Power system management program and power system management device
Patent Information
- Application Number
- JP2023128348
- Authority / Receiving Office
- JP · JP
- Patent Type
- Applications
- Current Assignee / Owner
- Filing Date
- 2023-08-07
- Publication Date
- 2025-02-20
Smart Images
Figure 2025024320000001_ABST
Abstract
Description
[Technical field]
[0001] An embodiment of the present invention relates to a power system management program and a power system management device. [Background technology]
[0002] Power flow calculations are sometimes performed for power systems that consist of multiple nodes and multiple branches. Here, a node refers to equipment that produces and consumes power (such as a generator or power load), and a branch refers to equipment that transmits power (such as a transmission line).
[0003] Power flow calculation is the process of calculating the node voltage (voltage magnitude |V| and phase angle θ) for each node in the power system being calculated, when either (1) the active power P and voltage magnitude |V| (PV-designated node) or (2) the active power P and reactive power Q (PQ-designated node) are known, so that these known quantities (measured values) are satisfied.
[0004] Also, "satisfying a known quantity" means that the known quantity S des The difference between the calculated voltage and the theoretical value S is zero. This is expressed as the power equation ΔS = S des -S=0 is satisfied.
[0005] Since the power equation is a nonlinear simultaneous equation, it cannot be solved as is. Conventionally, the equation has been solved, for example, by the Newton-Raphson method, which is a common method for solving nonlinear simultaneous equations. Summary of the Invention [Problem to be solved by the invention]
[0006] As the scale of the power systems being handled increases and power flows become more complex due to an increase in renewable energy generators, there have been cases where the calculations do not converge and the solution cannot be found when trying to solve power flow calculations using the Newton-Raphson method.
[0007] Therefore, the present invention has been made in consideration of the above circumstances, and an object of the present invention is to provide a power system management program and a power system management device that can make calculations converge more easily than in the prior art when solving the power equation ΔS=0 in performing power flow calculations in a power system. [Means for solving the problem]
[0008] In the power system management program according to the embodiment, when a power flow calculation is performed for a power system that is configured with a plurality of nodes and a plurality of branches, the computer des The power equation ΔS=S, which shows that the difference between the theoretical value S and des When solving -S=0, a first calculation unit performs an iterative calculation using the Tikhonov regularization method or the ridge regression analysis method until the corrected difference ΔS converges to a second threshold or less, and calculates node voltages indicating the magnitude and phase angle of the voltage of each of the nodes, and a second calculation unit takes over the node voltages calculated by the first calculation unit, and performs an iterative calculation using the Newton-Raphson method until the corrected difference ΔS converges to a first threshold or less to calculate the node voltages. [Brief description of the drawings]
[0009] [Figure 1] FIG. 1 is a block diagram illustrating a functional configuration of an information processing apparatus according to an embodiment. [Diagram 2] FIG. 2 is a graph showing the transition of the maximum absolute error value of ΔS when the Tikhonov regularization method is used in the embodiment. [Diagram 3] FIG. 3 is a flowchart illustrating a power flow calculation process performed by the information processing device according to the embodiment. [Figure 4] FIG. 4 is a table showing an example 1 of the experimental results obtained by the information processing device according to the embodiment. [Diagram 5] FIG. 5 is a table showing a second example of the experimental results obtained by the information processing device according to the embodiment. [Figure 6] FIG. 6 is an explanatory diagram of the power flow calculation. [Figure 7] FIG. 7 is an explanatory diagram of the Newton-Raphson method. [Figure 8] FIG. 8 is an explanatory diagram of a case where the power flow calculation using the Newton-Raphson method of the prior art does not converge. [Figure 9] FIG. 9 is a flowchart showing a power flow calculation process according to the conventional technology. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0010] Hereinafter, an embodiment of a power system management program and a power system management device of the present invention will be described with reference to the drawings.
[0011] First, the power flow calculation will be described with reference to Fig. 6. Fig. 6 is an explanatory diagram of the power flow calculation. In the power system in Fig. 6, capital letters indicate node constraint conditions, and lowercase letters indicate variables obtained by the power flow calculation. The numbers subscripted to the letters indicate the node numbers. Furthermore, P is active power, Q is reactive power, V is voltage, and θ is phase angle.
[0012] Then, it is necessary to determine the node voltage (voltage magnitude |V| and phase angle θ) so as to satisfy the node constraint conditions, which can be reduced to the problem of finding the zero points of the power equation. The power equation becomes a nonlinear simultaneous equation. Specifically, it becomes a simultaneous equation consisting of one equation related to the PV designated nodes and two equations related to the PQ designated nodes.
