Power system state estimation using parameterized potential functions for equality constraints

Abstract

Conventional state estimation methods based on constrained optimization problems with equality and / or inequality constraints rely on penalty-based heuristics that can generate very large weight values, resulting in mal-tuned gain matrices. Disclosed state estimation embodiments transform the constrained optimization problem into an unconstrained convex optimization problem, where violated equality and / or inequality constraints are represented as parameterized potential functions, each including a center of attraction parameter. This unconstrained convex optimization problem can be iteratively formulated using successively updated values ​​of the center of attraction parameter and solved until no equality and / or inequality constraints are violated, generating a final estimated state. This final estimated state may then be used to control a monitored system, such as a power system.

Description

[Technical Field]

[0001] background FIELD OF THE INVENTION FIELD Embodiments described herein relate generally to state estimation, and more particularly to state estimation of power systems using parameterized potential functions for equality constraints and, optionally, inequality constraints. [Background technology]

[0002] 2. Description of Related Art State estimation (SE) is used in management systems to estimate the most likely state of a power system (e.g., a power grid) network from a slightly redundant set of measurements of nodal and branch quantities (e.g., node voltage phasors, power injection, and branch power flows). State estimation is necessary in complex systems where the state cannot be directly observed and / or the state measurements are susceptible to noise or corruption. The state of each node in a power system network may be defined, for example, by node voltage magnitudes and node phase angles. Examples of management systems that utilize state estimation include, but are not limited to, supervisory control and data acquisition (SCADA) systems, energy management systems (EMS), distribution management systems (DMS), advanced DMS (ADMS), etc.

[0003] Traditionally, state estimation is solved as either an unconstrained nonlinear weighted least squares (WLS) problem or an equality-constrained nonlinear WLS problem to avoid numerical malalignment of nodes (e.g., buses) with no power injection. In these cases, the solution does not impose feasibility constraints on power injection. For example, the solution may estimate a distributed energy resource (DER) with a maximum output of 10 kilowatts (KW) to generate 12 KW. While such conditions can occur in state estimation for both transmission and distribution systems, they are more likely to occur in distribution systems due to lower telemetry redundancy and data quality. Therefore, management systems benefit from state estimation that constrains node metrics (e.g., power output) to feasible values. Summary of the Invention [Means for solving the problem]

[0004] overview Accordingly, a system, method, and non-transitory computer-readable medium are disclosed for state estimation of an electric power system using parameterized potential functions (e.g., quadratic functions) for at least the equality constraints. An objective of the embodiments is to constrain the solution of the SE problem to feasible values ​​of nodal metrics by satisfying all equality constraints within a tolerance. A further objective of the embodiments is to estimate the state of a system, such as an electric power system, which can be used to optimize and control the system.

[0005] In one embodiment of a method for estimating a state of a power system, the method includes: using at least one hardware processor to obtain a constrained optimization problem including a convex first objective function to be minimized subject to one or more equality constraints; converting the constrained optimization problem into an unconstrained convex optimization problem including a second objective function that is the sum of the first objective function and a parameterized potential function for each of at least one of the one or more equality constraints, where each parameterized potential function is defined by an equality function and a center of attraction parameter; and performing a solution process including solving the unconstrained convex optimization problem by finding inputs to the unconstrained convex optimization problem that minimize an output of the unconstrained convex optimization problem, where the one or more center of attraction parameters are updated when solving the unconstrained convex optimization problem to ensure that the inputs satisfy the one or more equality constraints within a tolerance, and the inputs represent an estimated state of the power system. The method may further include using the at least one hardware processor to control the power system based on the estimated state. The method may further include providing the estimated state of the power system via a human-to-machine interface of the energy management system. The method may further include using the estimated state in one or more of contingency analysis, Volt-Var optimization, or optimal power flow, such as distributed energy resource management. The first objective function may include an error calculation in which a value of the measurement function is subtracted from a value of the system telemetry given an input.

[0006] Each parametric potential function is

[0007]

number

[0008] The second objective function can be defined as follows:

[0009]

number

[0010] The method may further include executing, using at least one hardware processor, a first process that includes: performing an initial iteration of a solution process to find initial optimization inputs, the initial iteration of the solution process further including initializing a value of each center of attraction parameter in each parameterized potential function in the unconstrained convex optimization problem; determining whether the initial optimization inputs violate one or more equality constraints; outputting the initial optimization inputs as an estimated output state of the power system if it is determined that the one or more equality constraints are not violated; performing the solution process for one or more subsequent iterations if it is determined that at least one of the one or more equality constraints is violated until the one or more equality constraints are no longer violated, the subsequent iteration of the solution process further including updating a value of each center of attraction parameter in each parameterized potential function corresponding to the one or more equality constraints before solving the unconstrained convex optimization problem; and outputting the inputs found by the solution process in a final one of the one or more subsequent iterations as an estimated output state of the power system. The method may further include using the at least one hardware processor to control the power system based on the estimated output state. In one embodiment, the one or more equality constraints are determined to be violated when at least one of the one or more equality constraints is out of tolerance, and the one or more equality constraints are determined to be not violated when all of the one or more equality constraints are within tolerance. In the initial iteration and each of the one or more subsequent iterations, the unconstrained convex optimization problem may include parameterized potential functions for all of the one or more equality constraints. In each of the one or more subsequent iterations, the initial inputs used in solving the unconstrained convex optimization problem in the solution process of the subsequent iteration may be the inputs found by the solution process in the immediately preceding iteration.

[0011]

number

[0012]

number

[0013] In one embodiment of a method for estimating a state of an electrical power system, the method includes: using at least one hardware processor to obtain a constrained convex optimization problem including a first objective function to be minimized subject to one or more equality constraints; converting the constrained convex optimization problem to an unconstrained convex optimization problem including a second objective function that is a sum of the first objective function and a parameterized potential function for each of the one or more equality constraints, where each parameterized potential function is defined by an equality function and a center of attraction parameter; defining a system of equations including first-order optimality conditions of the unconstrained convex optimization problem and the one or more equality constraints with associated weights; and determining an estimated state of the electrical power system by solving the system of equations using a root-finding algorithm. The method may further include using the at least one hardware processor to control the electrical power system based on the estimated state.

