System and method for mitigating latency and uncertainty in electric vehicle fleet charging by optimally adjusting size of energy-time reserve to maintain vehicle ready service levels

Abstract

Electric vehicle supply equipment (EVSE) in an electric vehicle (EV) station may be controlled to charge an electric vehicle according to a scheduled departure time of the electric vehicle. However, interference and other uncertainties may accidentally change the power required for charging for any given period of time. The disclosed embodiments utilize an energy reserve distribution associated with a power infrastructure asset as a constraint in an optimization model to prevent the optimization from excessively relying on the last charge while still providing the optimization model with flexibility to balance competitive goals in a fast and scalable manner. Each energy reserve distribution may reduce energy available to the associated power infrastructure assets over time by increasing energy reserve over time.

Description

Technical Field

[0001] The embodiments described herein generally relate to energy management, and more particularly to using energy-time reserves to mitigate uncertainty in scheduled charging. Background Art

[0002] Electric vehicle (EV) fleets typically charge overnight at an EV depot that includes multiple charging stations and other EV supply equipment (EVSE). The control system of the EV depot determines how to distribute electrical power among the electric vehicles so as to charge their batteries to a desired state of charge before a scheduled time.

[0003] A deterministic charging strategy that minimizes the electricity cost may wait until the last minute to charge an electric vehicle without considering unexpected disturbances. These unexpected disturbances may affect the ability to charge the electric vehicle at the scheduled time, resulting in disruptions to fleet operations.

[0004] Thus, actual charging control is complicated by real-world uncertainties. In particular, public and commercial fleets are open systems exposed to environmental disturbances (e.g., weather, traffic, etc.). When replacing traditional vehicles with electric vehicles, maintaining on-time readiness becomes a major issue because the recharge time of an electric vehicle is typically significantly longer than the refueling time of a traditional vehicle. Although digital and real-time planning applications can improve the visibility of the EV fleet state, complex solutions increase costs and require maintenance. Additionally, unpredictable disturbances may still occur. Examples of such disturbances include, but are not limited to: an electric vehicle returning and plugging in late, an electric vehicle returning with a lower-than-planned state of charge, an electric vehicle accidentally unplugging or suffering a temporary charging fault, an electric vehicle unplugging due to unplanned maintenance, an electric vehicle being needed earlier than expected, a charging system suffering a temporary fault, a grid operator reducing the power demand limit, an unexpected reduction in on-site power generation (e.g., a reduction in solar power generation due to unexpected weather), etc. Such disturbances can reduce the time and / or power available to charge the electric vehicles, which may result in the electric vehicles not being ready to leave at their scheduled departure time.

[0005] Additionally, changes in energy demand, available charging time, departure time, etc. may unexpectedly change the power required for charging. The changed power demand may exceed the power capacity of the EVSE or unnecessarily increase the peak power demand of the EV depot at the point of common coupling with the grid, which may result in penalties imposed by the grid operator. To reliably prepare the electric vehicles before a business-critical deadline, the control system must be able to predict such uncertainties.

[0006] There are multiple heuristic solutions for reducing uncertainty. One solution is to charge the electric vehicle to a fully charged state as soon as possible. However, such a solution may impose peak power demands on the power grid. This can be mitigated by setting a power flow rate for each electric vehicle, for example, by dividing the amount of energy to be delivered to the electric vehicle by the amount of time before the electric vehicle is scheduled to depart. However, such a solution does not account for the uncertainty described above.

[0007] Solutions for addressing uncertainty may predict delays by subtracting a time buffer from the deadline for scheduling the charging of the electric vehicle. However, having all electric vehicles ready early is sub-optimal. It not only wastes time but may also increase peak power demands and potentially increase charging costs.

[0008] Scheduled charging based on an optimization problem (formulated as objectives and constraints) can potentially improve performance and achieve an appropriate balance between the risk of delays and the impact on the power grid and cost. Traditional methods either formulate the variability of arrival or departure times or employ a two-stage approach. Examples of traditional methods include U.S. Pat. Nos. 8,762,189, 9,148,027, 9,358,896, 9,406,412, 10,040,365, and 10,112,499, and European Patent No. 2768 693. The present disclosure addresses one or more problems that the inventors have identified in these methods. SUMMARY

[0009] Systems, methods, and non-transitory computer-readable media for using energy-time reserves to mitigate uncertainty in scheduled charging are disclosed. The goal of certain embodiments is to associate power infrastructure assets with an energy reserve profile that reduces the available charging power over time. A further goal of certain embodiments is to use the energy reserve profile as a constraint to implement optimization of the operational configuration of a power infrastructure site to mitigate unexpected disturbances. A further goal of certain embodiments is to improve on-time charging of flexible loads such as electric vehicles.

[0010] In an embodiment, a method includes using at least one hardware processor to: generate an optimization model for at least one power infrastructure site, wherein the at least one power infrastructure site includes one or more power infrastructure assets, wherein at least one of the one or more power infrastructure assets is associated with an energy reserve profile that decreases the energy available for the power infrastructure asset over time, and wherein the optimization model outputs a target value based on one or more variables representing an operating configuration of the at least one power infrastructure site, subject to constraints of the energy reserve profile associated with the at least one power infrastructure asset; solve the optimization model to determine values of the one or more variables that optimize the target value; and initiate control of one or more physical components in the at least one power infrastructure site based on the determined values of the one or more variables.

[0011] In an embodiment, the optimization model is periodically generated and solved to determine the one or more variables representing the operating configuration of the at least one power infrastructure site in a sliding time window that slides according to a time step. The energy reserve profile associated with the at least one power infrastructure asset may slide with the sliding time window according to the time step. The energy reserve profile associated with the at least one power infrastructure asset may be anchored to a scheduling event. The at least one power infrastructure site may be a depot, the at least one power infrastructure asset may be an electric vehicle, and the scheduling event may be the arrival or departure of the electric vehicle at the depot.

[0012] In an embodiment, the method further includes using at least one hardware processor to determine an energy reserve profile associated with at least one of the one or more power infrastructure assets by combining: an energy reserve profile that slides with the sliding time window according to a time step; and an energy reserve profile that is anchored to a scheduling event. The at least one power infrastructure site may be a depot, the at least one power infrastructure asset may be an electric vehicle, and the scheduling event may be the arrival or departure of the electric vehicle at the depot.

[0013] In an embodiment, the method further includes using at least one hardware processor to update an energy reserve profile associated with at least one of the one or more power infrastructure assets in response to one or more completion events.

[0014] In an embodiment, the one or more power infrastructure assets include one or more flexible loads each including a battery. The energy reserve profile associated with each of the one or more flexible loads may decrease the effective charging power of the battery available for the flexible load over time. Each of the one or more flexible loads may be an electric vehicle.

[0015] In an embodiment, at least one power infrastructure site includes a yard, one or more power infrastructure assets include electric vehicles, and one or more physical components include one or more charging stations, which are configured to be electrically connected to the electric vehicles to charge the electric vehicles. The determined values of one or more variables may associate each of the electric vehicles with one or both of the following: a period of time for charging at one of the one or more charging stations in at least one power infrastructure site or a power flow rate.

[0016] In an embodiment, the target value includes at least an energy cost, and optimizing the target value includes minimizing the target value.

[0017] In an embodiment, initiating control of one or more physical components includes controlling the setpoints of one or more physical components according to the determined values of one or more variables. One or more physical components may include non-intermittent distributed energy sources.

[0018] In an embodiment, initiating control includes communicating via at least one network with a control system for at least one power infrastructure site.

[0019] It should be understood that any feature in the above methods can be implemented alone or in any combination with any subset of other features. Thus, even though the appended claims indicate specific dependencies between features, the disclosed embodiments are not limited to these specific dependencies. Instead, any feature described herein can be combined with any other feature described herein, or implemented in any combination of features without any one or more of the other features described herein. Additionally, any method described above and elsewhere herein can be embodied, alone or in any combination, in executable software modules in a processor-based system (such as a server) and / or in executable instructions stored in a non-transitory computer-readable medium. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Details regarding both the structure and operation of the present invention can be gathered in part by studying the drawings, in which like reference numerals refer to like parts, and in which:

[0021] Figure 1 An example infrastructure in which one or more processes described herein can be implemented according to an embodiment is illustrated;

[0022] Figure 2 An example processing system that can be used to execute one or more processes described herein according to an embodiment is illustrated;

[0023] Figure 3 An example power distribution network of a power infrastructure site according to an embodiment is illustrated;

[0024] Figure 4 Illustrates an example data flow between various components of an optimized infrastructure according to an embodiment;

[0025] Figure 5 Illustrates an example process for reducing uncertainty in scheduling charging using an energy - time reserve according to an embodiment; and

[0026] Figures 6A to 6D Illustrates various examples of an energy - time reserve according to an embodiment. Detailed Description

[0027] In an embodiment, systems, methods, and non - transitory computer - readable media for reducing uncertainty in scheduling charging using an energy - time reserve are disclosed. After reading this specification, those skilled in the art will be clear how to implement the present invention in various alternative embodiments and alternative applications. However, although various embodiments of the present invention will be described herein, it should be understood that these embodiments are presented by way of example and illustration only, and not by way of limitation. Thus, this detailed description of the various embodiments should not be construed as limiting the scope or breadth of the present invention as set forth in the appended claims.

[0028] The term "power infrastructure site" refers to any infrastructure having a well - defined electrical boundary. Generally, a power infrastructure site includes a distribution network with interconnected loads and can be independently controlled. For example, a power infrastructure site can be a power supply station and / or a microgrid including multiple infrastructure assets. However, a power infrastructure site can also consist of a single infrastructure asset. Infrastructure assets can include generators, energy storage systems, loads, and / or any other components of the power infrastructure site.

[0029] The term "power supply station" refers to any power infrastructure site including at least one charging station configured to be electrically connected to a flexible load to charge and / or discharge the battery of the flexible load. It should be understood that a power supply station can also include non - flexible loads. As an example, a power supply station can be an electric vehicle (EV) station that provides private charging for a fleet of electric vehicles of a municipal public transportation system, an enterprise, a utility provider, or other entities, provides public charging for personal electric vehicles, provides private charging for personal electric vehicles (e.g., at the residence of a personal electric vehicle owner), etc.

[0030] The term "microgrid" refers to any power infrastructure site that includes a local power grid capable of operating independently of the rest of the power grid. A microgrid can include multiple infrastructure assets (e.g., (multiple) generators, (multiple) energy storage systems, (multiple) loads, etc.) connected under the same point of common coupling through a local distribution network. The infrastructure assets of a microgrid typically include at least some types of generators or energy storage systems, but can include any combination of infrastructure assets. It should be understood that a power supply station and a microgrid are not mutually exclusive, and in some instances, a power infrastructure site can include both a power supply station and a microgrid.

[0031] The term "flexible load" refers to any load that is flexible in at least one characteristic that can be represented by a variable in an optimization model. One such characteristic can be the location where the flexible load charges or discharges. A flexible load that is flexible in location can charge or discharge at any of multiple locations in one or more power infrastructure sites. Another such characteristic can be the timing of the flexible load charging or discharging. A flexible load that is flexible in timing can charge or discharge according to different timings in terms of start time, end time, time range, duration, etc. Another such characteristic can be the power flow rate of the flexible load charging or discharging. A flexible load that is flexible in power flow rate can charge at any of multiple different power flow rates (e.g., at any power flow rate within a power flow rate range). Another such characteristic can be the operating state of the flexible load. A flexible load that is flexible in operating state (e.g., water heater, air conditioner, compressor, etc.) can transition to another state with reduced power consumption (e.g., low power mode, off, discharge, etc.) to increase the amount of energy available for other loads and / or reduce the total amount of energy consumed. It should be understood that these are only examples of characteristics, and a flexible load can be flexible in other characteristics even if not specifically described herein. A flexible load can be flexible in only one characteristic, all characteristics, or any subset of characteristics. In contrast, the term "non-flexible load" refers to any load that is not flexible in any characteristic.

[0032] In an envisioned embodiment, the flexible load is an electric vehicle, and the power infrastructure site is an EV station. The electric vehicle can be flexible at least with respect to its location. In other words, since the electric vehicle is mobile, the electric vehicle can typically charge at any of the multiple available charging stations within any of the multiple EV stations. In particular, the electric vehicle includes an on-board battery that can be electrically connected to any of the multiple available charging stations within the EV station. Similar types of flexible loads include but are not limited to drones, robotic systems, mobile machines, mobile devices, power tools, etc.

