Power system tidal current calculation device, computer program for power system tidal current calculation device, and power system tidal current calculation method

Abstract

To provide a power system tidal current calculation device for calculating an appropriate quantity of electricity with which a tidal current calculation is settled even in a case where the tidal current calculation according to an initial value of the quantity of electricity at a node is non-settled.SOLUTION: A power system tidal current calculation device 1 comprises: a constraint condition creation section 32 which creates a power tidal current equation on the basis of data indicating a configuration of a power system which supplies power and data indicating a quantity of electricity at a node and for creating a constraint condition relating to power arithmetic for each node by linearly approximating the power tidal current equation on the basis of the created power tidal current equation; a virtual load settlement determination section 23 which determines that the virtual load is settled, when a virtual load calculated by computational processing relating to the power arithmetic including the constraint condition created by the constraint condition creation section 32 is within a predetermined allowable range; and a tidal current calculation execution section 22 which calculates a voltage at the node by performing the computational processing relating to the power arithmetic including the constraint condition until it is determined by the virtual load settlement determination section 23 that the virtual load is settled.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The present embodiment relates to a power system power flow calculation device that executes power flow calculation for performing monitoring and control in a power system, a computer program for the power system power flow calculation device, and a power system power flow calculation method. [Background technology]

[0002] In a power system, a plurality of electric power devices are arranged to generate and transmit electric power. The plurality of electric power devices are composed of a power supply device and a power feeding device. Electric power output from the power supply device is supplied to a load via the power feeding device. In order to appropriately perform monitoring and control in the power system, the electric power devices arranged in the power system are controlled. The electric power devices are controlled by an electric quantity calculated based on a power flow calculation. A power system control device that controls the electric power devices arranged in the power system is known. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Japanese Patent Application Publication No. 7-250431 [Patent Document 2] JP 2001-238355 A Summary of the Invention [Problem to be solved by the invention]

[0004] As described above, in order to appropriately monitor and control the power system, the power devices arranged in the power system are controlled by the electric quantity calculated based on the power flow calculation. Power flow calculation is a basic and important calculation in the monitoring and control of the power system. When performing the monitoring and control of the power system, the power flow calculation is widely used to calculate the target control object and the control quantity.

[0005] However, in recent years, power generation devices such as renewable energy power generation devices are often installed in power systems. This has resulted in the configuration of power systems becoming more complex. In controlling power systems, selecting a node to be controlled and calculating the electric quantities such as the power and voltage of the node to be controlled is a very complicated task. Depending on the state of the power system, there are cases where a solution for the power flow calculation cannot be obtained or the calculation does not converge. When the power flow calculation does not converge, the electric quantity of the node to be controlled cannot be calculated, which causes a problem that it is difficult to appropriately control the power system.

[0006] The object of the present invention is to provide a power system power flow calculation device, a computer program for the power system power flow calculation device, and a power system power flow calculation method that calculate appropriate electrical quantities at which the power flow calculation converges, even when the power flow calculation based on the initial values ​​of the electrical quantities at a node does not converge, in order to perform appropriate control of the power system. [Means for solving the problem]

[0007] The power system power flow calculation apparatus of this embodiment has the following features. (1) A constraint condition creation unit creates a power flow equation based on data indicating the configuration of a power system that supplies power and data indicating the amount of electricity at the node, and creates constraint conditions for power calculations for each node based on the created power flow equation. (2) A virtual load convergence determination unit is provided that determines that a virtual load calculated by a calculation process for the power calculation, including the constraint conditions created by the constraint condition creation unit, has converged when the virtual load is within a predetermined allowable range. (3) A power flow calculation execution unit performs calculation processing related to the power calculation including the constraint conditions and calculates voltages at the nodes until the virtual load convergence determination unit determines that the virtual load has converged. (4) The constraint condition creating unit creates the constraint conditions by linearly approximating the power flow equation. [Brief description of the drawings]

[0008] [Figure 1] FIG. 1 is a diagram showing a configuration of a power system power flow calculation device 1 according to a first embodiment. [Diagram 2] FIG. 1 is a diagram showing a program flow of a power system power flow calculation device 1 according to a first embodiment. [Diagram 3] Diagram showing cases where load flow calculations do not converge [Figure 4] Diagram showing equivalent circuits of power system branches [Diagram 5] Diagram showing transmission losses in modeled branches [Figure 6] FIG. 1 is a diagram showing a power system input to a power system power flow calculation device 1 according to a first embodiment. [Figure 7] FIG. 1 is a diagram showing reactive power Q of nodes 30, 31, 32, and 33 of a power system input to a power system power flow calculation device 1 according to a first embodiment. [Figure 8] A diagram explaining the relationship between the number of iterations of a load flow calculation and the error when the load flow calculation does not converge. [Figure 9] FIG. 1 is a diagram showing a case where a tap is operated by the calculation of the power system power flow calculation device 1 according to the first embodiment. [Figure 10] FIG. 1 is a diagram showing reactive power of a load for each node after adjustment by the calculation of the power system power flow calculation device 1 according to the first embodiment; [Figure 11] FIG. 1 is a diagram showing a relationship between the number of iterations of power flow calculation and an error in a power system power flow calculation device 1 according to a first embodiment. [Figure 12] FIG. 1 is a diagram showing voltages when transmission losses are reflected in virtual loads in a power system power flow calculation device 1 according to a first embodiment. [Figure 13] FIG. 1 is a diagram showing voltages in a case where transmission losses are not reflected in a virtual load in a power system power flow calculation device 1 according to a first embodiment. [Figure 14] FIG. 1 is a diagram showing a maximum error versus the number of iterations of power flow calculation in a power system power flow calculation device 1 according to a first embodiment. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0009] [1. First embodiment] [1-1. Configuration] With reference to Fig. 1, a power system power flow calculation apparatus 1 will be described as an example of this embodiment. The power system power flow calculation apparatus 1 calculates appropriate electric quantities at which the power flow calculation converges, even when the power flow calculation based on the initial values ​​of the electric quantities at the nodes of the power system does not converge. The electric quantities calculated by the power system power flow calculation apparatus 1 are the voltage at the node (sometimes called "node voltage" or "node voltage designated value"), the power (sometimes called "node injection amount"), and the tap ratio of the transformer. The electric quantities calculated by the power system power flow calculation apparatus 1 may include branch power flows calculated based on the node voltages. The power system is appropriately controlled based on the calculated electric quantities.

