SYSTEM AND METHOD FOR CONTROLLING A HYBRID ELECTRIC DISTRIBUTION SYSTEM - Patent application

Abstract

Power flow in the power distribution system is controlled using control commands generated based on values ​​of system parameters. In this regard, power generation forecast data, load forecast data, and real-time device status data of equipment are utilized to generate scheduling data for power generation and consumption, and a network topology of the system is also obtained. The values ​​of the system parameters are generated as a result of an unbalanced load flow analysis of the power distribution system using the scheduling data and the network topology. The unbalanced load flow analysis utilizes a compact multi-bus-based nodal admittance matrix to represent the relationship between nodal injected power and nodal voltages at multiple non-overlapping phases of a bus for a section of the power distribution system consisting of zero-impedance branches connected to impedance branches.

Description

[Technical Field]

[0001] The present invention relates generally to power distribution systems, and more particularly to unbalanced load flow analysis of hybrid power distribution systems with multiple slack buses. [Background technology]

[0002] The global energy system is facing significant changes, including a transition from a model with centralized power generation at power plants to a distributed power grid that includes renewable energy generation. As renewable energy generation further penetrates the energy market, traditional power system operation methods are undergoing significant change. The ongoing development and significant innovation of smart power grids are integrating an increasing number of distributed generation resources into the power distribution network. The emergence of hybrid power systems now provides greater flexibility in how power is accessed. To ensure the grid's fault-free function, it is essential to maintain the parameters controlling power flow within the grid at specified levels within acceptable ranges. However, due to the distributed nature of hybrid power grids, these parameters can fluctuate frequently. This makes it increasingly important to constantly monitor and maintain these parameters within acceptable ranges. However, doing so has traditionally been a complex task that is often difficult to achieve due to the grid's complex structure and the need for sensing at all levels of generation and distribution. One solution is to accurately and precisely measure and monitor power system behavior. Assessment, monitoring, and control of power system behavior can be achieved through accurate unbalanced load flow analysis of the power system. Inaccurate load flow analysis can cause operators to be unable to recognize and respond to abnormal system events in a timely manner, potentially resulting in grid-wide blackouts, outages, or both.

[0003] Three-phase unbalanced load flow analysis is an essential tool for observing and analyzing power system behavior. For example, load flow analysis can monitor power quality. It is always desirable to maintain the power load on each phase within a given percentage of each other. Three-phase load flow can report the difference between phases and send an alert when the difference exceeds an acceptable threshold. As an increasing proportion of renewable generation penetrates the distribution system, accurate load flow analysis to adequately capture system behavior becomes an increasingly challenging task.

[0004] Many challenges exist that affect the accuracy of load flow analysis in such hybrid power systems. For example, in bidirectional power flows with distributed generation, it is important to consider distribution systems with different voltage levels when analyzing load flow distribution within systems with different voltage levels. Furthermore, in integrating distribution systems with different voltage levels, it is difficult to find a single bus with sufficient capacity to handle the slack of the integrated system, and the slack must be shared among multiple generators. Therefore, to ensure efficient and continuous power flow in distribution systems with distributed generation, a better analytical method for determining and analyzing load flow in distribution systems is needed. Summary of the Invention

[0005] Load flow analysis or power flow analysis is a computational procedure for determining the steady-state operating characteristics of an electric power system network from given branch (wires, switches, phase jumpers, transformers, and regulators) and bus data. Such analysis is one of the fundamental power system analyses in the planning, design, and operation phases of an electric power system. It is used to calculate the steady-state performance of an electric power system under various possible operating conditions and to study the effects of changes in equipment configuration. Load flow analysis involves solving a set of nonlinear algebraic power simultaneous equations for two unknown variables: voltage magnitude (|V|) and phase angle (∠δ) at each node in the system.

[0006] Load flow analysis is used for various purposes, including verifying and checking the operation of an existing system under normal or outage conditions to determine whether the existing system can supply a planned additional load, or to verify and compare new alternatives for adding a system to supply the new load or improve system performance. Load flow analysis provides values ​​for various system parameters such as active and reactive power flow, maximum and minimum current flow in branch circuits, terminal voltages of all buses, power factors, transformer and generator load factors, system losses, transformer tap settings, voltage angles, line losses, and slack bus power. By conducting a load flow study on a power system, optimal operation of the power system is recommended. Methods used for load flow analysis include the Gauss-Seidel method, the Newton-Raphson method, and the fast separation method.

[0007] A balanced three-phase load refers to a condition in which all three phases carry the same magnitude of current with the same phase difference. An unbalanced load refers to a condition in which the three phases carry different currents. Inaccurate load flow analysis in an electrical distribution system can result in equipment damage or incorrect control measures being adopted, resulting in a failure to timely recognize and respond to system abnormal events. Accordingly, some example embodiments recognize that unbalanced load flow analysis is an essential tool for determining the behavior of an electrical distribution system and can be utilized to achieve optimization goals related to power distribution and delivery. For example, three-phase load flow can be used to report differences between phases and send alerts and / or initiate control actions when such differences exceed acceptable limits.

[0008] Some example embodiments recognize that distribution systems at different voltage levels may have different phase and neutral configurations. For example, a low-voltage distribution system may be configured as a three-phase, four-wire system, and its substations may be connected to a medium-voltage distribution system that may also be configured as a three-phase, three-wire system. The neutral-grounding configuration of a three-wire system is quite different from that of a four-wire system. Some example embodiments recognize that the three-phase, three-wire load approach traditionally lacks the accurate analytical capabilities of a four-wire low-voltage system due to the approximation of integrating neutral admittance into phase admittance. Such an approximation may be undesirable, for example, when the effects of neutral and grounding must be evaluated in the presence of single-phase renewable power injection, which can cause significant levels of network imbalance.

[0009] Some example embodiments also recognize that a single slack bus model is not effective in hybrid power distribution systems. When power distribution systems of different voltage levels are integrated, it becomes difficult to find a single bus with sufficient capacity to handle the slack of the integrated system, and the slack must be shared among multiple generators located on different buses. Therefore, some example embodiments recognize that a distributed slack bus model must be adopted, and specialized measures are needed to coordinate effective power sharing among participants in the power distribution system.

[0010] Some example embodiments recognize that sparse formulations for solving unbalanced three-phase, three-wire power systems using the Newton-Raphson method cannot be applied to effectively treat hybrid three-wire and four-wire systems. Some example embodiments recognize that three-phase, four-wire current injection methods, which apply the Newton-Raphson method to solve nonlinear current injection equations, also cannot be applied to effectively treat hybrid three-wire and four-wire systems.

[0011] Some example embodiments recognize that the convergence of component-based methods, such as backward / forward sweep algorithms, is highly dependent on the initial configuration of the variables to be solved for. Additionally, some example embodiments recognize that system-based methods, such as the Newton-Raphson algorithm, are computationally intensive. Therefore, example embodiments provide a hybrid system-based / component-based approach, in which a system-based algorithm is used to initialize the load flows using known scheduled configurations of generation, load, and voltage, and a component-based algorithm is used to update the load flows after receiving real-time updates of generation and load.

[0012] To achieve these objectives, example embodiments provide systems and methods for analyzing load flows in hybrid power systems to evaluate, monitor, and control the behavior of such hybrid power systems. Some example embodiments provide countermeasures for unbalanced load flow analysis of a distribution system. Some example embodiments provide countermeasures for controlling one or more parameters that control the behavior of such a distribution system according to the results of the unbalanced load flow analysis.

[0013] Some example embodiments relate to a three-phase unbalanced load flow analysis method for a hybrid three-wire-four-wire power distribution system with a distributed slack bus to accurately estimate system states under various phase and neutral configurations. Real-time load flow is obtained by hybrid component-based and system-based solution strategies. The inverse of a non-square mutual admittance matrix is ​​replaced by the product of the corresponding squared mutual admittance matrix. The singular admittance inverse matrix is ​​obtained by using a modified singular value decomposition. A composite three-bus node current model is used by merging zero-impedance branches and non-zero-impedance branches with mismatched phase sets. Residual active and reactive power are incorporated into the component-based and system-based algorithms to model the contribution of the distributed slack bus to mitigate global power imbalance and local voltage deviations.

