Optimal control method and optimal control device

Abstract

To quickly solve an optimal control problem in a power grid equipped with GFM inverters with current limiting functions.SOLUTION: An optimal control device 1 according to one embodiment of the present invention is provided with a calculation unit 112 that solves a first equation system that formulates a problem of optimal control for determining a state of a GFM inverter A1, for maintaining a dynamic reliability of a power grid A that includes one or more GFM inverters A1 with current limiting functions. The first equation system includes a second equation system that represents a dynamic model of the power grid A. The second equation system includes a third algebraic equation that re-formulates a first algebraic equation using a complementary variable as the first algebraic equation that shows an internal state of one or more GFM inverters A1, for each of a first conditional branch that is met when the current limiting function is in operation and a second conditional branch that is met when the current limiting function is not in operation.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present disclosure relates to an optimal control method and an optimal control device. [Background technology]

[0002] In recent years, there has been a demand for improved flexibility and resilience in power systems. For example, if a distribution substation loses its voltage source due to an event such as abnormal weather or a natural disaster, it is required that some or all of the feeders extending from the distribution substation operate autonomously. One possible solution to this problem is to introduce a grid-forming inverter (GFM inverter) into the power system (see, for example, Patent Document 1). A GFM inverter is a type of power conditioner system (PCS), and is equipped with a control function that autonomously establishes voltage and maintains stable operation.

[0003] Generally, a distributed energy system that establishes voltage independently from the power grid is called a "microgrid." When the entire feeder below the distribution substation is independent from the higher-level power grid, it is also called a "regional microgrid." In the following, we will focus on configurations that include GFM inverters for such power grids.

[0004] In the operation of power systems such as regional microgrids, transient fluctuations in voltage and frequency are expected to become apparent, making it important to maintain the dynamic reliability of the power system, including GFM inverters. The criteria for dynamic reliability here are whether power flow, frequency, voltage, and stability are within their operational limits, and these conditions are determined by evaluating a dynamic model. Therefore, it is considered necessary to build a dynamic model of the power system, including GFM inverters, and to use the dynamic model to control reliability in real time.

[0005] In conventional reliability control of power systems, in order to minimize the possibility of accident propagation in the power system, even if a primary accident occurs, preventive control and emergency control are often carried out to prevent the temporary accident from progressing to a secondary or tertiary accident. Preventive control is control that takes preventive measures in advance for the normal operating state of the power system, and emergency control is control that quickly suppresses the accident propagation by some method once the accident propagation begins to occur (for example, see Non-Patent Document 1).

[0006] Preventive control generally involves proactively reallocating generator output to maintain the reliability of the power grid even in the event of a major power grid failure. Meanwhile, emergency control includes control for quickly disconnecting generators and shedding loads after a fault occurs. This emergency control requires a response within several hundred milliseconds after the fault occurs. For this reason, a lookup table is prepared in advance that shows combinations of generators to be disconnected based on the supply and demand status and loads to be shedding based on the supply and demand status. Then, control devices such as protective relays execute control operations for disconnecting generators and shedding loads based on this lookup table, thereby realizing fast emergency control (see, for example, Non-Patent Document 2).

[0007] In both preventive control and emergency control, it is necessary to find the optimal state of the generator (hereinafter referred to as "optimal state") that can maintain the dynamic reliability of the power system by using a method such as solving an optimization problem in the power system in advance. The problem of finding the optimal state of the generator is called the dynamic security constrained optimal power flow problem (DSCOPF: Dynamic Security Constrained Optimal Power Flow problems) and has been widely studied (for example, see Non-Patent Document 3).

[0008] In general, analysis of the dynamic reliability of a power system is performed using differential-algebraic equations for the entire power system, taking into account the dynamic characteristics of generators and loads. Therefore, the optimal power flow problem (TSCOPF) in a power system is formulated as an optimal control problem (hereinafter referred to as the "optimal control problem") that requires the solution of differential-algebraic equations. There are two methods for solving optimal control problems: direct methods and indirect methods. The direct method is a method that discretizes the differential-algebraic equations and finds a solution that satisfies the equality constraints in the optimal control problem. The indirect method is a method that alternates between solving the differential-algebraic equations and performing optimization calculations.