[0010] The power system power flow calculation apparatus 1 is configured by a computer etc. The power system power flow calculation apparatus 1 has an input unit 11, an output unit 12, a calculation unit 13 and a storage unit 14.

[0011] The input unit 11 is composed of an operating device such as a keyboard, a mouse, a touch panel, or a transmitting / receiving circuit, and an external memory connection circuit. The input unit 11 is connected to the calculation unit 13. It is operated by an operator, and data indicating the configuration of the power system and data indicating the amount of electricity at the node are input from the input unit 11.

[0012] The data indicating the amount of electricity includes data on the voltage at the node (sometimes called "node voltage" or "node voltage designated value"), the power (sometimes called "node injection amount"), and the tap ratio of the transformer. The data indicating the configuration of the power system and the data indicating the amount of electricity at the node may be input to the input unit 11 by communication from an external device.

[0013] The calculation unit 13 is configured by a calculation processing unit in a computer or a software module. The calculation unit 13 is connected to the input unit 11, the output unit 12, and the storage unit 14. The calculation unit 13 controls the input unit 11, the output unit 12, and the storage unit 14.

[0014] The calculation unit 13 has an optimization problem creation unit 21, a power flow calculation execution unit 22, and a virtual load convergence determination unit 23. The optimization problem creation unit 21 has an objective function creation unit 31 and a constraint condition creation unit 32. The optimization problem creation unit 21 creates an objective function as an optimization problem related to the power calculation by the objective function creation unit 31. In addition, the optimization problem creation unit 21 creates constraint conditions related to the power calculation by the constraint condition creation unit 32.

[0015] The objective function creation unit 31 of the optimization problem creation unit 21 creates a power flow equation based on the data indicating the configuration of the power system and the data indicating the amount of electricity at the nodes input to the input unit 11, and creates an objective function related to the power flow for each node based on the created power flow equation. The power flow equation related to the power flow is called the power flow equation.

[0016] The constraint condition creating unit 32 of the optimization problem creating unit 21 includes a function linearizing unit 321, a transmission loss calculating unit 322, and a differential calculating unit 323. The function linearizing unit 321, the transmission loss calculating unit 322, and the differential calculating unit 323 are configured as software modules.

[0017] The constraint creating unit 32 creates constraints for power calculation by linearly approximating the power flow equation using the function linearizing unit 321. The function linearizing unit 321 linearly approximates the terms related to the phase angles and the terms related to the voltages for each node in the power flow equation.

[0018] The constraint condition creating unit 32 creates a constraint condition related to the power transmission loss occurring in the branch by the power transmission loss calculating unit 322, and sets the constraint condition as the first constraint condition for the power calculation. The power transmission loss calculating unit 322 calculates the power transmission loss occurring in the branch of the power system as the load of the nodes at both ends of the branch, and sets the first constraint condition.

[0019] The constraint condition creating unit 32 creates a constraint condition related to the tap ratio of the transformer by the differential calculation unit 323, and sets the constraint condition as a second constraint condition for the power calculation. The differential calculation unit 323 differentiates the term related to the tap ratio of the power flow equation, and sets the second constraint condition.

[0020] The power flow calculation executing unit 22 of the calculation unit 13 performs power flow calculation related to power calculation including constraint conditions and calculates node voltages until the calculated virtual load is determined to have converged by the virtual load convergence determining unit 23. The power flow calculation executing unit 22 executes a DC method power flow calculation and an AC method power flow calculation based on the NR method. The power flow calculation executing unit 22 may calculate the branch power flows based on the node voltages.

[0021] The power flow calculation executing unit 22 stores the node voltages when the virtual load convergence determining unit 23 determines that the virtual load has converged in the memory unit 14, and outputs them via the output unit 12. The power flow calculation executing unit 22 may store the branch power flows calculated based on the node voltages in the memory unit 14, and output them via the output unit 12.

[0022] The virtual load convergence determination unit 23 of the calculation unit 13 determines that convergence has occurred when the difference between the value of the virtual load calculated by the power flow calculation related to the power calculation including the constraint conditions created by the constraint condition creation unit 32 at the previous iteration and the value at the current iteration is within a predetermined allowable range. The virtual load convergence determination unit 23 performs a convergence determination for the power flow calculation that has been repeatedly executed, and determines that convergence has occurred when the difference between the value calculated by the power flow calculation and the previous value is equal to or less than a predetermined determination value ε.

[0023] The storage unit 14 is configured with a storage medium such as a semiconductor memory or a hard disk. The storage unit 14 is connected to the calculation unit 13. The calculation unit 13 controls writing and reading of data to and from the storage unit 14. The storage unit 14 stores node voltages calculated by the power flow calculation execution unit 22 of the calculation unit 13. The storage unit 14 may store branch power flows calculated based on the node voltages. The storage unit 14 may also store data indicating the configuration of the power system input to the input unit 11 and data indicating the amount of electricity at the nodes. The data indicating the amount of electricity includes data related to "node voltages", "node injection amounts", and transformer tap ratios.

[0024] The output unit 12 is composed of a display device such as a liquid crystal display, a printing device such as a printer, a transmission circuit, an external memory connection circuit, etc. The output unit 12 is connected to the calculation unit 13. The output unit 12 outputs the node voltages calculated by the power flow calculation execution unit 22 of the calculation unit 13. The output unit 12 outputs the calculated node voltages as display, printout, or electronic data. The output unit 12 may output a branch power flow calculated based on the node voltages. The output unit 12 may also output data indicating the configuration of the power system input to the input unit 11 and data indicating the amount of electricity at the node. The data indicating the amount of electricity includes data regarding the "node voltage", the "node injection amount", and the tap ratio of the transformer.