[0014] Some example embodiments describe a composite system and component-based three-phase unbalanced load flow method for hybrid three-wire and four-wire power distribution systems, in which the neutral conductor is explicitly modeled similarly to the phase wires, and the neutral ground is modeled as an equivalent ground admittance determined based on rated measurement accuracy and short-circuit current (particularly for ungrounded and solid-grounded scenarios). The transformer admittance matrix is ​​determined by relating the currents and voltages between the external high-potential and low-potential terminals to the currents and voltages between the internal high-potential and low-potential terminals, which allows for more accurate modeling of the transformer's neutral impact. Unlike traditional three-phase, three-wire load flow analysis methods that cannot calculate the currents on the neutral conductor and the voltages at the neutral ground, the disclosed method explicitly models the neutral configuration of the power distribution system, which can be used to monitor and control the operation of the power distribution system and for more efficient control. Some example embodiments explicitly model the different phase connections of generators, loads, and capacitors, replacing the approximate phase-to-ground connections used in traditional methods, significantly improving the accuracy of the load flow solution.

[0015] To enable load flow to be solved using a component-based algorithm, some example embodiments replace the inverse matrix of the mutual admittances of non-zero impedance branches with different phase numbers at the terminal bus with the inverse matrix of the product of the mutual admittances of the terminal bus in the corresponding reverse order of the admittance under study and the mutual admittance under study. This allows the effects of non-invertible and non-square matrices to be expressed as invertible square matrices through the multiplication of mutual admittance matrices. To improve the convergence of the load flow iterations and the consistency of the solution, some example embodiments utilize a modified singular value decomposition algorithm to solve the inverse matrix of the singular mutual admittance matrices or the products of the admittance multiplication. Zero values ​​in the diagonal matrix containing the square roots of the eigenvalues ​​are replaced with small values ​​defined by the maximum and minimum absolute values ​​of the admittance matrix under study.

[0016] To enable the system-based algorithm to solve for load flow, some example embodiments include merging zero-impedance branches with adjacent non-zero impedance branches to be considered. To account for the possibility of bidirectional flow, some example embodiments select the adjacent branch as one of the non-zero impedance branches that has a common terminal with the zero-impedance branch, and the phases present at the common terminal as seen by the non-zero impedance branch include all phases present at the common terminal as seen by the non-zero impedance branch. Some example embodiments utilize a nodal admittance model based on three buses to represent the relationship between node injection currents and branch currents injected from the three buses. In this model, corresponding nodes of the three buses include all phases of the terminal bus of the zero-impedance branch opposite the common bus, all phases of the terminal bus of the impedance branch opposite the common bus, and mismatched phases of the common bus as seen by the non-zero impedance branch.

[0017] Unlike traditional load flow methods that select a single slack bus to absorb system losses and mismatches, which is impractical in distribution systems with high renewable energy penetration, some example embodiments disclosed herein utilize multiple buses that function as slack buses to share system power imbalances and losses among participating distributed generators, such as synchronous generators and grid-forming inverters with limited but sufficient generating capacity. In addition to scheduled active power to supply the active power of load demands, participating generators also provide surplus active power according to a global participation factor defined by the corresponding active power droop control eco-efficiency. Meanwhile, in addition to scheduled reactive power to supply the reactive power of load demands, participating generators also provide surplus reactive power according to the global and local participation factors defined by the corresponding reactive power droop control eco-efficiency. The surplus reactive power consists of two parts: one part for mitigating global reactive power imbalances and losses in the entire system, and the other part for mitigating local voltage deviations from the schedule.

[0018] Some example embodiments provide a component-based load flow algorithm that can model multiple slack buses by extending a conventional backward / forward sweep algorithm, in which the surplus active and reactive power updates are incorporated into the forward sweep step based on the updated nodal injection currents at the root node and the voltage deviations at the voltage regulated buses.

[0019] In some example embodiments, a system-based load flow algorithm is provided that extends the traditional Newton-Raphson algorithm to model multiple slack buses. In some example embodiments, such an algorithm includes embedding active and reactive powers into the nodal power balance equations and adding two additional equations for active power residual imbalance and reactive power residual imbalance to the load flow formulation. The load flow is obtained by solving the formulated equations for the magnitude and phase angle of the nodal voltages and the residual active and reactive powers shared by the distributed slack buses.

[0020] To achieve the above objects and advantages, some example embodiments provide a system, method and program for controlling an electrical power distribution system.

[0021] For example, some example embodiments provide a control system for controlling power flow in an electrical distribution system. The control system includes circuitry configured to receive input data related to power generation forecast data indicative of power generation by a plurality of power sources over a finite time horizon, load forecast data indicative of power consumption by a plurality of loads, and device status data for one or more pieces of equipment in the electrical distribution system. The control system generates scheduling data for scheduling power generation by one or more power sources among the plurality of power sources and for scheduling power consumption by one or more loads among the plurality of loads based on the power generation forecast data and the load forecast data. The control system further determines a network topology of the electrical distribution system based on equipment status updates obtained from protective devices of the electrical distribution system and determines values ​​of one or more system parameters of the electrical distribution system. The one or more system parameters include dispatched power, dispatched load demand, branch current, and bus voltage of the electrical distribution system. The control system determines these parameters by performing an unbalanced load flow analysis for the electrical distribution system using the scheduling data and the network topology. The unbalanced load flow analysis utilizes a compact multi-bus-based nodal admittance model to represent the relationship between nodal injected currents and nodal voltages at multiple non-overlapping phases of a bus for a section of the power distribution system formed by a zero-impedance branch connected with an impedance branch. A control system generates one or more commands for controlling the power distribution system based on the determined values ​​of the one or more system parameters.

[0022] Some example embodiments further provide a computer-implemented method for controlling power flow in an electrical distribution system. The method includes receiving input data including generation forecast data indicative of power generation by a plurality of power sources over a finite time horizon, load forecast data indicative of power consumption by a plurality of loads, and real-time device status data for one or more pieces of equipment in the electrical distribution system. The method further includes generating scheduling data for scheduling power generation by one or more power sources of the plurality of power sources and for scheduling power consumption by one or more loads of the plurality of loads based on the generation forecast data and the load forecast data. The method further includes determining a network topology of the electrical distribution system and determining values ​​of one or more system parameters of the electrical distribution system based on equipment status updates obtained from protective devices of the electrical distribution system. These parameters include dispatched power, dispatched load demand, branch current, and bus voltage of the electrical distribution system. The parameters are determined by performing an unbalanced load flow analysis for the electrical distribution system using the scheduling data and the network topology. The unbalanced load flow analysis utilizes a compact multi-bus-based nodal admittance model to represent the relationship between nodal injected currents and nodal voltages at multiple non-overlapping phases of a bus for a section of the power distribution system formed by a zero-impedance branch connected with an impedance branch. The method further includes generating one or more commands for controlling the power distribution system based on the determined values ​​of the one or more system parameters.

[0023] The present invention will now be described in detail with reference to the accompanying drawings, in which the drawings are not necessarily to scale, with emphasis instead generally being placed upon illustrating the principles of embodiments of the present disclosure. [Brief explanation of the drawings]

[0024] [Figure 1A]FIG. 1 is a schematic diagram illustrating a power distribution system controlled by a power distribution control system, according to some example embodiments. [Figure 1B] FIG. 1 illustrates an exemplary hybrid power distribution system, according to some example embodiments. [Figure 2] 1 is a flowchart illustrating an exemplary method for controlling an electrical power distribution system, according to some example embodiments. [Figure 3] FIG. 1 illustrates a workflow for controlling power flow with unbalanced load flow in a power distribution system, according to some example embodiments. [Figure 4A] FIG. 1 illustrates a branch model of a distribution line connecting two buses having a three-wire configuration, according to some example embodiments. [Figure 4B] FIG. 1 illustrates a branch model of a distribution line connecting two buses, having a four-wire configuration, in accordance with some example embodiments. [Figure 5A] 1A-1C illustrate three typical neutral grounding scenarios, according to some example embodiments. [Figure 5B] 1A-1C illustrate three typical neutral grounding scenarios, according to some example embodiments. [Figure 5C] 1A-1C illustrate three typical neutral grounding scenarios, according to some example embodiments. [Figure 6A] FIG. 2 illustrates the internal windings and external terminal connections of a three-phase transformer, according to some example embodiments. [Figure 6B] FIG. 2 illustrates the internal windings and external terminal connections of a three-phase transformer, according to some example embodiments. [Figure 7] FIG. 1 illustrates an exemplary configuration having a zero-impedance branch between a first bus and a second bus connected with a non-zero-impedance branch between a second bus and a third bus, according to some example embodiments. [Figure 8] FIG. 1 is a one-line diagram used to represent the graphical connections of a radial power distribution system, according to some example embodiments. [Figure 9A]FIG. 1 illustrates some steps of a load flow analysis method for a hybrid three-wire and four-wire power distribution system with a distributed slack bus, according to some example embodiments. [Figure 9B] FIG. 1 illustrates some steps of a load flow analysis method for a hybrid three-wire and four-wire power distribution system with a distributed slack bus, according to some example embodiments. [Figure 9C] 9C illustrates an example convergence of the load flow analysis method of FIGS. 9A and 9B, according to some example embodiments. FIG. [Figure 10] FIG. 1 illustrates several parameters utilized in power generation by one or more power sources and considered for load flow analysis of a power distribution system, according to some example embodiments. [Figure 11] FIG. 1 illustrates multiple parameters describing the load demand of one or more loads that are considered for load flow analysis of an electrical distribution system, according to some example embodiments. [Figure 12] FIG. 1 illustrates several parameters describing a distribution network that are considered for load flow analysis of a distribution system, according to some example embodiments. [Figure 13] FIG. 1 illustrates several corrective actions that may be implemented as a result of a load flow analysis to maintain the safety of an electrical distribution system, according to some example embodiments. [Figure 14] FIG. 1 is a block diagram illustrating a system for implementing an electrical distribution control system, according to some example embodiments. DETAILED DESCRIPTION OF THE INVENTION