[0014] It should be understood that any of the features in the above methods may be implemented individually or with any subset of other features in any combination. Thus, to the extent that the appended claims suggest particular dependencies between features, the disclosed embodiments are not limited to those particular dependencies. Rather, any feature described herein may be combined with any other feature described herein, or may be implemented in any combination of features without any one or more other features described herein. Furthermore, any of the methods described above and elsewhere herein may be implemented individually or in any combination in executable software modules of a processor-based system, such as a server, and / or in executable instructions stored on a non-transitory computer-readable medium.

[0015] BRIEF DESCRIPTION OF THE DRAWINGS The details of the present invention, both as to its structure and operation, may be gleaned in part by study of the accompanying drawings, in which like reference numerals refer to like parts, and in which: [Brief explanation of the drawings]

[0016] [Figure 1] FIG. 1 illustrates an exemplary infrastructure in which one or more of the processes described herein may be implemented, according to one embodiment. [Figure 2] FIG. 1 illustrates an exemplary processing system in which one or more of the processes described herein may be performed, according to one embodiment. [Figure 3] FIG. 2 illustrates an exemplary data flow between systems and software modules in an exemplary infrastructure, according to one embodiment. [Figure 4] FIG. 10 illustrates the operation of a virtual measurement utilizing a center of attraction parameter, according to one embodiment. [Figure 5] FIG. 1 illustrates a solution process according to one embodiment. [Figure 6] FIG. 1 illustrates an overall algorithm for solving a constrained optimization problem, according to one embodiment. [Figure 7] FIG. 1 illustrates an overall algorithm for solving constrained optimization problems containing both equality and inequality constraints, according to one embodiment. [Figure 8] FIG. 1 illustrates an algorithm for solving a constrained optimization problem including equality constraints, according to one embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0017] Detailed Description In one embodiment, a system, method, and non-transitory computer-readable medium are disclosed for state estimation of a power system using parameterized potential functions for equality constraints and, potentially, inequality constraints. State estimation is generally considered to be performed on a power system, such as a power grid (e.g., of any scale, from a large-scale power system to a microgrid or smaller). A power system can be any network of electrical components (e.g., power system equipment) configured to generate, store, supply, transmit, distribute, and / or consume electrical power, including, but not limited to, power plants configured to generate electricity from combustible fuels (e.g., coal, natural gas, etc.) and / or renewable sources (e.g., wind, solar, nuclear, etc.), transmission systems configured to transport or transmit electricity from sources (e.g., generators) to loads, and distribution systems configured to deliver the supplied electricity to nearby homes, businesses, and / or other facilities. However, the techniques of this disclosure are not limited to power systems. Rather, the techniques of this disclosure may be applied to any system whose state is estimated using a WLS problem with one or more equality constraints.

[0018] As used herein, the term "network" refers to the interconnection of components in a system whose state is estimated. In the case of an electric power system, these components generally include electrical components, such as generators, distributed energy resources (e.g., renewable energy sources, battery energy storage (BES) systems, etc.), loads, transformers, transmission and distribution lines, etc. It should be understood that other types of systems may be represented as networks as well.

[0019] As used herein, the terms "node" or "bus" generally refer to any point in a network whose state is estimated when solving an SE problem. In the case of an electric power system, the state of each node may be defined as the magnitude and phase angle of the voltage at that node. However, the state of a node in an electric power system may be defined in other ways. It should be understood that the state of a node in other types of systems is defined in a manner appropriate to that type of system.

[0020] After reading this description, it will be apparent to one skilled in the art how to implement the invention in various alternative embodiments and alternative applications. However, while various embodiments of the invention are described herein, it is understood that these embodiments are presented for purposes of example and illustration only, and not limitation. Therefore, this detailed description of various embodiments should not be construed as limiting the scope or breadth of the invention, which is set forth in the appended claims.

[0021] 1. System Overview Infrastructure 1 illustrates an exemplary infrastructure in which one or more of the processes of the present disclosure may be implemented, according to one embodiment. The infrastructure may include a management system 110 (e.g., comprising one or more servers) that hosts and / or executes one or more of the various functions, processes, methods, and / or software modules described herein. Examples of management system 110 include, but are not limited to, an EMS, a DMS, an ADMS, a SCADA system, etc. Management system 110 may comprise dedicated servers or, alternatively, may be implemented in a computing cloud in which resources of one or more servers are dynamically and elastically allocated to multiple tenants based on demand. In either case, the servers may be co-located (e.g., in a single data center) and / or geographically distributed (e.g., across multiple data centers). Management system 110 may also include or be communicatively connected to software 112 and / or one or more databases 114. Additionally, the management system 110 may be communicatively connected to one or more user systems 130 and / or power systems 140 (e.g., electrical grids) via one or more networks 120.

[0022] The network 120 may comprise the Internet, and the EMS 110 may communicate with the user systems 130 and / or the power systems 140 over the Internet using standard transmission protocols such as HyperText Transfer Protocol (HTTP), HTTP Secure (HTTPS), File Transfer Protocol (FTP), FTP Secure (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), as well as proprietary protocols. While the management system 110 is shown connected to various systems through a single set of networks 120, it should be understood that the management system 110 may be connected to various systems through a different set of one or more networks. For example, management system 110 may be connected to a subset of user systems 130 and / or power systems 140 via the Internet, but may be connected to one or more other user systems 130 and / or power systems 140 via an intranet. Additionally, while only a few user systems 130 and power systems 140, one instance of software 112, and one set of databases 114 are shown, it should be understood that the infrastructure may include any number of user systems, power systems, software instances, and databases.