[0013] A PV-designated node is a node, such as node 2, for which P and V are designated. A PQ-designated node is a node, such as node 3, for which P and Q are designated.
[0014] Specifically, there are three unknowns (lowercase letters) and three equations, which are nonlinear simultaneous equations, as shown below.
number
[0015] Conventionally, the Newton-Raphson method (NR method), which is one of the common methods, has been applied as a method for solving such nonlinear simultaneous equations. The outline of the method is as follows.
[0016] Here, Fig. 7 is an explanatory diagram of the Newton-Raphson method. The goal is to find a zero point of the power equation g. In other words, if y is a voltage, g(y)=0, and the voltage y is repeatedly corrected based on the following iterative calculation.
number
[0017] When trying to solve load flow calculations using the Newton-Raphson method, in many cases the calculations converge and the problem can be solved, as shown in Figure 7. Figure 7 shows a case where the calculations converge on the third iterative calculation. However, there were also cases where the calculations did not converge and the problem could not be solved.
[0018] Figure 8 is an explanatory diagram of a case where power flow calculation using the conventional Newton-Raphson method does not converge. (a) is an example where the correction amount is too large and diverges. Specifically, for the initial value B1, the solution moves to point B2 in the first iteration, and moves to point B3 in the second iteration, resulting in divergence. In other words, it does not converge to the solution A1.
[0019] Also, (b) is an example where the same value is repeated. Specifically, for an initial value C1, the first iteration moves to point C2, and the second iteration returns to point C1. In other words, it does not converge to solution A2.
[0020] 9 is a flowchart showing a power flow calculation process according to the conventional technique. In step S101, input data is read. In step S102, a node admittance matrix is created. In step S103, the magnitude of the node injected power or node voltage is set.
[0021] In step S104, an initial value of the node voltage is set. In step S105, a mismatch calculation of the node injection power is performed. In step S106, it is determined whether the calculation has converged. If Yes, the process ends, and if No, the process proceeds to the Newton-Raphson method.
[0022] In the Newton-Raphson method, the maximum number of iteration loops is set in step S111. The node voltage is set in step S112. The correction equation is solved and the voltage correction amount is reflected in step S113.
[0023] In step S114, a mismatch calculation of node injection power is performed. In step S115, it is determined whether the calculation has converged. If Yes, the process ends, and if No, the process returns to step S111.
[0024] However, there are cases where the Newton-Raphson method does not converge and is unable to solve the problem, as shown in Fig. 8. Therefore, below we will explain a technology that can make the calculations converge more easily than conventional technology when solving the power equation ΔS=0 in case of performing a power flow calculation for a power system.
[0025] 1 is a block diagram showing a functional configuration of an information processing device 1 according to an embodiment. The information processing device 1 is a computer device, and includes a storage unit 2, an input unit 3, a display unit 4, and a processing unit 5. The information processing device 1 also includes a communication interface for communicating with other devices, but for the sake of brevity, illustration and description of the communication interface are omitted.
[0026] The storage unit 2 is composed of a ROM (Read Only Memory), a RAM (Random Access Memory), an HDD (Hard Disk Drive), an SSD (Solid State Drive), etc. The storage unit 2 stores various information such as a program for operating the processing unit 5, measurement information related to the power system, various setting values, and power flow calculation results.
[0027] The input unit 63 includes a keyboard, a mouse, and the like. The display unit 64 is composed of an LCD (Liquid Crystal Display) or the like.
[0028] The processing unit 5 is, for example, a CPU (Central Processing Unit) and executes various types of arithmetic processing. The processing unit 5 includes an acquisition unit 51, a calculation unit 52, and a control unit 53 as functional components.
[0029] The acquisition unit 51 acquires, for example, measurement information related to the power system from an external device or the like.
[0030] The calculation unit 52 calculates and sets various values. For example, when performing a power flow calculation for a power system configured with a plurality of nodes and a plurality of branches, the calculation unit 52 (first calculation unit) calculates a measured value S des The power equation ΔS=S, which shows that the difference between the theoretical value S and des When solving -S = 0, an iterative calculation is performed until the corrected difference ΔS using Tikhonov regularization method or ridge regression analysis method (hereinafter referred to as Tikhonov regularization method) converges to a second threshold or less, and the node voltages indicating the magnitude and phase angle of the voltage at each node are calculated.
[0031] In addition, the calculation unit 52 (second calculation unit) takes over the node voltages calculated by the Tikhonov regularization method, and calculates the node voltages by performing iterative calculations until the difference ΔS corrected using the Newton-Raphson method converges to a first threshold value or less.
[0032] The control unit 53 performs various controls and judgments.