[0025] [Description of the embodiment] While the above drawings illustrate embodiments disclosed herein, other embodiments are contemplated, as noted in the description. The present disclosure illustrates exemplary embodiments by way of representation and not limitation. Numerous other modifications and embodiments can be devised by those skilled in the art which fall within the scope and spirit of the principles of the embodiments disclosed herein.

[0026] The following description provides only exemplary embodiments and is not intended to limit the scope, applicability, or configuration of the present disclosure. Rather, the following description of exemplary embodiments provides those skilled in the art with an enabling description for implementing one or more exemplary embodiments. Various changes may be made in the function and arrangement of elements without departing from the spirit and scope of the disclosed subject matter as set forth in the appended claims.

[0027] In the following description, specific details are set forth to provide a thorough understanding of example embodiments. However, it will be apparent to those skilled in the art that the present disclosure may be practiced without these specific details. For example, systems, processes, and other elements of the disclosed subject matter may be shown as components in block diagram form to avoid obscuring the embodiments in unnecessary detail. In other instances, well-known processes, structures, and techniques may be shown without unnecessary detail to avoid obscuring the embodiments. Additionally, the same reference numbers and names in the various drawings refer to the same elements.

[0028] Also, particular embodiments may be described as a process that is depicted as a flowchart, a flow diagram, a data flow diagram, a structure diagram, or a block diagram. While a flowchart may describe operations as a sequential process, many of the operations may be performed in parallel or simultaneously. Additionally, the order of operations may be rearranged. A process may be terminated when its operations are completed, but may have additional steps not discussed or included in the diagram. Moreover, not all operations in any process that are specifically described may occur in all embodiments. A process may correspond to a method, a function, a procedure, a subroutine, a subprogram, etc. When a process corresponds to a function, the termination of the function may correspond to a return of the function to the calling function or the main function.

[0029] Furthermore, embodiments of the disclosed subject matter may be implemented, at least in part, either manually or automatically. The manual or automatic implementation may be performed or at least assisted by a machine, hardware, software, firmware, middleware, microcode, hardware description languages, or any combination thereof. When implemented in software, firmware, middleware, or microcode, the program code or code segments to perform the necessary tasks may be stored on a machine-readable medium. A processor(s) may perform the necessary tasks.

[0030] Renewable energy sources are gaining increasing acceptance in the modern world due to ecological and environmental concerns associated with the depletion of non-renewable resources. The adoption of such clean energy sources is becoming more prevalent in the electrical energy industry. As renewable power sources become more prevalent in the power grid, significant challenges arise in hybrid power distribution systems due to the complexity and heterogeneity of renewable and conventional energy sources. For example, renewable power sources typically fluctuate in terms of output power, voltage output, output current frequency, and hours of availability per day. Solar power plants may provide low or no power under certain operating conditions. Therefore, power grids must ensure that they adequately address such changes due to suddenness and fluctuations in the power provided by renewable sources.

[0031] Electrical energy is typically generated and / or delivered in three phases for several operational advantages. For transmission purposes, such three-phase power supplies employ three-wire or four-wire supply systems. To ensure the smooth operation of a distribution system, load flow analysis must be performed for proper planning and uninterrupted operation. A transmission and distribution system becomes unbalanced when the source voltages and / or load impedances within the system are mismatched. For example, the source voltages may not be the same magnitude and / or may not be at equal phase angles relative to each other. In another example, the load impedances may not be equal to each other. Differences in voltage and / or load impedances result in an unbalanced distribution system. On the other hand, in a balanced system, the magnitude and phase angle differences between the voltage sources are always equal (e.g., a three-phase system with a 4.16 kV voltage source per phase and any two phases 120 degrees apart), and the load impedances are equal (e.g., a three-phase system with the same resistive, inductive, or capacitive loads on all wires).

[0032] Some of the negative effects of an unbalanced three-phase system are overheating of the three-phase motor, shortened machine life due to overheating, and power loss. 2 These include increased R and reduced motor drive reliability. Therefore, performing accurate load flow analysis in such unbalanced power distribution systems is crucial; otherwise, operators may not be able to recognize and respond to system abnormalities in a timely manner, potentially leading to widespread outages. System abnormalities include, for example, equipment damage due to unbalanced load impedance or power supply voltage, thermal damage to equipment due to overheating, and increased power losses resulting in line failure. Three-phase unbalanced load flow analysis is widely used in power distribution systems. For example, load flow analysis can be used to monitor power quality. Maintaining the power loads on each phase within a given percentage of each other is an effective technique. Three-phase load flow reports the difference between the phases and sends an alert when the difference exceeds a preset percentage.

[0033] Because load impedances vary greatly in distribution systems, one of the primary causes of unbalanced three-phase systems occurs when the load impedance of one conductor is not equal to the load impedance of the other conductors. This occurs because one conductor with a load impedance draws a different current than the other two conductors. Such unbalanced systems can be analyzed using standard techniques applying mesh analysis or nodal analysis. However, with the introduction of hybrid distribution systems, it is highly likely that one or more voltage sources in the distribution system will differ in terms of the magnitude of their supply voltage and / or active / reactive power from other voltage sources in the distribution system. This complicates the unbalanced load flow analysis process, making it extremely cumbersome and / or nearly impossible for hybrid three-wire and four-wire distribution systems, especially considering that such systems have multiple slack buses.

[0034] Many challenges affect the accuracy of load flow analysis in unbalanced distribution systems. The first challenge stems from bidirectional flows from distributed generation, which require that distribution systems with different voltage levels be considered together when analyzing the load flow distribution within those systems. Distribution systems with different voltage levels may have different phase and neutral configurations. For example, a low-voltage distribution system may be configured as a three-phase, four-wire system, and its substation may be connected to a medium-voltage distribution system that may also be configured as a three-phase, three-wire system. The neutral-grounding configuration of a three-wire system is completely different from that of a four-wire system. Traditional three-phase, three-wire load flow analysis approaches cannot accurately analyze four-wire low-voltage systems due to the approximation that merges the neutral admittance into the phase admittance. This approximation can be undesirable when the effects of neutral and grounding need to be evaluated, especially when there is the injection of single-phase renewable power, which can cause significant levels of network imbalance. Another challenge affecting the accuracy of load flow analysis in unbalanced distribution systems is that a single slack bus model is no longer valid. When integrating distribution systems with different voltage levels, it is difficult to find a single bus with sufficient capacity to handle the slack of the integrated system, and the slack must be shared among multiple generators.

[0035] Some example embodiments described herein provide a three-phase unbalanced load flow analysis method for hybrid three-wire-four-wire power distribution systems with a distributed slack bus to more accurately estimate system states under various phase and neutral configurations. Real-time load flow is obtained through hybrid component-based and system-based solution strategies. The inverse of a non-square mutual admittance matrix is ​​replaced by the product of the corresponding squared mutual admittance matrix. The singular admittance inverse matrix is ​​found using a modified singular value decomposition. A composite three-bus node current model is used by merging zero- and non-zero-impedance branches with mismatched phase sets. Residual active and reactive power are incorporated into the component-based and system-based algorithms to model the contribution of the distributed slack bus to mitigate global power imbalance and local voltage deviations.