[0023] User system 130 may include any type of computing device capable of wired and / or wireless communication, including, but not limited to, a desktop computer, a laptop computer, a tablet computer, a smartphone or other mobile phone, a server, a game console, a television, a set-top box, an electronic kiosk, a point-of-sale terminal, an embedded controller, a programmable logic controller (PLC), etc. However, it is generally contemplated that user system 130 comprises a personal computer, a mobile device, or a workstation through which an agent of the operator of power system 140 can interact with management system 110. These interactions may include inputting data (e.g., parameters for configuring one or more of the processes described herein) and / or receiving data (e.g., output of one or more processes described herein) via a graphical user interface provided by management system 110 or a system between management system 110 and user system 130. A graphical user interface may comprise a screen (e.g., a web page) that includes a combination of content and elements such as text, images, video, animation, 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., including elements that include or are derived from data stored in one or more databases (e.g., database 114).

[0024] The management system 110 may execute software 112 comprising one or more software modules that implement one or more of the processes of the present disclosure. Additionally, the management system 110 may comprise, be communicatively coupled to, or have access to one or more databases 114 that store data inputs to and / or data outputs from one or more of the processes of the present disclosure. Any suitable database (including cloud-based databases, proprietary databases, and unstructured databases) may be utilized, including, but not limited to, MySQL®, Oracle®, IBM®, Microsoft® SQL, Access™, PostgreSQL™, etc.

[0025] 1.2. Exemplary Processing Device 2 is a block diagram illustrating an exemplary wired or wireless system 200 that may be used in connection with various embodiments described herein. For example, system 200 may 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 may represent components of management system 110, user system 130, power system 140, and / or other processing devices described herein. System 200 may be a server or any conventional personal computer, or any other processor-enabled device capable of wired or wireless data communication. Other computer systems and / or architectures may also be used, as will be apparent to those skilled in the art.

[0026] System 200 preferably includes one or more processors 210. Processor 210 may comprise a central processing unit (CPU). Additional processors may be provided, such as a graphics processing unit (GPU), auxiliary processors for managing input / output, auxiliary processors for performing floating-point operations, dedicated microprocessors with architectures suitable for high-speed execution of signal processing algorithms (e.g., digital signal processors), processors lower in the main processing system (e.g., back-end processors), additional microprocessors or controllers for dual or multiprocessor systems, and / or coprocessors. Such auxiliary processors may be separate processors or may be integrated with processor 210. Examples of processors that may be used with system 200 include, but are not limited to, any processor available from Intel Corporation of Santa Clara, California (e.g., Pentium®, Core i7™, Xeon®, etc.), any processor available from Advanced Micro Devices, Incorporated (AMD) of Santa Clara, California, any processor available from Apple Inc. of Cupertino (e.g., A series, M series, etc.), any processor available from Samsung Electronics Co., Ltd. of Seoul, Korea (e.g., Exynos®, etc.).

[0027] Processor 210 is preferably connected to communication bus 205. Communication bus 205 may include a data channel for facilitating information transfer between storage and other peripheral components of system 200. Additionally, communication bus 205 may provide a set of signals used for communication 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, for example, an industry standard architecture (ISA), an extended industry standard architecture (EISA), a Micro Channel Architecture (MCA), a peripheral component interconnect (PCI) local bus, a bus architecture conforming to standards promulgated by the Institute of Electrical and Electronics Engineers (IEEE), including the IEEE 488 general-purpose interface bus (GPIB), IEEE 696 / S-100, etc.

[0028] System 200 preferably includes a main memory 215 and may also include a secondary memory 220. Main memory 215 provides storage of instructions and data for programs executing on processor 210, such as one or more of the functions and / or modules (e.g., software 112) described herein. It should be understood that the programs stored in memory and executed by processor 210 may be written and / or compiled according to 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), including read only memory (ROM), Rambus dynamic random access memory (RDRAM), ferroelectric random access memory (FRAM), and the like.

[0029] Secondary memory 220 may optionally include internal media 225 and / or removable media 230. Removable media 230 is read from and written to in any known manner. Removable storage media 230 may be, for example, a magnetic tape drive, a compact disc (CD) drive, a digital versatile disc (DVD) drive, other optical drive, a flash memory drive, etc. Secondary memory 220 is a non-transitory computer-readable medium on which computer-executable code (e.g., software 112) and / or other data is stored. Computer software or data stored in secondary memory 220 is loaded into main memory 215 for execution by processor 210.

[0030] In alternative embodiments, secondary memory 220 may include other similar means for allowing computer programs or other data or instructions to be loaded into system 200. Such means may include, for example, a communications interface 240 that allows software and data to be transferred to system 200 from an external storage medium 245. Examples of external storage medium 245 may include an external hard disk drive, an external optical drive, an external magneto-optical drive, etc. Other examples of secondary memory 220 may include semiconductor-based memory 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).

[0031] As described above, system 200 may include a communications interface 240. Communications interface 240 allows software and data to be transferred between system 200 and an external device (e.g., a printer), a network, or other information source. For example, computer software or executable code may be transferred to system 200 from a network server (e.g., platform 110) via communications interface 240. Examples of communications interface 240 include an internal 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 communications port, an infrared interface, an IEEE 1394 Firewire, and any other device capable of interfacing system 200 with a network (e.g., network 120) or another computing device.Communications interface 240 preferably implements industry published protocol standards such as the Ethernet IEEE 802 standard, Fibre Channel, digital subscriber line (DSL), asynchronous digital subscriber line (ADSL), frame relay, asynchronous transfer mode (ATM), integrated digital services network (ISDN), personal communications service (PCS), transmission control protocol / Internet protocol (TCP / IP), serial line Internet protocol / point to point protocol (SLIP / PPP), etc., but may also implement customized or non-standard interface protocols.

[0032] The software and data transferred via communications interface 240 are typically in the form of electrical communications signals 255. These signals 255 may be provided to communications interface 240 via communications channel 250. In one embodiment, communications channel 250 may be a wired or wireless network (e.g., network 120) or any of a variety of other communications links. Communications channel 250 carries signals 255 and may be implemented using a variety of wired or wireless communications means, including wire or cable, optical fiber, conventional telephone line, cellular phone link, wireless data communications link, radio frequency (“RF”) link, or infrared link, to name just a few.