[0033] However, the disclosed method is not limited to electric vehicles or other mobile loads. Instead, the disclosed method can be applied to any load (whether mobile or stationary) as long as the load has one or more flexible characteristics that can be defined in terms of the variable(s) in the optimization model. For example, a flexible load can consist solely of a stationary or mobile battery, or can be a system that consumes electricity but does not have any on-board battery for storing electricity. A stationary flexible load typically does not have flexibility in terms of location, but can have flexibility in terms of timing, power flow rate, operating state, etc. For the purposes of the present disclosure, it is generally assumed that a flexible load includes or consists of an energy storage device. Although the energy storage device is primarily described herein as a battery, it should be understood that the energy storage device can include or consist of any other mechanism or component for storing energy, such as a supercapacitor, compressed gas, etc.

[0034] The power infrastructure site can also include one or more flexible generators. The term "flexible generator" refers to any generator that can be controlled to increase and / or decrease the power generation. Examples of flexible generators include, but are not limited to, diesel generators, hydrogen fuel cells, distributed energy sources whose power output can be curtailed, etc. The optimization of the power infrastructure site can optimize the variables of both the flexible load and the flexible generator.

[0035] As used herein, the term "distribution network" refers to the interconnection of electrical components within a power infrastructure site that distribute electricity to flexible loads. These electrical components can include one or more intermittent and / or non-intermittent distributed energy sources, including renewable energy sources (e.g., solar generators, wind generators, geothermal generators, hydroelectric generators, fuel cells, etc.) and / or non-renewable energy sources (e.g., diesel generators, natural gas generators, etc.), one or more battery energy storage systems (BESS), etc. Additionally or alternatively, if the power infrastructure site includes a power supply station, these electrical components can include charging stations. Despite the term "charging", the term "charging station" encompasses stations that are capable of discharging a load (e.g., drawing power from the on-board battery of the load) in addition to charging the load (e.g., supplying power to the on-board battery of the load), as well as stations that are only capable of charging the load and stations that are only capable of discharging the load. The electrical components in the power infrastructure site can be regarded as "nodes" of the distribution network, and the electrical connections between these electrical components can be regarded as "edges" connecting the nodes within the distribution network. The distribution network of the power infrastructure site can be connected to other distribution networks (e.g., during normal operation) or can be isolated (e.g., in the case of microgrid independent operation).

[0036] 1. Example infrastructure

[0037] Figure 1 FIG. illustrates an example infrastructure in which one or more of the disclosed processes may be implemented. The infrastructure may include an Energy Management System (EMS) 110 (e.g., including one or more servers) that hosts and / or executes one or more of the various functions, processes, methods, and / or software modules described herein. The EMS 110 may include dedicated servers or, alternatively, may be implemented in a computing cloud where resources of one or more servers are dynamically and elastically allocated to multiple tenants based on demand. In either case, the servers may be collocated and / or geographically distributed. The EMS 110 may also include or be communicatively connected to software 112 and / or one or more databases 114. Additionally, the EMS 110 may be communicatively connected to one or more user systems 130, power infrastructure sites 140, and / or power markets 150 via one or more networks 120.

[0038] The network 120 may include the Internet, and the EMS 110 may communicate with the (multiple) user systems 130, the (multiple) power infrastructure sites 140, and / or the (multiple) power markets 150 via the Internet using standard transport protocols such as Hypertext Transfer Protocol (HTTP), HTTP Secure Protocol (HTTPS), File Transfer Protocol (FTP), FTP Secure Protocol (FTPS), Secure Shell FTP (SFTP), Extensible Messaging and Presence Protocol (XMPP), Open Field Message Bus (OpenFMB), IEEE Smart Energy Profile Application Protocol (IEEE 2030.5), etc., as well as proprietary protocols. Although the EMS 110 is illustrated as being connected to various systems via a single set of the (multiple) networks 120, it should be understood that the EMS 110 may be connected to various systems via different sets of one or more networks. For example, the EMS 110 may be connected to a subset of the user systems 130, power infrastructure sites 140, and / or power markets 150 via the Internet, but may be connected to one or more other user systems 130, power infrastructure sites 140, and / or power markets 150 via an intranet. Additionally, although only a few user systems 130 and power infrastructure sites 140, one power market 150, one instance of software 112, and one set of the (multiple) databases 114 are illustrated, it should be understood that the infrastructure may include any number of user systems, power infrastructure sites, power markets, software instances, and databases.

[0039] The user system 130 can include any type or types of computing devices capable of wired and / or wireless communication, including but not limited to desktop computers, laptop computers, tablet computers, smartphones or other mobile phones, servers, gaming consoles, televisions, set-top boxes, electronic kiosks, point-of-sale terminals, embedded controllers, programmable logic controllers (PLCs), etc. However, it is generally envisioned that the user system(s) 130 includes personal computers, mobile devices, or workstations, through which agents of the operator(s) of the power infrastructure site(s) 140 can interact with the EMS 110 as users. These interactions can include entering data (e.g., parameters for configuring one or more of the processes described herein) and / or receiving data (e.g., outputs of one or more of the processes described herein) via a graphical user interface provided by the EMS 110 or an intermediate system between the EMS 110 and the user system(s) 130. The graphical user interface can include a screen (e.g., a web page) that includes a combination of content and elements such as text, images, videos, animations, references (e.g., hyperlinks), frames, inputs (e.g., text boxes, text areas, check boxes, radio buttons, drop-down menus, buttons, forms, etc.), scripts (e.g., JavaScript), etc., thus including elements that contain data stored in one or more databases (e.g., the database(s) 114) or elements derived from such data.

[0040] The EMS 110 can execute software 112, which includes one or more software modules that implement one or more of the disclosed processes. Additionally, the EMS 110 can include one or more databases 114 that are communicatively coupled to or otherwise accessible to the one or more databases and that store data input to and / or output from one or more of the disclosed processes. Any suitable database can be used, including but not limited to MySQL TM , Oracle TM , IBM TM , Microsoft SQL TM , Access TM , PostgreSQL TM , etc., thus including cloud-based databases, proprietary databases, and unstructured databases (e.g., MongoDB TM ).

[0041] The EMS 110 can communicate with the power infrastructure site(s) 140 and / or the power market(s) 150 via an application programming interface (API). For example, the EMS 110 can "push" data (i.e., actively transmit data) to each power infrastructure site 140 via the API of the control system 142 of the power infrastructure site 140. The control system 142 can be a supervisory control and data acquisition (SCADA) system. Alternatively or additionally, the control system 142 of the power infrastructure site 140 can "pull" data (i.e., initiate data transmission via a request) from the EMS 110 via the API of the EMS 110. Similarly, the EMS 110 can push data to the power market interface 152 of the power market 150 via the API of the power market interface 152, and / or the power market interface 152 can pull data from the EMS 110 via the API of the EMS 110.

[0042] 2. Example processing system

[0043] Figure 2 is a block diagram illustrating an example wired or wireless system 200 that can be used in conjunction with various embodiments described herein. For example, the system 200 can be used as or in conjunction with one or more of the functions, processes, or methods described herein (e.g., for storing and / or executing software 112), and can represent components of the EMS 110, the user system(s) 130, the power infrastructure site(s) 140, the control system 142, the power market interface 152, and / or other processing devices described herein. The system 200 can be a server or any conventional personal computer, or any other processor-enabled device capable of wired or wireless data communication. Those skilled in the art will appreciate that other computer systems and / or architectures can also be used.

[0044] The system 200 preferably includes one or more processors 210. The processor(s) 210 can include a central processing unit (CPU). Additional processors can be provided, such as a graphics processing unit (GPU), a secondary processor for managing input / output, a secondary processor for performing floating-point mathematical operations, a dedicated microprocessor having an architecture suitable for rapidly executing signal processing algorithms (e.g., a digital signal processor), a secondary processor subordinate to the main processing system (e.g., a backend processor), additional microprocessors or controllers and / or coprocessors for a dual-processor or multi-processor system. Such secondary processors can be discrete processors or can be integrated with the processor 210. Examples of processors that can be used with the system 200 include, but are not limited to, any processors provided by Intel Corporation of Santa Clara, California (e.g., Pentium TM , Core i7 TM , XeonTM etc.), any processor provided by Advanced Micro Devices, Inc. (AMD) of Santa Clara, California, any processor provided by Apple Inc. of Cupertino (e.g., A series, M series, etc.), any processor provided by Samsung Electronics Co., Ltd. of Seoul, South Korea (e.g., Exynos TM ), any processor provided by NXP Semiconductors N.V. of Eindhoven, the Netherlands, and so on.

[0045] Processor 210 is preferably connected to communication bus 205. Communication bus 205 may include data channels for facilitating information transfer between the storage devices of system 200 and other peripheral components. In addition, communication bus 205 may provide a set of signals for communicating with processor 210, including a data bus, an address bus, and / or a control bus (not shown). Communication bus 205 may include any standard or non-standard bus architecture, such as an Industry Standard Architecture (ISA), Extended Industry Standard Architecture (EISA), Micro Channel Architecture (MCA), Peripheral Component Interconnect (PCI) local bus, bus architectures conforming to standards published by the Institute of Electrical and Electronics Engineers (IEEE), including the IEEE 488 General-Purpose Interface Bus (GPIB), IEEE 696 / S-100, etc.

[0046] System 200 preferably includes main memory 215 and may also include secondary memory 220. Main memory 215 provides instruction and data storage for programs executed on processor 210 (such as one or more functions and / or modules discussed herein (e.g., software 112)). It should be understood that programs stored in the memory and executed by processor 210 may be written and / or compiled in any suitable language, including but not limited to C / C++, Java, JavaScript, Perl, Visual Basic,.NET, etc. Main memory 215 is typically semiconductor-based memory, such as dynamic random access memory (DRAM) and / or static random access memory (SRAM). Other semiconductor-based memory types include, for example, synchronous dynamic random access memory (SDRAM), Rambus dynamic random access memory (RDRAM), ferroelectric random access memory (FRAM), etc., including read-only memory (ROM).

[0047] The auxiliary memory 220 may optionally include an internal medium 225 and / or a removable medium 230. Reading and / or writing to the removable medium 230 is performed in any well-known manner. The removable storage medium 230 may be, for example, a tape drive, a compact disc (CD) drive, a digital versatile disc (DVD) drive, other optical drives, a flash memory drive, and the like. The auxiliary memory 220 is a non-transitory computer-readable medium on which computer-executable code (e.g., software 112) and / or other data are stored. The computer software or data stored on the auxiliary memory 220 is read into the main memory 215 for execution by the processor 210.

[0048] In an alternative embodiment, the auxiliary memory 220 may include other similar devices for allowing a computer program or other data or instructions to be loaded into the system 200. Such devices may include, for example, a communication interface 240 that allows software and data to be transferred from an external storage medium 245 to the system 200. Examples of the external storage medium 245 may include an external hard disk drive, an external optical drive, and / or an external magneto-optical drive, and the like. Other examples of the auxiliary memory 220 may include semiconductor-based memories such as programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable read-only memory (EEPROM), and flash memory (a block-oriented memory similar to EEPROM).

[0049] As mentioned above, the system 200 may include a communication interface 240. The communication interface 240 allows software and data to be transferred between the system 200 and external devices (e.g., a printer), a network, or other information sources. For example, computer software or executable code may be transferred from a network server (e.g., the platform 110) to the system 200 via the communication interface 240. Examples of the communication interface 240 include a built-in network adapter, a network interface card (NIC), a Personal Computer Memory Card International Association (PCMCIA) network card, a CardBus network adapter, a wireless network adapter, a Universal Serial Bus (USB) network adapter, a modem, a wireless data card, a communication port, an infrared interface, an IEEE 1394 FireWire, and any other device capable of interfacing the system 200 with a network (e.g., the (one or more) networks 120) or another computing device. The communication interface 240 preferably implements industry-released protocol standards such as the Ethernet IEEE 802 standards, Fibre Channel, Digital Subscriber Line (DSL), Asymmetric Digital Subscriber Line (ADSL), Frame Relay, Asynchronous Transfer Mode (ATM), Integrated Services Digital Network (ISDN), Personal Communication Services (PCS), Transmission Control Protocol / Internet Protocol (TCP / IP), Serial Line Internet Protocol / Point-to-Point Protocol (SLIP / PPP), etc., but may also implement custom or non-standard interface protocols.

[0050] Software and data transmitted via the communication interface 240 typically take the form of electrical communication signals 255. These signals 255 can be provided to the communication interface 240 via the communication channel 250. In an embodiment, the communication channel 250 can be a wired or wireless network (e.g., the network(s) 120), or any other type of communication link. The communication channel 250 carries the signals 255 and can be implemented using various wired or wireless communication means, including wires or cables, optical fibers, conventional telephone lines, cellular telephone links, wireless data communication links, radio frequency (“RF”) links, or infrared links, to name a few.