[0025] The configuration of the power system power flow calculation device 1 has been described above.

[0026] [1-2. Effect] Next, an overview of the operation of the power system power flow calculation apparatus 1 of this embodiment will be described.

[0027] The optimization problem creating unit 21 creates an objective function as an optimization problem related to the power calculation by the objective function creating unit 31. The optimization problem creating unit 21 also creates constraint conditions related to the power calculation by the constraint condition creating unit 32.

[0028] The objective function creation unit 31 of the optimization problem creation unit 21 creates a power flow equation based on data indicating the configuration of the power system that supplies power and data indicating the amount of electricity at the node, and creates an objective function related to the power flow for each node based on the created power flow equation. The objective function is used for power calculation. The objective function is created as an optimization problem related to the power calculation.

[0029] The constraint condition creating unit 32 of the optimization problem creating unit 21 creates constraint conditions for power calculation using a function linearizing unit 321, a power transmission loss calculating unit 322, and a differential calculating unit 323.

[0030] A function linearizer 321 in the constraint generator 32 linearly approximates the terms relating to the phase angles and the voltages for each node in the power flow equation to generate constraints for the power calculation.

[0031] The transmission loss calculation unit 322 of the constraint creating unit 32 calculates the transmission loss occurring in the branch of the power system as the load of the nodes at both ends of the branch, and sets it as a first constraint on the power calculation.

[0032] The differential calculation unit 323 of the constraint creating unit 32 differentiates the term of the power flow equation relating to the tap ratio of the transformer arranged in the power system, and sets the differentiated term as a second constraint relating to the power calculation.

[0033] The virtual load convergence determination unit 23 determines that the virtual load calculated by the calculation process for the power calculation including the constraint conditions created by the constraint condition creation unit 32 has converged when it is within a predetermined allowable range. The calculation process for the power calculation uses the objective function created by the objective function creation unit 31.

[0034] The power flow calculation executing unit 22 performs calculation processing related to power calculation including constraint conditions until it is determined that the calculated virtual load has converged by the virtual load convergence determining unit 23, and calculates the voltage at the node (sometimes called the "node voltage" or the "node voltage designated value"). The power flow calculation executing unit 22 calculates the node voltage that reduces the objective function created by the objective function creating unit 31 through the power calculation. The node voltage is a voltage corresponding to the tap ratio of the transformer. The node voltage that reduces the objective function is calculated by solving the optimization problem. The power flow calculation executing unit 22 may calculate the branch power flow based on the node voltage.

[0035] In order to appropriately perform supervisory control in a power system, power flow calculations are widely used to select nodes to be controlled and to calculate the amount of electricity. However, depending on the state of the power system, power flow calculations may not converge and an appropriate solution may not be obtained. When power flow calculations do not converge, it is difficult to appropriately control the power system.

[0036] A typical case where a power flow calculation does not converge is shown in Figure 3. In Figure 3, the horizontal axis y represents the voltage of the power system, and the vertical axis g(y) represents the value of the power flow equation. The point where the curve in the graph intersects with the horizontal axis, g(y) = 0, is the solution that should be calculated. (a): A case where the algorithm does not converge with a flat start, but converges if the initial values ​​are appropriately adjusted (Figure 3 (a)). (b): The same value is repeated, but the voltage can be adjusted appropriately to converge (Figure 3 (b)). (c): Even if the initial values ​​and voltages are modified, the system does not converge and there is no solution, resulting in divergence (Figure 3 (c)).

[0037] The power system power flow calculation apparatus 1 of this embodiment targets the above case (c). In order to converge the power flow calculation in the case (c), the power system power flow calculation apparatus 1 corrects the set values.

[0038] First, the power system power flow calculation apparatus 1 calculates the "node injection amount," "node voltage designated value," and "tap ratio" that are as close as possible to the initially set values ​​for the "node injection amount," "node voltage designated value," and "tap ratio" (also called "minimizing the shift amount") and that place the entire node in an appropriate voltage range. After that, the power system power flow calculation apparatus 1 uses the calculated "node injection amount," "node voltage designated value," and "tap ratio" in the AC method power flow calculation based on the NR method, and sets the new "node injection amount" and "node voltage" as the solution.

[0039] In order to calculate a solution quickly and robustly by optimization calculation, including calculation by a commercial solver, it is preferable that the constraint conditions are linear. Since the power flow equation is nonlinear, there is a problem that it is difficult to use it for calculation by optimization calculation at a practical level. When the power flow equation is nonlinear and nonconvex, it is preferable to linearize it in order to calculate a solution by optimization calculation. Power system power flow calculation device 1 linearly approximates the power flow equation.

[0040] Currently, there are solvers that can handle complex nonlinear problems. However, these solvers deal with the non-convergence of load flow calculations without alleviating the original problem, and therefore have problems in terms of performance and robustness.

[0041] In the DC method (direct current method), which is a linearization technique in the prior art, only active power (P) and voltage phase angle (θ) are handled. The power system power flow calculation device 1 of the present embodiment is characterized in that in addition to active power (P) and voltage phase angle (θ), voltage (V) and reactive power (Q) are also handled in the linearized power flow equation. Hereinafter, active power may be represented as P, reactive power as Q, voltage as V, and voltage phase angle as θ.

[0042] The DC method does not take transmission losses into account, making it difficult to obtain accurate voltages. Since transmission losses are not included in the linearization of the power flow equation, there is a problem in that errors occur in the calculated voltage values.

[0043] The power system power flow calculation device 1 calculates the transmission loss, simulates it by reflecting it as a virtual load on the node, and calculates a solution close to the voltage value calculated by the normal power flow equation. The power system power flow calculation device 1 of this embodiment is characterized by calculating the transmission loss and calculating the voltage close to the AC method.

