JPH06261453A - Power system simulation equipment - Google Patents

Abstract

PURPOSE:To make it possible to quickly perform a simulation for a power system by efficiently paralleling a portion for solving simultaneous linear equations. CONSTITUTION:With respect to the portion for solving simultaneous linear equations among the simulation calculations for a power system, part of the advance and regression substitution calculations is replaced with the calculations with inverse matrix factors when performing the advance and regression substitution. At first, bus lines are separated to several independent groups in step 51, and advance substitution calculations are made in parallel. Then in step 52, the products of inverse matrix factors and vectors are calculated by parallel processing for each line for the remaining buses. In step 53, buses are separated to groups likewise in step 51 and parallel regression substitution calculations are performed. By paying attention to a resolution passgraph during LU resolution, paralleled by replacing with calculations using inverse matrix factors for the trunk portion of the graph. By doing this, simulation for power system can be performed at a high speed.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an apparatus for simulating a phenomenon of a power system by using a parallel computer, and more particularly to a power system simulation apparatus suitable for a case where high speed transient stability calculation is required.

[0002]

2. Description of the Related Art (Public example closest to the invention: A. Abur, "A
Parallel Scheme for the Forward / Backward Substitut
ions in Solving Sparse Linear Equations ”, IEEE Tr
ans. on Power Systems, Vol.3-4, pp.1471 (1988-11)
) As one of the means for accelerating the simulation, there is a method of performing parallel calculation using a parallel computer. As a method of parallelizing the transient stability calculation, which is a kind of power system simulation, for example, there is the following method.

The transient stability calculation solves an equation consisting of an ordinary differential equation representing the dynamic characteristics of a generator and a system circuit equation. Normally, the ordinary differential equation and the circuit equation are alternately solved at each time step. Go. Of these, the ordinary differential equations are independent for each generator, and therefore can be easily parallel-calculated by assigning each generator to an individual processor.
On the other hand, the circuit equation becomes a simultaneous linear equation in the dimension of the number of busbars in the system, and some ingenuity is required for parallelization.

A simultaneous linear equation is usually an LU of a coefficient matrix.
Solve by decomposition and forward / backward substitution. Of these, LU decomposition may be calculated only when the circuit conditions change, but forward / backward substitution needs to be calculated every time. As a method of processing this forward / backward substitution in parallel, for example, IEEE Transactions on
Power Systems, Vol. 3, No. 4, pp. 1471 to 1478. This method utilizes a decomposition path graph when performing LU decomposition, divides the decomposition path graph into several subgraphs, assigns each subgraph to a processor, and performs forward / backward substitution for each subgraph. By using this method, each processor can perform forward / backward substitution processing in parallel while exchanging data as necessary.

[0005]

In the above prior art, when the decomposition path graph is divided into subgraphs, the portion corresponding to the trunk of the graph is redundantly included in each subgraph, so that the same arithmetic operation is performed by a plurality of processes. There was a problem that it would be duplicated. That is, even if the data is divided and parallelized, there is a problem that the efficiency of parallelization is reduced due to the overlap of arithmetic operations in a plurality of processes.

An object of the present invention is to provide a device capable of high-speed simulation by devising parallelization so that the same calculation is not duplicated and improving the efficiency of parallelization. Another object of the present invention is to provide a device capable of simulating at higher speed by omitting unnecessary calculation as much as possible. Another object of the present invention is to provide a simulation device capable of reflecting the result in actual control by performing a simulation based on online information.

[0007]

In order to achieve the above object, a part of forward / backward substitution calculation when solving simultaneous linear equations, in particular, a part corresponding to the trunk of a decomposition path graph of LU decomposition is replaced with calculation by an inverse matrix factor. I tried to calculate in parallel. Also, the forward / backward substitution calculation for the elements included in the constant vector of the simultaneous linear equations and not corresponding to the generator bus is omitted. In addition, an input means for taking in the online information of the power system is provided, and the simulation is performed based on the taken online information.

[0008]

By replacing a part of the forward / backward substitution calculation, particularly the stem part of the decomposition path graph, with the calculation by the inverse matrix factor, the same arithmetic operation is not duplicated in a plurality of processors.

The calculation by the inverse matrix factor is to solve a linear equation by calculating an inverse matrix of an LU-decomposed matrix or a matrix obtained by further decomposing them and sequentially calculating a product of the inverse matrix and a constant vector. Is. The product of a matrix and a vector can be calculated independently for each row of the matrix, and thus can be calculated in parallel by assigning each row to a processor.

Usually, when the inverse matrix is taken, the number of non-zero elements of the matrix increases and the amount of calculation increases. However, the main part of the decomposition path graph originally has many non-zero elements, and the inverse matrix is taken only for this part, so the calculation amount does not increase so much. By this method, parallel calculation can be performed without increasing the overall calculation amount, so that efficient parallelization can be achieved and high-speed simulation can be performed.

