Analysis method and analysis apparatus

Abstract

To reduce an amount of load-flow calculation of a power system including at least one or more of one or more power supplies with output uncertainty and one or more load devices with load-amount uncertainty.SOLUTION: An analysis method according to an aspect of the present invention includes: determining the factor coefficient of LODF (Line Outage Distribution Factors) in a sensitivity method on the basis of data related to a power system including at least one or more of one or more power supplies with output uncertainty and one or more load devices with load-amount uncertainty; determining an approximate model that directly relates a probability distribution of the outputs of one or more power supplies included in the power system and the load amounts of one or more load devices to a probability distribution of the tidal current of each branch in the power system; and calculating the probability distribution of the tidal current of each branch after a malfunction occurs in one of the branches in the power system on the basis of the factor coefficient and the approximate model.SELECTED DRAWING: Figure 3

Description

[Technical Field]

[0001] The present disclosure relates to an analysis method and an analysis apparatus. [Background Art]

[0002] Conventionally, power flow calculation for calculating power flow, voltage and the like in a power system is known. Methods of power flow calculation are generally classified into alternating current (AC) power flow calculation and direct current (DC) power flow calculation. AC power flow calculation is a method for obtaining power flow by strictly solving a power equation represented by a non-linear equation. As an example, the Newton method, which obtains a solution to a non-linear equation through iterative convergence calculation, is known. DC power flow calculation simplifies AC power flow calculation into a simple linear theory problem and is a method for calculating approximate values of power flow at high speed through conversion. As an example of its application, the sensitivity method disclosed in Non-Patent Document 1 is known.

[0003] In addition, when an accident such as disconnection of one or more power transmission lines occurs in a power system, the power flow flowing through each power transmission line of the power system changes greatly before and after the accident occurs. Due to the influence of this change, there is a risk of causing damage to power transmission lines, banks and the like in the power system. As a countermeasure, a contingency analysis method is used to estimate the power flow before and after the occurrence of an accident, and quantitatively evaluate the reliability of the power system in advance (see, for example, Patent Document 1). Generally, in hypothetical fault analysis, the power flow calculations described above are performed for each hypothetical fault, both before and after the occurrence of the fault. In hypothetical fault analysis targeting actual power systems, the number of hypothetical faults becomes enormous. In particular, when hypothetical fault analysis is used in monitoring and control devices that monitor power systems, the monitoring and control devices need to process a large number of system conditions after a fault in a short time and promptly process alarms. Therefore, the sensitivity method based on the above-mentioned DC power flow calculation, which enables high-speed calculation, is widely used in hypothetical fault analysis. Patent document 1 and non-patent document 2 show that hypothetical fault analysis can be further accelerated by using the sensitivity method in combination with distributed parallel processing, and that power flows before and after the occurrence of a hypothetical fault can be estimated by simple linear calculations using the sensitivity method.

[0004] On the other hand, Patent Documents 2 and 3 describe a stochastic tidal flow calculation method that uses a probabilistic approach to calculate tidal flow, which assumes that the values ​​of physical quantities such as loads follow a normal distribution. [Prior art documents] [Patent Documents]

[0005] [Patent Document 1] Japanese Patent Publication No. 2000-270477 [Patent Document 2] Japanese Patent Publication No. 2003-37937 [Patent Document 3] Japanese Patent Publication No. 2005-57821 [Non-patent literature]

[0006] [Non-Patent Document 1] Allen J. Wood, Bruce F. Wollenberg, Gerald B. Sheble, “Wollenberg, Power Generation, Operation, and Control 3rd Edition”, Wiley-Interscience, 2013 [Non-Patent Document 2] Shinji Kitagawa, et al., "Study on Accelerating Hypothetical Accident Analysis Using Distributed Parallel Processing," Proceedings of the Institute of Electrical Engineers of Japan, PE, Power Engineering Research Committee, September 30, 1999, 1999(151), pp. 65-70. [Overview of the project] [Problems that the invention aims to solve]

[0007] In recent years, many renewable energy sources have begun to be introduced into power grids. Typical examples of renewable energy include natural energy sources such as solar and wind power, and the output of these renewable energy sources fluctuates depending on natural phenomena such as weather. Therefore, there are concerns that fluctuations in renewable energy output may destabilize the power grid, and it is extremely important to estimate the power flow of the power grid and to evaluate its reliability in advance.