[0036] These and other principles of various example embodiments are described herein, first describing the structure and operation of a power distribution system utilizing some of the novel power distribution control principles, followed by a description of the underlying load flow analysis algorithms and parameters utilized.

[0037] 1A is a schematic diagram illustrating a power distribution system 100A controlled by a power distribution control system 102, according to some example embodiments. The power distribution system 100A includes the power distribution control system 102 communicatively coupled to a data acquisition system 106 via a communication network 104. The data acquisition system 106 is communicatively coupled to the electrical components of the power distribution system 100A via the communication network 104. In this regard, the data acquisition system 104 acquires sensor data and operational data related to the operation and performance of the electrical components of the power distribution system 100A. The power distribution system 100A further includes one or more generators 10A, one or more loads 20A, one or more transformers 30A, one or more loads 40A, one or more inverters 50A, and one or more inverters 60A. Generator 10A, loads 20A and 40A, and inverters 50A and 60A are electrically coupled to one another via multiple buses 70A, 70B, 70C, 70D, 70E, and 70F. Furthermore, generator 10A, loads 20A and 40A, and inverters 50A and 60A are communicatively coupled to data acquisition system 106 and power distribution control system 102 via communications network 104. To this end, generator 10A, loads 20A and 40A, and inverters 50A and 60A can each be considered to include appropriate electronics for collecting operational and attribute data of the respective components. For example, the appropriate electronics can capture and / or provide load values ​​related to current, voltage, power consumption, generator output values, rotational speed, AC frequency, primary and secondary winding voltages, etc.

[0038] Distribution control system 102 includes circuitry for collecting, transferring, and processing data. Additionally, distribution control system 102 may include suitable storage media for storing data and computer programs. Distribution control system 102 may periodically process data and issue control commands and / or corrective actions to balance power flow within the distribution system whenever the system experiences an unbalanced condition. Communications network 104 may include one or more media for enabling data communication between components of distribution system 100A. Data acquisition system 106 includes suitable interfaces, sensing circuits, transducers, etc. for collecting data from other components of distribution system 100A.

[0039] Loads 20A and 40A may be any type of resistive, inductive, or capacitive load in the power grid. Generator 10A may be a dispatchable source of electrical energy, such as a hydroelectric generator, a coal-fired generator, a diesel generator, or a gas-fired generator. In some example embodiments, generator 10A may be a synchronous generator. Generator 10A may also provide scheduled active power for the active power supply of the load demands and provide surplus active power according to a global participation factor defined by a corresponding active power droop control environmental efficiency. In some example embodiments, in addition to the scheduled reactive power for the reactive power supply of the load demands, participating generator 10A may also provide surplus reactive power according to a global and local participation factor defined by a corresponding reactive power droop control environmental efficiency. The surplus reactive power includes two components: a portion for mitigating global reactive power imbalances and losses throughout the system, and a portion for mitigating local voltage deviations from the schedule.

[0040] The transformer 30A may include a step-up or step-down transformer optionally coupled to the loads 20A, 40A, and the generator 10A. The bus pairs connected by wires / links from the available buses 70A-70F may include three-wire and / or four-wire architectures to support power transmission between components. The multiple buses 70A-70F, acting as slack buses, share system power imbalances and losses among the participating distributed generators, such as the participating distributed generators, the synchronous generator 10A, and grid-forming inverters 50A and 60A with finite but sufficient generating capacity. The inverters 50A and 60A may include grid-forming inverters that provide power in the system, making the distribution system a hybrid system.

[0041] Aspects of some example embodiments include explicitly modeling the neutral ground as an equivalent ground admittance determined based on rated measurement accuracy and short circuit current, particularly for ungrounded and solidly grounded scenarios. An admittance matrix for the transformer can be determined by relating the currents and voltages at the external high and low voltage terminals to the currents and voltages at all internal high and low voltage terminals, allowing for more accurate modeling of the effects of the transformer neutral.

[0042] FIG. 1B illustrates an exemplary hybrid power distribution system 100B configured with a combination of three-wire and four-wire sections, according to some example embodiments. The system 100B includes three buses with three wires, including bus-1, bus-2, and bus-3. The system further includes three buses with four wires, including bus-4, bus-5, and bus-6. The three-wire section includes only phase wires, and the generator 10B and the load 20B may be delta-connected (i.e., connected between the phase wires). The four-wire section includes phase and neutral wires, and the neutral wire is grounded (80) at least at one point along the section. The renewable generators, such as inverters 50B and 60B, and their loads 40B may be wye-connected (i.e., connected between the phase wires and the neutral wire). The generator 10B may be a conventional synchronous generator, and the inverters 50B and 60B may be grid-forming inverter-based generators and grid-following inverter-based generators. A transformer 30B may be used to connect the three-wire section and the four-wire section.

[0043] FIG. 2 is a flowchart illustrating an example method 200 for controlling a power distribution system 100B according to some example embodiments. The method 200 includes receiving 202 forecast generation data, load forecast data, and real-time device status data associated with one or more generating, consuming, or transmitting equipment in the power distribution system 100B over a time horizon. For example, the forecast generation data may include a generation schedule for the generator 10B and inverters 50B and 60B over a predefined or user-defined period. According to some example embodiments, the forecast generation data for the generator 10B and inverters 50B and 60B may be obtained from a database or directly from the generator and inverter operators. The load forecast data may be obtained in a similar manner, for example, by querying a database or by directly measuring state parameters of the loads 20B and 40B over a period of time. The real-time device status of the generators, inverters, buses, transformers, and loads in the power distribution system may also be obtained by appropriate means and measures, such as using one or more sensors. In some example embodiments, the data received in step 202 may be obtained in response to one or more queries, or may be obtained using any suitable approach.

[0044] Method 200 further includes generating 204 scheduling data for scheduling power generation and consumption in power distribution system 100B. The power generation schedule is generated based on the power generation forecast data obtained in step 202 using economic dispatch and unit commitments to balance total power generation with known total load demand. Similarly, the power consumption schedule may be generated based on the load forecast data obtained in step 202 and real-time weather or environmental updates. Method 200 includes determining a network topology of power distribution system 100B in step 206. The network topology may be determined based on real-time device status data, power generation forecast data, and load forecast data using connectivity analysis with full connection tracking. According to some example embodiments, as part of determining the network topology of the power distribution system, method 200 may include explicitly modeling the neutral conductor as a phase conductor and the neutral ground as an equivalent ground admittance. Method 200 proceeds to step 208, where system parameters are determined by performing an unbalanced load flow analysis of the power distribution system using the scheduling data and the network topology. In some example embodiments, power flow in the system may be bidirectional, and performing the unbalanced load flow analysis may comprise solving for an initial load flow of the power distribution system using the scheduling data and the real-time device status data according to a system-based model. The system-based model is based on a nodal admittance matrix of the power distribution system generated using admittance matrices of each component and each node in the network topology of the power distribution system. Each branch with an energized phase is modeled as a node, and each branch with a branch impedance below a threshold is modeled as a zero-impedance branch.

[0045] The system parameters determined in step 208 include dispatched generation schedules and dispatched loads for the system operator / dispatcher to maintain power balance in the distribution system, and branch current / power flows and bus phase voltages for maintaining system safety and good quality of service. A detailed description of the unbalanced load flow analysis is provided below in this disclosure. Based on the results of the unbalanced load flow analysis, the one or more system parameters thus determined are used to take corrective actions for the distribution system. In this regard, the method comprises step 210 of generating one or more commands for controlling the distribution system based on the determined values ​​of the one or more system parameters. For example, if the results of the unbalanced load flow analysis indicate that the voltages supplied by one or more generators are below a threshold, control commands instructing an increase in generation and / or a reduction in load on each branch of the distribution system may be generated and provided to associated equipment to timely balance the power flow in the system.