[0051] Computer-executable code (e.g., a computer program such as software 112) is stored in the main memory 215 and / or the secondary memory 220. The computer program can also be received via the communication interface 240 and stored in the main memory 215 and / or the secondary memory 220. Such a computer program, when executed, enables the system 200 to perform the various functions of the disclosed embodiments described elsewhere herein.

[0052] In this specification, the term “computer-readable medium” is used to refer to any non-transitory computer-readable storage medium for providing computer-executable code and / or other data to or within the system 200. Examples of such media include the main memory 215, the secondary memory 220 (including the internal memory 225 and / or the removable media 230), the external storage medium 245, and any peripheral device communicatively coupled to the communication interface 240 (including a network information server or other network device). These non-transitory computer-readable media are means for providing executable code, programming instructions, software, and / or other data to the system 200.

[0053] In embodiments implemented using software, the software can be stored on a computer-readable medium and loaded into the system 200 via the removable media 230, the I / O interface 235, or the communication interface 240. In such an embodiment, the software is loaded into the system 200 in the form of electrical communication signals 255. The software, when executed by the processor 210, preferably causes the processor 210 to perform one or more of the processes and functions described elsewhere herein.

[0054] In an embodiment, the I / O interface 235 provides an interface between one or more components of the system 200 and one or more input and / or output devices. Example input devices include, but are not limited to, sensors, keyboards, touchscreens or other touch-sensitive devices, cameras, biometric sensing devices, computer mice, trackballs, pen-based pointing devices, etc. Examples of output devices include, but are not limited to, other processing devices, cathode ray tubes (CRTs), plasma displays, light emitting diode (LED) displays, liquid crystal displays (LCDs), printers, vacuum fluorescent displays (VFDs), surface conduction electron emission displays (SEDs), field emission displays (FEDs), etc. In some cases, the input and output devices may be combined, such as in the case of a touch panel display (e.g., in a smart phone, tablet computer, or other mobile device).

[0055] The system 200 may also include optional wireless communication components that facilitate wireless communication over a voice network and / or a data network (e.g., in the case of the user system 130 being a smart phone or other mobile device). The wireless communication components include an antenna system 270, a radio system 265, and a baseband system 260. In the system 200, radio frequency (RF) signals are transmitted and received over the air by the antenna system 270 under the management of the radio system 265.

[0056] In an embodiment, the antenna system 270 may include one or more antennas and one or more multiplexers (not shown) that perform a switching function to provide transmit and receive signal paths to the antenna system 270. In the receive path, the received RF signal may be coupled from the multiplexer to a low noise amplifier (not shown) that amplifies the received RF signal and sends the amplified signal to the radio system 265.

[0057] In an alternative embodiment, the radio system 265 may include one or more radios configured to communicate at various frequencies. In an embodiment, the radio system 265 may combine a demodulator (not shown) and a modulator (not shown) in one integrated circuit (IC). The demodulator and modulator may also be separate components. In the incoming path, the demodulator removes the RF carrier signal, leaving a baseband received audio signal that is sent from the radio system 265 to the baseband system 260.

[0058] If the received signal contains audio information (e.g., a user system 130 including a smart phone or other mobile device), the baseband system 260 decodes the signal and converts it to an analog signal. The signal is then amplified and sent to a speaker. The baseband system 260 also receives analog audio signals from a microphone. These analog audio signals are converted by the baseband system 260 to digital signals and encoded. The baseband system 260 also encodes the digital signals for transmission and generates a baseband transmitted audio signal, which is routed to the modulator section of the radio system 265. The modulator mixes the baseband transmitted audio signal with an RF carrier signal, thereby generating an RF transmitted signal, which is routed to the antenna system 270 and may be amplified by a power amplifier (not shown). The power amplifier amplifies the RF transmitted signal and routes it to the antenna system 270, where the signal is switched to an antenna port for transmission.

[0059] The baseband system 260 is also communicatively coupled to the processor(s) 210. The processor(s) 210 can access data stores 215 and 220. The processor(s) 210 are preferably configured to execute instructions (i.e., computer programs such as the disclosed software) that may be stored in the main memory 215 or the secondary memory 220. The computer programs may also be received from the baseband processor 260 and stored in the main memory 210 or the secondary memory 220, or executed upon receipt. Such computer programs, when executed, cause the system 200 to perform the various functions of the disclosed embodiments.

[0060] 3. Example power infrastructure site

[0061] Figure 3 A single-line diagram of an example distribution network of an example power infrastructure site 140 according to an embodiment is illustrated. As a non-limiting example, the power infrastructure site 140 can be an EV yard for charging electric vehicles as flexible loads. The power infrastructure site 140 is connected to the power grid 310 and can purchase power from the grid (e.g., from the power market 150). According to the time-of-use (ToU) rate, the purchase price of power can vary within a day (e.g., higher during the day than at night) and across days (e.g., higher in summer than in winter). The ToU rate can assign peak rates, partial peak rates, and off-peak rates to respective time periods (e.g., each hourly interval of a day), representing the power price during these time periods.

[0062] The power distribution network of the power infrastructure site 140 may include nodes representing one or more distributed energy sources in the power infrastructure site 140, including, for example, one or more battery energy storage systems 320 and / or one or more generators 330 (illustrated as generators 330A and 330B). The generator(s) 330 may include renewable energy sources (e.g., solar generators, wind generators, geothermal generators, hydroelectric generators, fuel cells, etc.) and / or non-renewable energy sources (e.g., diesel generators, natural gas generators, etc.). For example, generator 330A may be a solar generator including a plurality of photovoltaic cells that convert sunlight into electricity, and generator 330B may be a diesel generator that burns diesel fuel to generate electricity.

[0063] The power distribution network of the power infrastructure site 140 may also include nodes representing one or more charging stations 340 in the power infrastructure site 140. In the example shown, the power infrastructure site 140 is a power supply station including a plurality of charging stations 340A, 340B, 340C, 340D, 340E, 340F, and 340G. Each charging station 340 may include one or more chargers 342. For example, charging station 340F is illustrated with two chargers 342. Each charger 342 is configured to be electrically connected to a flexible load 350 to supply power to and / or release power from one or more energy storage devices (e.g., batteries) of the flexible load 350. In the case of powering or charging the battery of the flexible load 350, power may flow from the generator 330 and / or the power grid 310 through the power distribution network to the battery of the flexible load 350. Conversely, in the case of discharging the battery of the flexible load 350, power may flow from the battery of the flexible load 350 into the power distribution network and into the battery energy storage system 320, the power grid 310, and / or another flexible load 350. At any given time, some chargers 342 may be connected to flexible loads 350 (illustrated as flexible loads 350A, 350B, 350C, 350E, 350F1, and 350F2), while other chargers 342 may be unconnected to flexible loads 350 and available to receive incoming flexible loads 350.

[0064] In an embodiment, two or more power infrastructure sites 340 may be connected via a transmission network (not shown) or within the same distribution network. In such a case, power may be transmitted between the two power infrastructure sites 340. For example, a first power infrastructure site 140 may transmit power from one or more of its infrastructure assets (e.g., (multiple) battery energy storage systems 320, (multiple) generators 330, and / or (multiple) flexible loads 350) over the network to a second power infrastructure site 140 to charge one or more infrastructure assets (e.g., (multiple) battery energy storage systems 320 and / or (multiple) flexible loads 350) of the second power infrastructure site 140.

[0065] One or more charging stations 340 or individual chargers 342 may be configured to start charging a flexible load 350 (e.g., at a settable power flow rate), terminate charging the flexible load 350, start discharging the flexible load 350 (e.g., at a settable power flow rate), terminate discharging the flexible load 350, etc., under the control of a control system 142, an EMS 110, and / or another controller. For example, the charging station 340 and / or charger 342 may include a processing system 200 that receives commands from a controller (e.g., the control system 142 and / or the EMS 110) via a communication interface 240, processes the commands using a processor 210 and a main memory 215, and controls actuators (e.g., one or more switches) according to the processed commands to start or terminate charging or discharging.

[0066] It should be understood that the power infrastructure site 140 may include other loads in addition to the flexible load 350. For example, the power infrastructure site 140 may include auxiliary loads for operating various functions of the power infrastructure site 140. However, if these auxiliary loads are flexible in at least one characteristic (e.g., operating state), then even the auxiliary loads may be considered flexible loads 350. It should also be understood that each battery energy storage system 320 can function as both a power source (i.e., when discharging) and a load (i.e., when charging), and may also be considered a flexible load 350.

[0067] The parameters (e.g., voltage, current, set points, etc.) of each node within the distribution network of the power infrastructure site 140 can be monitored and / or simulated by the EMS 110 (e.g., during a load flow analysis). Thus, the EMS 110 can monitor and / or simulate the parameters of the nodes within the distribution network and control one or more physical components of the power infrastructure site 140, such as the (multiple) charging stations 340, the (multiple) chargers 342, the (multiple) generators 330, the (multiple) battery energy storage systems 320, etc., based on these parameters. Such control can be performed periodically or in real time and can be performed directly or indirectly (e.g., via the control system 142).

[0068] The illustrated power infrastructure site 140 includes a certain number of charging stations 340. However, it should be understood that the power infrastructure site 140 can include any number of charging stations 340, including only a single charging station 340. Additionally, each charging station 340 can include any number of chargers 342, including only a single charger 342. In its simplest form, the power infrastructure site 140 can consist of only a single charging station 340 (such as a charging station 340 in a residence, a public parking space, etc.) constituted by a single charger 342. Additionally, while all flexible loads 350 are illustrated as being connected to a charging station, one or more flexible loads 350 can be connected to the distribution network without any intermediate charging station 340.

[0069] A single EMS 110 can manage a single power infrastructure site 140 or multiple power infrastructure sites 140. In the case where the EMS 110 manages multiple power infrastructure sites 140, the managed power infrastructure sites 140 can be the same, similar, or different from each other. For example, a homogeneous mix of power infrastructure sites 140 can consist of multiple power supply stations for one or more fleets of electric vehicles. In contrast, a heterogeneous mix of power infrastructure sites 140 can include a mix of the (multiple) power supply stations, the (multiple) residential charging stations 340, the (multiple) public charging stations 340, the (multiple) microgrids, etc.

[0070] 4. Example data stream

[0071] Figure 4Illustrated is an example data flow among various components of an optimized infrastructure according to an embodiment. Software 112 hosted on platform 110 may implement optimizer 410. Optimizer 410 may generate an optimization model that outputs a target value based on one or more variables and inputs including a schedule for one or more flexible loads 350 in one or more power infrastructure sites 140. The optimization model represents a specific software-based implementation of an optimization problem. Optimizer 410 may solve the optimization model to determine values of one or more variables that optimize the target value while subject to zero, one, or more constraints (e.g., inequality and / or equality constraints representing limitations on physical and / or technical capabilities, load flexibility, and / or generators, etc.). Such optimization may include minimizing the target value (e.g., if the target value represents cost) or maximizing the target value (e.g., if the target value represents a performance metric). The determined values of the (one or more) variables may represent an operating configuration (e.g., set points, schedules, etc.) of one or more power infrastructure sites 140 over a certain time period. Optimizer 410 may also initiate control of one or more physical components in one or more power infrastructure sites 140 based on the determined values of the one or more variables.

[0072] Optimizer 410 may update and solve the optimization model periodically based on real-time or updated data. For example, the optimizer may update and solve an optimization model for one or more power infrastructure sites 140 operating in a sliding time window representing an optimization cycle. The sliding time window advances continuously or successively to cover the next time period for which the operation of one or more power infrastructure sites 140 is to be optimized. It should be understood that the start of the sliding time window may be the current time or some future time (e.g., future 1 minute, 5 minutes, 10 minutes, 15 minutes, 30 minutes, 1 hour, 24 hours, etc.), such that the optimization is performed prior to the future time period (for which the optimization is being performed) covered by the sliding time window. In an embodiment, the sliding time window may advance according to a time step (e.g., every 15 minutes) and utilize the latest available data within a time range (e.g., a time range extending into the past and of size equal to the time step). The size of the sliding time window may be any suitable duration (e.g., 15 minutes, 30 minutes, 1 hour, 24 hours, etc.).