[0008] However, conventional technologies have problems such as requiring an enormous amount of computation to calculate power flow for power grids that include power sources that generate electricity based on renewable energy, and thus incurring significant costs such as computation time.

[0009] To elaborate, fluctuations in renewable energy output caused by natural phenomena are probabilistic. in Although there is uncertainty in the output fluctuations, the probability distribution deviates from the normal distribution used in Patent Documents 2 and 3. Therefore, the stochastic power flow calculations in Patent Documents 2 and 3 have the problem that the power flow of a power system including power sources that generate electricity based on renewable energy cannot be accurately calculated. As a countermeasure to this problem, it is conceivable to introduce the Monte Carlo method into the stochastic power flow calculations in Patent Documents 2 and 3. However, in order to obtain sufficient accuracy with the Monte Carlo method, tens of thousands to hundreds of thousands of calculation points are required for the fluctuations in the output of renewable energy. Furthermore, in stochastic power flow calculations, power flow calculations are performed for each calculation point, so the amount of computation becomes enormous.

[0010] Furthermore, when evaluating the reliability of a power grid that includes power sources that generate electricity based on renewable energy, the above-mentioned hypothetical accident analysis is performed. However, in the hypothetical accident analysis, the hypothetical accident is number Because tidal flow calculations are required, the amount of computation increases even further, making the aforementioned cost issues, such as computation time, even more pronounced.

[0011] Furthermore, the aforementioned problem arises not only when there is one or more power sources with uncertain output, but also when the power system includes one or more load devices with uncertain load quantities.

[0012] The present disclosure aims to provide an analysis method and an analysis apparatus that can reduce the computational complexity of power flow calculations for a power system that includes at least one power source with uncertainty in its output and at least one load device with uncertainty in its load. [Means for solving the problem]

[0013] An analysis method according to one aspect of the present disclosure includes: determining factor coefficients for LODF (Line Outage Distribution Factors) in a sensitivity method based on data relating to a power system including at least one power source having uncertainty in output and at least one load device having uncertainty in load; determining an approximate model that directly relates the probability distribution of the output of the one or more power sources and the load of the one or more load devices included in the power system to the probability distribution of the power flow at each branch in the power system; and calculating the probability distribution of the power flow at each of the branches after a fault occurs at any one of the branches in the power system, based on the factor coefficients and the approximate model.

[0014] An analysis device according to one aspect of the present disclosure includes: a factor coefficient determination unit that determines a factor coefficient of LODF (Line Outage Distribution Factors) in a sensitivity method based on data relating to a power system including at least one of one or more power sources having uncertainty in output and one or more load devices having uncertainty in load amount; an approximate model determination unit that determines an approximate model that directly correlates the probability distribution of the output of the one or more power sources included in the power system and the probability distribution of the load amount of the one or more load devices with the probability distribution of the power flow of each branch in the power system; and a probabilistic power flow calculation unit that calculates the probability distribution of the power flow of each of said branches after a fault occurs in any one of said branches in the power system based on said factor coefficient and said approximate model. [Effects of the Invention]

[0015] According to one aspect of the present disclosure, it is possible to reduce the amount of calculation for power flow calculation of a power system including at least one of one or more power sources having uncertainty in output and one or more load devices having uncertainty in load amount. [Brief Description of the Drawings]

[0016] [Figure 1] It is a diagram showing an example of the electrical configuration of an analysis device according to an embodiment of the present disclosure. [Figure 2] It is a diagram showing an example of a power system. [Figure 3] It is a flowchart showing an example of probabilistic power flow calculation processing in an analysis device. [Figure 4] It is a diagram showing verification results regarding the accuracy of probabilistic power flow calculation. [Figure 5] It is a diagram showing verification results regarding the calculation speed of probabilistic power flow calculation. [Mode for Carrying Out the Invention]

[0017] The following describes preferred forms relating to this disclosure with reference to the drawings. Unless otherwise specified in the following description, the scope of this disclosure is not limited to the forms described below. The scope of this disclosure includes equivalents of such forms.