[0033] Computer-executable code (e.g., computer programs such as software 112) is stored in main memory 215 and / or secondary memory 220. Computer programs may also be received via communications interface 240 and stored in main memory 215 and / or secondary memory 220. Such computer programs, when executed, enable system 200 to perform various functions of embodiments of the present disclosure as described elsewhere herein.

[0034] In this description, the term "computer-readable medium" is used to refer to any non-transitory computer-readable storage medium used to provide computer-executable code and / or other data to or within system 200. Examples of such media include main memory 215, secondary memory 220 (including internal memory 225 and / or removable media 230), external storage media 245, and any peripheral devices (including network information servers or other network devices) communicatively coupled to communication interface 240. These non-transitory computer-readable media are means for providing executable code, programming instructions, software, and / or other data to system 200.

[0035] In embodiments implemented using software, the software may be stored on a computer-readable medium and loaded into system 200 via removable medium 230, I / O interface 235, or communication interface 240. In such embodiments, the software is loaded into system 200 in the form of electrical communication signals 255. When executed by processor 210, the software preferably causes processor 210 to perform one or more of the processes and functions described elsewhere herein.

[0036] In one embodiment, I / O interface 235 provides an interface between one or more components of system 200 and one or more input and / or output devices. Examples of input devices include, but are not limited to, sensors, keyboards, touchscreens or other touch-sensitive devices, cameras, biosensing 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-emitter displays (SEDs), field emission displays (FEDs), etc. In some cases, input and output devices may be combined, such as in the case of touch-sensitive displays (e.g., smartphones, tablets, or other mobile devices).

[0037] System 200 may also include optional wireless communication components that facilitate wireless communication over voice and / or data networks (e.g., in the case of user system 130 being a smartphone or other mobile device). The wireless communication components include antenna system 270, radio system 265, and baseband system 260. In system 200, radio frequency (RF) signals are transmitted and received wirelessly by antenna system 270 under the control of radio system 265.

[0038] In one embodiment, antenna system 270 may include one or more antennas and one or more multiplexers (not shown) that perform switching functions to provide transmit and receive signal paths for antenna system 270. In the receive path, the received RF signal may be coupled from the multiplexer to a low noise amplifier (not shown), which amplifies the received RF signal and sends the amplified signal to radio system 265.

[0039] In alternative embodiments, the radio system 265 may comprise one or more radios configured to communicate over various frequencies. In one embodiment, the radio system 265 may combine a demodulator (not shown) and a modulator (not shown) into a single integrated circuit (IC). The demodulator and modulator may also be separate components. In the incoming path, the demodulator removes the RF carrier signal, leaving the baseband received audio signal, which is sent from the radio system 265 to the baseband system 260.

[0040] If the received signal contains audio information (e.g., in the case of a user system 130 capable of operating as a telephone), the baseband system 260 decodes and converts the signal 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 to digital signals and encoded by the baseband system 260. The baseband system 260 also encodes the digital signals for transmission and generates baseband transmit audio signals, which are routed to a modulator portion of the radio system 265. The modulator mixes the baseband transmit audio signal with an RF carrier signal to generate an RF transmit signal, which is routed to the antenna system 270 and may pass through a power amplifier (not shown). The power amplifier amplifies the RF transmit signal and routes it to the antenna system 270, where the signal is switched to an antenna port for transmission.

[0041] The baseband system 260 is also communicatively coupled to the processor 210. The processor 210 may access data storage areas 215 and 220. The processor 210 is preferably configured to execute instructions (i.e., computer programs, such as the software of the present disclosure), which may be stored in the main memory 215 or the secondary memory 220. 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, enable the system 200 to perform various functions of embodiments of the present disclosure.

[0042] 1.3. Example Data Flow 3 illustrates an exemplary data flow between management system 110, user system 130, and power system 140, according to one embodiment. Power system 140 may include a monitoring module 310 and a control module 320. Software 112 of management system 110 may include a state estimation module 330, a control and optimization module 340, and a human-to-machine interface (HMI) 350. Database 114 of management system 110 may store a system model 360. It should be understood that communication between various systems may be performed via network 120. Additionally, communication between pairs of modules may be performed via an application programming interface (API) provided by one of the modules.

[0043] The monitoring module 310 may monitor and collect data output by one or more sensors in the network of the power system 140. The monitoring module 310 may also derive data from the collected data. The monitoring module 310 may send or “push” the collected and / or derived data to the state estimation module 330 as system telemetry (e.g., via the API of the state estimation module 330). Alternatively, the state estimation module 330 may retrieve or “pull” system telemetry from the monitoring module 310 (e.g., via the API of the monitoring module 310). The system telemetry may include measurements at each of one or more nodes or other points in the network of the power system 140. The system telemetry may be communicated from the monitoring module 310 to the state estimation module 330 in real time, as the data is collected and / or derived, or periodically. As used herein, the term “real time” includes events occurring simultaneously, as well as events occurring contemporaneously, as dictated by normal delays resulting from latencies in processing, memory access, communication, and the like.

[0044] State estimation module 330 receives system telemetry from monitoring module 310 and uses the system telemetry in combination with system model 360 to generate an estimated state of power system 140. In particular, state estimation module 330 may formulate an optimization problem based on system telemetry and system model 360 and implement one or more of the processes for state estimation described herein to solve the optimization problem. State estimation module 330 may generate an estimated state of power system 140 in real time or periodically (e.g., each time new system telemetry is received). The estimated state may include estimated voltage magnitudes and phase angles of each node in the network of power system 140. State estimation module 330 may send or “push” the estimated state of power system 140 to optimization and control module 340 (e.g., via an API of optimization and control module 340). Alternatively, optimization and control module 340 may retrieve or “pull” the estimated state of power system 140 from state estimation module 330 (e.g., via an API of state estimation module 330). The estimated states may be communicated from the state estimation module 330 to the optimization and control module 340 in real time, as the estimated states are generated, or periodically.