[0073] Optimizer 410 can collect data from one or more scheduling systems 420, one or more telemetry systems 430, one or more control systems 142 of one or more electric power infrastructure sites 140, and / or one or more power market interfaces 152 of one or more power markets 150, and use the data for optimization (e.g., as input to an optimization model). It should be understood that these are only examples of data flows, and Optimizer 410 can collect data from other systems (e.g., may include (a) site management system(s) 440). For example, Optimizer 410 can receive solutions from other optimizers, and the solutions can be incorporated into the input of the optimization model. In this case, Optimizer 410 can focus on one aspect of the overall optimization and thus does not have to integrate every detail of the optimization into the optimization model.

[0074] In an embodiment, Optimizer 410 can combine the data collected from multiple electric power infrastructure sites 140 into a single virtual site model and perform a single overall optimization on the virtual site model to optimize the operation of the multiple electric power infrastructure sites 140 as a single unit. The virtual site model can represent a system-of-systems for multi-tenant charging, which aggregates multiple electric power infrastructure sites 140 (e.g., EV yards) of multiple tenants (e.g., EV fleet operators).

[0075] Optimizer 410 can output data to one or more scheduling systems 420, one or more control systems 142 of one or more electric power infrastructure sites 140, one or more site management systems 440, and / or one or more power market interfaces 152 of one or more power markets 150. It should be understood that these are only examples of data flows, and Optimizer 410 can output data to other systems (e.g., potentially including one or more telemetry systems 430). For example, Optimizer 410 can output its solution or other data to one or more other optimizers, and each optimizer can incorporate the data into the input of its own optimization model. In this case, Optimizer 410 can focus on one aspect of the overall optimization and thus does not have to integrate every detail of the optimization into the optimization model.

[0076] (Multiple) scheduling systems 420, (multiple) telemetry systems 430, and / or (multiple) site management systems 440 may be hosted on the EMS 110 or external to the EMS 110. In either case, when collecting data, the optimizer 410 may receive data by pulling data from the respective system via the API of the respective system or by the respective system pushing data to the optimizer 410 via the API of the optimizer 410. Similarly, the optimizer 410 may output data by pushing data to the respective system via the API of the respective system or by the respective system pulling data via the API of the optimizer 410.

[0077] Each scheduling system 420 may manage the schedules and routes of flexible loads 350 (e.g., fleets of electric vehicles). The optimizer 410 may receive scheduling information from each scheduling system 420. The scheduling information provided by the scheduling system 420 may include a planned schedule for the flexible load 350. For example, for each flexible load 350, the planned schedule may include: a scheduled arrival time at which the flexible load 350 is expected to arrive at the power infrastructure site 140, a scheduled departure time at which the flexible load 350 is expected to leave the power infrastructure site 140, an auxiliary task schedule defining a period of time during which the flexible load 350 is expected to perform or carry out an auxiliary task (e.g., pre-conditioning the cabin and / or battery of an electric vehicle, performing cleaning, maintenance, or repair, etc.), a power flow schedule defining the power flow rate or distribution for charging or discharging the flexible load 350, a priority of the flexible load 350 relative to other flexible loads 350 (e.g., indicating the relative cost of delaying the charging of the flexible load 350), a preferred power infrastructure site 140 to be assigned to the flexible load 350, etc. Additionally, if the flexible load 350 has a route, the scheduling information may include: for each flexible load 350, the route assigned to the flexible load 350.

[0078] After solving the optimization model, the optimizer 410 may output data associated with the scheduling system 420 to the scheduling system 420 or an intermediate system. For example, in the case where the optimizer 410 performs optimization for multiple power infrastructure sites 140, the optimizer 410 may output a ranked list of the power infrastructure sites 140, e.g., sorted from the power infrastructure site 140 with the largest capacity to the power infrastructure site 140 with the smallest capacity. Such information may be used by the scheduling system 420 or an intermediate system to update the route assignment of the flexible loads 350 (e.g., by rerouting one or more flexible loads 350 from a power infrastructure 140 with a smaller capacity to a power infrastructure site 140 with a larger capacity). Additionally or alternatively, the optimizer 410 may output a ranked list of the flexible loads 350, e.g., sorted from the flexible load 350 that will be charged first to an acceptable state of charge (SoC) to the flexible load 350 that will be charged last to an acceptable state of charge (e.g., reflecting which electric vehicle can be ready first or maintain the longest unplugged time). As another example, the optimizer 410 or an intermediate system may provide suggestions for improving the schedule and / or provide data from which such suggestions can be derived. For example, if the flexible load 350 is an electric vehicle, such data may identify electric vehicles that are frequently late, such that the routes of the electric vehicles can be changed (e.g., assigned to another electric vehicle, split with another electric vehicle, etc.). More generally, the scheduling system 420 or an intermediate system may analyze the data provided by the optimizer 410 to identify inefficiencies (e.g., bottlenecks, scheduling electric vehicles that require extremely fast charging, etc.) and / or inaccurate parameters (e.g., actual energy consumed for preconditioning, etc.) in the scheduling of the flexible loads 350, and update the schedule of the flexible loads 350 (e.g., re-optimize the EV route assignment) in order to eliminate or mitigate such inefficiencies and / or reflect more accurate parameters.

[0079] Each telemetry system 430 may collect telemetry information of one or more flexible loads 350. The telemetry system 430 may be located on each flexible load 350 and transmit real-time telemetry information to the optimizer 410. For example, in the case where the flexible load 350 is an electric vehicle, the telemetry system 430 may be embedded (e.g., as software or hardware) in the electronic control unit (ECU) of the electric vehicle and communicate via a wireless communication network (e.g., a cellular communication network). Alternatively, the telemetry system 430 may be located external to the flexible load 350. In this case, the telemetry system 430 may collect real-time telemetry information of multiple flexible loads 350 and forward or relay the collected telemetry information to the optimizer 410 in real time. It should be understood that as used herein, the term "real-time" not only contemplates events that occur simultaneously, but also includes events separated by delays caused by normal time delays in processing, communication, etc. and / or caused by the use of time steps (e.g., a sliding time window with respect to optimization).

[0080] The optimizer 410 may receive telemetry information from each telemetry system 430. The telemetry information provided by the telemetry system 430 may include one or more parameters of each flexible load 350 for which the telemetry system 430 collects data. For each flexible load 350, these (multiple) parameters may include the estimated arrival time of the flexible load 350 at the scheduled power infrastructure site 140, the current state of charge of the energy storage device (e.g., a battery) carried by the flexible load 350, etc. It should be understood that these parameters may change over time, and the optimizer 410 may periodically receive updated telemetry information reflecting any changes (e.g., and use it as an input to the optimization model during the current optimization cycle). Real-time telemetry information reduces the uncertainty in the optimization model.

[0081] Each site management system 440 may manage infrastructure assets (including flexible loads 350) and personnel within one or more power infrastructure sites 140. After solving the optimization model, the optimizer 410 may output site information to each site management system 440. For example, the site information may include a ranked list of flexible loads 350, e.g., sorted from the flexible load 350 that can maintain the longest amount of unplugged time to the flexible load 350 that can maintain the shortest amount of unplugged time. Such information may be used by the site management system 440, e.g., to determine which flexible loads 350 can be served, etc. Additionally or alternatively, the site information may include the assignment or mapping of flexible loads 350 to charging stations 340. Such a mapping may be used, e.g., to automatically route the flexible load 350 to the mapped charging station 340 by transmitting routing instructions (such as the location of its mapped charging station 340) to the navigation system within each flexible load 350.

[0082] Each control system 142 can provide independent control of the power infrastructure site 140. After solving the optimization model, the optimizer 410 can output control information associated with the control of the power infrastructure site 140 to the control system 142 associated with the power infrastructure site 140. Such control information can be provided to the control system 142 of each power infrastructure site 140 managed by the optimizer 410. The control information can include one or more control instructions that trigger one or more control operations at the control system 142 and / or other information used during one or more control operations at the control system 142. The control instructions can include, but are not limited to, instructions for controlling set points associated with physical components of the power infrastructure site 140 (e.g., the power flow rate associated with the charging station 340), instructions for charging the flexible load 350, instructions for discharging the flexible load 350, instructions for performing pre-regulation of the flexible load 350 (e.g., cooling of the cockpit and / or battery of an electric vehicle, heating of the cockpit of an electric vehicle, etc.). Other information can include, but is not limited to, a ranked list of charging stations 340 (e.g., sorted from the charging station 340 with the largest capacity to the charging station 340 with the smallest capacity), a charging schedule for the flexible load 350, an assignment or mapping of the flexible load 350 to the charging station 340, etc.

[0083] The optimizer 410 can also receive data from each control system 142. For example, the control system 142 can report events detected within the corresponding power infrastructure site 140 (e.g., the charger 342 of the charging station 340 is plugged into the flexible load 350), the detected state of charge of the flexible load 350 that has been plugged in, the actual power flow or power flow rate between the charging station 340 and the connected flexible load 350, etc. This data can be received by the optimizer 410 periodically and used as input to the optimization model during the current optimization cycle.

[0084] The power market interface 152 can provide an interface with the power market 150, in which the utility operating the power grid 310 is a participant. In particular, the power market 150 can enable the operator of the power infrastructure site 140 to purchase electricity from the utility or other energy providers (e.g., the provider operating the power grid 310), sell electricity to energy providers (e.g., the provider operating the power grid 310), obtain service commitments from energy providers, provide service commitments to energy providers, etc. The optimizer 410 can receive pricing information from the power market interface 152. For example, the pricing information can include price forecasts for electricity from the power grid 310 in one or more future time periods (e.g., including the optimization period), (multiple) uncertainty parameters of the price forecasts, applicable electricity tariff rates, etc. The optimizer 410 can incorporate the pricing information into the input of the optimization model. For example, the objective value output by the optimization model can include the energy cost derived from the pricing information, in which case the optimization objective value can include minimizing the objective value, thereby minimizing the energy cost.

[0085] The optimizer 410 can receive a forecast of DER power generation from the power market interface 152. Alternatively, the optimizer 410 can receive a weather forecast from the power market interface 152 or other external systems (e.g., weather forecast services) and derive the forecast of DER power generation by itself. It should be understood that the electricity generated by renewable energy sources such as solar generators and wind turbines may vary significantly according to the weather. The optimizer 410 can incorporate the forecast of DER power generation into the input of the optimization model, e.g., to determine how much DER power generation is available for the (multiple) power infrastructure sites 140 during the current optimization period.

[0086] The optimizer 410 can obtain service commitments from the power market 150 via the power market interface 152. For example, the optimizer 410 can determine the energy demand required during the optimization period based on the solution of the optimization model (e.g., including the values of one or more variables in the optimization model that optimize the objective value output by the optimization model). The optimizer 410 can send a request for a service commitment from the power market 150 for the determined energy demand during the corresponding optimization period to the power market interface 152. In response, the optimizer 410 can receive a service commitment for the energy demand from the energy provider via the power market interface 152 during the corresponding optimization period. If no energy provider on the power market 150 commits to providing service, the optimizer 410 can update and re-run the optimization model (e.g., impose constraints on the energy demand), and / or initiate or execute other remedial actions.

[0087] Optimizer 410 may obtain other services from power market 150 via power market interface 152. For example, optimizer 410 may receive service pricing for one or more services offered by an energy provider on power market 150 from power market interface 152. Optimizer 410 may incorporate the service pricing into the inputs of the optimization model. Based on the solution of the optimization model, optimizer 410 may determine to purchase one or more services and request service commitments for the (multiple) services from power market 150 via power market interface 152. In response, optimizer 410 may receive the requested service commitments for the (multiple) services via power market interface 152. If no energy provider on power market 150 commits to the service, optimizer 410 may update the inputs of the optimization model to exclude the service pricing and re-run the optimization model, and / or initiate or perform other remedial actions. In an embodiment, optimizer 410 may receive a schedule for the requested service commitments via power market interface 152.

[0088] Optimizer 410 may provide service commitments to power market 150 via power market interface 152. For example, optimizer 410 may provide flexibility information for one or more power infrastructure sites 140 managed by the optimizer to power market 150 via power market interface 152. The flexibility information may include a price-versus-flexibility curve per kilowatt (kW) in the (multiple) power infrastructure sites 140. Energy providers on power market 150 may purchase flexibility from optimizer 410 via power market interface 152. Such flexibility may be used for curtailment (e.g., demand response) when needed. In an embodiment, optimizer 410 may receive a schedule for the provided service commitments via power market interface 152.

[0089] It should be understood that the depicted data flows are merely examples. Optimizer 410 may interface with a set of systems that is fewer, more, or different than the depicted systems. Each system may be used to collect data for incorporation into the inputs of an optimization model solved by optimizer 410, and / or may be a destination for data output by optimizer 410. Examples of additional data that may be collected and used as inputs to the optimization model include, but are not limited to, weather, the status of the (multiple) power infrastructure sites 140, financial figures associated with the (multiple) power infrastructure sites 140, uncertainty estimates (e.g., planned schedules for flexible load 350), etc.