[0018] Figure 1 shows an example of the electrical configuration of the analysis device 1 according to this embodiment. Analysis device 1 is a device that calculates the power flow cross-section (probability distribution of power flow at each branch) before and after a hypothetical fault occurs, targeting a power system that includes one or more power sources that output electricity based on renewable energy, i.e., one or more power sources with uncertainty in output, and one or more load devices with uncertainty in load amount, and outputs the calculation results of each power flow cross-section as analysis results. These analysis results are used in hypothetical fault analysis, which is one of the reliability assessments of power systems. Reliability assessments of power systems are generally classified into static security assessment (SSA), voltage security assessment (VSA), and dynamic security assessment (DSA). Static security assessment evaluates the impact of a fault on the power system when a fault occurs in the power system, using line overload and voltage drop as indicators. Voltage security assessment evaluates the impact of a fault on the system, using voltage stability as an indicator. Furthermore, dynamic reliability evaluation assesses the impact of the accident on the power system using transient stability as an indicator. The analysis results from the analysis device 1 of this embodiment are used for static reliability evaluation, which is part of the reliability evaluation. In the following explanation, "power sources that generate electricity based on renewable energy, and load equipment with uncertain load amounts" will be referred to as "uncertainty nodes."

[0019] The analysis device 1 of this embodiment performs stochastic power flow calculations. In addition, instead of obtaining the probability distribution of power flow at each branch in the power system using a general stochastic power flow calculation with the Monte Carlo method, the analysis device 1 uses an approximate model Y. The approximate model Y is a function that directly relates the probability distribution of the output of each uncertainty node included in the power system to the probability distribution of power flow at each branch. By using the approximate model Y, the analysis device 1 can significantly reduce the amount of computation required to obtain the probability distribution of power flow at each branch before and after an accident, thereby significantly reducing many costs such as computation time. The sensitivity method and the approximate model Y will be described in detail later.

[0020] [Electrical and functional configuration of analysis device 1] As shown in Figure 1, the analysis device 1 includes a computer comprising a processing unit 10, a storage device 12, an input I / F device 14, and an output I / F device 16. This computer can be a personal computer, a supercomputer, or the like. The processing unit 10 includes at least one processor, such as a CPU (Central Processing Unit). Some of the functions of the processing unit 10 may be configured by circuits such as an FPGA (Field Programmable Gate Array). The storage device 12 is a recording medium that the processing unit 10 can read. The storage device 12 includes, for example, non-volatile memory and volatile memory. Non-volatile memory is, for example, ROM (Read Only Memory), EPROM (Erasable Programmable Read Only Memory), or EEPROM (Electrically Erasable Programmable Read Only Memory). Volatile memory is, for example, RAM (Random Access Memory). The input I / F device 14 is a device that includes an input interface circuit to which an input device is connected by wire or wireless, and receives data input from the external device and outputs the received data to the processing unit 10. The output I / F device 16 is a device that includes an output interface circuit to which an output device is connected by wire or wireless, and outputs various types of data to the output device under the control of the processing unit 10. Typical examples of input devices include keyboards, recording media readers, and other computers. Typical examples of output devices include displays, printers, recording media recorders, and other computers.

[0021] The storage device 12 in this embodiment stores the program PR for probabilistic current calculation. The analysis device 1 functions as an input data acquisition unit 100, an approximate model determination unit 102, a factor coefficient determination unit 104, a probabilistic current calculation unit 106, and a result output unit 108 when the processing unit 10 executes the program PR. The input data acquisition unit 100 is a functional unit that acquires input data used to determine the approximate model Y and the factor coefficient d in the sensitivity method, which will be described later, from external devices via the input I / F device 14. Details of the input data will be described later. The approximate model determination unit 102 is a functional unit that determines the approximate model Y based on the input data. The factor coefficient determination unit 104 is a functional unit that determines the factor coefficient d based on the input data. The probability power flow calculation unit 106 calculates the probability distribution of power flow at each branch after an accident occurs in the power system, based on the factor coefficient d and the approximate model Y. The result output unit 108 is a functional unit that outputs the calculation results of the probability distribution of power flow at each branch after an accident to output devices via the output I / F device 16.