[0044] Non-convergence of power flow calculation is often caused by an imbalance in reactive power. Of the initially set values ​​for the "node injection amount," "node voltage designation value," and "tap ratio," it is preferable to change the "tap ratio." However, since the "tap ratio" is reflected in the coefficients of the power flow equation as a node admittance matrix, there is a problem that it is difficult to use it in the calculation process compared to other variables such as the "node injection amount" and the "node voltage designation value." The power system power flow calculation device 1 of this embodiment is characterized by calculating the derivative of the "node injection amount" by the "tap ratio" and executing an optimization calculation by the power flow equation.

[0045] (Reading input data) The calculation unit 13 of the power system power flow calculation apparatus 1 controls the input unit 11 and reads in input data. The input data is input to the input unit 11 by communication, input by an operator, or the like. The input data is input to the calculation unit 13 via the input unit 11 and stored in the storage unit 14. Data indicating the configuration of the power system and data indicating the amount of electricity at the nodes are read in as input data. The data indicating the amount of electricity includes initial values ​​of the "node injection amount," "node voltage designated value," and "tap ratio" at each node.

[0046] (Creating power flow equations) The optimization problem generator 21 generates a power flow equation using the objective function generator 31 and the constraint condition generator 32. ij =g ij +jb ij Then, the node admittance matrix Y is a matrix with the following (i, j) elements according to (Equation 2.1).

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[0047] In (Equation 2.1), Ni is the set of nodes connected to node i. Each component may be divided into real and imaginary parts and expressed as in (Equation 2.2). It may also be expressed as a matrix as in (Equation 2.3).

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[0048] G is a matrix with the following (i,j) elements as given by (Eq. 2.4). B is a matrix with the following (i,j) elements as given by (Eq. 2.5).

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[0049] Moreover, the matrix excluding the shunt components of G and B is expressed as (equation 2.6).

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[0050] Y' has the following (i,j) components according to (equation 2.7). Furthermore, (equation 2.7) has components according to (equation 2.8) and (equation 2.9).

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[0051] Using the components of the nodal admittance matrix in (equation 2.10) and (equation 2.11) and the voltages of each node, the power flow equations are given by the following (equation 2.12) and (equation 2.13). N is the set of all nodes. If N is the number of nodes, the power flow equations become a set of 2N nonlinear simultaneous equations.

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[0052] The optimization problem generator 21 generates power flow equations (equation 2.12) and (equation 2.13) using the objective function generator 31 and the constraint condition generator 32.

[0053] (Differentiation by tap ratio) Optimization problem creation unit 21 performs differentiation with respect to the tap ratio of the power flow equation using differential calculation unit 323 of constraint condition creation unit 32. Figure 4 shows an equivalent circuit of a branch having an LTC (on-load tap changer), where NF is i, NT is j, the tap ratio is NF:NT=1:t, and the admittance of the branch is G+jB.

[0054] When the tap ratio t of a branch is changed, the admittance that may be affected is expressed by the following (Equation 2.14), (Equation 2.15), and (Equation 2.16). A prime is added to Y to distinguish them.

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[0055] When calculating the differential of the power flow equation with respect to the tap ratio, differential calculation unit 323 extracts terms in (Equation 2.12) and (Equation 2.13) that include the tap ratio in their admittance. Terms in (Equation 2.12) and (Equation 2.13) that do not include the tap ratio become zero. The terms of the power flow equation that include the tap ratio in their admittance are the following (Equation 2.17), (Equation 2.18), (Equation 2.19), and (Equation 2.20).

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[0056] The differential calculation unit 323 differentiates (Equation 2.17), (Equation 2.18), (Equation 2.19), and (Equation 2.20) with respect to the tap ratio t to calculate the following (Equation 2.21), (Equation 2.22), (Equation 2.23), and (Equation 2.24). (Equation 2.21), (Equation 2.22), (Equation 2.23), and (Equation 2.24) show the differentiation of the node injection power with respect to the tap ratio. (Equation 2.21), (Equation 2.22), (Equation 2.23), and (Equation 2.24) are used in the calculation related to the optimization calculation described later.

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[0057] The optimization problem creating unit 21 differentiates the power flow equation with respect to the tap ratio using differential calculation unit 323 of constraint condition creating unit 32 to calculate (equation 2.21), (equation 2.22), (equation 2.23), and (equation 2.24). Differential calculation unit 323 differentiates the terms in the power flow equation related to the tap ratios of the transformers arranged in the power system to create constraint conditions for the objective function. The optimization problem creating unit 21 sets (equation 2.21), (equation 2.22), (equation 2.23), and (equation 2.24) calculated by differential calculation unit 323 as constraint conditions for the objective function.

[0058] (Derivation of the linearized power flow equation) The optimization problem creating unit 21 derives a linearized power flow equation by the function linearizer 321 of the constraint condition creating unit 32. In general, a linear approximation of a power flow equation can be expressed in the form shown in the following (Equation 3.1). In the case of a power system with N nodes, the equation becomes a set of 2N linear simultaneous equations.

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[0059] The function linearization unit 321 derives the following (Equation 3.2) and (Equation 3.3) based on (Equation 2.12).

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[0060] The function linearization unit 321 derives the following (Equation 3.4) based on (Equation 3.2).

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[0061] Similarly, function linearization unit 321 derives the following (Equation 3.5) and (Equation 3.6) based on (Equation 2.12).

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[0062] The normal DC load flow calculation is expressed by the following (Equation 3.7). (Equation 3.7) is a natural extension of the normal DC load flow calculation.

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[0063] The optimization problem creating unit 21 derives (equation 3.2), (equation 3.4), (equation 3.5), and (equation 3.6) as linearized power flow equations using the function linearizer 321 of the constraint condition creating unit 32.

[0064] (Preconditions for objective function) The optimization problem creating unit 21 creates objective functions for calculating the "node injection amount," "node voltage specification value," and "tap ratio" using the objective function creating unit 31 and the constraint condition creating unit 32. As an example, when a solution for the power flow calculation cannot be obtained with a predetermined node constraint condition and a predetermined tap ratio, the power system power flow calculation device 1 of this embodiment adjusts the node constraint condition and the tap ratio to obtain a converged solution.