[0046] FIG. 3 illustrates a workflow 300 for controlling power flow in a distribution system, such as system 100B of FIG. 1B, using unbalanced load flow, according to some example embodiments. In particular, workflow 300 illustrates different inputs and outputs of an unbalanced load flow analysis method 304. Generation and consumption forecasts over a time horizon and real-time device status 302 are received by a distribution control system performing unbalanced load flow analysis. Based on the data received in 302, scheduled generation data 351, scheduled load demand data 353, and grid network topology 355 are determined and provided as load flow inputs to a three-phase unbalanced load flow analysis algorithm 360. The three-phase unbalanced load flow analysis algorithm 360 provides dispatched generation schedule 371, dispatched load 373, branch current 375, and bus voltage 377 as load flow results. The dispatched generation amount may include corresponding amounts of both scheduled generation and surplus generation. The surplus generation is used to compensate for active power losses and forecast errors in the scheduled generation. The dispatched load may differ slightly from the scheduled load. The scheduled load is typically determined based on a pre-determined voltage level. If the load contains a constant current or impedance load component, the dispatched load will differ from the scheduled load if the actual voltage level determined by the load flow solution differs from the pre-determined voltage level. These load flow results are used to perform a condition assessment of the distribution system. For example, as part of the condition assessment, the dispatched generation schedule 371 may be used to determine upper / lower limit generation violation data 381 for generators and / or inverters in the distribution system. In some example embodiments, the dispatched load 373 may be used to determine load current capacity and quality 383 associated with the loads in the distribution system. In some example embodiments, the branch current 375 may be used to determine phase / neutral overload 385 and current imbalance 387 in the distribution system.Similarly, in some example embodiments, bus voltage 377 may be used to determine undervoltage / overvoltage 389 and voltage imbalance 391 in the distribution system. The results of the situation assessment are then automatically or semi-automatically analyzed to suggest and / or implement corrective actions to maintain the safety of the distribution system (306).

[0047] (Modeling of distribution lines with 3-wire and 4-wire configurations) 1B in conjunction with FIGS. 4A and 4B, a detailed model of components in power distribution system 100B will now be described. FIG. 4A illustrates a branch model of a power distribution line connecting two buses in a three-wire configuration, according to some example embodiments. FIG. 4B illustrates a branch model of a power distribution line connecting two buses in a four-wire configuration, according to some example embodiments.

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[0051] If only two phases or one phase are present, the corresponding series and shunt admittances reduce to a 2x2 or 1x1 matrix.

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[0053] Similarly, if only two-phase or one-phase wires are present, the corresponding series and shunt admittances reduce to a 3 × 3 or 2 × 2 matrix.

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[0055] Y ps and Y sp If is a square matrix, then equation (4c) above can be used to derive the phase-to-ground voltage and injected phase current at one terminal bus given the phase-to-ground voltage and injected phase current at the opposite terminal bus.

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[0058] Equations (5) and (6) define the current and voltage distribution matrices using the transformed branch admittance matrices when the mutual admittance matrix is ​​a square matrix.

[0059] For devices such as transformers with specific connections, Y ps or Y sp Considering that can be singular or close to it, we modify the singular value decomposition (SVD) to compute the inverse of the matrix.

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[0064] (Neutral point representation of different earthing systems) In some example embodiments, each phase, including the neutral, for each bus is explicitly modeled, with each neutral being grounded via an equivalent admittance that is evaluated or approximated based on a grounded neutral scenario.

[0065] Figures 5A, 5B, and 5C illustrate three typical neutral grounding scenarios according to some example embodiments. Figure 5A depicts a solid neutral grounding scenario 500A. Figure 5B depicts an ungrounded neutral scenario 500B. Figure 5C depicts a resistive or reactive neutral grounding scenario 500C. According to some example embodiments, the neutral is treated as a node, and the neutral ground rod is represented as an equivalent admittance connected between the neutral and ground.

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[0076] Then, the relationship between the node phase-to-ground voltage and the branch phase current can be expressed using equation (4c).

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[0080] Equations (20) and (21) define the current and voltage distribution matrices using the transformed branch admittance matrices when the mutual admittance matrix is ​​a square matrix.

[0081] In addition to transformers, boost regulators are also well known as a type of voltage control equipment used in current / power distribution systems. A boost regulator is essentially a transformer in which a high voltage winding (shunt) and a low voltage winding (series) are connected with each voltage on one side or against each other. The output voltage can then be the sum or difference of the winding voltages.

[0082] A boost regulator is a zero-impedance branch type. Additionally, a switch or phase jumper can be treated as a zero-impedance branch to be modeled.

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[0084] (Modeling of distributed generators, loads and capacitors) Distributed generators can be conventional synchronous generators, equivalent synchronous generators (such as substations connected to the mains grid), or electronics-based generators (such as grid-forming or grid-following inverters). Distributed generators can be connected phase-to-neutral using a wye connection, or phase-to-phase using a delta connection.

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[0092] The local surplus reactive power generation component of each participating generator increases or decreases independently based on its own local voltage conditions, however the global surplus reactive power generation components of all participating generators increase or decrease simultaneously.

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[0095] (Unbalanced Load Flow in Distribution Systems) Although power distribution systems may employ a radial configuration, flows can be bidirectional due to distributed generation and multiple generators participating in balancing active and reactive power. Due to the complex connections of large-scale distribution systems, traditional load flow analysis methods, such as the Gauss-Seidel method, Newton's method, and backward / forward sweep methods, face challenges in efficiently obtaining accurate solutions and are unable to meet real-time applications. Some example embodiments provide a component-based algorithm for hybrid systems that uses a system-based model to solve initial load flows based on scheduled generation, loads, and controller settings, and updates the load flows using the component-based model upon receiving updates to dispatched generation, loads, and controller settings.

[0096] (Zero-impedance branch connected to a non-zero-impedance branch with mismatched phase connection) The system-based algorithmic model is based on a nodal admittance matrix of the system, which is generated using the admittance matrices of each component / branch, where each energized phase (including the neutral point) of each branch is modeled as a node. However, some branch types, such as phase jumpers, boost regulators, and switches, do not have nodal admittance matrices due to negligible branch impedances. Such branches are sometimes called zero-impedance branches. A phase or wiring jumper is a short conductor used to connect two points in an electrical circuit, especially for phase connection changes of single-phase loads. Switches used in power distribution systems include circuit breakers and sectionalizing or linking switches.

[0097] To formulate the nodal admittance of a zero-impedance branch, the zero-impedance branch is merged with the adjacent non-zero-impedance branch to be considered. To allow for the possibility of bidirectional flow, the adjacent branch is selected as one of the non-zero-impedance branches that has a common terminal with the zero-impedance branch, and the phases present at the common terminal as seen from the non-zero-impedance branch include all phases present at the common terminal as seen from the zero-impedance branch.

[0098] 7 shows an example configuration 700 with a zero-impedance branch 704 between bus m and bus p connected with a non-zero-impedance branch 708 between bus p and bus s. p 706 is the matching phase Φ p1 and the mismatch phase Φ p2 The zero-impedance branch 704 can be divided into two subsets: the phase Φ m 702 at bus m and the partial phase Φ p1 The impedance branch is connected to the phase Φ s Take the 710 bus p All phases Φ in p Connect with Φ p =Φ p1 ∪Φ p2 Φ p1 and Φ p2 represent a phase set that matches between the zero-impedance branch and the non-zero-impedance branch, and a phase set that does not match between the zero-impedance branch and the non-zero-impedance branch, respectively.

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[0103] This three-bus model includes a complete phase set for bus m, a mismatched phase set for bus p, and a complete phase set for bus s.

[0104] Extending the above strategy to a single zero-impedance branch connecting to multiple impedance branches from the same bus, a compact multi-bus-based nodal admittance model can be used to represent the relationship between nodal injected currents and nodal voltages at multiple non-overlapping phases of the bus for a section formed by zero-impedance branches connected to impedance branches.

[0105] (Distributed Slack Bus) In traditional load flow analysis, one bus is selected to absorb all system losses and mismatches. This slack bus serves as a power balancing bus, referencing the voltage angles of all buses and compensating for the difference between the scheduled generation and the combined load and losses. The slack bus is therefore considered a voltage source with a large power capacity, i.e., an "infinite power source." However, in practical distribution systems, especially those with a high penetration rate of distributed generation, it is difficult to find a bus that can allocate all of the system's slack, and the slack must be distributed among the set of participating distributed generators.

[0106] In some example embodiments, the buses / nodes of the system are classified into five different types, including reference (Vθ) buses / nodes, fV buses / nodes, fQ buses / nodes, PV buses / nodes, and PQ buses / nodes.

[0107] The reference (Vθ) bus / node is a bus / node for which the magnitude and phase angle of the corresponding voltage are known, while the active and reactive power injection is adjustable. It is selected from buses with larger capacity generators, such as the equivalent synchronous generator bus of a substation.

[0108] An fV bus / node is a bus / node where the voltage magnitude and frequency are given while the corresponding phase angle, active power injection, and reactive power injection are adjustable. This type of bus / node includes grid-forming inverter-based generators with constant frequency and constant voltage control, and synchronous generators with constant frequency and constant voltage control.