[0022] Next, we will describe the sensitivity method and the approximate model Y in detail.

[0023] [Sensitivity method] When a fault occurs in a power system, the faulty section is generally shut off at high speed to prevent equipment damage and the spread of the fault, but as a result, power flow and supply-demand balance change. The sensitivity method is a technique that rapidly calculates the change in power flow before and after a fault occurs, using a sensitivity that indicates the impact of each fault on power flow, for each case where a transmission line or bank in the power system is cut, and when the output of a node in the power system changes. The sensitivity that indicates the degree to which a fault in one transmission line or bank affects the power flow changes of each transmission line is called LODF (Line Outage Distribution Factors). Also, the sensitivity that indicates the degree to which a change in the output or load of one uncertainty node affects the power flow changes of each transmission line is G science fiction These are called Generation Shift Factors.

[0024] In the analysis device 1 of this embodiment, the probability current calculation unit 106 calculates the probability distribution of currents at each branch after an accident based on the LODF, and this LODF will be explained below.

[0025] [LODF] In the sensitivity method, the following three assumptions are introduced about the power system in order to treat it as a simple linear theory problem by converting the power equation, which is expressed as a nonlinear equation, into a linear equation.

[0026] (Assumption 1) The reactive power in each branch is at an appropriate value and can be excluded from the calculation, and the resistance of each branch is zero. (Assumption 2) The voltage value of all nodes is 1.0 [pu]. (Assumption 3) The difference in phase angles between each node is sufficiently small.

[0027] Based on these assumptions, the power equation is expressed by the following linear equation (1).

[0028]

number

[0029] Furthermore, in LODF, the factor coefficient d indicates the degree to which a power line k severance accident has an impact on the power flow change of power line l. l、k As shown in Non-Patent Document 2 and other documents mentioned above, it is defined by the following equation (2).

[0030]

number

[0031] Equation (2) can be expressed as follows (3) when busbars n and m are not slack nodes, using the elements of the inverse of the admittance matrix and the reactances of transmission lines k and l.

[0032]

number

[0033] Then, the tidal flow rate in power line l after an accident occurs in power line k can be expressed using equation (3) as shown in equation (4).

[0034]

number

[0035] Therefore, if a fault occurs in one transmission line k within the power system, the tidal flow rate to the other transmission lines can be calculated using equation (4).

[0036] [Approximate Model Y] When uncertainty nodes are included in the power grid, performing stochastic power flow calculations based on the Monte Carlo method becomes computationally intensive.

[0037] Furthermore, even when calculating the probability distribution of power flow in each transmission line after an accident using equation (4) above, the addition of power flows is an addition operation of probability distributions, requiring calculations using convolution integrals or similar methods. For example, consider an accident in the power system shown in Figure 2 in which the transmission lines of branch 2 are disconnected. The probability distribution of power flow in each branch's transmission lines after the accident can be obtained by adding the probability distribution of power flow in branch 2's transmission line before the accident to the other transmission lines. In this case, instead of multiplying the factor coefficient d related to branch 2's transmission line by the probability distribution of power flow in the other branch's transmission lines, it is necessary to perform a convolution integral on the probability distribution of power flow in branch 2's transmission line and the probability distribution of power flow in the other branch's transmission lines, which significantly increases the computational complexity compared to a simple addition operation.

[0038] Thus, when uncertainty nodes are included in the power grid, a massive amount of computation is required using the Monte Carlo method to calculate the probability distribution of power flow, and the computational cost required to add power flow values ​​together also increases significantly.

[0039] Therefore, the analysis device 1 of this embodiment uses the above-mentioned approximate model Y instead of general stochastic power flow calculations. As described above, the approximate model Y is a function that directly relates the probability distribution of the output of one or more uncertainty nodes included in the power system to the probability distribution of the power flow at each branch.