[0065] Optimization problem preparation unit 21 of power system power flow calculation apparatus 1 prepares an objective function for the following optimization problem. Objective function preparation unit 31 and constraint condition preparation unit 32 of optimization problem preparation unit 21 formulate the optimization problem by linear programming (LP) based on the linearized power flow equations (Equation 3.2), (Equation 3.4), (Equation 3.5), and (Equation 3.6) derived by function linearizer 321, and minimize the objective function. As a result, calculation unit 13 of power system power flow calculation apparatus 1 solves the problem quickly and robustly.

[0066] The objective function generating unit 31 and the constraint condition generating unit 32 derive an objective function as an optimization problem under the following conditions: <Decision variables> Generator P output Generator Q output or terminal voltage V ·Load P, Q <Objective function> Minimizing deviation from initial node constraints <Restrictions> ·Linearized power flow equation Node voltage V upper and lower limits Generator P upper and lower limits Generator Q upper and lower limits · Load sign retention Phase angle of reference node = 0 Change in power injected at both ends due to tap ratio change in a branch with LTC (on-load tap changer) Tap ratio upper and lower limits The values ​​of the decision variables other than the terminal voltage V may be fixed at predetermined values ​​and not changed. When the connection node of the generator is specified as PV, V is the decision variable, and when it is specified as PQ, Q is the decision variable. The phase angle of the reference node may be any value, but there is no loss of generality if it is set to zero.

[0067] The sets and subscripts related to the calculations by the objective function creating unit 31 and the constraint condition creating unit 32 are as follows:

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[0068] The parameters related to the calculations by the objective function creating unit 31 and the constraint condition creating unit 32 are as follows:

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[0069] The variables related to the calculations by the objective function creating unit 31 and the constraint condition creating unit 32 are as follows:

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[0070] (Constraints due to linearized power flow equations) The node injected powers P, Q and voltages (V, θ) are required to satisfy the constraints on the linearized power flow equation. The constraint condition creating unit 32 derives (Equation 4.1) and (Equation 4.2) as the constraint conditions based on the linearized power flow equation. The constraint condition creating unit 32 derives the constraint conditions on the linearized power flow equation based on (Equation 4.1) and (Equation 4.2).

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[0071] (Constraints due to upper and lower limits of node voltage V) The constraint condition is that the node voltage be within a range of predetermined upper and lower limits. The constraint condition creating unit 32 derives (Equation 4.3) as the constraint condition based on the upper and lower limits of the node voltage V.

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[0072] (Constraints due to upper and lower limits of generator P) The constraint condition is that the generator P (active power) is within a range of predetermined upper and lower limits. The constraint condition creating unit 32 derives (Equation 4.4) as the constraint condition based on the upper and lower limits of the generator P.

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[0073] (Constraints due to upper and lower limits of generator Q) The constraint condition is that the generator Q (reactive power) is within a range of predetermined upper and lower limits. The constraint condition creating unit 32 derives (Equation 4.5) as the constraint condition based on the upper and lower limits of the generator Q.

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[0074] (Constraint due to load sign retention) Regarding preservation of the sign of the loads, the following constraints are subject to: When the specified load is zero, it will be fixed at zero during optimization. If the given load is >0, it is set to ≥0 during optimization (without changing the sign) If the given load is <0, it is set to ≦0 during optimization (without changing the sign) Based on the above constraints, the constraint creating unit 32 derives (Equation 4.6), (Equation 4.7), (Equation 4.8), (Equation 4.9), (Equation 4.10), and (Equation 4.11) as constraints by preserving the sign of the load.

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[0075] (Constraints due to reference node phase angle) The constraint condition is that the reference node phase angle is set to 0. The constraint condition creating unit 32 derives (Equation 4.12) as the constraint condition based on the reference node phase angle.

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[0076] (Constraints due to changes in injected power caused by tap ratio changes) In a branch having an LTC (on-load tap changer), the injected power at both ends of the branch changes due to a change in the tap ratio. dPi / dt and dQi / dt are calculated from the current voltage and tap ratio based on (Equation 2.21), (Equation 2.22), (Equation 2.23), and (Equation 2.24). The constraint condition generator 32 derives (Equation 4.13), (Equation 4.14), (Equation 4.15), and (Equation 4.16) as constraint conditions due to changes in injected power caused by a change in the tap ratio.

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[0077] (Tap ratio upper and lower limits) The tap change of the LTC (on-load tap changer) is performed within the range of upper and lower limits. The constraint condition creating unit 32 derives (Equation 4.17) and (Equation 4.18) as the constraint conditions based on the upper and lower limits of the tap ratio of the LTC (on-load tap changer).

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[0078] (Constraints due to node injection amount) The node injection power is (Total power generation of generators connected to the node) - (Load) + (Power change due to tap ratio change) The constraint condition creating unit 32 derives (Equation 4.19) and (Equation 4.20) as the constraint conditions based on the node injection amount.

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[0079] (Derivation of the objective function) The objective function generator 31 derives the objective function according to (Equation 4.21) based on the weighted shift amount according to the initial node constraint condition or the tap ratio. The weighting is set arbitrarily by the user.

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[0080] (Calculation of transmission loss) The constraint condition creating unit 32 calculates the transmission loss by the transmission loss calculation unit 322 and reflects it in the constraint condition by the node injection amount. The linearized power flow equations (Equation 4.1) and (Equation 4.2) do not include active transmission loss and reactive transmission loss, as in the normal DC power flow calculation. The transmission loss calculation unit 322 calculates the transmission loss and includes the transmission loss in the constraint condition by the node injection amount.

[0081] When the resistance of branch m is Rm, the reactance is Xm, and the active power flow is PFm, the active transmission loss and the reactive transmission loss are approximately as shown in (Equation 5.1) and (Equation 5.2) on the condition that V = 1. The transmission loss calculation unit 322 derives the active transmission loss (Equation 5.1) and the reactive transmission loss (Equation 5.2).