[0109] An fQ bus / node is a bus / node where the corresponding reactive power injection and frequency are known, while the corresponding phase angle and active power injection are adjustable. This type of bus / node includes grid-forming inverter-based generators with constant frequency control and synchronous generators with constant frequency control.

[0110] A PV bus / node is a bus / node in which the corresponding active power injection and voltage magnitude are known, while the corresponding phase angle and reactive power injection are adjustable. This type of bus / node includes grid-forming inverters with constant voltage control and synchronous generators with constant voltage control, such as static synchronous compensators (STATCOMs).

[0111] A PQ bus / node is a bus / node where the corresponding active and reactive power injections are known, while the corresponding phase angles and voltage magnitudes are adjustable. This type of bus / node contains a grid-following inverter with constant PQ control, a load, and a synchronous generator with constant PQ control.

[0112] The distributed slack bus model is implemented by a set of buses including a reference bus, an fV bus, an fQ bus, and a PV bus, and mitigates the system's active and reactive power mismatches by sharing the active and reactive power mismatches among participating generators and resolving additional local reactive power demands through voltage regulation of the participating generators. The frequency of the distribution system is maintained by active power regulation of the reference bus, the fV bus, and the fQ bus. The voltage of the distribution system is maintained by reactive power regulation of the reference bus, the fV bus, and the PV bus.

[0113] (Component-based analysis of load flow using distributed slack bus) Conventional backward / forward sweep algorithms are designed to solve the load flow of a radial distribution system with a single slack bus and all other PQ buses, and cannot solve the load flow of a system with multiple slack buses. In some example embodiments, the backward / forward sweep algorithm with surplus active and reactive power updates is extended to enable solving the load flow of a distribution system with distributed slack buses.

[0114] 8 is a single-line diagram used to represent the graphical connection 800 of the radial power distribution system shown in FIG. 1B. Bus 1 may be selected as the reference bus. Bus 6 may be selected as the fV bus. Bus 1 and Bus 6 together function as distributed slack buses.

[0115] The objective of the load flow calculation is to determine the amplitude and phase angle of each energized phase on all buses, as well as the surplus active and reactive power generated by the distributed slack buses.

[0116] A radial power distribution system can be represented as a graph, where buses are modeled as nodes in the graph and branches are modeled as links in the graph. One of the reference buses is taken as the root. The connectivity relationships between nodes can be obtained by performing a full connectivity trace. Based on the trace results, the nodes can be divided into multiple layers based on the number of branches connected to the root. The root belongs to the first layer, and the higher the layer number, the farther the node is from the root.

[0117] Assuming the total number of layers is D, the load flow calculation can be realized by an iterative procedure. In this iterative procedure, two calculation stages are performed in each iteration. The first stage, called the "backward sweep," is a sweep from the nodes connected to the last layer D back to the first layer to calculate the power / current flowing through the branches and the power / current injected into the nodes. In addition to the scheduled power, load, or compensation from generation, the injected power of the distributed slack bus includes the allocation of global surplus active power generation and global reactive power generation for all distributed slack buses, and local surplus reactive power for voltage deviation correction based on the latest global surplus power and bus voltage. The global surplus active power and global reactive power generation are updated after the current / power accumulation in the first layer. The other stage, called the "forward sweep," is a sweep from the root node to the nodes in the last layer to calculate the amplitude and phase angle of the voltage at each node.

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[0119] Backward sweep is the summation process of node currents or powers with updating of surplus active and reactive powers. In this process, the nodes are iterated from the last layer D connected nodes to the first layer nodes. During backward propagation, voltages and surplus active and reactive powers are assumed to be constant as of the last iteration.

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[0129] The forward sweep is the voltage drop calculation process accompanied by the update of the residual reactive power. The voltage calculation is repeated from the nodes connected to the first layer to the nodes in the last layer D. During the forward propagation, the phase currents of each branch are kept at the values ​​obtained in the backward sweep.

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[0134] Component-based methods such as the backward / forward sweep algorithm are easy to implement, but their convergence is highly dependent on the initial settings of voltage and residual power.

[0135] (System-based analysis method for load flow with distributed slack buses) The load flow in a power distribution system with a distributed slack bus can also be solved using a system-based load flow analysis method, in which each phase of all buses is modeled as a node, except for the common phase of the common bus between the zero-impedance branch and a selected adjacent impedance branch. The adjacent impedance branch is selected as the branch connected to the zero-impedance branch that has a larger number of phases connected to the common bus than the zero-impedance branch.

[0136] The nodal admittance matrix, which represents the relationship between nodal injection current and nodal voltage, is formed by integrating the branch nodal admittance matrices for all non-zero impedance branches, including zero-impedance branches and branches merged by selected adjacent impedance branches. Ground impedances, constant impedance loads, and capacitors are all treated as nodal self-admittances to be considered in the nodal admittance matrix.

[0137] For a given nodal admittance matrix, the load flow is expressed as a set of nodal active and reactive power balance equations and one additional uncertain power unbalance equation for the entire system. The uncertain variables in the load flow are the amplitudes and angles of the nodal voltages for all phases of each bus except for the phase of a given reference bus, and the system power unbalance, including the active and reactive power unbalances.

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[0145] System-based methods such as the Newton-Raphson algorithm have good convergence properties but require extensive computations to repeatedly invert the Jacobian matrix.

[0146] (Hybrid System-Based and Component-Based Load Flow Algorithms with Distributed Slack Buses) To overcome the shortcomings of component-based and system-based algorithms, some example embodiments provide hybrid system-based and component-based algorithms.

[0147] 9A and 9B together illustrate example steps and convergence of a method 900 for load flow analysis of a hybrid three-wire / four-wire distribution system with a distributed slack bus, according to some example embodiments. The load flow analysis includes steps 902-910 for load flow initialization and steps 912-920 for load flow update. The method 900 includes a step 902 of obtaining scheduled generation, load, and controller settings. According to some example embodiments, obtaining data in step 902 may be performed in the manner described with reference to step 202 of FIG. 2. Next, zero-impedance branches are merged with adjacent non-zero-impedance branches 904, and distributed generator participation factors are calculated 906. The load flow initialization then proceeds to step 908, where a load flow model with a distributed slack bus is formulated and the Newton-Raphson algorithm is used to solve 910 the load flow equations for the system with a distributed slack bus. The solution of the load flow equations is used to update 912 the generation, load, and controller settings and the method 900 proceeds to load flow update.

[0148] In step 914, the method 900 comprises determining current and voltage allocation matrices based on the branch node admittance matrices and singular value decomposition, as described in equations (5)-(6), (20)-(21), and (7)-(9). Then, a backward sweep is performed to calculate the bus injection current and update the surplus active power and surplus reactive power (916), and a forward sweep is performed to calculate the bus voltage (918). Next, the load flow convergence is checked (920); if the convergence criteria are not met, the control returns to step 912 to update the generation, load, and controller settings. If the convergence criteria are met, the method ends and outputs the load flow results. The load flow convergence check may be performed by using the maximum voltage mismatch for all nodes between two iterations.

[0149] FIG. 9C illustrates an example convergence of a method 900 for load flow analysis of a hybrid three-wire and four-wire distribution system with a distributed slack bus, according to some example embodiments. As shown in FIG. 9C, the convergence process is a process for solving the load flow of the example system shown in FIG. 8. In this solution, the maximum real and maximum imaginary voltage mismatch between two consecutive iterations is used to verify the convergence of the load flow. If the allowable voltage mismatch is 0.0025 per unit, the load flow is considered to have converged in iteration 19 of FIG. 9C if the maximum voltage mismatch is below the allowable limit after 19 backward / forward sweeps.

[0150] Thus, the load flow analysis method for a hybrid three-wire / four-wire power distribution system with a distributed slack bus provides a power distribution system that can analyze the load flow to timely detect the occurrence of system abnormal events, thereby facilitating the timely implementation of appropriate corrective measures and preventing system equipment failures. The load flow analysis leads to corrective measures that can modify the generation and / or consumption of power, thereby significantly optimizing the overall efficiency of the power distribution.