[0040] More specifically, the stochastic power flow calculation for a power system containing N uncertainty nodes and M branches can be simplified as shown in equation (5) below.

[0041]

number

[0042] The Monte Carlo method described above is used to calculate stochastic currents using N sets of independent variables ζ1, ζ2, ...ζ N This method involves setting up a vast number of calculation points and, for each calculation point, calculating the power equation corresponding to the function g in equation (5) using a convergence calculation, for example, the Newton-Raphson method, to obtain the output variable y, which is the probability distribution of the tidal current at each branch. Therefore, the computational complexity is enormous, calculated by multiplying the number of calculation points by the computational complexity of the convergence calculation.

[0043] On the other hand, the approximate model Y of this embodiment corresponds to an approximate function with function g as the function to be approximated, and consists of N sets of independent variables ζ1, ζ2, ...ζ N This function approximates the above function g, which is the response function of the stochastic current calculation for . In other words, the approximate model Y is a function that approximates the N sets of independent variables ζ1, ζ2, ...ζ N It is also a function or numerical model that directly relates the input (i.e., the probability distribution of the output of each node) to the estimated values ​​of the M-group output variable y in equation (5) (i.e., the probability distribution of the current of each branch).

[0044] The approximate model Y uses functions represented as linear combinations of multiple basis functions, each belonging to an orthogonal polynomial system and each weighted according to the topology of the power system by weight coefficients, as shown in equations (6A) and (6B). Here, K is the number of basis functions.

[0045]

number

[0046] In this embodiment, the function represented by equation (6B) is a function based on a polynomial chaos expansion. For more information on polynomial chaos expansions, see, for example, "Kazuaki Iwamura, et al., "Arbitrary Polynomial Chaos Based Simulation of Probabilistic Power Flow Including Renewable Energies", IFAC-PapersOnLine, Volume 53, Issue 2, 2020, Pages 12145-12150". Hereinafter, this document will be referred to as "Non-Patent Document 3".

[0047] In a polynomial chaos expansion, the polynomials of the basis functions are arbitrary. In this case, the more basis functions K there are, the higher the accuracy of the approximation. However, the number of basis functions K and the number of uncertainty nodes N in the power system must satisfy the following relationship (7). In equation (7), d is the highest degree of all basis functions, and equation (7) is used to calculate the highest degree d of the basis functions and the number of basis functions K.

[0048]

number

[0049] On the other hand, each coefficient of the weight coefficient matrix C is obtained using the selection method, as described in Non-Patent Document 3. The selection method is a technique for obtaining each coefficient by substituting the representative random variable value of the orthogonal polynomial that constitutes the basis function vector (equation (6C)) into equation (5), and obtaining the corresponding estimated value Y by tidal flow calculation. In this case, the root of a single-variable polynomial of the order (d+1) one order higher than the highest order d of the basis function is usually used to select the representative random variable value. When there are N random variables (i.e., the number of uncertainty nodes), (d+1) calculation points are calculated for each random variable. If the number of zeros is m, the relationship between the highest order d and the number of random variables N is as shown in equation (8).

[0050]

number

[0051] Since the zeros are found for each basis function of the orthogonal polynomial, they can be expressed in matrix form as shown in equation (9).

[0052]

number

[0053] The matrix on the left side of equation (9) is m × K (where K is less than or equal to m). Therefore, by selecting K linearly independent rows from this matrix on the left side, we obtain the K × K square matrix shown in equation (10). Then, by finding the inverse of the matrix on the left side of equation (10), we can find the weight coefficient matrix C.

[0054]

number

[0055] [Applying the approximate model Y to LODF] By applying the probability distribution of the tidal current at each branch, obtained by the approximate model Y, to equation (2) above, the probability distribution of the tidal current at each branch after the accident can be determined. In this case, L Two possible methods for applying the approximate model Y to the ODF are the following first and second methods.

[0056] The first method involves first determining the probability distribution of power flow in each branch before the accident using an approximate model Y, and then calculating the probability distribution of power flow after the accident for each branch using equation (2). Specifically, in this first method, the estimated value of the above output variable after the accident in transmission line l when transmission line k is severed is expressed as shown in equation (11). Therefore, if an accident occurs in a transmission line, the probability distribution of power flow in each of the other transmission lines can be individually determined using equation (11).