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[0082] (Reflection of transmission loss in virtual load) The branch transmission losses FNPi, FNQi can be modeled as shown in Fig. 5 and expressed as virtual loads at both end nodes of the branch. The constraint condition creating unit 32 derives (Equation 5.3) applied to the active power load FNPi and (Equation 5.4) applied to the reactive power load FNQi as virtual loads at both end nodes of the branch using the transmission loss calculating unit 322. The constraint condition creating unit 32 reflects FNPi, FNQi applied to (Equation 5.3) and (Equation 5.4) using the transmission loss calculating unit 322 in the constraints (Equation 4.19) and (Equation 4.20) based on the nodal injection amount described above.

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[0083] (Virtual load convergence judgment) Changing the virtual load changes the branch power flow, which in turn changes the transmission loss. Changing the transmission loss further changes the virtual load. Changing the virtual load further changes the branch power flow. Repeating this operation will cause the virtual load to converge to a constant value.

[0084] The virtual load convergence determination unit 23 iterates the power flow calculation to determine whether it has converged, and determines that it has converged if the difference from the previous value is equal to or less than a predetermined determination value ε. A numerical value equivalent to the convergence allowable error of the power flow calculation is selected as the determination value. When the virtual load convergence determination unit 23 determines that it has converged, it ends the iteration of the power flow calculation. The virtual load convergence determination unit 23 performs the convergence determination using (Equation 5.5) and (Equation 5.6). In (Equation 5.5) and (Equation 5.6), k represents the number of iterations.

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[0085] The calculation unit 13 of the power system power flow calculation apparatus 1 calculates appropriate "node injection amount," "node voltage designated value," and "tap ratio" based on the above.

[0086] The calculation of the "node injection amount", "node voltage designated value", and "tap ratio" is realized by the computer program shown in Fig. 2. The computer program shown in Fig. 2 is built into the calculation unit 13 of the power system power flow calculation apparatus 1.

[0087] (Step S01: Reading input data) The calculation unit 13 of the power system power flow calculation apparatus 1 controls the input unit 11 to read in input data. The input data is input to the input unit 11 by communication, input by an operator, or the like. The input data is input to the calculation unit 13 via the input unit 11 and stored in the memory unit 14. Data indicating the configuration of the power system and the amount of electricity at each node is read in as input data. The data indicating the amount of electricity includes initial values ​​of "node injection amount," "node voltage designated value," and "tap ratio" at each node. As an example, the configuration of the power system shown in FIG. 6 is as follows. Number of nodes: 57 Number of branches: 80 Number of generators: 7

[0088] (Step S02: AC power flow calculation using the NR method) The calculation unit 13 of the power system power flow calculation device 1 performs AC power flow calculation of the power system in the initial state by the NR method. The operation of step S02 is performed by the power flow calculation execution unit 22 of the calculation unit 13. The power flow calculation execution unit 22 performs power calculation based on the initial values ​​of the "node injection amount", "node voltage specification value", and "tap ratio" inputted to the power system.

[0089] (Step S03: Determining non-convergence) The calculation unit 13 of the power system power flow calculation device 1 determines whether the power flow calculation executed in step S02 has not converged. If it is determined that the power flow calculation has not converged, the program proceeds to step S04. If it is not determined that the power flow calculation has not converged, the program proceeds to step S11. As an example, in this embodiment, the reactive power Q of nodes 30, 31, 32, and 33 that are far from the generators in the power system shown in Figure 6 is large, so the power flow calculation using initial values ​​does not converge. The reactive power Q of nodes 30, 31, 32, and 33 in the initial state is assumed to be as shown in Figure 7.

[0090] (Step S04: Iterative loop) If it is determined that the power flow calculation has not converged, the calculation unit 13 of the power system power flow calculation device 1 repeats the power flow calculation in an iterative loop. The calculation unit 13 repeats the processes of steps S05 to S07 in a loop up to a predetermined number of times.

[0091] (Step S05: Solving the optimization problem) The calculation unit 13 of the power system power flow calculation apparatus 1 solves the optimization problem. The operation of step S05 is executed by the power flow calculation execution unit 22 of the calculation unit 13. The power flow calculation execution unit 22 repeats the operation of step S05 in a loop until the virtual load converges.

[0092] When the reactive power Q of nodes 30, 31, 32, and 33 has the value shown in Fig. 7, the load flow calculation by the conventional technology does not converge as shown in Fig. 8. The allowable error is set to 0.001 pu on a 100 MVA basis. The behavior of the maximum node error up to 21 iterations using the NR method is shown in Fig. 8.

[0093] (Step S06: Calculate transmission loss and reflect virtual load) The calculation unit 13 of the power system power flow calculation device 1 calculates the transmission loss and reflects it in the virtual load. The operation of calculating the transmission loss in step S06 is executed by the power flow calculation execution unit 22 of the calculation unit 13. The operation of reflecting the virtual load in step S06 is executed by the constraint condition creation unit 32 of the calculation unit 13. The power flow calculation execution unit 22 repeats the operation of step S06 in a loop until the virtual load converges. As an example, in this embodiment, the power flow calculation execution unit 22 adjusts the node voltage, load reactive power (QL), and tap ratio of the PV designated location.

[0094] The constraint condition creating unit 32 calculates the transmission loss occurring in the branch of the power system as the load of the nodes at both ends of the branch, and reflects it as a constraint condition. In (Equation 4.21), the weight of the load reactive power (QL) is set to 2.0, and the other weights are set to 1.0. As an example, the power flow calculation executing unit 22 operates two taps shown in FIG. 9 by executing an optimization calculation. Tap down has the effect of raising the voltage of nodes 30, 31, 32, and 33 where the voltage is lowered. Moreover, tap up has the effect of raising the voltage of nodes 30, 31, 32, and 33.