[0151] 10 illustrates parameters 1000 utilized for power generation by one or more power sources considered for load flow analysis of a power distribution system, according to some example embodiments. The parameters 1000 include a generator control mode 1010, a power generation set point 1020, a voltage set point 1030, a governor set point 1040, and a phase connection type 1050. The power generation control mode 1010 further includes a reference value (constant voltage and constant phase angle) 1011, a PQ value (constant active and reactive power) 1013, a PV value (constant active power and constant voltage) 1015, fV (constant frequency and constant voltage) 1017, and fQ (constant frequency and constant reactive power) 1019. The power generation set points 1020 include active power (P) 1021, reactive power (Q) 1023, a maximum value of P 1025, and a maximum value of Q 1027. The voltage set point 1030 includes a voltage magnitude (V) 1031 and a phase angle (θ) 1033. The governor set point 1040 includes a droop factor 1041 and a distribution factor 1043. The phasing type 1050 can be wye 1051 or delta 1053.

[0152] 11 illustrates parameters 1100 describing the load demand of one or more loads considered for load flow analysis of a power distribution system, according to some example embodiments. The parameters 1100 include a load regulation mode 1110, a power consumption setpoint 1120, and a phase connection type 1130. The load regulation mode 1110 includes a constant active and reactive power (Const PQ) 1112, a constant current (Const I) 1114, and a constant impedance (Const Z) 1116. The power consumption setpoint 1120 includes an active power (P) 1122 and a reactive power (Q) 1124. The phase connection type 1130 can be a wye 1132 or a delta 1134.

[0153] FIG. 12 shows parameter 1200 for explaining a power distribution network considered for load flow analysis of a power distribution system according to some embodiments. The power distribution network parameter 1200 includes impedance / admittance parameters and maximum power 1210 of wire segments, impedance parameters, maximum power, and real-time tap positions 1220 of transformers and voltage regulators, real-time settings 1230 of capacitors and grounding rods, maximum power and real-time states 1240 of switches or phase switches (phase jumpers), and system requirements 1250. The system requirements 1250 include maximum voltage and minimum voltage 1252, maximum voltage imbalance 1254, and maximum current imbalance 1256.

[0154] FIG. 13 shows some corrective measures 1300 implemented as a result of load flow analysis to maintain the safety of a power distribution system according to some embodiments. The corrective measures 1300 include changes in active power generation (distributed generation) 1310, changes in reactive power generation (capacitors) 1320, rebalancing of loads (changing the connection phase of single-phase loads using phase switches) 1330, reduction of load demand (opening load switches) 1340, and adjustment of tap positions of transformers / regulators 1350.

[0155] FIG. 14 is a block diagram showing a system 1400 for implementing some components of the power distribution control system of FIG. 1A according to some embodiments. Component 1411 includes a processor 1440, a computer-readable memory 1412, a storage 1458, and a user interface 1449 having an optional display 1452 and a keyboard 1451, which are connected via a bus 1456. For example, when the user interface 1449 communicating with the processor 1440 and the computer-readable memory 1412 receives an input from the surface of the user interface 1457 or the keyboard 1453 by the user, it acquires data and stores it in the computer-readable memory 1412.

[0156] Component 1411 may include a power supply 1454. Depending on the application, power supply 1454 may optionally be located outside component 1411. Linked via bus 1456 is a user input interface 1457 adapted to connect to a display device 1448, which may include, among other things, a computer monitor, a camera, a television, a projector, or a mobile device. Network interface controller (NIC) 1434 is adapted to connect to a network 1436 via bus 1456, so that image data or other data can be rendered to a third-party display device, a third-party imaging device, and / or a third-party printing device external to component 1411.

[0157] Continuing to refer to FIG. 14 , particularly electronic data, may be transmitted via a communication channel of the network 1436 and / or stored in a storage system 1458 for archiving and / or further processing. Furthermore, time-series data or other data may be received wirelessly or via a wired connection from a receiver 1446 (or an external receiver 1438) and transmitted wirelessly or via a wired connection from a transmitter 1447 (or an external transmitter 1439), both of which are connected via a bus 1456. The component 1411 may be connected to an external sensing device 1444 and an external input / output device 1441 via an input interface 1408. For example, the external sensing device 1404 may include a sensor that collects data before, during, and after the machine's collected time-series data. The component 1411 may be connected to another external computer 1442. The output interface 1409 may be used to output processed data from the processor 1440. In addition, the user interface 1449, which is in communication with the processor 1440 and the non-transitory computer-readable storage medium 1412, receives input from the surface of the user interface 1449 by a user and retrieves and stores data in the non-transitory computer-readable storage medium 1412.

[0158] The foregoing description provides only exemplary embodiments and is not intended to limit the scope, applicability, or configuration of the present disclosure. Rather, the following description of exemplary embodiments will provide those skilled in the art with an enabling description for implementing one or more exemplary embodiments. Various changes may be made in the function and arrangement of elements without departing from the spirit and scope of the disclosed subject matter as set forth in the appended claims.

[0159] Specific details are given in the following description to provide a thorough understanding of the embodiments. However, it will be understood by those skilled in the art that the embodiments may be practiced without these specific details. For example, systems, processes, and other elements in the disclosed subject matter may be shown as components in block diagram form to avoid obscuring the embodiments in unnecessary detail. In other instances, well-known processes, structures, and techniques may be shown without unnecessary detail to avoid obscuring the embodiments. Moreover, like reference numbers and names in the various drawings indicate like elements. Moreover, particular embodiments may be described as a process that is shown as a flowchart, a flow diagram, a data flow diagram, a structure diagram, or a block diagram. Although a flowchart may describe operations as a sequential process, many of the operations can be performed in parallel or simultaneously. In addition, the order of operations may be rearranged. A process may be terminated upon completion of its operations, but may have additional steps not discussed or included in the diagram. Moreover, not all operations in any process specifically described may occur in all embodiments. A process may correspond to a method, a function, a procedure, a subroutine, a subprogram, etc. If the process corresponds to a function, the termination of the function may correspond to the function returning to the calling function or to the main function.

[0160] Furthermore, embodiments of the disclosed subject matter may be implemented, at least in part, either manually or automatically. Manual or automated implementations may be performed by, or at least assisted by, a machine, hardware, software, firmware, middleware, microcode, hardware description languages, or any combination thereof. When implemented in software, firmware, middleware, or microcode, program code or code segments to perform the necessary tasks may be stored on a machine-readable medium. A processor(s) may perform the necessary tasks. The various methods or processes outlined herein may be coded as software executable by one or more processors employing any one of a variety of operating systems or platforms. Additionally, such software may be written using any of a number of suitable programming languages ​​and / or programming or scripting tools, and compiled as executable machine-language code or intermediate code that runs on a framework or virtual machine. Typically, the functionality of the program modules may be combined or distributed as desired in various embodiments.

[0161] The embodiments of the present disclosure may be implemented as a method, an example of which is provided. The order of actions performed as part of this method may be determined in any suitable manner. Thus, embodiments may be configured to perform actions in an order different from that illustrated, including performing some actions simultaneously, even though they are shown as a series in the illustrated embodiments. Furthermore, the use of order terms such as "first," "second," etc. to modify claim elements in the claims does not, in itself, imply any priority, precedence, or order among the claim elements or the chronological order in which the method actions are performed, but is merely used as a label to distinguish between claim elements having the same name (except for the use of order terms). While the present disclosure has been described with reference to certain exemplary preferred embodiments, it should be understood that various other adaptations and modifications are possible within the spirit and scope of the present disclosure. Therefore, it is the object of the appended claims to cover all such variations and modifications that are within the true spirit and scope of the present disclosure.

Claims

1. 1. A control system for controlling power flow in an electrical distribution system, comprising: Equipped with a circuit, The circuit comprises: receiving input data including power generation forecast data indicative of power generation by a plurality of power sources over a finite time horizon, load forecast data indicative of power consumption by a plurality of loads, and real-time device status data for one or more pieces of equipment in the power distribution system; generating scheduling data for scheduling power generation by one or more power sources among the plurality of power sources and for scheduling power consumption by one or more loads among the plurality of loads based on the power generation forecast data and the load forecast data; and performing an unbalanced load flow analysis of the distribution system using the scheduling data and a network topology of the distribution system to determine values ​​of one or more system parameters including dispatched generation, dispatched load demand, branch current, and bus voltage of the distribution system, wherein the unbalanced load flow analysis utilizes a compact multi-bus based nodal admittance model to represent relationships between nodal injected currents and nodal voltages at multiple non-overlapping combinations of buses and phases for sections formed by zero-impedance branches connected to impedance branches in the distribution system, and the circuitry further comprises: a control system configured to generate one or more commands for controlling the electrical distribution system based on the determined values ​​of the one or more system parameters.

2. the power distribution system is a hybrid three-wire / four-wire three-phase power distribution system; The control system of claim 1 , wherein the network topology of the power distribution system is determined by explicitly modeling a neutral conductor as a phase conductor and a neutral-grounding conductor as an equivalent ground admittance.