[0057]

number

[0058] The second method involves calculating the probability distribution of tidal currents at individual branches after an accident by finding a corresponding approximate model Y after the accident occurs. More specifically, the approximate model Y expressed by equations (6A) and (6B) above has a basis function that remains unchanged even if the power system configuration (topology) changes due to an accident, as long as the number of uncertainty nodes N and the above random variable ζ for those uncertainty nodes do not change. This means that by simply changing the weight coefficient matrix C in equations (6A) and (6B) to coefficients that represent the topology of the power system after the accident, an approximate model Yc corresponding to the state after the accident can be obtained. Therefore, in the second method, first, the weight coefficient matrix Cc corresponding to the state after the accident is obtained to obtain the approximate model Yc corresponding to the state after the accident, and this approximate model Yc is used to obtain the probability distribution of the power flow at the branch after the accident. In this disclosure, "Cc" and "Yc" correspond to the letters "C" and "Y" with the symbol "~" added, respectively.

[0059] The weight coefficient matrix Cc corresponding to the period after the accident is determined based on the weight coefficient matrix C corresponding to the period before the accident and the factor coefficient d. More specifically, equation (11) above can be transformed into the form of a linear combination of basis functions, as shown in equation (12), by using the corresponding approximation model Y before the accident occurred.

[0060]

number

[0061] In equation (12), each basis function in the basis function vector is weighted by the coefficients of the weight coefficient matrix Cc. Furthermore, as shown in equation (12A), this weight coefficient matrix Cc is determined before the accident occurs by the corresponding weight coefficient matrix C and the factor coefficient d. Then, by applying equation (12) to each branch in the power system, equation (13) is derived, which represents the corresponding approximate model Yc after an accident occurs. Therefore, if an accident occurs in one transmission line, the probability distribution of the power flow in the other transmission lines can be determined by the matrix calculation in equation (13).

[0062]

number

[0063] [Operation of Analysis Device 1] Figure 3 is a flowchart showing an example of the probabilistic current calculation process in the analysis device 1. In the analysis device 1, first, the input data acquisition unit 100 acquires input data (step Sa1). The input data includes at least the factor coefficient d of the LODF, data necessary for determining the approximate model Y, and data related to assumed accidents. The data necessary for determining the factor coefficient d includes data related to the power system, such as the system configuration, the impedance of each line, the capacity of each load, the capacity of each power source and each power source, and the voltage specification value. The data necessary for determining the approximate model Y includes one or more basis functions and data showing the output of each uncertainty node. The basis functions are set in advance by the designer or the like using appropriate polynomials. The data related to assumed accidents includes data that identifies one or more branches in the power system where an accident may occur.

[0064] Next, the factor coefficient determination unit 104 calculates the factor coefficient d of the LODF according to equation (3) based on the input data (step Sa2).

[0065] Next, the approximation model determination unit 102 performs processing to determine the weight coefficient matrix C of the approximation model Y based on the input data. Specifically, the approximation model determination unit 102 determines equation (10) using the zeros obtained for each basis function by the selection method, and determines the weight coefficient matrix C by finding the inverse matrix of the left side of equation (10) (step Sa4). Once the weight coefficient matrix C is determined, the approximation model Y is determined. Note that the processing in steps Sa3 and Sa4 may be performed before or simultaneously with step Sa2.

[0066] Next, the probability current calculation unit 106 calculates the probability distribution of currents at each branch after an accident for each assumed accident, based on the data related to the assumed accident (step Sa5). This calculation is performed using the first or second method described above, based on the approximate model Y and factor coefficient d, as described above. The result output unit 108 then outputs the probability distribution of the power flow at each branch after the occurrence of each assumed accident as an analysis result to the output device (step Sa6).

[0067] Based on these analysis results, a reliability assessment can be performed to determine whether or not there are any overloaded branches by comparing the tidal flow rate of each branch with the transmission capacity limit for each assumed fault. Alternatively, the analysis device 1 may function as an assumed fault analysis device by equipping the processing device 10 with a function unit to perform this determination.