[0045] Optimization and control module 340 receives the estimated states from state estimation module 330 and uses the estimated states in combination with system model 360 to determine an optimal configuration of one or more components of power system 140, and then controls power system 140 to transition to the optimal configuration. In particular, optimization and control module 340 may generate control signals that are sent to control module 320 of power system 140. For example, the control signals may be sent via an API of control module 320. The control signals may be communicated from optimization and control module 340 of management system 110 to control module 320 of power system 140 in real time as the estimated states are received and analyzed, periodically, or in response to user action. Optimization and control module 340 may control power system 140 automatically (e.g., without user intervention), semi-automatically (e.g., requiring user approval or confirmation), and / or in response to manual user input.

[0046] The control module 320 of the power system 140 receives control signals from the optimization and control module 340 and controls one or more components of the power system 140 according to the control signals. Examples of such control include setting set points (e.g., for active power and / or reactive power for distributed energy resources), adjusting the power output of a generator, adjusting the charging or discharging of a BES system, adjusting the power input to a load, opening or closing a switch (e.g., a circuit breaker), etc.

[0047] Human-to-machine interface 350 may generate a graphical user interface that is sent to user system 130 and receive input to the graphical user interface via user system 130. The graphical user interface may provide information regarding the estimated state of power system 140 determined by state estimation module 330, the optimal configuration of power system 140 determined by optimization and control module 340, control decisions or recommendations determined by optimization and control module 340, a visual representation of system model 360, etc. Additionally, the graphical user interface may provide input that allows a user of user system 130 to configure settings for state estimation module 330, configure settings for optimization and control module 340, configure system model 360, specify or approve controls that are sent to control module 320 for power system 140, analyze power system 140, etc.

[0048] The system model 360 may be stored in the database 114 and may be accessed by modules such as the state estimation module 330 and the optimization and control module 340 via any known means (e.g., via an API of the database 114, a direct query of the database 114, etc.). The database 114 may store a system model 360 for each power system 140 managed by the management system 110. Each system model 360 models the network of the power system 140 in any suitable manner. For example, the system model 360 may include a one-line diagram representing the components of the network and their relationships to one another. It should be understood that the one-line diagram may be implemented as a data structure capable of being automatically analyzed by software modules including the state estimation module 330 and the optimization and control module 340.

[0049] The estimated state output by state estimation module 330 may be used as input to any downstream functions that may benefit from the estimated state of power system 140. These downstream functions may be performed by optimization and control module 340, human-to-machine interface 350, and / or other modules within management system 110 or an external system. If the downstream function is performed by another module, state estimation module 330 may send or “push” the estimated state of power system 140 to the other module (e.g., via an API of the implementing module or relayed through optimization and control module 340). Alternatively, the other module may retrieve or “pull” the estimated state of power system 140 from state estimation module 330 (e.g., via an API of state estimation module 330) or from optimization and control module 340 (e.g., via an API of optimization and control module 340). The estimated state may be communicated to the implementing module in real time as the estimated state is generated or periodically.

[0050] As an example of a downstream function, the estimated state may be stored and displayed to a user within a graphical user interface of human-to-machine interface 350 in response to a triggering event. The triggering event may be a user requesting the estimated state, an estimated state satisfying an alert condition, etc. If the estimated state satisfies an alert condition, the user may be prompted via the graphical user interface or other means (e.g., notification sent via email message, text message, voice message, etc.) to take preventative or corrective control action (e.g., via graphical user interface input, manually, etc.).

[0051] Generally, a baseline model for one or more downstream functions may be generated using the estimated states, which may include voltage magnitudes and phase angles of each node in the network within power system 140. The downstream functions may utilize this baseline model to perform any type of analysis on power system 140, including optimal power flow, distributed energy resource (DER) management, contingency analysis, etc. The analysis may be performed in response to a user action or automatically in real time or periodically. In some cases, the analysis may be provided to a user via human-to-machine interface 350. In other cases, optimization and control module 340 may automatically (i.e., without user intervention) or semi-automatically (e.g., with user approval or confirmation) initiate a control action based on the analysis. Initiating a control action may include sending a control command to control module 320 of power system 140, which may respond by controlling power system 140 according to the control command.

[0052] As an example, the estimated state may be used by the optimization and control module 340 as input to a contingency analysis. The contingency analysis may utilize the estimated state of the power system 140 in a baseline model of the power system 140 (e.g., system model 360) to perform a “what-if” analysis for various hypothetical scenarios (e.g., failure of a component of the power system 140). For example, the estimated state of each node (e.g., voltage magnitude and phase angle) may be used to calculate the amount of power generation or consumption at that node for use in the contingency analysis. The contingency analysis may be performed in real time (e.g., when the estimated state is output by the state estimation module 330), periodically, and / or in response to a trigger event (e.g., user request, achievement of one or more monitoring criteria, etc.). If the contingency analysis detects a problem, the user may execute preventative or corrective control actions (e.g., via input in a graphical user interface of the human-to-machine interface 350, manually, etc.). Alternatively or additionally, optimization and control module 340 may automatically or semi-automatically perform contingency analysis of one or more what-if scenarios and, if a problem is detected, initiate preventative or corrective control action via communication with control module 320 of power system 140.

[0053] As an additional example, the estimated states may be used by the optimization and control module 340 as input to Volt-Var optimization. The Volt-Var optimization may utilize the estimated states (e.g., voltage magnitude and phase angle) and the system model 360 (or other model) as a baseline to determine optimal voltage levels and reactive power to achieve efficient operation of the power system 140 (e.g., by reducing system losses, peak demand, and / or energy consumption). The Volt-Var optimization may be performed in real time (e.g., when the estimated states are output by the state estimation module 330), periodically, and / or in response to a trigger event (e.g., a user request, achievement of one or more monitoring criteria, etc.). The optimization and control module 340 may automatically or semi-automatically initiate control actions via communication with the control module 320 of the power system 140 to adapt the power system 140 to the optimal voltage levels and reactive power as determined by the Volt-Var optimization. The control actions may include controlling switchable capacitors, on-load tap changers, etc.