[0095] As an example, the power flow calculation executing unit 22 adjusts the load reactive power (QL) of the nodes 30, 31, and 32 by performing an optimization calculation. The load reactive power (QL) initial value for each node and the calculated load reactive power (QL) adjustment value are shown in Fig. 10. As an example, in this embodiment, the power flow calculation converges without the power flow calculation executing unit 22 adjusting the node voltage.

[0096] (Step S07: Determining convergence of the objective function reflecting the virtual load) The calculation unit 13 of the power system power flow calculation apparatus 1 performs a convergence determination of the virtual load. The operation of step S07 is executed by the virtual load convergence determination unit 23 of the calculation unit 20. The virtual load convergence determination unit 23 calculates the degree of convergence of the virtual load by power flow calculation. The virtual load convergence determination unit 23 performs a convergence determination of the virtual load by iteratively solving the optimization problem, and determines that the virtual load has converged when the difference from the previous value is equal to or smaller than a predetermined determination value ε.

[0097] As an example, in this embodiment, it is assumed that the power flow calculation using the NR method converges at the third iteration. Figure 11 shows the relationship between the number of iterations of the power flow calculation and the error when the convergence judgment conditions are 100 MVA base and 0.001 pu.

[0098] (Step S08: Determine whether the virtual load is non-convergent) The calculation unit 13 of the power system power flow calculation device 1 judges whether the virtual load is non-converged based on the degree of convergence calculated in step S07. The operation of step S08 is executed by the virtual load convergence determination unit 23 of the calculation unit 13. If the virtual load convergence determination unit 23 judges that the virtual load is non-converged, the program proceeds to step S04. If the virtual load is not judged to be non-converged, the program proceeds to step S09.

[0099] (Step S09: Reflect the optimization calculation results to the nodes and taps) If it is not determined in step S08 that the virtual load has not converged, the calculation unit 13 of the power system power flow calculation device 1 reflects the optimization calculation result in the nodes and taps. The operation in step S09 is executed by the power flow calculation execution unit 22 of the calculation unit 13.

[0100] (Step S10: AC power flow calculation using the NR method) The calculation unit 13 of the power system power flow calculation device 1 performs AC power flow calculation using the NR method after reflecting the optimization calculation results in the nodes and taps. The operation of step S10 is performed by the power flow calculation execution unit 22 of the calculation unit 13. The power flow calculation execution unit 22 calculates the voltages at the nodes (sometimes referred to as "node voltages") using AC power flow calculation using the NR method. The power flow calculation execution unit 22 may calculate the branch power flows based on the node voltages.

[0101] (Step S11: Writing the results) The calculation unit 13 of the power system power flow calculation device 1 writes the result calculated by the AC power flow calculation to the storage unit 14. The operation of step S11 is executed by the power flow calculation execution unit 22 of the calculation unit 13. The power flow calculation execution unit 22 stores in the storage unit 14 the appropriate node voltages calculated in step S02 or step S10 and the branch power flows calculated based on the node voltages.

[0102] The results of power flow calculations using the linearized objective function (equation 4.21) are shown in Figures 12 and 13. Figure 12 shows the voltages at each node calculated by solving the optimization problem when transmission losses are reflected in the virtual load. It can be seen that these are almost the same values ​​as the voltages resulting from the power flow calculation using the NR method, which is also shown. Figure 13 shows the voltages at each node calculated by solving the optimization problem when transmission losses are not reflected in the virtual load. It can be seen that there is a difference from the voltages resulting from the power flow calculation using the NR method, which is also shown. The voltages calculated using the NR method are close to the actual voltage values ​​in the power system. The effectiveness of reflecting transmission losses in the virtual load can be confirmed.

[0103] As an example, the virtual load reflecting the transmission loss converged after four iterations of the power flow calculation. The allowable error was set to 0.001 pu on a 100 MVA basis. Figure 14 shows the maximum error versus the number of iterations of the power flow calculation at all nodes.

[0104] The calculation unit 13 causes the output unit 12 to output the result of the AC power flow calculation. The appropriate node voltage calculated in step S02 or step S10 or the branch power flow calculated based on the node voltages is output from the output unit 12.

[0105] Output unit 12 outputs the results of the AC power flow calculation calculated by calculation unit 13. Output unit 12 displays, prints out, or outputs as electronic data the calculated appropriate node voltages and the branch power flows calculated based on the node voltages. An external device connected to output unit 50 may be an I / O device such as a printer or monitor, an external storage device, or an external control device or computer device.

[0106] An operator refers to the node voltages output from power system power flow calculation apparatus 1 and the branch power flows calculated based on the node voltages, and controls the power system with appropriate control variables.

[0107] The above is the operation of the power system power flow calculation device 1.

[0108] [1-3. Effects] (1) According to this embodiment, the power system power flow calculation device 1 includes a constraint condition creation unit 32 that creates a power flow equation based on data indicating the configuration of a power system supplying power and data indicating electric quantities at nodes, and creates constraint conditions for power calculation for each node based on the created power flow equation, a virtual load convergence determination unit 23 that determines that a virtual load calculated by calculation processing for the power calculation including the constraint conditions created by the constraint condition creation unit 32 has converged when the virtual load calculated by the calculation processing for the power calculation including the constraint conditions created by the constraint condition creation unit 32 is within a predetermined allowable range, and a power flow calculation execution unit 22 that performs calculation processing for the power calculation including the constraint conditions until it is determined that the virtual load has converged by the virtual load convergence determination unit 23, and calculates a voltage at the node. The constraint condition creation unit 32 creates the constraint conditions by linearly approximating the power flow equation. Therefore, even if the power flow calculation based on the initial values ​​of the electric quantities at the nodes does not converge, it is possible to provide a power system power flow calculation device that calculates appropriate electric quantities at which the power flow calculation converges.

[0109] In conventional technology, power flow equations are generally nonlinear simultaneous equations. Therefore, when calculating a solution using the power flow equations, if the correction amount is too large, if the same value is repeated, or if the input data is inappropriate, such as when the supply and demand are not balanced, the power flow calculation may not converge.