[0068] [Performance Verification] Figure 4 shows the verification results regarding the accuracy of the stochastic current calculation in this embodiment, and Figure 5 shows the verification results regarding the calculation speed of the stochastic current calculation in this embodiment. The verification was performed by comparing the stochastic power flow calculation of this embodiment with that of a general stochastic power flow calculation using the Monte Carlo method, using the power system shown in Figure 2 above. Hereinafter, the "general stochastic power flow calculation using the Monte Carlo method" will be referred to as the "conventional method," and the stochastic power flow calculation of this embodiment will be referred to as the "approximate model method."

[0069] The power system in Figure 2 has a reference voltage of 154kV and a system reference capacity of 1000MVA, and includes four busbars and four branches. Busbar 0 is the slack, and busbars 1, 2, and 3 are connected to loads, a synchronous generator G, and a wind turbine WT, respectively. The wind turbine WT corresponds to the uncertainty node in this disclosure. That is, the output of the wind turbine WT fluctuates stochastically. In this verification, wind power generation data from one year at 5-minute intervals is used as trial points in the Monte Carlo method as historical power generation data for the wind turbine WT. In this case, the number of trial points is 105 and 120. Furthermore, as a hypothetical accident, a break in the transmission line of branch 2 between busbar 0 and busbar 1 is assumed, resulting in the disconnection of both ends of the transmission line of branch 2.

[0070] In the verification, the tidal flow was calculated using the conventional method for each trial point, both before and after the accident. The accuracy of this calculation was then considered as the true value, and the calculation results of the approximation model method were used for both before and after the accident, with the mean squared error (R) from the true value being used. MS The accuracy was evaluated as E). In the approximation model method, a function based on polynomial chaos expansion was used for the approximation model Y, and the second method described above was used to calculate the tidal flow after the accident. As shown in Figure 4, the error of the approximation model method was sufficiently small in all three branches (branch 0, branch 1, and branch 2), confirming that the tidal currents could be determined with high accuracy. Furthermore, even in the case of a small-scale power system, as shown in Figure 2, when comparing the time required for power flow calculations before and after an accident using the conventional method and the approximate model method, as shown in Figure 5, the conventional method requires approximately 630 times longer to calculate than the approximate model method, demonstrating that the approximate model method is extremely fast. Although not shown in the figure, when comparing the time required for power flow calculations after an accident using the first method and the second method in the approximate model method, the second method is faster. 1 If the method is used 、 It has been confirmed that this method requires approximately three times the computation time compared to the second method.

[0071] As described above, the analysis method of this embodiment includes: determining the factor coefficient d of the LODF (Line Outage Distribution Factors) in the sensitivity method based on data relating to a power system that includes at least one power source with uncertainty in output and at least one load device with uncertainty in load amount; determining an approximate model Y that directly relates the probability distribution of the output of one or more power sources and the load amount of one or more load devices included in the power system to the probability distribution of the power flow at each branch in the power system; and calculating the probability distribution of the power flow at each branch after a fault occurs at any one branch in the power system, based on the factor coefficient d and the approximate model Y. This method significantly reduces the computational effort required for power flow calculations in power systems, compared to conventional methods using the Monte Carlo method, for power systems that include at least one uncertainty node with one or more power sources having uncertainty in their output and one or more load devices having uncertainty in their load, i.e., uncertainty nodes where the probability distribution of the output or load is unspecified. This reduces costs such as computation time.

[0072] Furthermore, in this embodiment, the approximate model Y is a function represented by a linear combination of multiple basis functions, each belonging to an orthogonal polynomial system, and each weight corresponding to the topology of the power system is given by a weight coefficient. According to this approximate model Y, the probability distribution of the output of each uncertainty node may be unspecified, and there is no need to restrict the probability distribution to a normal distribution, as described in Patent Documents 2 and 3 above.