[0090] For example, the optimizer 410 can interact with a weather forecasting service to receive a weather forecast for an optimization period from the weather forecasting service. Incorporating the weather forecast into the optimization model can improve the estimation of energy demand. For example, as described above, the weather forecast can be used to predict DER power generation, which can be incorporated into the inputs of the optimization model. Additionally or alternatively, the optimizer 410 can utilize the weather forecast in a preconditioning model to more accurately estimate the energy demand of the preconditioning flexible load 350. For example, more energy may be required to precondition (e.g., cool or heat) an electric vehicle during relatively hot or cold time periods compared to during mild time periods.

[0091] It should be understood that the above examples are not restrictive. The optimizer 410 can utilize other inputs and / or generate other outputs not specifically described herein. The optimizer 410 can utilize a modular "building block" architecture so that new inputs can be easily incorporated into the optimization model and / or existing inputs can be easily removed from the optimization model. Some of these inputs may represent solutions to the outputs of other optimization systems. Additionally, as described in the various examples, the optimizer 410 can provide additional outputs (e.g., a ranked list) that describe the capacity constraints of EV power supply devices (EVSEs) such as the charging station 340. These additional outputs can be used by other systems (e.g., the scheduling system 420, the site management system 440, etc.), so the optimizer 410 does not have to integrate every detail of the optimization.

[0092] 5. Optimization:

[0093] The optimizer 410 can solve an optimization model that implements an optimization problem in software form for one or more electric power infrastructure sites 140. The optimization model can be generated from the models of the (multiple) electric power infrastructure sites 140. For example, the model of each electric power infrastructure site 140 managed by the optimizer 410 can be stored in a data structure (e.g., the (multiple) databases 114) in the memory. The optimization model can be derived from the model of a single electric power infrastructure site 140 to optimize the operation of the single electric power infrastructure site 140, or can be derived from the models of multiple electric power infrastructure sites 140 to optimize the operation across the multiple electric power infrastructure sites 140. In an embodiment, the optimization model minimizes an objective value based on one or more variables and inputs, the inputs including the scheduling of generators 330 and / or flexible loads 350 in the (multiple) electric power infrastructure sites 140 represented by the models of the (multiple) electric power infrastructure sites 140.

[0094] The variables can represent controllable parameters within one or more power infrastructure sites 140. Examples of controllable parameters include, but are not limited to, setpoints of physical components, amounts of power output by distributed energy resources, power flow rates for charging or discharging flexible loads 350, states of charge reached by charging flexible loads 350 or battery energy storage systems 320, times to start charging or discharging flexible loads 350, times to terminate charging or discharging flexible loads 350, durations of charging or discharging flexible loads 350, assignments or mappings of flexible loads 350 to charging stations 340 or power infrastructure sites 140, etc. Generally, the optimization model will include multiple variables, which potentially include a mix of different types of controllable parameters. In an embodiment, the variables in the optimization model at least include power consumption and / or power generation within one or more power infrastructure sites 140, or are related thereto.

[0095] Mathematically, the optimization model can be expressed as:

[0096]

[0097] Subject to

[0098] ec i (x) = 0, i = 1, …, n ec

[0099] ic j (x) ≤ 0, j = 1, …, n ic

[0100] where x includes the values of all the variables, f(x) is the primary objective function that calculates an estimated target value resulting from the operation of one or more power infrastructure sites 140 using x as the values of the operating variables, ec represents equality constraints, and n ec represents the number of equality constraints (n ec ≥ 0), ic represents inequality constraints, and n ic represents the number of inequality constraints (n ic ≥ 0). It should be understood that the primary objective function f(x) represents the model of one or more power infrastructure sites 140. Generally, the values x of one or more variables represent the operating configurations of one or more power infrastructure sites 140.

[0101] As depicted, there can be zero, one, or more auxiliary objective functions g(x). The auxiliary objective function g(x) can penalize one or more attributes of the value x by adding to the objective value output by the primary objective function f(x) in the same unit of measure as the primary objective function f(x) (e.g., monetary cost). This penalty serves to drive the optimization model away from solutions for values x having those (multiple) attributes. Alternatively, the auxiliary objective function g(x) can reward one or more attributes of the value x by subtracting from the objective value output by the primary objective function f(x) in the same unit of measure as the primary objective function f(x) (e.g., monetary cost). In contrast to a penalty, a reward serves to bias the optimization model towards solutions for values x having those (multiple) attributes.

[0102] The solution of the optimization model can include the value x that minimizes the objective value output as the sum of the primary objective function f(x) and any auxiliary objective function g(x) while satisfying all constraints (e.g., within tolerances). In an embodiment, in contrast to hard constraints, at least some of the constraints can be probabilistic constraints. Additionally, at least some of the constraints can limit parameters associated with the flexible load 350 (e.g., parameters associated with an electric vehicle).

[0103] In an embodiment where the objective value includes an energy cost, the primary objective function f(x) takes into account the (multiple) energy prices during the optimization period when calculating the objective value. For example, the primary objective function f(x) can determine the power demand profile generated by the value x and use the (multiple) energy prices and the power demand profile (e.g., calculate the product of the power demand profile and the (multiple) energy prices) to determine the objective value as its output. The primary objective function f(x) can also take into account other costs associated with the operation of the (multiple) power infrastructure sites 140 during the optimization period, such as grid charges, network service costs, indirect capital costs, etc.

[0104] The primary objective function f(x) and / or the auxiliary objective function g(x) (if any) can include mixed integer programming, linear programming, quadratic programming, mixed integer linear programming (MILP), mixed integer quadratic programming (MIQP), etc. Generally, using linear programming can improve the computational speed and scalability of the optimization model, which is particularly advantageous when the primary objective function f(x) and / or the (multiple) auxiliary objective functions g(x) (if any) include a large number of variables or other parameters (e.g., for a large number of flexible loads 350). There are many commercial and open-source modeling languages available for defining the objective function f(x) and any auxiliary objective function g(x).

[0105] The objective function f(x) and / or the auxiliary objective function(s) g(x) (if any) can be trained in any known manner. For example, the objective function f(x) can be trained using supervised machine learning. In this case, a training data set (X, Y) can be used, where X represents a set of historical values of the variable(s), and Y represents the benchmark objective values of the historical values of these variable(s). In this case, the training can be expressed as:

[0106] min(Y - f(X))

[0107] wherein f(X) (e.g., the weights in f(X)) is updated to minimize the error between the benchmark objective value Y and the corresponding objective value output by f(X). Alternatively, the objective function f(x) can be trained in other ways using historical data. Any auxiliary objective function g(x) can be trained in the same, similar, or different manner as the primary objective function f(X), and / or trained together with the primary objective function f(X).

[0108] Although the optimization model is expressed as a minimization problem in this article, it should be understood that the optimization model can also be expressed as a maximization problem in this article:

[0109]

[0110] subject to zero, one, or more constraints. However, for simplicity of description, it is generally assumed in this article that the optimization model is constructed as a minimization problem. Those skilled in the art will understand how to convert between a minimization problem and a maximization problem, and which problem may be more appropriate in a given situation.

[0111] The optimization model is solved to determine the value(s) of one or more variables that optimize the objective value. In other words, the optimization model is evaluated to determine the value x that optimizes (e.g., minimizes) the objective value output by the optimization model. Solving the optimization model can include iteratively executing the optimization model using different sets of values of x in each iteration until the objective value converges. After each iteration, the value of x for the next iteration can be determined using any known technique (e.g., gradient descent). The objective value can be determined to have converged when the objective value is within a tolerance of a specific value, when the improvement rate of the objective value relative to the previous iteration meets a threshold (e.g., the rate of decrease of the objective value in a minimization problem is below the threshold), and / or when one or more other criteria are met. Once the objective value has converged, the value x that produces the final objective value can be output as the solution of the optimization model. These values of x can represent the optimal operating configurations of the power infrastructure site(s) 140.

[0112] The optimization model can be a stochastic optimization model that is robust to uncertainty. Any suitable technique can be used to solve the optimization model. These techniques include, but are not limited to: stochastic multi-stage optimization, chance-constrained optimization, Markowitz mean-variance optimization, etc. There are many commercial and open-source solvers available for solving the optimization model.

[0113] In an embodiment, multiple optimization models each including a different primary objective function f(x) can be solved. Each primary objective function f(x) can represent a different scenario. Such an embodiment can be used to evaluate multiple different "what-if" scenarios. Alternatively or additionally, each primary objective function f(x) can represent a different goal. The final solution can be determined from the solutions by selecting one of the solutions output from the multiple optimization models, combining the solutions in any suitable manner, etc.

[0114] 6. Process overview

[0115] Embodiments of the process of using energy-time reserves to mitigate uncertainty in scheduling charging will be described in detail below. It should be understood that the described process can be embodied in one or more software modules executed by one or more hardware processors, e.g., as software 112 executed by the (multiple) processors 210 of the EMS 110. The described process can be implemented as instructions represented in source code, object code, and / or machine code. These instructions can be directly executed by the (multiple) hardware processors 210, or alternatively, can also be executed by a virtual machine or container operating between the object code and the hardware processors 210. Additionally, the disclosed software can be built on or interface with one or more existing systems.

[0116] Alternatively, the described process can be implemented as a hardware component (e.g., a general-purpose processor, an integrated circuit (IC), an application-specific integrated circuit (ASIC), a digital signal processor (DSP), a field-programmable gate array (FPGA), or other programmable logic device, discrete gate or transistor logic, etc.), a combination of hardware components, or a combination of hardware components and software components. To clearly illustrate the interchangeability of hardware and software, various illustrative components, blocks, modules, circuits, and steps are generally described herein according to their functions. Whether this function is implemented as hardware or software depends on the specific application and the design constraints imposed on the overall system. A person skilled in the art can implement the described function in different ways for each specific application, but such implementation decisions should not be construed as causing a departure from the scope of the present invention. Additionally, the functional grouping within a component, block, module, circuit, or step is for ease of description. Without departing from the present invention, a specific function or step can be moved from one component, block, module, circuit, or step to another.

[0117] Figure 5 FIG. 500 illustrates an example process for mitigating uncertainty in scheduling charging using an energy - time reserve, according to an embodiment. Process 500 may be implemented by optimizer 410. Although process 500 is illustrated by a certain arrangement and ordering of sub - processes, process 500 may be implemented by fewer, more, or different sub - processes and different arrangements and / or orderings of sub - processes. Additionally, it should be understood that any sub - process that does not depend on the completion of another sub - process may be executed before, after, or in parallel with that other independent sub - process, even if the sub - processes are described or illustrated in a particular order.

[0118] In sub - process 510, as described elsewhere herein, an optimization model is generated from a model of one or more power infrastructure sites 140. The power infrastructure site(s) may include one or more power infrastructure assets. The power infrastructure asset(s) may include one or more charging stations 340 and / or one or more flexible loads 350, but may also include other infrastructure assets (including one or more non - flexible loads) or be composed of them. One or more (and potentially all) of these power infrastructure assets may be associated with an energy reserve profile. Each power infrastructure asset associated with an energy reserve profile may be associated with a different or independent energy reserve profile from one or more other power infrastructure assets, and / or may be associated with the same energy reserve profile as one or more power infrastructure assets.

[0119] The optimization model may output an objective value based on one or more variables (i.e., values x), subject to any energy reserve profile associated with the power infrastructure asset(s). In an embodiment, the energy reserve profile reduces the energy available to the associated power infrastructure asset over time. For example, if the power infrastructure asset is a charging station 340, the energy reserve profile may reduce the energy that the charging station can deliver to a load in the optimization. As another example, if the power infrastructure asset is a flexible load 350, the solution of the optimization model schedules the charging of flexible load 350 further into the future, and the less energy is available for charging that flexible load 350 in the optimization. Conceptually, such a constraint reserves energy for the power infrastructure asset to mitigate future uncertainty. The further into the future charging by or of the power infrastructure asset is scheduled, the more energy is reserved to address greater uncertainty. In other words, the magnitude of the energy reserve may be proportional to the risk. In the event of a disruption during the actual operation of the power infrastructure site(s) 140, the reserved energy may be used to prevent an operational interruption.