[0054] As a further example, the estimated states may be used as input to optimal power flow by optimization and control module 340. Optimal power flow may utilize the estimated states and system model 360 (or other model) as a baseline for managing power generation in power system 140. For example, optimal power flow may determine optimal set points for generators in power system 140 to meet the demands of power system 140 while minimizing operating costs and / or satisfying one or more other criteria. Optimal power flow may be performed in real time (e.g., when the estimated states are output by state estimation module 330), periodically, and / or in response to a trigger event (e.g., a user request, achievement of one or more monitoring criteria, etc.). Optimization and control module 340 may automatically or semi-automatically initiate control actions via communication with control module 320 of power system 140 to adapt power system 140 to the set points determined by optimal power flow.

[0055] As a further example, the estimated state may be used by the optimization and control module 340 as input to distributed energy resource (DER) management, which can be thought of as a type of optimal power flow. DER management may utilize the estimated state and system model 360 (or other model) to manage distributed energy resources in the power system 140. For example, DER management may manage setpoints for active and reactive power, power factor, and / or voltage at the distributed energy resources or their interconnections with other nodes in the network. DER management may be performed in real time (e.g., when the estimated state is output by the state estimation module 330), periodically, and / or in response to a trigger event (e.g., a user request, achievement of one or more monitoring criteria, etc.). The optimization and control module 340 may automatically or semi-automatically initiate control actions via communication with the control module 320 of the power system 140 to adapt the power system 140 to the setpoints determined by the DER management.

[0056] 2. Process Overview An embodiment of a process for power system state estimation using parameterized potential functions for equality constraints will now be described in detail. It should be understood that the described process may be embodied in one or more software modules executed by one or more hardware processors, for example, as software 112 executed by processor 210 of management system 110. The described process may be implemented as instructions expressed in source code, object code, and / or machine code. These instructions may be executed directly by hardware processor 210 or may be executed by a virtual machine or container operating between the object code and hardware processor 210. Furthermore, the software of the present disclosure may be built on or interfaced with one or more existing systems.

[0057] Alternatively, the described processes may be implemented as hardware components (e.g., general-purpose processors, integrated circuits (ICs), application-specific integrated circuits (ASICs), digital signal processors (DSPs), field-programmable gate arrays (FPGAs) or other programmable logic devices, discrete gate or transistor logic, etc.), a combination of hardware components, or a combination of hardware and software components. To clearly illustrate this interchangeability of hardware and software, various illustrative components, blocks, modules, circuits, and steps are described herein generally in terms of their functionality. Whether such functionality is implemented as hardware or software depends on the particular application and design constraints imposed on the overall system. Those skilled in the art may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the invention. Furthermore, the grouping of functions within a component, block, module, circuit, or step is for ease of description. Particular functions or steps may be moved from one component, block, module, circuit, or step to another without departing from the invention.

[0058] Additionally, while the processes described herein are shown with a particular arrangement and order of subprocesses, each process may be implemented with fewer, more, or different subprocesses, and with a different arrangement and / or order of the subprocesses. Furthermore, even if the subprocesses are described or illustrated in a particular order, it should be understood that any subprocess that is not dependent on the completion of another subprocess may be performed before, after, or in parallel with other independent subprocesses.

[0059] 2.1. Introduction Throughout this disclosure, equality constraints are expressed in the following form:

[0060]

number

[0061] The constrained optimization problem can be expressed as:

[0062]

number

[0063] Subject to the following conditions:

[0064]

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[0065] Constrained optimization problems may also include inequality constraints. Throughout this disclosure, inequality constraints are expressed in the following form:

[0066]

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[0067]

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[0068] Existing methods for enforcing equality constraints in state estimation include elimination, feasible direction, Lagrangian (e.g., Hachtel's matrix formula), augmented Lagrangian (using multipliers), and penalty function methods. Penalty function methods generally require the weight of each equality constraint to be set to a very large value to ensure that violations of the equality constraints are zero.

[0069] In one embodiment, instead of the above method, a parameterized potential function is used for each equality constraint. In the context of parameterized potential functions, the term "parameterized" refers to the inclusion of adjustable parameters in the potential function, and the term "potential" refers to the analogy between an unconstrained objective function and a generalized potential field (e.g., a particle in a potential field is pulled toward a zero-force point). Although not required for the embodiment, the parameterized potential function may be a quadratic function. Each parameterized potential function may be expressed as follows:

[0070]

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[0071]

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[0072]

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[0073]

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[0074]

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[0075]

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[0076]

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[0077]

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[0078] The following system of equations has the same solution as the KKT condition for the constrained optimization problem:

[0079]

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[0080]

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[0081] 2.2. Equality Constraint Algorithm 5 illustrates a solution process 500 according to one embodiment. The solution process 500 may be implemented by the state estimation module 330 in the software 112 of the management system 110.

[0082] In sub-process 510, an unconstrained convex optimization problem is prepared based on the equality constraints. In particular, a parameterized potential function may be generated for each equality constraint and summed with the objective function from the constrained optimization problem for the second objective function to be minimized. The unconstrained convex optimization problem may again be expressed as:

[0083]

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[0084]

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[0085]

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[0086]

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[0087] 6 illustrates a global equality constraint (EC) algorithm 600 for solving a constrained optimization problem including an equality constraint, according to one embodiment. The EC algorithm 600 may be implemented by the state estimation module 330 in the software 112 of the management system 110. The EC algorithm 600 operates to convert a constrained optimization problem, including an objective function to be minimized subject to one or more equality constraints, into an unconstrained convex optimization problem and then solve the unconstrained convex optimization problem. In solving the unconstrained convex optimization problem, the EC algorithm 600 may iteratively perform the solution process 500.

[0088] First, in sub-process 610, a constrained optimization problem is obtained. This obtaining process may involve finding a representation of the constrained optimization problem, or of one or more components of the constrained optimization problem, such as the objective function to be minimized and the equality functions of the equality constraints that condition the objective function. The constrained optimization problem may again be expressed as:

[0089]

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[0090] Subject to the following conditions:

[0091]

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[0092] The components of the constrained optimization problem, such as the objective function and any equality constraints or functions, may be stored in memory that persists across iterations of the solution process 500 and can be easily accessed at each iteration of the solution process 500 without having to be regenerated or redetermined at each iteration.