[0009] When a direct method is used to solve an optimal control problem, the state variables at all time steps in the discretized differential algebraic equations are used as variables in the optimal control problem, which increases the size of the variables in the problem and makes the amount of calculation extremely large. On the other hand, when an indirect method is used to solve an optimal control problem, the calculations for solving the differential algebraic equation and the optimization problem are performed independently, so the size of the variables in the problem becomes relatively small and the solution can be found relatively quickly. For example, Non-Patent Document 4 discloses that by using the adjoint method, which is a type of indirect method, to solve the optimal control problem, it is possible to execute a single control in about 10 seconds for a power system with several thousand nodes.

[0010] In order to protect internal components, GFM inverters are equipped with a current limiting function that limits the current when an overcurrent is detected. This current limiting function makes the characteristics of GFM inverters discontinuous and complex. For this reason, it is difficult to use the conventional solution method described in Non-Patent Document 4 to solve the optimal control problem in a power system that includes a GFM inverter. On the other hand, Non-Patent Document 5 discloses an analysis method for a GFM inverter having a current limiting function that limits an excessive current caused by the occurrence of a system fault or the like. [Prior art documents] [Non-patent literature]

[0011] [Non-Patent Document 1] Sekine, "Reliability Control of Power Systems", Journal of the Institute of Electrical Engineers of Japan, 1969, Vol. 9, pp.1626-1634 [Non-patent document 2] Special Committee on Issues and Solutions for Grid Stabilization Systems Caused by Environmental Changes Surrounding the Power System, "Issues and Solutions for Grid Stabilization Systems Caused by Environmental Changes Surrounding the Power System," Electrical Cooperative Research Association, Vol. 77, No. 1, 2021 [Non-patent document 3] Yan Xu, Zhao Yang Dong, Zhao Xu, Rui Zhang, Kit Po Wong, “Power system transient stability-constrained optimal power flow : A comprehensive review“, 2012 IEEE Power and Energy Society General Meeting, 2012 [Non-patent document 4] Zhihao Li, Guoqiang Yao, Guangchao Geng, Quanyuan Jiang, “An Efficient Optimal Control Method for Open-Loop Transient Stability Emergency Control”, IEEE Transactions on Power Systems, Vol.32, No.4, pp.2704-2713, 2017 [Non-patent document 5] Du Wei, Liu Yuan, Huang Renke, Francis K. Tuffner, Xie Jing, Huang Zhenyu, "Positive-Sequence Phasor Modeling of Droop-Controlled, Grid-Forming Inverters with Fault Current Limiting Function", [online], 12 July 2022, IEEE, [Searched on January 12, 2024], Internet <URL:https: / / ieeexplore.ieee.org / document / <9817530>

Summary of the Invention

Problems to be Solved by the Invention

[0012] Non-Patent Document 5 discloses a method for analyzing a power system including the GFM inverter by using algebraic equations formulated for each conditional branch of an If-then rule as a logic for simulating the current limiting function of the GFM inverter. However, the method of Non-Patent Document 5 involves a combinatorial problem of algebraic equations to be solved, and it is not easy to solve the combinatorial problem. Also, when the method of Non-Patent Document 5 is used for an optimal control problem, the calculation time becomes exponentially long with respect to the variable size.

[0013] An object of the present disclosure is to provide an optimal control method and an optimal control device that can quickly solve an optimal control problem in a power system including a GFM inverter having a current limiting function.

Means for Solving the Problems

[0015] An optimal control device according to one embodiment of the present disclosure includes a calculation unit that solves a first system of equations that formulates an optimal control problem for determining the state of one or more GFM inverters having a current limiting function, while maintaining the dynamic reliability of the power system including the GFM inverters. The first system of equations includes a second system of equations that represents a dynamic model of the power system. The second system of equations includes a third algebraic equation that is a reformulation of the first algebraic equation using complementary variables as a first algebraic equation that represents the internal state of the one or more GFM inverters, for each of a first conditional branch that is true when the current limiting function is operating and a second conditional branch that is true when the current limiting function is not operating. [Effects of the Invention]

[0016] According to one aspect of the present disclosure, it is possible to quickly solve an optimal control problem in a power system including a GFM inverter with a current limiting function. [Brief explanation of the drawings]

[0017] [Figure 1] 1 is a diagram illustrating an example of a functional configuration of an optimization control device according to an embodiment of the present disclosure, together with a power system that is an optimization control target. [Figure 2] 10 is a flowchart showing an example of the operation of the optimization control device. [Figure 3]FIG. 1 is a diagram illustrating a power system that is an optimal control target according to an operation example. [Figure 4] FIG. 4 is a diagram showing a response waveform when preventive control is not executed in the power system of FIG. 3. [Figure 5] FIG. 4 is a diagram showing a response waveform when preventive control is being executed in power system A of FIG. 3. DETAILED DESCRIPTION OF THE INVENTION