3. power flow in the distribution system is bidirectional; 2. The control system of claim 1, wherein to perform the unbalanced load flow analysis, the circuitry is configured to solve for an initial load flow of the power distribution system using the scheduling data and the real-time device state data according to a system-based model.

4. the system-based model is based on a nodal admittance matrix of the power distribution system; the nodal admittance matrix is ​​generated using admittance matrices of each component and each node in the network topology of the power distribution system; The control system of claim 3 , wherein each branch having a conducting phase is modeled as a node, and each branch having a branch impedance below a threshold is modeled as a zero-impedance branch.

5. a nodal admittance of the zero-impedance branch is formulated by merging the zero-impedance branch with a corresponding adjacent non-zero-impedance branch having a common terminal with the zero-impedance branch; The control system of claim 4 , wherein the phases present at the common terminal as seen from the non-zero impedance branch include all phases present at the common terminal as seen from the zero impedance branch.

6. 4. The control system of claim 3, wherein to generate the one or more commands, the circuitry is configured to update the initial load flow based on a component-based model using the values ​​of the one or more system parameters.

7. the component-based model is based on a representation of the electrical distribution system as a graph; In the graph, the buses are modeled as nodes of the graph and branches of a radial configuration are modeled as links of the graph; The nodes of the graph are divided into layers based on the number of branches connected to a root node; The control system of claim 6 , wherein one of the plurality of buses is modeled as the root node belonging to a first layer of the plurality of layers.

8. To update the initial load flow based on the component-based model, the circuit Calculating the injection power of nodes and the power flow of branches connected to each phase from the last layer of the plurality of layers to the first layer of the plurality of layers by using the latest voltages, the global surplus active power, and the global surplus reactive power determined in the last iteration; updating global surplus active power and global surplus reactive power for the participating generators based on the calculated injected power and the node and branch power flows in the first layer; 8. The control system of claim 7, configured to calculate voltage magnitudes and phase angles of each node connected to each phase from the root node toward the nodes in the last layer using the latest power flows and node and branch injected powers.

9. a power flow in a branch between a first bus and a second bus having a different number of phases is calculated based on a corresponding current flowing into the branch through the first bus, the corresponding current being determined as a weighted combination of a current flowing into the branch through the second bus of the branch and a voltage at the second bus of the branch; the weighted contribution of the current is expressed using a matrix calculated based on a self-admittance matrix of the first bus of the branch, a mutual admittance matrix between the first bus and the second bus of the branch, and an inverse matrix of a product of the mutual admittance matrix between the first bus and the second bus of the branch and the mutual admittance matrix between the second bus and the first bus; 9. The control system of claim 8, wherein the weighted voltage contributions are represented using a matrix determined based on a self-admittance matrix of the first bus and the second bus of the branch, a mutual admittance matrix between the first bus and the second bus of the branch, and an inverse matrix of a product of the mutual admittance matrix between the first bus and the second bus of the branch and the mutual admittance matrix between the second bus and the first bus.

10. a voltage at the second bus of a branch between a first bus and a second bus having a different number of phases is calculated as a weighted combination of a current flowing through the first bus of the branch into the branch and a voltage at the first bus of the branch; the weighted contribution of the current is expressed as a matrix determined based on a mutual admittance matrix between the second bus and the first bus of the branch and an inverse matrix of a product of a mutual admittance matrix between the second bus and the first bus of the branch and a mutual admittance matrix between the first bus and the second bus; 9. The control system of claim 8, wherein the weighted voltage contributions are represented using a matrix based on a self-admittance matrix of the first bus of the branch, a mutual admittance matrix between the second bus and the first bus of the branch, and an inverse matrix of a product of the mutual admittance matrix between the second bus and the first bus of the branch and the mutual admittance matrix between the first bus and the second bus.

11. The circuit further comprises: Check the convergence of the load flow by using the maximum voltage mismatch of all nodes between two iterations; The control system of claim 8 , configured to generate the one or more commands based on determined branch currents, node voltages, load consumption, and generated power.

12. the plurality of buses share a global active power and global reactive power mismatch among the plurality of power sources; The control system of claim 1 , wherein the circuitry is further configured to provide additional reactive demand to meet voltage regulation needs of the plurality of power sources.

13. 1. A computer-implemented method for controlling power flow in an electrical distribution system, comprising: receiving input data including power generation forecast data indicative of power generation by a plurality of power sources over a finite time horizon, load forecast data indicative of power consumption by a plurality of loads, and real-time device status data for one or more pieces of equipment in the power distribution system; generating scheduling data for scheduling power generation by one or more power sources among the plurality of power sources and for scheduling power consumption by one or more loads among the plurality of loads based on the power generation forecast data and the load forecast data; performing an unbalanced load flow analysis of the distribution system using the scheduling data and a network topology of the distribution system to determine values ​​of one or more system parameters including dispatched generation, dispatched load demand, branch current, and bus voltage of the distribution system; The unbalanced load flow analysis utilizes a compact multi-bus-based nodal admittance model to represent the relationship between nodal injected currents and nodal voltages at multiple non-overlapping combinations of buses and phases for a section formed by zero-impedance branches connected to impedance branches in the power distribution system, and the method further includes: A computer-implemented method comprising generating one or more commands for controlling the electrical power distribution system based on the determined values ​​of the one or more system parameters.

14. the power distribution system is a hybrid three-phase three-wire and four-wire three-phase power distribution system; 14. The computer-implemented method of claim 13, wherein the network topology of the power distribution system is determined by explicitly modeling a neutral conductor as a phase conductor and a neutral-grounding conductor as an equivalent ground admittance.

15. power flow in the distribution system is bidirectional; 14. The computer-implemented method of claim 13, wherein performing the unbalanced load flow analysis includes solving for an initial load flow for the power distribution system using the scheduling data and the real-time device status data according to a systems-based model.

16. the system-based model is based on a nodal admittance matrix of the power distribution system; the nodal admittance matrix is ​​generated using admittance matrices of each component and each node in the network topology of the power distribution system; 16. The computer-implemented method of claim 15, wherein each branch having an energized phase is modeled as a node and each branch having a branch impedance below a threshold is modeled as a zero-impedance branch.

17. 16. The computer-implemented method of claim 15, wherein generating the one or more commands comprises updating the initial load flow based on a component-based model using the values ​​of the one or more system parameters.

18. the component-based model is based on a representation of a radial configuration of the electrical distribution system as a graph; In the graph, the buses are modeled as nodes of the graph and branches of the radial configuration are modeled as links of the graph; 18. The computer-implemented method of claim 17, wherein the nodes of the graph are divided into multiple layers based on the number of branches connected to a root node, and one of the multiple buses is modeled as the root node belonging to a first layer of the multiple layers.

19. updating the initial load flow based on the component-based model Calculating the injection power of nodes and power flows of branches connected to each phase from the last layer of the plurality of layers to the first layer of the plurality of layers by using the latest voltages, global surplus active power, and global surplus reactive power determined in the last iteration; updating global surplus active power and global reactive power for the participating generators based on the calculated injected power and the node and branch power flows in the first layer; 20. The computer-implemented method of claim 18, comprising: calculating voltage magnitudes and phase angles of each node connected to each phase from the root node toward the nodes in the last layer using the latest power flows and node and branch injected powers.

20. 1. A non-transitory computer-readable medium storing computer-executable instructions that, when executed by a computer, cause the computer to perform a method for controlling power flow in an electrical power distribution system, the method comprising: receiving input data including power generation forecast data indicative of power generation by a plurality of power sources over a finite time horizon, load forecast data indicative of power consumption by a plurality of loads, and real-time device status data for one or more pieces of equipment in the power distribution system; generating scheduling data for scheduling power generation by one or more power sources among the plurality of power sources and for scheduling power consumption by one or more loads among the plurality of loads based on the power generation forecast data and the load forecast data; performing an unbalanced load flow analysis of the distribution system using the scheduling data and a network topology of the distribution system to determine values ​​of one or more system parameters including dispatched generation, dispatched load demand, branch currents, and bus voltages of the distribution system, wherein the unbalanced load flow analysis utilizes a compact multi-bus based nodal admittance model to represent the relationship between nodal injection currents and nodal voltages at multiple non-overlapping combinations of buses for sections formed by zero-impedance branches connected to impedance branches in the distribution system, and the method further comprises: generating one or more commands for controlling the electrical power distribution system based on the determined values ​​of the one or more system parameters.

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