[0110] According to this embodiment, the constraint condition creating unit 32 of the power system power flow calculation apparatus 1 creates the constraint condition for the power calculation by linearly approximating the power flow equation, so that the number of corrections to the input data for the power calculation can be reduced. The operator can quickly grasp the corrections to the input data for the power calculation and the correction values.

[0111] An operator can more easily select a node to be controlled and can more quickly calculate the voltage at the node. The operator can control the power system with an appropriate control amount by referring to the voltage at the node calculated by the power system power flow calculation apparatus 1.

[0112] (2) According to this embodiment, the constraint condition creating unit 32 of the power system power flow calculation apparatus 1 calculates the power transmission loss occurring in the branch of the power system as the load of the nodes at both ends of the branch and sets it as the first constraint condition for the power calculation, so that the power flow calculation can be performed with the power transmission loss occurring in the branch as the virtual load of the node. This makes it possible to calculate the voltage at the node that is more suitable for the actual power system by the power calculation.

[0113] An operator can refer to the voltages at the nodes calculated by the power system power flow calculation apparatus 1 and control the power system with appropriate control variables.

[0114] (3) According to this embodiment, the constraint condition creating unit 32 of the power system power flow calculation apparatus 1 differentiates the term related to the tap ratio of the transformer arranged in the power system in the power flow equation and sets it as the second constraint condition for the power calculation, so that the voltage at the node when the transformer tap is switched can be calculated by the power calculation. By differentiating the term related to the transformer tap ratio in the power flow equation, the change in the tap ratio can be converted into a change in the "node injection amount", which is the power at the node.

[0115] This makes it possible to prevent the power flow calculation from becoming non-convergent. Also, it is possible to calculate voltages at nodes by power calculations that are more suited to the actual power system.

[0116] An operator can refer to the voltages at the nodes calculated by the power system power flow calculation apparatus 1 and control the power system with appropriate control variables.

[0117] (4) The power flow calculation executing unit 22 calculates the branch power flow at the node based on the calculated voltage at the node, so that an amount of electricity that is more suited to an actual power system can be calculated by power calculation.

[0118] 2. Other embodiments Although the embodiments including the modified examples have been described, these embodiments are presented as examples and are not intended to limit the scope of the invention. These embodiments can be implemented in various other forms, and various omissions, substitutions, and modifications can be made without departing from the gist of the invention. These embodiments and their modifications are included in the scope of the invention and its equivalents as well as in the scope and gist of the invention. The following is an example.

[0119] (1) In the above embodiment, the function linearizer 321, the transmission loss calculator 322, and the differential calculator 323 are built into the objective function creator 31. However, the function linearizer 321, the transmission loss calculator 322, or the differential calculator 323 may be configured by an external device to the power system power flow calculation apparatus 1. [Explanation of symbols]

[0120] 1... Power system power flow calculation device 11 Input section 12 Output section 13... Arithmetic section 14...Storage section 21. Optimization problem creation section 22. Power flow calculation execution unit 23 Virtual load convergence determination unit 31... Objective function creation part 32. Constraint Condition Creation Section 321 Function Linearization 322 Transmission loss calculation unit 323...Differential calculation section

Claims

1. a constraint condition creating unit that creates a power flow equation based on data indicating a configuration of a power system that supplies power and data indicating an electric quantity at a node, and creates a constraint condition for a power calculation for each node based on the created power flow equation; a virtual load convergence determination unit that determines that a virtual load calculated by a calculation process related to the power calculation including the constraint conditions created by the constraint condition creation unit has converged when the virtual load is within a predetermined allowable range; a power flow calculation execution unit that performs a calculation process related to the power calculation including the constraint condition and calculates a voltage at the node until the virtual load convergence determination unit determines that the virtual load has converged; the constraint condition creation unit creates the constraint condition by linearly approximating the power flow equation; Power system power flow calculation device.

2. the constraint condition creation unit calculates a transmission loss occurring in a branch of the power system as a load of the nodes at both ends of the branch, and sets the calculated transmission loss as a first constraint condition for the power calculation; The power system load flow calculation apparatus according to claim 1 .

3. the constraint condition creation unit differentiates a term in the power flow equation related to a tap ratio of a transformer arranged in the power system, and sets the differentiated term as a second constraint condition for the power calculation. The power system load flow calculation apparatus according to claim 1 .

4. the power flow calculation execution unit calculates a branch power flow at the node based on the calculated voltage at the node. The power system load flow calculation apparatus according to claim 1 .

5. On the computer, a constraint condition creating step of creating a power flow equation based on data indicating a configuration of a power system that supplies power and data indicating an electric quantity at a node, and creating a constraint condition for a power calculation for each node based on the created power flow equation; a virtual load convergence determination step of determining that a virtual load calculated by a calculation process related to the power calculation including the constraint conditions created in the constraint condition creation step has converged when the virtual load is within a predetermined allowable range; a power flow calculation execution step of performing a calculation process related to the power calculation including the constraint conditions and calculating a voltage at the node until it is determined that the virtual load has converged in the virtual load convergence determination step; The constraint condition creating step creates the constraint condition by linearly approximating the power flow equation. A computer program for power system load flow calculation equipment.

6. a constraint condition creation step of creating a power flow equation based on data indicating a configuration of a power system that supplies power and data indicating an electric quantity at a node, and creating a constraint condition for a power calculation for each node based on the created power flow equation; a virtual load convergence determination step of determining that a virtual load calculated by a calculation process related to the power calculation including the constraint conditions created by the constraint condition creation step has converged when the virtual load is within a predetermined allowable range; a power flow calculation execution step of performing a calculation process related to the power calculation including the constraint condition and calculating a voltage at the node until it is determined that the virtual load has converged by the virtual load convergence determination step, the step of creating the constraint condition comprises linearly approximating the power flow equation to create the constraint condition; Power system power flow calculation method.

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