[0018] Preferred embodiments of the present disclosure will be described below with reference to the drawings. The dimensions and scale of each part in the drawings may differ from the actual dimensions and scale, and some parts may be shown schematically to facilitate understanding. Furthermore, unless otherwise specified in the following description to the effect that the present disclosure is limited, the scope of the present disclosure is not limited to the embodiments described below. The scope of the present disclosure includes equivalents of the embodiments.

[0019] 1. Embodiment FIG. 1 is a diagram showing an example of the functional configuration of an optimization control device 1 according to this embodiment, together with a power system A that is the object of optimization control. The optimal control device 1 is a device that performs optimal control to maintain the dynamic reliability of a power system A by solving an optimal control problem in the power system A that includes one or more GFM inverters A1. Here, the power system A can have any configuration, and may be either a large-scale system or an autonomous system, and may be either a transmission system or a distribution system. The optimal control problem in this embodiment is a problem of determining the optimal state of the GFM inverter A1 that can maintain the dynamic reliability of the power system A.

[0020] As shown in FIG. 1, the optimal control device 1 of this embodiment includes a computer equipped with a processing device 10, a storage device 12, an input I / F device 14, and an output I / F device 16, and this computer may be a personal computer, a supercomputer, or the like. The processing device 10 includes at least one processor, such as a CPU (Central Processing Unit). Some of the functions of the processing device 10 may be configured using circuits such as an FPGA (Field Programmable Gate Array). The storage device 12 is a recording medium readable by the processing device 10. The storage device 12 includes, for example, a nonvolatile memory and a volatile memory. The nonvolatile memory is, for example, a ROM (Read Only Memory), an EPROM (Erasable Programmable Read Only Memory), or an EEPROM (Electrically Erasable Programmable Read Only Memory). The volatile memory is, for example, a RAM (Random Access Memory). The input I / F device 14 is a device including an input interface circuit to which an input device is connected by wire or wirelessly, and receives data input from the external device and outputs the received data to the processing device 10. The output I / F device 16 is a device including an output interface circuit to which an output device is connected by wire or wirelessly, and outputs various data to the output device under the control of the processing device 10. Typical examples of input devices include a keyboard, a recording medium reader, and another computer. Typical examples of output devices include a display, a printer, a recording medium recorder, and another computer.

[0021] The storage device 12 of this embodiment stores a program PR for realizing optimal control. The processing device 10 executes the program PR, and the optimal control device 1 functions as a storage unit 110, a calculation unit 112, and an execution unit 114.

[0022] Each functional unit will be described in detail below. In the following description, it is assumed that the power system A includes i GFM inverters A1, where i=1, 2, 3, . . . , m, and m is a natural number. The optimal control device 1 of this embodiment solves an optimal control problem for preventive control.

[0023] The storage unit 110 is a functional unit that stores a first system of equations that formulates an optimal control problem in a power system A that includes a GFM inverter A1. This first system of equations includes a second system of equations that represents a dynamic model of the power system A. This second system of equations includes differential-algebraic equations, specifically, a first differential equation DE1 and a first algebraic equation AE1 that represent a model of the GFM inverter A1, and a second algebraic equation AE2 that represents the relationship between the power flow and voltage in the power system A. The first differential equation DE1, the first algebraic equation AE1, and the second algebraic equation AE2 are derived from the method disclosed in the above-mentioned Non-Patent Document 5.

[0024] More specifically, the first differential equation DE1 expresses the dynamic characteristics f of the i-th GFM inverter A1 in the power system A. i is a differential equation expressed by the following equation (1A): In this formula (1A), "E i " indicates the internal state of the GFM inverter A1. In this embodiment, the internal state E i is the internal voltage only, and E i ∈C 1 "C" represents the set of all complex numbers. Also, in formula (1A), "V i (t)" indicates the terminal voltage of the GFM inverter A1, and "I i (t)" indicates the output current of the GFM inverter A1.

[0025]

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[0026] The first algebraic equation AE1 is an algebraic equation that represents the internal state of the GFM inverter A1 for each of the first conditional branch that is true when the current limiting function is not operating and the second conditional branch that is true when the current limiting function is operating, and includes the following algebraic equations (1B), (1C), and (1D).