[0073] Furthermore, in this embodiment, calculating the probability distribution of power flow in each branch after a fault occurs in any one branch of the power system, based on the factor coefficient d and the approximate model Y, includes determining a matrix of weight coefficients Cc corresponding to the topology of the power system after a fault occurs in any one branch of the power system, based on the matrix of weight coefficients C corresponding to the state before the fault occurred and the factor coefficient d, and calculating the probability distribution of power flow in each branch after a fault occurs in any one branch of the power system by performing a matrix operation between the matrix of weight coefficients corresponding to the topology of the power system after a fault occurs in any one branch of the power system and a matrix of multiple basis functions. This method reduces the computational complexity and computation time compared to the method (the first method described above) that calculates the probability distribution of power flow in each branch after an accident occurs in any one branch of the power system, based on an approximate model Y and factor coefficient d for each branch.

[0074] Furthermore, in this embodiment, the approximate model Y is a function based on a polynomial chaotic expansion. This method significantly reduces the computational complexity required for power system power flow calculations compared to conventional stochastic power flow calculations using the Monte Carlo method, while maintaining high accuracy.

[0075] 2. Variations Specific variations added to the embodiments illustrated above are shown below. Two or more forms arbitrarily selected from the following examples may be combined as appropriate, provided they do not contradict each other.

[0076] The analysis device 1 is not limited to a single computer; it may be implemented using multiple computers. Specifically, each functional unit of the processing unit 10 of the analysis device 1 may be implemented by the processors of each of the multiple computers. In this case, each step shown in Figure 3 is assigned to one of the multiple computers and executed by each computer. [Explanation of Symbols]

[0077] 1...Analysis device, 10...Processing device, 12...Storage device, 14...Input I / F device, 16...Output I / F device, 100...Input data acquisition unit, 102...Approximate model determination unit, 104...Factor coefficient determination unit, 106...Probability current calculation unit, 108...Result output unit, C, Cc...Weight coefficient matrix, PR...Program, Y, Yc...Approximate model, d...Factor coefficient.

Claims

1. The analysis device is Based on data relating to a power system that includes at least one power source with uncertainty in output and at least one load device with uncertainty in load quantity, the factor coefficients of LODF (Line Outage Distribution Factors) in the sensitivity method are determined. To determine an approximate model that directly relates the probability distribution of the output of one or more power sources included in the power system, and the load of one or more load devices, to the probability distribution of the power flow at each branch within the power system, The probability distribution of power flow in each of the aforementioned branches after an accident occurs in any one of the aforementioned branches within the power system is calculated based on the factor coefficient and the approximate model. An analysis method that includes this.

2. The aforementioned approximate model is, Each of these functions belongs to an orthogonal polynomial system and is represented as a linear combination of multiple basis functions, each weighted according to the topology of the power system by a weight coefficient. The analysis method according to claim 1.

3. Calculating the probability distribution of power flow in each of the aforementioned branches after an accident occurs in any one of the aforementioned branches within the power system, based on the factor coefficient and the approximate model, is: The matrix of weight coefficients corresponding to the topology of the power system after a fault occurs in any one of the branches within the power system is determined based on the matrix of weight coefficients corresponding to the power system before the fault occurred and the factor coefficients. The probability distribution of power flow in each of the branches after a fault occurs in any one of the branches within the power system is calculated by performing a matrix operation between the matrix of weight coefficients corresponding to the topology of the power system after a fault occurs in any one of the branches within the power system and the matrix of the plurality of basis functions. The analysis method according to claim 2, which includes the following:

4. The aforementioned approximation model is a function based on a polynomial chaotic expansion. The analysis method according to claim 2 or claim 3.

5. A factor coefficient determination unit that determines the factor coefficients of LODF (Line Outage Distribution Factors) in the sensitivity method based on data relating to a power system that includes at least one power source with uncertainty in output and at least one load device with uncertainty in load amount, An approximation model determination unit determines an approximation model that directly relates the probability distribution of the output of one or more power sources included in the power system and the load amount of one or more load devices to the probability distribution of the power flow at each branch within the power system. A probability power flow calculation unit calculates the probability distribution of power flow in each of the branches after an accident occurs in any one of the branches within the power system, based on the factor coefficient and the approximation model. An analytical device that includes [this component].

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