[0120] Each energy reserve profile can define the energy reserve for each of a plurality of discrete time points, or define the energy reserve as a continuous function of time starting from the current time or anchored to another time point. In either case, the shape of the energy reserve profile can be referred to herein as a "curve" because even when using a set of discrete time points, the value at time points outside the set can be interpolated such that the energy reserve at any time point can be determined. The shape of the energy reserve profile can be learned empirically and / or selected by an operator or other user (e.g., via the graphical user interface of the EMS 110) of the power infrastructure site(s) 140 based on a degree of risk tolerance (similar to an economic discount rate).

[0121] As a non-limiting example, the energy reserve profile can be defined as a set of breakpoints, each breakpoint represented as a tuple of a time point and an energy reserve. Each breakpoint represents the energy reserve at a particular time step. For example, the energy reserve profile can be represented by a plurality of breakpoints: {time = 0 seconds, reserve = 0%}; {time = 3600 seconds, reserve = 10%}; {time = 7200 seconds, reserve = 25%}; and so on. The energy reserve at time points not represented in the set of breakpoints can be interpolated (e.g., via linear interpolation) from the nearest pair of breakpoints on either side of the unrepresented time point. Using the above example, the energy reserve at the 4000-second time point can be linearly interpolated as: 10% + (4000 - 3600) / (7200 - 3600)*(25% - 10%) = 11.67%. The breakpoints can be defined at a granularity corresponding to the granularity at which the optimizer 410 performs optimization (e.g., every 15 minutes).

[0122] In an embodiment, each energy reserve profile is added as a constraint to the optimization model. Mathematically, the constraint for the energy reserve profile can be expressed as:

[0123]

[0124] where, P a,t is the effective charging power available for power infrastructure asset a at time t, is the nominal power available for power infrastructure asset a, and is the energy reserved for power infrastructure asset a at time t, as defined by the energy reserve profile. This constraint can be transformed into an inequality constraint ic(a, t) as follows:

[0125]

[0126] In sub-process 520, the optimization model is solved to determine the values of one or more variables that optimize the objective value. In other words, the optimization model is evaluated to determine the value x that optimizes (e.g., minimizes) the objective value output by the optimization model. Solving the optimization model can include iteratively executing the optimization model with different sets of values x in each iteration until the objective value converges. After each iteration, the value x for the next iteration can be determined using any known technique (e.g., gradient descent). The objective value can be determined to have converged when it is within a tolerance of a specific value, when the rate of improvement of the objective value relative to the previous iteration meets a threshold (e.g., the rate of decrease of the objective value in a minimization problem is below the threshold), and / or when one or more other criteria are met. Once the objective value has converged, the value x that results in the final objective value can be output as the solution to the optimization model. These values x can represent the optimal operating configurations of the (multiple) power infrastructure sites 140.

[0127] It should be understood that the optimization model is restricted by the constraints imposed by the (multiple) energy reserve distributions. Although the solution to the optimization model may still wait until the last possible moment to charge the power infrastructure assets (e.g., to obtain a better electricity price), it will have to maintain an energy reserve proportional to the risk of disruption, taking into account the amount of future uncertainty. If a disruption actually occurs during the operation of the (multiple) power infrastructure sites 140 and the disruption affects the energy available to the power infrastructure assets, the energy reserve can be used to avoid an interruption in the scheduled charging. It is worth noting that if the optimization model includes multiple constraints representing multiple energy reserve distributions for multiple power infrastructure assets, the energy reserves of the multiple power infrastructure assets are pooled into an energy reserve pool that can act as insurance against asset-specific disruptions.

[0128] In sub-process 530, control of the (multiple) power infrastructure sites 140 for which the optimization was performed in sub-process 520 can be initiated based on the solution to the optimization model. This control can include configuring one or more physical components in the (multiple) power infrastructure sites 140 based on the determined value x representing the operating configuration. These physical components can include physical infrastructure assets such as the (multiple) battery energy storage systems 320, the (multiple) generators 330, the (multiple) charging stations 340, the (multiple) chargers 342, the (multiple) flexible loads 350, the (multiple) auxiliary loads, etc.

[0129] As described above, the solution to the optimization model includes the values x of one or more variables that optimize the objective value in sub-process 520. The value x can represent the operating configuration of the (multiple) power infrastructure sites 140. For example, the value x can include the future charging pattern (e.g., power flow rate, charging time period, etc.) for each flexible load 350, which charges the flexible load 350 to the target state of charge according to the scheduled time. Since the (multiple) energy reserve distributions are included as (multiple) constraints in the optimization model, the solution will be robust to disturbances during the actual operation of the power infrastructure sites 140 according to the operating configuration.

[0130] In the case where the flexible load 350 is an electric vehicle, the scheduled time can be the departure time, and the target state of charge can be the state of charge required for the electric vehicle to complete its scheduled route. Charging can also include or otherwise account for pre-conditioning of the electric vehicle (e.g., cooling the electric vehicle before it departs, pre-conditioning the battery of the electric vehicle, etc.), as well as charging the battery of the electric vehicle. However, the pre-conditioning can be a flexible operating state, which can be terminated or abandoned when it is necessary to charge the electric vehicle according to the scheduled departure time, or when the optimizer 410 determines that the power can be better used elsewhere.

[0131] Sub-process 530 can include the optimizer 410 generating control information and sending the control information to one or more control systems 142. Then, each control system 142 can control the (multiple) physical components in its corresponding power infrastructure site 140. Alternatively, the optimizer 410 can directly control the (multiple) physical components (i.e., without an intermediate control system). In either case, the control can include setting the set points of the physical components, actuating switches, turning the physical components on or off, or otherwise changing the physical or operating state of the physical components, etc. The set points of the physical components can include values such as voltage, current, output power, input power, power flow rate, state of charge, temperature, etc. For example, the control can include controlling the (multiple) set points (e.g., output power) of non-intermittent distributed energy resources. It should be understood that although intermittent distributed energy resources (e.g., solar or wind generators or other weather-dependent generators) can be controlled in a similar manner, intermittent distributed energy resources can generally only be controlled to curtail the output power to be lower than its potential output power, which essentially wastes energy.

[0132] In an embodiment, process 500 may be executed periodically to determine a value x representing the operating configuration of power infrastructure site(s) 140 in a sliding time window and initiate control of power infrastructure site(s) 140 to conform to those operating configurations within an optimization period represented by the sliding time window. The sliding time window and the corresponding optimization period may be of any suitable time length, such as one hour, twelve hours, twenty-four hours, multiple days, etc. The sliding time window may slide based on a time step (i.e., expiration of a time interval) and process 500 may be executed within the optimization period currently represented by the sliding time window after each time step. For example, the time step may be one minute, five minutes, ten minutes, fifteen minutes, thirty minutes, one hour, one day, or any other time interval. The sliding time window may start from the current time and end in the future, or may start in the future and end further in the future. In the former case, process 500 is executed at the start of each optimization period, while in the latter case, process 500 is executed before each optimization period (e.g., one minute, five minutes, ten minutes, fifteen minutes, thirty minutes, one hour, one day, etc. in advance). The periodic execution of process 500 may be automatically executed (i.e., without user intervention) or semi-automatically executed (e.g., with user confirmation) after each time step. In either case, once the execution of process 500 is initiated, each sub-process of process 500 (including control initiation in sub-process 530) may be automatically executed.

[0133] In an alternative or additional embodiment, process 500 may be executed in response to a trigger event other than a time step. For example, process 500 may be executed in response to a user operation. In particular, the user may execute optimizer 410 using one or more inputs of a graphical user interface provided by software 112. In this case, control initiation in sub-process 530 may be executed automatically, semi-automatically, or manually. In the semi-automatic case, the graphical user interface may display the operating configuration output by sub-process 520 to the user and request user confirmation before optimizer 410 executes sub-process 530. In the manual case, the graphical user interface may provide the operating configuration output by sub-process 520 to the user and the user may manually configure power infrastructure site(s) 140.

[0134] 7. Example energy reserve distribution

[0135] Figures 6A to 6DIllustrated are various examples of energy - time reserves according to an embodiment. Each energy reserve profile is illustrated as the amount of power available to an associated power infrastructure asset or the amount of energy reserve not available to the associated power infrastructure asset at multiple time points (e.g., represented as breakpoints at any time step) before and after a single time step. Each energy reserve profile decreases the energy available to the power infrastructure asset (e.g., charging station 340 or flexible load 350) or increases the energy reserve not available to the power infrastructure asset from a start time (e.g., representing the start of an optimization period) to an end time (e.g., representing the end of an optimization period). At each time point, the energy available to the power infrastructure asset or the energy reserve not available to the power infrastructure asset can be represented as a percentage of a nominal power P nom In the example shown, the energy reserve at each time point is indicated as a percentage of the nominal power P nom .

[0136] In an embodiment, the energy reserve profile can be defined relative to the maximum charging power of a particular power infrastructure asset, represented as a nominal power P nom . The energy reserve profile can be a piece - wise linear function from 100% of the nominal power P nom at the start of the optimization period to a defined value (e.g., percentage) of the nominal power P nom at the end of the optimization period (e.g., 80% of P nom ). However, it should be understood that the energy reserve profile can be represented by another type of function, can start at less than 100% of the nominal power P nom , and / or can end at 0% of the nominal power P nom .

[0137] Generally, each energy reserve profile defines a time - varying "curve" of available charging power, where the future available charging power is equal to or less than the nominal power P nom . The difference between the curve and the nominal power P nom is considered the future energy reserve for protection against uncertainty and should be sized proportionally to the amount of risk. The shape of the curve and the corresponding energy reserve amount can reflect the weighted uncertainty, impact, and risk tolerance of factors affecting charging and asset utilization (e.g., the amount of time the flexible load 350 is plugged in, energy demand, the departure time of the flexible load 350, etc.). The curve can be derived in any way and can be based on an estimate of charging power availability. Examples of how the curve of the energy reserve profile can be derived include, but are not limited to: a discount rate, similar to economic discounting (e.g., multiplying P nom by an x% multiplier per time step); a discount slope (e.g., decreasing from P nomLinear discount (x%); event-based discount penalty (e.g., from P for the period after the scheduled arrival time); nom Discount of x% to account for delays, from P if the electric vehicle has not been inspected and cleaned nom Discount of x% etc.); state-based discount penalty (e.g., from P if communication with the telemetry system of the electric vehicle is lost) nom Discount of x%, if the asset monitoring system indicates abnormal behavior or a higher risk of equipment failure in the associated power infrastructure asset, from P nom Discount of x% etc.); empirically estimated discount distributions based on past performance, actual telemetry, environmental conditions (e.g., snow, extreme heat, etc.), etc.; probability forecasts from the scheduling system 420; manual inputs from the fleet supervisor to account for unmeasured phenomena or risk tolerances; and so on. It should be noted that any factor or combination of factors can be incorporated into the energy reserve distribution for a given power infrastructure asset, providing unlimited flexibility in the amount and type of information that can be "factored into" the constraints of the optimization problem.

[0138] In an embodiment, the energy reserve distribution can slide with the sliding time window of the optimizer 410. The sliding time window defines the optimization period optimized by the optimizer 410. After each advancement of the sliding time window (e.g., continuously or according to a time step), the energy reserve distribution can slide by the same amount. In other words, the start of the energy reserve distribution can be fixed to the start of the sliding time window. Alternatively, the end of the energy reserve distribution can be fixed to the end of the sliding time window.

[0139] In an embodiment, each power infrastructure asset is associated with an independent energy reserve profile. In an alternative embodiment, each power infrastructure asset may be associated with the same energy reserve profile, or a subset of power infrastructure assets may be associated with the same energy reserve profile while different subsets are associated with different energy reserve profiles. As another possible embodiment, power infrastructure assets of the same type (e.g., the same type of charging station 340, the same type of battery, the same model of electric vehicle, etc.) may be associated with the same energy reserve profile while different types of power infrastructure assets are associated with different energy reserve profiles. As additional examples of embodiments, all power infrastructure assets within the same power infrastructure site 140 may be associated with the same energy reserve profile and different power infrastructure sites 140 may have different energy reserve profiles, all electric vehicles within the same EV fleet may be associated with the same energy reserve profile and different EV fleets may have different energy reserve profiles (e.g., to reflect the specific risk tolerance of each fleet operator), each charging station 340 may be associated with an energy reserve profile different from that of other charging stations 340 (e.g., to reflect the historical reliability of the corresponding charging station 340), each electric vehicle may be associated with an energy reserve profile different from that of other electric vehicles (e.g., to reflect the historical reliability of the corresponding electric vehicle), any electric vehicle assigned to a specific route may be associated with the same energy reserve profile and different routes may have different energy reserve profiles (e.g., to reflect the historical latency of the corresponding route), etc. It should be understood that the energy reserve profiles may be associated with different subsets of power infrastructure assets in any manner to reflect differences in historical reliability, risk tolerance, and / or other factors.