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[0030] In addition, in formula (1B), the symbol " - " means complex conjugate, "Z i " is a constant that indicates the impedance of the GFM inverter A1, and Z i ∈C 1 Also, equation (1D) expresses the output current I i This is the formula that represents the phase angle of (t).

[0031] The second algebraic equation AE2 is an algebraic equation that represents the relationship between the power flow and voltage in the network of power system A, and is expressed by the following equation (1E): In this equation (1E), w(t) is a variable other than the GFM inverter A1, such as a variable related to the load bus.

[0032]

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[0033] In the above equations, the complex conjugate of I and E(0) are set appropriately.

[0034] Here, when the if-then rule of the first conditional branch in formula (1B) is satisfied, that is, when the non-current limiting operation is performed, E i ’ By eliminating (t), the following equation (2) is obtained.

[0035]

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[0036] In this equation (2), I i (t), and V i (t) is found by solving the algebraic equations (1C) and (1D).

[0037] On the other hand, if the if-then rule of the second conditional branch in equation (1B) is satisfied, that is, if the current is limited, the following equation (3) is determined regardless of equation (1D), and V i (t) is found by solving equation (1D).

[0038]

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[0039] However, the "I" used to determine the first and second conditional branches i (t)" is also a state variable of equation (1D). In other words, solving the second system of equations representing the dynamic model of power system A requires calculations to simultaneously solve equation (1B), which indicates the first and second conditional branches included in the first algebraic equation AE1, as well as equations (1C), (1D), and (1E). In general, solving algebraic equations including the first and second conditional branches requires calculations using a combinatorial problem solution method, which requires a large amount of calculation and takes a long time to solve. Furthermore, even when trying one of multiple possible combinations, it is necessary to solve nonlinear equations, such as performing convergence calculations using the Newton-Raphson method.

[0040] Therefore, in this embodiment, instead of equations (1A) to (1D), a system of equations formulated using complementary variables is used as the second system of equations representing the dynamic model of power system A, thereby reducing the amount of calculation and increasing the speed. Such a system of equations is detailed below.

[0041] For each of the first and second conditional branches, the above equation (1B) representing the internal state of the GFM inverter A1 is converted into the form of the following equation (4) based on equation (1C).

[0042]

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[0043] Equation (4) is a formulation of a combinatorial problem that seeks a set of algebraic equations that satisfy the complementarity conditions of the first conditional branch and the second conditional branch. This combinatorial problem can be reformulated by introducing a complementarity variable. Specifically, I i , E i , V i , and Z i Considering that all are complex numbers, the complementary variable a i , and b i When this is introduced into equation (4), equation (4) is reformulated as a third algebraic equation AE3 indicating the complementarity condition. In this embodiment, the third algebraic equation AE3 is expressed by the following equation (6).

[0044]

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[0046] The complementarity condition of this equation (6) can be accurately approximated by a nonlinear function shown in the following equation (7), for example: In equation (7), "ε" is a small positive real number.

[0047]

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[0048] Therefore, in the second system of equations representing the dynamic model of power system A, equation (4) can be replaced with equation (7). In this case, the second system of equations is formulated as the following equations (8A) to (8D) based on equations (5) to (7).

[0049]

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[0053] However, the complementary variable a i , and b i is expressed as the following equation (8E).

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[0055] Of the second system of equations, when equations (8A) and (8D) are expressed using vector variables x, y, and p, they become general vector equations shown in equations (9A) and (9B). Therefore, the amount of calculation required to solve the second system of equations representing the dynamic model of power system A is reduced, and as a result, the amount of calculation required to solve the optimal control problem is reduced and the solution can be found more quickly.

[0056]

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[0058] In this embodiment, the system contraction method is applied to the second algebraic equation AE2 that indicates the relationship between the power flow and voltage of the power system A, thereby achieving a significant reduction in the amount of calculation. For this system reduction method, for example, the system reduction method shown in Non-Patent Document 6 is used. Non-Patent Document 4 is "PW Sauer, et al., "Power System Dynamics and Stability 2nd Edition", Wiley IEEE Press, 2018".