[0093] In sub-process 620, the constrained optimization problem is transformed into an unconstrained convex optimization problem in which each of the equality constraints is expressed as a parameterized potential function. The unconstrained convex optimization problem may be expressed as:

[0094]

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[0095]

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[0096]

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[0097]

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[0099] An example of EC pseudocode implementing one embodiment of the EC algorithm 600 is provided below.

[0100]

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[0101]

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[0102] 2.3. Inequality Constraint Algorithm 7 illustrates a global inequality constraint (IC) algorithm 700 for solving a constrained optimization problem containing both equality and inequality constraints, according to one embodiment. The IC algorithm 700 may be implemented by the state estimation module 330 in the software 112 of the management system 110. The IC algorithm 700 operates to convert an IC-EC optimization problem, including an objective function to be minimized subject to one or more equality constraints and one or more inequality constraints, over one or more iterations to an EC convex optimization problem (i.e., a problem subject to equality constraints but no inequality constraints), and then solves the EC convex optimization problem using the EC algorithm 600, which converts the EC convex optimization problem to a fully unconstrained convex optimization problem (i.e., a problem subject to no inequality or equality constraints).

[0103] First, in sub-process 710, an IC-EC optimization problem is obtained. This obtaining process may include finding a representation of the IC-EC optimization problem or a representation of one or more components of the IC-EC optimization problem, such as the objective function to be minimized, inequality functions of the inequality constraints conditioned on the objective function, and equality functions of the equality constraints conditioned on the objective function. The IC-EC optimization problem may be expressed as follows:

[0104]

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[0105] Subject to the following conditions:

[0106]

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[0107] Equivalently:

[0108]

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[0109] Subject to the following conditions:

[0110]

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[0111] In sub-process 720, a convex optimization problem is generated from the constrained optimization problem without any inequality constraints. In other words, the IC-EC optimization problem is converted into an EC-only optimization problem without a representation of the inequality constraints. That is, the EC optimization problem does not include a parameterized potential function for any inequality constraints. Therefore, the convex optimization problem can be expressed as follows:

[0112]

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[0114]

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[0115]

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[0120] In IC algorithm 700, EC algorithm 600 is utilized to solve an inequality-unconstrained or EC optimization problem that is still subject to equality constraints. However, in alternative embodiments, different algorithms may be used to solve the EC optimization problem and / or to convert the EC optimization problem to a fully unconstrained convex optimization problem. Thus, EC algorithm 600 in IC algorithm 700 may be replaced with any other suitable algorithm for solving an EC optimization problem.

[0121] An example of IC pseudocode implementing one embodiment of IC algorithm 700 is provided below.

[0122]

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[0123]

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[0124]

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[0125] 2.4. Alternative Implementation of the Equality Constraint Algorithm 8 shows an EC algorithm 800 for solving a constrained optimization problem including equality constraints, according to an alternative embodiment. The EC algorithm 800 may be implemented by the state estimation module 330 in the software 112 of the management system 110. The constrained optimization problem may again be expressed as:

[0126]

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[0127] Subject to the following conditions:

[0128]

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[0129] In sub-process 810, an unconstrained parametric convex optimization problem is generated based on the equality constraints, thereby converting the constrained optimization problem to an unconstrained convex optimization problem. In particular, a parameterized potential function (e.g., a quadratic function) may be generated for each equality constraint and summed with the objective function from the constrained optimization problem for the second objective function to be minimized. The unconstrained convex optimization problem may be expressed as:

[0130]

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[0131]

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[0132]

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[0133] Sub-process 840 outputs the solution from sub-process 830. For example, the solution may be output as an estimated state to optimization and control module 340. Optimization and control module 340 may then utilize the estimated state to optimize and / or control power system 140, as described elsewhere herein.

[0134]

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[0135] Subject to the following conditions:

[0136]

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[0137] The unconstrained SE problem generated in sub-process 810 can be expressed as follows:

[0138]

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[0139] The system of equations defined in sub-process 820 can be expressed as follows:

[0140]

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[0141] The Newton-Raphson iteration equation for the system of equations used in sub-process 830 can be expressed as follows:

[0142]

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[0143]

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[0144] 3. Usage example

[0145]

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[0146]

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[0147] In some cases, one or more of these downstream functions may automatically (e.g., without user intervention) or semi-automatically (e.g., after user approval or confirmation) issue control commands to the system's control module 320, thereby controlling the system. Thus, state estimation may be used to monitor and control systems such as power system 140. For example, if the voltage at a measurement point is too low, a corresponding generator in power system 140 may be controlled to increase its reactive power output, thereby increasing the voltage at that measurement point.

[0148]

number

[0149] The above description of the embodiments of the present disclosure is provided to enable those skilled in the art to make or use the present invention. Various modifications to the 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. It should therefore be understood that the description and drawings presented herein represent presently preferred embodiments of the invention and, therefore, represent the subject matter broadly contemplated by the present invention. It is further understood that the scope of the present invention fully encompasses other embodiments that may become apparent to those skilled in the art, and therefore, the scope of the present invention is not limited.

[0150] 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 "A, B, C, or any combination thereof," include any combination of A, B, and / or C, and may include multiples of A, multiples of B, or multiples of C. 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 "A, B, C, or any combination thereof" may be A only, B only, C only, A and B, A and C, B and C, or A and B and C, and any such combination may include one or more members of its components A, B, and / or C. For example, a combination of A and B may include one A and multiple Bs, multiple As and one B, or multiple As and multiple Bs.