[0033] The following is a specific description of the processing performed by the calculation unit 52 and the control unit 53. The Tikhonov regularization method is a regression analysis that adds a regularization term to a loss function to minimize it, and is a representative numerical solution method for ill-conditioned linear equations.
[0034] Here, an "ill-conditioned linear equation" means that in a linear equation Xw=y, when a small perturbation ΔX or Δy is applied to X or y, the change Δw in the solution w changes significantly.
[0035] For example, if the objective variable is y^, the actual observation value (measurement value) is y, the observation error is ε, the explanatory variable is X, and the regression coefficient is w, the formula for calculating the regression coefficient w using the least squares method can be expressed as follows.
number
[0036] Note that ||·|| means the L2 norm, and X, y, and y^ are vectors.
[0037] In the Tikhonov regularization method, a regularization term (α||w|| 2 ) is added to the formula.
number
[0038] Note that I is a unit matrix.
[0039] The main features of Tikhonov’s regularization method are the following three features: (Feature 1) Due to the effect of the regularization term (= penalty term), the absolute value of the regression coefficient is sought to be as small as possible. Therefore, it is possible to suppress error sensitivity. In other words, it is possible to obtain regression coefficients that correspond to ill-conditioned linear equations. This is equivalent to suppressing overfitting of the regression coefficient w.
[0040] (Feature 2) In ordinary least squares, "X T Even if "X" does not have an inverse, "X TSince "X+αI" can have an inverse matrix, it is possible to find an estimate. This is where the name "regularization term" comes from. Regular is the opposite of singular, which is used when there is no inverse matrix.
[0041] (Feature 3) Since multiplication with a transposed matrix is performed, the computational cost is high.
[0042] Next, we describe the implementation of Tikhonov regularization. Applying the Tikhonov regularization method to obtain the power equation ΔS=0, it can be expressed as the following equation.
number
[0043] Note that ΔS is the theoretical voltage and current value S at the current step (k in the iterative calculation process) and the specified node injection power S des (Measured value) and the difference between.
[0044] And the Jacobian matrix is as follows:
number
[0045] In addition, S 1 is the vector of nodal injected powers for PV- or PQ-designated nodes. Also, S 2 is the vector of nodal injection powers for the PQ-specified nodes. Also, |V 1 | is a vector of voltage magnitudes for the PQ designated nodes.
[0046] 2 is a graph showing the transition of the maximum absolute error of ΔS when the Tikhonov regularization method is used in the embodiment. When the node voltage is calculated using only the Tikhonov regularization method, the difference ΔS approaches zero to some extent, but it was confirmed that the convergence situation (maximum absolute error of ΔS) reaches a plateau at a certain point and there are cases where it does not converge.
[0047] For this reason, we use the Tikhonov regularization method to calculate "non-ill-conditioned" node voltages to bring ΔS closer to zero to a certain extent, and then use the NR method to achieve convergence. In other words, by finding non-ill-conditioned node voltages using the Tikhonov regularization method, we can provide good initial values to the NR method, which has the effect of making it easier for the NR method to converge.
[0048] 3 is a flowchart showing a power flow calculation process by the information processing device 1 according to the embodiment. In step S1, the acquisition unit 51 reads input data. In step S2, the calculation unit 52 creates a node admittance matrix. In step S3, the calculation unit 52 sets a node injection power.
[0049] In step S4, the calculation unit 52 sets an initial value of the node voltage. In step S5, the calculation unit 52 performs a mismatch calculation of the node injection power. In step S6, the control unit 53 determines whether the calculation has converged. If Yes, the process proceeds to step S7. If No, the process proceeds to the Tikhonov regularization method.
[0050] In the process of the Tikhonov regularization method, in step S11, the calculation unit 52 sets the maximum number of iteration loops. In step S12, the calculation unit 52 sets a node voltage. In step S13, the calculation unit 52 solves a correction equation and reflects the voltage correction amount.
[0051] In step S14, the calculation unit 52 performs a mismatch calculation of node injection power. In step S15, the control unit 53 determines whether the calculation has converged, and if Yes, the process proceeds to processing of the Newton-Raphson method, and if No, the process returns to step S11.
[0052] In the process of the Newton-Raphson method, in step S21, the calculation unit 52 sets the maximum number of iteration loops. In step S22, the calculation unit 52 sets a node voltage. In step S23, the calculation unit 52 solves a correction equation and reflects the voltage correction amount.
[0053] In step S24, the calculation unit 52 performs a mismatch calculation of the node injection power. In step S25, the control unit 53 determines whether the calculation has converged, and if Yes, the process proceeds to step S7, and if No, the process returns to step S21.
[0054] In step S7, the calculation unit 52 sets the node injection power.