[0059] The system reduction method is described in detail. Generally, loads are divided into three types: constant impedance, constant current, and constant power. When a load has a constant current or constant power characteristic, the nodal equations for system calculations become nonlinear. Therefore, in system calculations, it is often assumed that all loads in a power system A have a constant impedance characteristic. Under this assumption, the load admittance matrix Y L can be incorporated as part of the system admittance, and the internal voltage E of the GFM inverter A1, the terminal voltage V, and the voltage V of the load node L The relational expression (10) below holds between Y and the output current I of the GFM inverter A1. G is the coupling admittance of the GFM inverter A1.

[0060]

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[0061] By solving this equation (10), the following equations (11) and (12) are obtained.

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[0064] From equations (11) and (12), the terminal voltage V and the voltage V at the load node are L By eliminating the above, the following equations (13A) and (13B) or (14A) and (14B) are obtained.

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[0069] In the formulas (13B), (14A), and (14D), Y red is the contracted admittance, which corresponds to the determinant enclosed in "()" on the right side of equation (13A). The fourth algebraic equation AE4 represented by equations (13A) and (13B) or equations (14A) and (14B) can be used as equation (8D), which is the second algebraic equation AE2. In this embodiment, the following equation (15D) is used for the fourth algebraic equation AE4.

[0070]

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[0071] In this way, by converting equation (8D), which is the second algebraic equation AE2, into equation (15D), which is the fourth algebraic equation AE4 obtained by the contraction method, the size of the second algebraic equation AE2 is reduced to a matrix containing only GFM inverter A1, and the second algebraic equation AE2 is linearized. As a result, the amount of calculation required for the second algebraic equation AE2, which represents the relationship between the power flow and voltage in power system A, is significantly reduced, and further reductions in the amount of calculation required to solve the optimal control problem and further speedup are achieved.

[0072] Here, the optimal control problem in power system A is formulated as the above-mentioned first system of equations including the following equations (16A) to (16F).

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[0079] In the first system of equations, t∈[0,T], where T is the terminal time. If the optimal control problem is, for example, an optimization problem for preventive control, the parameter p corresponds to the initial value of the output command value of the GFM inverter A1. The vector variable x is a state variable and includes the phase difference angle δ and angular velocity ω of the GFM inverter A1. The vector variable y is an output variable and includes the output current and terminal voltage of the power system A. Equation (16A) shows that the optimal control problem is a minimization problem of the objective function φ(p). Equation (16E) shows the constraints on the dynamic reliability of the power system A.

[0080] Moreover, equations (16B) and (16C) correspond to the second system of equations of the dynamic model of power system A. Then, by using equations (8A) to (8D) formulated using complementary variables instead of equations (16B) and (16C), it becomes possible to solve the optimal control problem in power system A using the adjoint method, which allows for relatively fast solution.

[0081] In the optimal control device 1 of this embodiment, the storage unit 110 stores the first system of equations as described above, and the storage unit 110 of this embodiment stores, as a second system of equations included in this first system of equations, a system of equations in which a dynamic model of the power system A is formulated using complementary variables. Note that in this embodiment, as described above, equation (15D) to which a contraction method is applied is used for equation (8D) included in the second system of equations.

[0082] The calculation unit 112 is a functional unit that executes an optimal control calculation, which is a calculation for solving the first system of equations stored in the storage unit 110 using the adjoint method. The optimal control calculation will be described in detail later.

[0083] The execution unit 114 is a functional unit that executes optimal control to put each GFM inverter A1 into an optimal state based on the calculation results of the calculation unit 112. The execution unit 114 of this embodiment has the following functions: acquire system information about the power system A; calculate initial values ​​for a second system of equations that represents a dynamic model of the power system A; calculate an output variable y for the GFM inverter A1 by having the calculation unit 112 solve a first system of equations that formulates an optimal control problem; and control the state of each GFM inverter A1 using a control input based on the output variable y. Although not shown, the optimization control device 1 includes a device necessary for acquiring system information. An example of the device is a measuring device that measures appropriate physical quantities in the power system A.

[0084] FIG. 2 is a flowchart showing an example of the operation of the optimization control device 1. In the optimization control device 1, first, the execution unit 114 acquires system information of the power system A by performing measurements on the power system A in real time (step Sa1). When the optimization control is a preventive control, the system information is, for example, the supply and demand state of the load, and is acquired by measuring the load of the power system A. Note that when the load cannot be measured, the execution unit 114 may identify the supply and demand state of the load using a state estimation technique.