Claims

1. 1. A method for estimating a state of an electric power system, the method comprising: obtaining a constrained optimization problem including a convex first objective function to be minimized subject to one or more equality constraints; converting the constrained optimization problem into an unconstrained convex optimization problem including a second objective function that is the sum of the first objective function and a parameterized potential function for each of at least one of the one or more equality constraints, each parameterized potential function being defined by an equality function and a center of attraction parameter; performing a solution process that includes solving the unconstrained convex optimization problem by finding an input to the unconstrained convex optimization problem that minimizes an output of the unconstrained convex optimization problem; Including, one or more center of attraction parameters are updated to ensure that the inputs satisfy, within a tolerance, the one or more equality constraints when solving the unconstrained convex optimization problem; the input represents an estimated state of the power system; method.

2. The method of claim 1 , further comprising using the at least one hardware processor to control the power system based on the estimated conditions.

3. Each parametric potential function is [Equation 1] The method of claim 1.

4. The second objective function is [Equation 2] The method of claim 3.

5. using said at least one hardware processor, performing an initial iteration of the solution process to find initial optimization inputs, the initial iteration of the solution process further comprising initializing a value for each center of attraction parameter in each parameterized potential function in the unconstrained convex optimization problem; determining whether the initial optimization inputs violate the one or more equality constraints; outputting the initial optimization input as an estimated output state of the power system if the one or more equality constraints are determined not to be violated; if it is determined that at least one of the one or more equality constraints is violated, performing the solution process over one or more subsequent iterations until the one or more equality constraints are no longer violated, the subsequent iterations of the solution process further comprising updating the value of each center of attraction parameter in each parameterized potential function corresponding to the one or more equality constraints before solving the unconstrained convex optimization problem; outputting the input found by the solution process in a final one of the one or more subsequent iterations as the output estimated state of the power system; The method of claim 1 , further comprising performing a first process comprising:

6. The method of claim 5 , further comprising using the at least one hardware processor to control the power system based on the output estimated state.

7. 6. The method of claim 5, wherein the one or more equality constraints are determined to be violated when at least one of the one or more equality constraints is outside the tolerance, and the one or more equality constraints are determined to be not violated when all of the one or more equality constraints are within the tolerance.

8. The method of claim 5 , wherein in the initial iteration and each of the one or more subsequent iterations, the unconstrained convex optimization problem includes parameterized potential functions for all of the one or more equality constraints.

9. 6. The method of claim 5, wherein in each of the one or more subsequent iterations, initial inputs used in solving the unconstrained convex optimization problem in the solution process of the subsequent iteration are the inputs found by the solution process in a immediately preceding iteration.

10. 6. The method of claim 5, wherein in each of the one or more subsequent iterations, updating the value of each center of attraction parameter comprises calculating the value of each center of attraction parameter based on a previous value of that center of attraction parameter in a immediately preceding iteration.

11. 11. The method of claim 10, wherein in each of the one or more subsequent iterations, updating the value of each center of attraction parameter comprises calculating the value of each center of attraction parameter further based on a value of the equality function for a corresponding one of the one or more equality constraints given the input found by the solution process in a immediately preceding iteration. 【Request 12】 【Number 3】 The method of claim 11.

13. the constrained convex optimization problem further includes one or more inequality constraints, and the method further comprises using the at least one hardware processor to: performing the first process while ignoring the one or more inequality constraints to find the output estimated state as a first initial optimization input; determining whether the first initial optimization input violates the one or more inequality constraints; using the first initial optimization input as a final estimated state of the power system if it is determined that the one or more inequality constraints are not violated; If it is determined that at least one of the one or more inequality constraints is violated, over one or more outer iterations until the one or more inequality constraints are no longer violated. converting the constrained optimization problem into an inequality-unconstrained convex optimization problem including the first objective function and an inequality-parameterized potential function for each of at least one of the one or more inequality constraints, each inequality-parameterized potential function being defined by an inequality function and a center of attraction parameter; determining a value for each center of attraction parameter in each inequality parameterized potential function in the inequality unconstrained convex optimization problem; executing the first process using the inequality unconstrained convex optimization problem as the constrained optimization problem in the first process; outputting the input found by the first process in a final one of the one or more outer iterations as the final estimated state of the power system; The method of claim 5 further comprising:

14. 14. The method of claim 13, wherein in each of the one or more outer iterations, for each of the one or more inequality constraints that are violated, an inequality parameterized potential function is added to the inequality-constrained free convex optimization problem, and is not added for the one or more inequality constraints that are not violated. 【Request 15】 【Number 4】 The method of claim 13.

16. The method of claim 1 , further comprising using the estimated states in one or more of a contingency analysis, a Volt-Var optimization, or an optimal power flow.

17. The method of claim 1 , wherein the first objective function comprises an error calculation in which a value of a measurement function is subtracted from a value of a system telemetry given the input.

18. at least one hardware processor; When executed by the at least one hardware processor, obtaining a constrained optimization problem including a convex first objective function to be minimized subject to one or more equality constraints; transforming the constrained optimization problem into an unconstrained convex optimization problem including a second objective function that is the sum of the first objective function and a parameterized potential function for each of at least one of the one or more equality constraints, each parameterized potential function being defined by an equality function and a center of attraction parameter; solving the unconstrained convex optimization problem by finding an input to the unconstrained convex optimization problem that minimizes an output of the unconstrained convex optimization problem, wherein one or more center of attraction parameters are updated to ensure that the input satisfies the one or more equality constraints within a tolerance when solving the unconstrained convex optimization problem, and wherein the input represents an estimated state of the power system. with software configured to A system comprising:

19. 1. A method for estimating a state of an electric power system, the method comprising: obtaining a constrained convex optimization problem including a first objective function to be minimized subject to one or more equality constraints; converting the constrained convex optimization problem into an unconstrained convex optimization problem including a second objective function that is the sum of the first objective function and a parameterized potential function for each of the one or more equality constraints, each parameterized potential function being defined by an equality function and a center of attraction parameter; defining a system of equations including first-order optimality conditions of the unconstrained convex optimization problem and the one or more equality constraints with associated weights; determining an estimated state of the power system by solving the system of equations using a root-finding algorithm; and A method comprising:

20. The method of claim 19 , further comprising using the at least one hardware processor to control the power system based on the estimated conditions.

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