[0055] 4 is a table showing an example 1 of the experimental results by the information processing device 1 of the embodiment. For data sets 1 to 21, the NR method, which is a conventional technique, was benchmarked to confirm the superiority of the Tk method (Tikhonov regularization method) + NR method (processing of FIG. 3). The number of nodes, the number of branches, and the number of generators for data sets 1 to 21 are as shown in the figure.
[0056] The prerequisites are as follows: Repeated calculation: 20 times Initial voltage: Flat start (voltage 1, phase angle 0 for all nodes) Convergence criteria: max(|ΔS|)≦0.001 ·Tk method convergence criteria: max(|ΔS|)≦50 ·Tk method α: 0.01
[0057] As shown in Figure 4, there were nine cases (data groups) where the NR method did not converge. On the other hand, the Tk method + NR method converged in all of these cases, confirming that it is easier to converge calculations than conventional technology. Note that in cases where the NR method converged, it was clear that the Tk method + NR method would also converge (because the initial voltage was in a more favorable condition than the NR method), so those experiments were omitted.
[0058] 5 is a table showing Example 2 of the experimental results obtained by the information processing device 1 according to the embodiment. For the same data groups 1 to 21 as in FIG. 4, the NR method, which is a conventional technique, was benchmarked to confirm the high versatility (high convergence) of the Tk method + NR method.
[0059] Incidentally, there is a condition number as an index to measure the degree of ill-conditioning of a simultaneous equation, and the low condition number of the Jacobian is one of the reasons for its high versatility. And in all nine cases where the NR method did not converge, the Tk method + NR method had a lower condition number of the Jacobian than the NR method. Therefore, it can be said that the Tk method + NR method is more versatile than the NR method.
[0060] As described above, according to this embodiment, when solving the power equation ΔS=0 in performing a power flow calculation for a power system, the Tk method+NR method is used, which makes it easier for the calculation to converge than with conventional techniques.
[0061] The program (power system management program) executed by the information processing device 1 of this embodiment is provided as a file in an installable or executable format recorded on a computer-readable recording medium such as a CD-ROM, a flexible disk (FD), a CD-R, or a DVD (Digital Versatile Disk).
[0062] The program may be stored on a computer connected to a network such as the Internet and provided by being downloaded via the network.The program may be provided or distributed via a network such as the Internet.The program may be provided by being pre-installed in a ROM or the like.
[0063] The program has a modular structure including the above-mentioned units 51 to 53, and in terms of actual hardware, the CPU reads the program from the storage medium and executes it, causing the units 51 to 53 to be loaded onto a main memory device and generated on the main memory device.
[0064] Although an embodiment of the present invention has been described, this embodiment is presented as an example and is not intended to limit the scope of the invention. This novel embodiment can be implemented in various other forms, and various omissions, substitutions, and modifications can be made without departing from the spirit of the invention. This embodiment and its modifications are included in the scope and spirit of the invention, and are included in the invention and its equivalents described in the claims.
[0065] For example, the information processing device 1 is not limited to being realized by a normal computer device, and may be realized in other forms such as cloud computing technology. [Explanation of symbols]
[0066] 1...information processing device, 2...storage unit, 3...input unit, 4...display unit, 5...processing unit, 51...acquisition unit, 52...calculation unit, 53...control unit
Claims
1. Computer, When performing a load flow calculation for a power system consisting of multiple nodes and multiple branches, the measured value S ｄｅｓ The power equation ΔS = S, which shows that the difference between the theoretical value S and ｄｅｓ a first calculation unit that calculates node voltages indicating the magnitude and phase angle of the voltage of each of the nodes by performing an iterative calculation until a difference ΔS corrected by using Tikhonov's regularization method or ridge regression analysis method when solving −S=0 converges to a second threshold or less; a second calculation unit that takes over the node voltage calculated by the first calculation unit and calculates the node voltage by performing iterative calculation until a difference ΔS corrected using a Newton-Raphson method converges to a first threshold or less.
2. When performing a load flow calculation for a power system consisting of multiple nodes and multiple branches, the measured value S ｄｅｓ The power equation ΔS = S, which shows that the difference between the theoretical value S and ｄｅｓ a first calculation unit that calculates node voltages indicating the magnitude and phase angle of the voltage of each of the nodes by performing an iterative calculation until a difference ΔS corrected by using Tikhonov's regularization method or ridge regression analysis method when solving −S=0 converges to a second threshold or less; a second calculation unit that takes over the node voltage calculated by the first calculation unit and calculates the node voltage by performing an iterative calculation until a difference ΔS corrected using a Newton-Raphson method converges to a first threshold or less.