[0085] Next, based on the system information acquired in step Sa1, the execution unit 114 calculates the initial values ​​of a second system of equations that represent the current power flow cross section of power system A, i.e., the dynamic model of power system A (step Sa2). In this embodiment, the initial values ​​are calculated for the active power and reactive power flowing through each node of power system A, as well as the magnitude and phase of the voltage, the magnitude and phase of the current, and so on.

[0086] Next, the execution unit 114 causes the calculation unit 112 to execute an optimal control calculation for solving, by the adjoint method, the first system of equations (16A), (8A) to (8D), and (16D) to (18F) that formulates the optimal control problem in the power system A. In this embodiment, this optimal control calculation includes the following steps Sa3 to Sa5.

[0087] Specifically, in the optimal control calculation, the calculation unit 112 first solves a second system of equations representing a dynamic model of the power system A (step Sa3). In this embodiment, the second system of equations is Equations (8A) to (8C) and (15D) formulated using complementary variables, and the calculation unit 112 finds the state variable x by solving this second system of equations. When a hypothetical fault is assumed, the state variable x is the series value of the phase difference angle δ of each GFM inverter A1 during fault fluctuation. Next, the calculation unit 112 uses adjoint sensitivity analysis to calculate the gradient of the objective function φ(p) in equation (16A) (step Sa4). Then, based on the calculation result of step Sa4, the calculation unit 112 solves the optimal control problem with equation (16A) as the objective function to obtain the output variable y (step Sa5). To solve the optimal control problem, an appropriate solution algorithm of a mathematical optimization method can be used.

[0088] Next, the execution unit 114 controls the state of each GFM inverter A1 to an optimal state based on the output variable y calculated in step Sa5 (step Sa6). Specifically, in step Sa6, the execution unit 114 calculates a reallocation value, which is a value obtained by reallocating active power and reactive power to each node of the power system A. Next, the execution unit 114 determines the control input amount of each GFM inverter A1 based on this reallocation value. Then, the execution unit 114 controls the state of each GFM inverter A1 to an optimal state by inputting a command value to each GFM inverter A1 based on the control input amount (step Sa6).

[0089] The optimal control device 1 repeatedly executes the series of processes from step Sa1 to step Sa6 at regular intervals, thereby maintaining the state of each GFM inverter A1 in an optimal state (optimal state) that can maintain the dynamic reliability of the power system A. As described above, in this embodiment, the optimal control problem is solved at high speed, so the cycle of the series of processes from step Sa1 to step Sa6 is kept to a practical time.

[0090] Next, an example of the operation of the optimum control by the optimum control device 1 will be described.

[0091] FIG. 3 is a diagram showing power system A that is the object of optimal control. As shown in the figure, the target power system A is a system including nine buses and three generators. In this operation example, node 1 is a slack bus, node 2 is a synchronous generator SG, and node 3 is a GFM inverter A1.

[0092] In addition, in the first system of equations that formulates the optimal control problem in power system A, the above-mentioned equation (16A), which is the objective function, is changed to the following equation (17), which indicates maximization of the amount of power generation.

[0093]

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[0094] The following equation (18) expresses the constraints on the stability, which is one of the dynamic reliability of the power system A, as the phase difference angle δ of each GFM inverter A1 when node 1, which is a slack node, is used as the reference. i (t) (where i=1, ..., n g ) is an equation expressed using

[0095]

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[0096] In this embodiment, in order to reduce the number of constraints on stability, the following equation (19) is defined, and equation (18) is simplified to equation (20).

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[0099] Furthermore, by using the exterior point penalty function "max{g(x(p),y(p),p),0}", the optimal control problem in power system A was converted into an optimization problem with no constraints on the state variables, as shown in equation (21). In equation (21), r is a penalty coefficient, and its value is a sufficiently large positive number.

[0100]

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[0101] Fig. 4 is a diagram showing response waveforms when preventive control is not being executed in power system A of Fig. 3. Fig. 5 is a diagram showing response waveforms when preventive control is being executed in power system A of Fig. 3. If a hypothetical fault C occurs in power system A and preventive control is not performed, as shown in Figure 4, after the fault occurs, a large number of spike-like noises D with sharp waveforms will occur in the output of GFM inverter A1, causing power system A to become unstable. In contrast, when preventive control using the optimal control of the optimal control device 1 is being executed, as shown in Figure 5, noise D does not occur in the output of the GFM inverter A1, and it can be seen that the power system A is maintained stable.