[0140] Figure 6A Illustrated is an energy reserve profile that slides with the sliding time window of the optimizer 410 according to time steps. Figure 6A The time t in may correspond to the start of the optimization period being optimized by the optimizer 410. The energy reserve profile will bias the optimization model towards a solution that charges the associated power infrastructure asset (e.g., a flexible load 350 such as an electric vehicle) at time t (i.e., immediately). This is because if the optimization solution schedules charging of the power infrastructure asset at time t (i.e., the energy reserve at time t is 0%), the optimization solution does not have to account for any energy reserve. In other words, the entire energy capacity is available for charging. Since the energy reserve profile slides with the sliding time window of the optimizer 410, when the start of the optimization period becomes time t+1 (e.g., the sliding time window slides such that the start of the sliding time window becomes time t+1), if the optimization solution schedules charging of the power infrastructure asset at the start of the optimization period, the optimization solution can again benefit from the entire energy capacity.

[0141] It should be understood that the optimized solution need not schedule to charge the power infrastructure at time t or immediately. For example, the optimized solution can schedule to charge the power infrastructure assets at a later time, provided that the benefits obtained by doing so can offset the impact of the loss of available energy capacity imposed on the optimization model due to the energy reserve distribution. For example, in order for the optimized solution to schedule to charge the power infrastructure assets at time t + 3, it will need to consider that the available energy will be reduced by x3% due to the constraints imposed by the energy reserve distribution at time t + 3. In other words, when scheduling to charge the power infrastructure assets at time t + 3, the optimized solution will have to set aside x3% of the energy reserve of P nom to mitigate the future uncertainty over three time steps. However, the optimized solution can still do so to obtain a lower electricity price or other compensatory benefits for waiting until time t + 3 to start charging the power infrastructure assets. If necessary, the optimized solution can address the energy reserve by scheduling the power infrastructure assets to charge for a longer time, assigning the power infrastructure assets to fast chargers, etc., to ensure that the power infrastructure assets are charged according to the scheduled time (e.g., scheduled departure time).

[0142] In an alternative or additional embodiment, the energy reserve distribution can be anchored to a scheduling event. In this case, once the event has occurred or been scheduled, the energy reserve distribution is fixed in time and is not affected by the advancement of the sliding time window of the optimizer 410 (i.e., does not slide with it). For example, the (multiple) power infrastructure sites 140 can include power supply stations (e.g., EV stations), the associated power infrastructure assets can be electric vehicles, and the scheduling event can be the arrival, plug-in, unplugging, or departure of an electric vehicle at the power supply station. In this case, the start of the energy reserve distribution associated with the electric vehicle can be set to the scheduled arrival or plug-in time of the electric vehicle at the power infrastructure site 140. Alternatively, the end of the energy reserve distribution associated with the electric vehicle can be set to the scheduled unplugging or departure time of the electric vehicle from the power infrastructure site 140.

[0143] Figure 6BIllustrates the energy reserve distribution anchored to the scheduled arrival time a of a power infrastructure asset. Similarly, the energy reserve distribution biases the optimization model towards solutions that charge the associated power infrastructure asset (e.g., a flexible load 350 such as an electric vehicle) at the scheduled arrival time a. Conceptually, this makes sense because charging the power infrastructure asset immediately upon its arrival eliminates the risk of intervening disturbances reducing the available energy of the power infrastructure asset. However, similarly, the optimization solution freely schedules charging the power infrastructure asset at a later time, as long as it maintains the energy reserves required by the energy reserve distribution and satisfies any other constraints (e.g., achieving a sufficient state of charge at the scheduled departure time). Anchoring the energy reserves to the arrival time can be used to capture the probability of the power infrastructure asset being late (e.g., by assigning non-zero energy reserves for time steps after the scheduled arrival time). Since the energy reserve distribution is anchored to the arrival time a, when the start of the optimization period becomes a + 1 (e.g., the sliding time window slides such that the start of the sliding time window becomes time a + 1), the optimization solution must set aside x1% of the energy reserves of P nom , even if it schedules to charge the power infrastructure asset at the start of the optimization period. Alternatively, the energy reserves at the start of the optimization period can be driven to 0% of P nom via some mechanism (e.g., by always multiplying the energy reserves at the first breakpoint by zero), such that the optimization solution can always benefit from the full energy capacity when it schedules to charge the power infrastructure asset at the start of the optimization period.

[0144] Figure 6C Illustrates the energy reserve distribution anchored to the scheduled departure time d of a power infrastructure asset. Similarly, the energy reserve distribution biases the optimization solution towards solutions that charge the associated power infrastructure asset (e.g., a flexible load 350 such as an electric vehicle) immediately at the start of the optimization period, but the optimization solution freely schedules charging the power infrastructure at a later time, as long as it maintains the energy reserves required by the energy reserve distribution and satisfies any other constraints. Since the energy reserve distribution is anchored to the scheduled departure time d, when the start of the optimization period becomes d - 4 (e.g., the sliding time window slides such that the start of the sliding time window becomes time d - 4), the optimization solution must set aside x1% of the energy reserves of P nom , even if it schedules to charge the power infrastructure asset at the start of the optimization period. Alternatively, the energy reserves at the start of the optimization period can be driven to 0% of P nom via some mechanism (e.g., by always multiplying the energy reserves at the first breakpoint by zero), such that the optimization solution can always benefit from the full energy capacity when it schedules to charge the power infrastructure asset at the start of the optimization period.

[0145] At a time step before or at the scheduled departure time d (i.e., d - 1), the energy reserve can become 100%. In this case, the optimal solution will be forced to schedule charging the power infrastructure asset in advance carefully. This is because the optimal solution is constrained by the 100% energy reserve and is prevented from scheduling the charging too close to the scheduled departure time d. The effect of a 100% energy reserve at a time step before the scheduled departure time d is the same as the effect of shifting the scheduled departure time forward by one time step to buffer some time before the departure (i.e., forcing the optimization to prepare the power infrastructure asset in advance). However, it should be understood that this is not a necessary condition for any embodiment.

[0146] In alternative or additional embodiments, the energy reserve profile associated with a power infrastructure asset can be determined by combining two or more different energy reserve profiles. For example, an energy reserve profile that slides with the sliding time window of the optimizer 410 (e.g., according to time steps) can be combined with an energy reserve profile that is anchored to a scheduling event. Alternatively, two or more different energy reserve profiles that slide with the sliding time window of the optimizer 410 can be combined, two or more different energy reserve profiles that are anchored to the same scheduling event can be combined, two or more different energy reserve profiles that are anchored to different scheduling events can be combined, etc. It should be understood that any number of the same type and / or different types of energy reserve profiles can be combined in any way to produce a final energy reserve profile for use with any given power infrastructure asset.

[0147] Figure 6D Illustrated by combining Figure 6A the sliding energy reserve profile depicted in Figure 6BThe energy reserve distribution depicted in (i.e., the scheduled arrival time anchored to the power infrastructure asset) determines the energy reserve distribution. The energy reserve distribution can be linearly combined by multiplying the energy reserve distributions, selecting the maximum value of the energy reserves for each break point, or in any other suitable way (e.g., by taking the average of the energy reserve amounts for each corresponding break point). For an optimization period starting at the scheduled arrival time a, the energy reserve is 0% at the scheduled arrival time a, increases to x1% at time a + 1, increases to x2% at time a + 2, and so on. When the start of the optimization period becomes a + 1 (e.g., the sliding time window slides such that the start of the sliding time window becomes time a + 1), the energy reserve is x6% at time a + 1, increases to x7% at time a + 2, and so on. The energy reserve x6% represents a combination of 0% in the sliding energy reserve distribution and x1% in the anchored energy reserve distribution (e.g., x6% = (0% + x1%) / 2), the energy reserve x7% represents a combination of x1% in the sliding energy reserve distribution and x2% in the anchored energy reserve distribution (e.g., x7% = (x1% + x2%) / 2), and so on.

[0148] As another example, the energy reserve distributions can be combined according to hierarchies. For example, each power infrastructure site 140 can be associated with an energy reserve distribution representing the corresponding reliability, each fleet operator can be associated with an energy reserve distribution representing the corresponding risk tolerance, each charging station 340 can be associated with an energy reserve distribution representing the corresponding reliability, each route can be associated with an energy reserve distribution representing the corresponding uncertainty, and / or each electric vehicle can be associated with an energy reserve distribution representing the corresponding reliability. In this case, for a given electric vehicle, the energy reserve distribution of the electric vehicle, the energy reserve distribution of the route to which the electric vehicle is assigned, the energy reserve distribution of the charging station 340 at which the electric vehicle is scheduled to charge, the energy reserve distribution of the fleet operator operating the electric vehicle, and the energy reserve distribution of the power infrastructure site 140 including the charging station 340 at which the electric vehicle is scheduled to charge can all be combined into a single composite energy reserve distribution. More generally, one or more individual energy reserve distributions at different hierarchical levels and / or other individual energy reserve distributions related to the charging of a given power infrastructure asset can be combined into a single composite energy reserve distribution, and the single composite energy reserve distribution can be used to constrain the optimization involving the power infrastructure asset.

[0149] The energy reserve distribution can be generated and / or updated periodically (e.g., hourly or other time steps) in response to events, etc. For example, the energy reserve distribution associated with a power infrastructure asset can be obtained, generated (e.g., as a composite of multiple energy reserve distributions), or updated in response to one or more completion events. Completion events can include an electric vehicle arriving at the power infrastructure site 140, an electric vehicle plugging into the charging station 340, an electric vehicle unplugging from the charging station 340, an electric vehicle leaving the power infrastructure site 140, etc.

[0150] 8. Example embodiment

[0151] The disclosed embodiments associate an energy reserve distribution with one or more power infrastructure assets in one or more power infrastructure sites 140. Each energy reserve distribution models the available charging power as a time-varying value rather than a fixed value. When the (multiple) energy reserve distributions are included as constraints in the optimization model, the optimization model anticipates a reduction in the future available charging power. In essence, the optimization model will trade off the cost of uncertainty and charging schedule disruptions against other technical constraints or financial objectives. Thus, the optimization model will reduce the reliance on future charging with associated uncertainties and bias towards charging the flexible loads 350 (e.g., electric vehicles) earlier. This mitigates future uncertainties to improve the average reliability of on-time charging (e.g., for an EV fleet).

[0152] Each energy reserve distribution reflects an energy reserve that provides a buffer against disturbances not reflected in the optimization model. The longer the optimization model waits to charge the flexible loads 350, the more energy the optimization model must reserve for the flexible loads 350, and the less energy is available for the overall optimization solution. Notably, the energy reserves of multiple power infrastructure assets are functionally pooled by the optimization model for added protection.

[0153] In an embodiment, the (multiple) power infrastructure sites 140 are EV yards, and the energy reserve distribution is associated with each charging station 340 in the (multiple) power infrastructure sites 140 and / or the electric vehicles scheduled to be charged in the (multiple) power infrastructure sites 140 (e.g., as flexible loads 350). Each charging station 340 can have a nominal power P nom . The nominal power P nom can be defined as the most restrictive among the capabilities of the charging station 340, the charger 342, the connected electric vehicle, etc. Alternatively, the nominal power P nomIt can be defined in other ways, such as absolute power (e.g., in kilowatts or kilowatt-hours), percentage of charging power, EV range, and / or percentage of state of charge of the battery, etc. In any case, the energy reserve distribution can be based on the nominal power P nom and defined as a constraint in the optimization model of the optimizer 410 executed by the EMS 110, so as to provide protection against future uncertainties in the form of energy reserves.

[0154] Such embodiments can improve the reliability of charging optimization for an EV fleet and reduce the probability that an electric vehicle fails to be charged on time due to unplanned disturbances. Additionally, the disclosed embodiments are mathematically compact and easy to handle, enabling fast execution, short response times, and scalability of optimization for large EV fleets. The use of individual power infrastructure assets and / or the energy reserve distribution defined at a higher level provides flexibility in estimating weighted uncertainties, impacts, and risk tolerances at different levels of detail in space or time (e.g., per vehicle per minute, per site per day, etc.).

[0155] Embodiment 1: A method includes using at least one hardware processor to: generate an optimization model for at least one power infrastructure site, where the at least one power infrastructure site includes one or more power infrastructure assets, where at least one of the one or more power infrastructure assets is associated with an energy reserve distribution that reduces the energy available for the power infrastructure asset over time, and where the optimization model outputs a target value based on one or more variables representing the operating configuration of the at least one power infrastructure site, while being constrained by the energy reserve distribution associated with the at least one power infrastructure asset; solve the optimization model to determine the values of the one or more variables that optimize the target value; and based on the determined values of the one or more variables, initiate control of one or more physical components in the at least one power infrastructure site.