[0102] As described above, the optimal control device 1 of this embodiment includes a calculation unit 112 that solves a first system of equations that formulates an optimal control problem for determining the state of one or more GFM inverters A1 that have a current limiting function and that maintains the dynamic reliability of the power system A including the GFM inverters. The first system of equations includes a second system of equations that represents a dynamic model of the power system A. The second system of equations includes a third algebraic equation that is obtained by reformulating the first algebraic equation using complementary variables as a first algebraic equation that represents the internal state of the one or more GFM inverters A1, for each of a first conditional branch that is true when the current limiting function is operating and a second conditional branch that is true when the current limiting function is not operating.

[0103] According to this configuration, the first algebraic equation AE1 representing the internal state of the GFM inverter A1 for each of the first and second conditional branches becomes a third algebraic equation representing the complementarity condition, so that the solution can be found relatively easily. Furthermore, of the second system of equations, the first differential equation DE1 that represents the dynamic characteristics of the GFM inverter A1 and the second algebraic equation AE2 that represents the relationship between the power flow and voltage in the power system A are converted into general vector equations. This reduces the amount of calculation required to solve the second system of equations that represents the dynamic model of the power system A, thereby reducing the amount of calculation required to solve the optimal control problem and speeding up the solution process.

[0104] In the optimal control device 1 of this embodiment, the second system of equations includes a second algebraic equation AE2 that represents the relationship between the power flow and voltage in the power system A, and a fourth algebraic equation AE4 that is obtained by applying a system reduction method to the second algebraic equation AE2.

[0105] According to this configuration, the amount of calculation for the second algebraic equation AE2 can be significantly reduced, and the amount of calculation required to solve the optimal control problem can be reduced and the speed of the solution can be increased.

[0106] The optimization control device 1 of this embodiment includes an execution unit 114 that executes control of the GFM inverter A1 based on the calculation result of the calculation unit 112.

[0107] This configuration allows the GFM inverter A1 to be in an optimal state.

[0108] In the optimal control device 1 of this embodiment, the calculation unit 112 solves the first system of equations by the adjoint method. This configuration further reduces the amount of calculation required to solve the optimal control problem and further speeds up the solution process.

[0109] 2. Variations The above-described embodiment can be modified as follows, for example.

[0110] (Variation 1) The optimal control device 1 of the above-described embodiment may solve the optimal control problem for emergency control rather than preventive control.

[0111] (Variation 2) The program PR that causes a computer to function as the optimization control device 1 may be implemented by distributing it on an appropriate recording medium or via an electric communication line. [Explanation of symbols]

[0112] 1...optimal control device, 10...processing device, 12...storage device, 14...input I / F device, 16...output I / F device, 110...memory unit, 112...calculation unit, 114...execution unit, A...power system, A1...GFM inverter, AE1...first algebraic equation, AE2...second algebraic equation, AE3...third algebraic equation, AE4...fourth algebraic equation.

Claims

1. a first step of solving a first system of equations that formulates an optimal control problem for determining the state of one or more GFM inverters with current limiting capabilities that maintains dynamic reliability of a power system including the GFM inverters; The first system of equations is: a second system of equations describing a dynamic model of the power system; The second system of equations is: For each of a first conditional branch that is established when the current limiting function is operating and a second conditional branch that is established when the current limiting function is not operating, a third algebraic equation is included that is reformulated as a first algebraic equation that represents an internal state of the one or more GFM inverters using a complementary variable. Optimal control methods.

2. The second system of equations is: a fourth algebraic equation obtained by applying a system reduction method to the second algebraic equation as a second algebraic equation expressing a relationship between a power flow and a voltage in the power system having the one or more GFM inverters; 2. The optimal control method of claim 1.

3. a second step of controlling the one or more GFM inverters based on the calculation result in the first step; 2. The optimal control method of claim 1.

4. In the first step, the first system of equations is solved by an adjoint method; 4. The optimum control method according to claim 1.

5. a calculation unit that solves a first system of equations that formulates an optimal control problem for determining a state of one or more GFM inverters having a current limiting function, the GFM inverters maintaining dynamic reliability of the power system; The first system of equations is: a second system of equations describing a dynamic model of the power system; The second system of equations is: For each of a first conditional branch that is established when the current limiting function is operating and a second conditional branch that is established when the current limiting function is not operating, a third algebraic equation is included that is reformulated as a first algebraic equation that represents an internal state of the one or more GFM inverters using a complementary variable. Optimal control device.

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