[0156] Embodiment 2: The method according to Embodiment 1, wherein the optimization model is periodically generated and solved to determine the one or more variables representing the operating configuration of the at least one power infrastructure site in a sliding time window that slides according to a time step.

[0157] Embodiment 3: The method according to Embodiment 2, wherein the energy reserve distribution associated with the at least one power infrastructure asset slides with the sliding time window according to the time step.

[0158] Embodiment 4: The method according to Embodiment 2, wherein the energy reserve distribution associated with the at least one power infrastructure asset is anchored to a scheduling event.

[0159] Example 5: The method according to Example 4, wherein the at least one power infrastructure site is a station, wherein the at least one power infrastructure asset is an electric vehicle, and wherein the scheduling event is the arrival or departure of the electric vehicle at the station.

[0160] Example 6: The method according to Example 2, further comprising using the at least one hardware processor to determine the energy reserve distribution associated with at least one of the one or more power infrastructure assets by combining: the energy reserve distribution that slides with the time step along with the sliding time window; and the energy reserve distribution anchored to the scheduling event.

[0161] Example 7: The method according to Example 6, wherein the at least one power infrastructure site is a station, wherein the at least one power infrastructure asset is an electric vehicle, and wherein the scheduling event is the arrival or departure of the electric vehicle at the station.

[0162] Example 8: The method according to any one of Examples 1 to 7, further comprising using the at least one hardware processor to update the energy reserve distribution associated with at least one of the one or more power infrastructure assets in response to one or more completion events.

[0163] Example 9: The method according to any of the preceding examples, wherein the one or more power infrastructure assets include one or more flexible loads each including a battery.

[0164] Example 10: The method according to Example 9, wherein the energy reserve distribution associated with each of the one or more flexible loads reduces the effective charging power of the battery available for that flexible load over time.

[0165] Example 11: The method according to Example 9 or 10, wherein each of the one or more flexible loads is an electric vehicle.

[0166] Example 12: The method according to any of the preceding examples, wherein the at least one power infrastructure site includes a station, wherein the one or more power infrastructure assets include electric vehicles, and wherein the one or more physical components include one or more charging stations configured to be electrically connected to the electric vehicles to charge the electric vehicles.

[0167] Example 13: The method according to Example 12, wherein the determined value of the one or more variables associates each of the electric vehicles with one or both of the following: a period of time or a power flow rate for charging at one of the one or more charging stations in the at least one power infrastructure site.

[0168] Example 14: The method according to any of the preceding examples, wherein the target value at least includes an energy cost, and wherein optimizing the target value includes minimizing the target value.

[0169] Example 15: The method according to any of the preceding examples, wherein initiating control of one or more physical components includes controlling the set points of the one or more physical components based on the determined value of the one or more variables.

[0170] Example 16: The method according to Example 15, wherein the one or more physical components include non-intermittent distributed energy sources.

[0171] Example 17: The method according to any of the preceding examples, wherein initiating control includes communicating via at least one network with a control system for the at least one power infrastructure site.

[0172] Example 18: A system, comprising at least one hardware processor; and software configured to perform the method according to any one of Examples 1 to 17 when executed by the at least one hardware processor.

[0173] Example 19: A non-transitory computer-readable medium having instructions stored thereon, wherein the instructions, when executed by a processor, cause the processor to perform the method according to any one of Examples 1 to 17.

[0174] The above description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles described herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, it should be understood that the description and drawings presented herein represent the current preferred embodiments of the invention and thus represent the broad subject matter contemplated by the invention. It should further be understood that the scope of the invention fully encompasses other embodiments that may be obvious to those skilled in the art, and thus the scope of the invention is not limited.

[0175] As used herein, the terms "comprising", "comprise", and "comprises" are open-ended. For example, "A comprises B" means that A can include any of the following: (i) only B; or (ii) a combination of B and one or more (and potentially any number of) other components. In contrast, the terms "consisting of", "consist of", and "consists of" are closed-ended. For example, "A consists of B" means that A includes only B and no other components in the same context.

[0176] Combinations described herein such as "at least one of A, B, or C", "one or more of A, B, or C", "at least one of A, B, and C", "one or more of A, B, and C", and "any combination of A, B, C, or thereof" include any combination of A, B, and / or C and can include multiple A's, multiple B's, or multiple C's. Specifically, combinations such as "at least one of A, B, or C", "one or more of A, B, or C", "at least one of A, B, and C", "one or more of A, B, and C", and "any combination of A, B, C, or thereof" can be only A, only B, only C, A and B, A and C, B and C, or A and B and C, and any such combination can include one or more members of its constituent elements A, B, and / or C. For example, a combination of A and B can include one A and multiple B's, multiple A's and one B, or multiple A's and multiple B's.

Claims

1. A method, comprising using at least one hardware processor to: Generate an optimization model for at least one power infrastructure site, wherein, The at least one power infrastructure site includes one or more power infrastructure assets, where at least one of the one or more power infrastructure assets is associated with an energy reserve profile that decreases the energy available for that power infrastructure asset over time, and where the optimization model outputs a target value based on one or more variables representing the operating configuration of the at least one power infrastructure site, subject to the constraint of the energy reserve profile associated with the at least one power infrastructure asset; Solving the optimization model to determine values of the one or more variables that optimize the target value; and Based on the determined values of the one or more variables, initiating control of one or more physical components in the at least one power infrastructure site.

2. The method according to claim 1, wherein, Periodically generating and solving the optimization model to determine the one or more variables representing the operating configuration of the at least one power infrastructure site in a sliding time window that slides according to a time step.

3. The method according to claim 2, wherein, The energy reserve profile associated with the at least one power infrastructure asset slides with the sliding time window according to the time step.

4. The method according to claim 2, wherein, The energy reserve profile associated with the at least one power infrastructure asset is anchored to a scheduling event.

5. The method according to claim 4, wherein, The at least one power infrastructure site is a depot, where the at least one power infrastructure asset is an electric vehicle, and where the scheduling event is the arrival or departure of the electric vehicle at the depot.

6. The method according to claim 2, further comprising using the at least one hardware processor to determine the energy reserve distribution associated with at least one of the one or more power infrastructure assets by combining: The energy reserve distribution that slides with the sliding time window according to the time step; and The energy reserve distribution anchored to the scheduling event.

7. The method according to claim 6, wherein, The at least one power infrastructure site is a depot, where the at least one power infrastructure asset is an electric vehicle, and where the scheduling event is the arrival or departure of the electric vehicle at the depot.

8. The method according to claim 2, further comprising using the at least one hardware processor to update the energy reserve distribution associated with at least one of the one or more power infrastructure assets in response to one or more completion events.

9. The method according to claim 1, wherein, The one or more power infrastructure assets include one or more flexible loads each including a battery.

10. The method as claimed in claim 9, wherein, The energy reserve profile associated with each of the one or more flexible loads decreases the effective charging power of the battery available for that flexible load over time.

11. The method as claimed in claim 9, wherein, Each of the one or more flexible loads is an electric vehicle.

12. The method according to claim 1, wherein, The at least one power infrastructure site includes a depot, where the one or more power infrastructure assets include electric vehicles, and where the one or more physical components include one or more charging stations configured to be electrically connected to the electric vehicles to charge the electric vehicles.

13. The method according to claim 12, wherein, The determined values of the one or more variables associate each of the electric vehicles with one or both of: a time period for charging at one of the one or more charging stations in the at least one power infrastructure site or a power flow rate.

14. The method according to claim 1, wherein, The target value includes at least an energy cost, and optimizing the target value includes minimizing the target value.

15. The method according to claim 1, wherein, Initiating control of one or more physical components includes controlling the set points of the one or more physical components according to the determined values of the one or more variables.

16. The method according to claim 15, wherein, The one or more physical components include non-intermittent distributed energy.

17. The method according to claim 1, wherein,Initiating control includes communicating via at least one network with a control system for the at least one electric power infrastructure site.

18. The method according to claim 1, wherein, The energy reserve profile reserves energy for the electric power infrastructure assets to mitigate future uncertainties.

19. The method according to claim 1, wherein, The energy reserve profile defines an energy reserve for each of a plurality of discrete time points or defines the energy reserve as a continuous function of time starting from the current time or anchored to another time point.

20. A system, comprising: At least one hardware processor; and software configured to, when executed by the at least one hardware processor, generate an optimization model for at least one electric power infrastructure site, where the at least one electric power infrastructure site includes one or more electric power infrastructure assets, where at least one of the one or more electric power infrastructure assets is associated with an energy reserve profile that reduces the energy available for that electric power infrastructure asset over time, and where the optimization model outputs a target value based on one or more variables representing an operating configuration of the at least one electric power infrastructure site, while being constrained by the energy reserve profile associated with the at least one electric power infrastructure asset, solve the optimization model to determine values of the one or more variables that optimize the target value, and initiate control of one or more physical components in the at least one electric power infrastructure site based on the determined values of the one or more variables.

21. The system according to claim 20, wherein, Periodically generate and solve the optimization model to determine the one or more variables representing the operating configuration of the at least one electric power infrastructure site in a sliding time window that slides according to a time step, and where the energy reserve profile associated with the at least one electric power infrastructure asset: slides with the sliding time window according to the time step; is anchored to a scheduling event; or is generated by combining a first energy reserve profile that slides with the sliding time window according to the time step and a second energy reserve profile that is anchored to a scheduling event.

22. The system according to claim 20, wherein, Periodically generate and solve the optimization model to determine the one or more variables representing the operating configuration of the at least one electric power infrastructure site in a sliding time window that slides according to a time step.

23. The system according to claim 22, wherein, The energy reserve profile associated with the at least one electric power infrastructure asset slides with the sliding time window according to the time step.

24. The system according to claim 22, further comprising updating the energy reserve distribution associated with at least one of the one or more electric power infrastructure assets in response to one or more completion events using the at least one hardware processor.

25. The system according to claim 20, wherein, The one or more electric power infrastructure assets include one or more flexible loads each including a battery; and where the energy reserve profile associated with each of the one or more flexible loads reduces the effective charging power of the battery available for that flexible load over time.

26. The system according to claim 20, wherein, The energy reserve profile reserves energy for the electric power infrastructure assets to mitigate future uncertainties.

27. The system according to claim 20, wherein, The energy reserve profile defines an energy reserve for each of a plurality of discrete time points or defines the energy reserve as a continuous function of time starting from the current time or anchored to another time point.

28. A non-transitory computer-readable medium having instructions stored thereon, wherein, The instructions, when executed by a processor, cause the processor to perform the following operations: Generate an optimization model for at least one power infrastructure site, where the at least one power infrastructure site includes one or more power infrastructure assets, where at least one of the one or more power infrastructure assets is associated with an energy reserve profile that reduces the energy available for that power infrastructure asset over time, and where the optimization model outputs a target value based on one or more variables representing the operating configuration of the at least one power infrastructure site, subject to the constraint of the energy reserve profile associated with the at least one power infrastructure asset; Solve the optimization model to determine the values of the one or more variables that optimize the target value; and Based on the determined values of the one or more variables, initiate control of one or more physical components in the at least one power infrastructure site.

29. The non-transitory computer-readable medium according to claim 28, wherein, Periodically generate and solve the optimization model to determine the one or more variables representing the operating configuration of the at least one power infrastructure site in a sliding time window that slides according to a time step.

30. The non-transitory computer-readable medium according to claim 29, wherein, The energy reserve profile associated with the at least one power infrastructure asset slides with the sliding time window according to the time step.

31. The non-transitory computer-readable medium according to claim 29, further comprising updating the energy reserve distribution associated with at least one of the one or more power infrastructure assets in response to one or more completion events using the at least one hardware processor.

32. The non-transitory computer-readable medium according to claim 28, wherein The one or more power infrastructure assets include one or more flexible loads each including a battery; and where the energy reserve profile associated with each of the one or more flexible loads reduces the effective charging power of the battery available for that flexible load over time.

33. The non-transitory computer-readable medium according to claim 28, wherein The energy reserve profile reserves energy for the power infrastructure asset to mitigate future uncertainties.

34. The non-transitory computer-readable medium according to claim 28, wherein The energy reserve profile defines an energy reserve for each of a plurality of discrete time points, or defines the energy reserve as a continuous function of time starting from the current time or anchored to another time point.

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