Further, by omitting the processing for the elements which do not correspond to the generator bus in the constant vector of the simultaneous linear equations, the simulation can be performed at a higher speed. The ordinary differential equation requires the voltage value of the generator bus, and the other bus voltage values are not required unless otherwise specified. Furthermore, since the designated current value is 0 for the constant impedance load bus, the element of the constant vector of the corresponding simultaneous linear equations is also 0. If unnecessary calculations are omitted in consideration of these, the simulation speed can be increased. In addition, the decomposition path graph becomes simpler by that amount, and especially the number of elements in the trunk is reduced, so that parallelization can be efficiently performed.

Furthermore, by taking in the online information, it is possible to carry out a simulation corresponding to the phenomenon actually occurring in the power system. If a sufficiently fast processor is used, the simulation can be executed faster than the actual phenomenon, and the result can be reflected in the decision of the control policy.

[0013]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of the present invention will be described below with reference to the drawings.

FIG. 1 is a configuration diagram when the present invention is applied to an online stability monitoring device of a power system. Online information such as circuit conditions and power flow conditions of the power system is captured via the data input unit 11 and sent to the simulator 12. The simulator 12 performs transient stability calculation assuming various accidents every predetermined time cycle, for example, every 10 minutes, and presents the result to the operator via the display unit 14.

The simulator 12 comprises one host processor 15, a plurality of node processors 16 and a database 13. The database 13 stores data necessary for simulation such as line constants and generator constants. Each node processor 16 has a local memory 17, respectively. There is also a shared memory 18 accessible by all processors.

The general procedure of the simulation is shown in FIG. First, in step 21, conditions such as circuit conditions, power flow conditions, and accident conditions are set. Next, in step 22, the power flow in the initial state is calculated. Up to this point, the host processor 15 mainly performs the processing, and if necessary, the node processor 1
6 is used, or data required for later calculation is transferred to the local memory 17 via the node processor 16. Next, in step 23, the time is advanced one by one, in step 24, the ordinary differential equation is solved by numerical integration, and in step 2
Repeat the procedure of solving the circuit equation in 5, and proceed with the calculation. In step 26, it is judged whether the time has advanced to a predetermined end time or the phase difference angle of the generator has diverged beyond a certain value, and if so, the calculation ends.

Steps 24 and 25 are the main part of the transient stability calculation, and are mainly performed in parallel by a plurality of node processors 16. In the following, a method of performing parallel calculation with three node processors will be described by taking a simple system having three generators and nine busbars shown in FIG. 3 as an example.

First, in step 24, since the ordinary differential equation is independent for each generator, each generator may be assigned to the node processor 16. In the example of FIG. 3, since there are three generators and three node processors, one-to-one allocation is performed and calculation is performed independently. As the calculation method, a numerical integration method such as the Runge-Kutta method is used.

Next, the step 25 will be described in detail.

The circuit equation is for solving simultaneous linear equations such as equation (1).

[0021]

[Formula 1] YV = I (Formula 1) Here, Y is a node admittance matrix, V is a variable vector in which bus voltages are arranged, and I is a constant vector in which bus currents are arranged. The simultaneous linear equations are usually solved by the operations of LU decomposition and forward / backward substitution.

The LU factorization is a factorization of the coefficient matrix Y into two matrices L and U as shown in equation 2.

[0023]

## EQU00002 ## Y = LU (Expression 2) where L is a lower triangular matrix and U is an upper triangular matrix. Since the admittance matrix Y changes only when the system condition changes, LU decomposition may be performed only at that time.

LU decomposition is performed by the host processor 15,
The result is transferred to the node processor 16.

The forward / backward substitution is to solve the equations 3 and 4 by using the result of LU decomposition.

[0026]

LX = I ... (Equation 3)

[0027]

## EQU00004 ## UV = X (Expression 4) where X is a variable vector. Since the matrix L has a lower triangular shape, the mathematical expression 3 can be solved in order from the element above X by the substitution operation without calculating the inverse matrix. This is called forward substitution. Similarly, in the equation 4, a solution can be obtained by substituting the elements below V in order. This is called backward substitution. But,
In general, assignment operations must follow a certain order, so they cannot be simply parallelized. Less than,
A method of parallelizing this part will be described.

FIG. 4 is an example of a decomposition path graph when LU decomposition is performed for the system of FIG. The decomposition path graph shows the relationship between the elements of the LU decomposed matrix, and it is necessary to perform forward substitution from the top of the graph and backward substitution from the bottom. For example, forward substitution for bus d must occur after forward substitution for bus a.
On the contrary, since the bus a and the bus c have no relation to each other, the forward substitution can be performed independently.

Therefore, first, for example, P1, P2 and P in FIG.
As shown in FIG. 3, the graph is divided into independent branches and leaves and a trunk portion W. Then, as shown in FIG. 5, P1 to P3
Forward substitution for the part of P (step 51), calculation by the inverse matrix factor for the part of W (step 52), P
Calculation is performed in the order of backward substitution (step 53) for the portions 1 to P3.

Among these, the forward substitution in step 51 and the backward substitution in step 53 can be calculated in parallel for each node processor because P1 to P3 are independent. The result is stored in the shared memory 18 as needed.

The calculation by the inverse matrix factor in step 52 is performed as follows. The inverse matrix factor is an inverse matrix of the matrices L and U or a matrix obtained by further decomposing them. Here, the inverse matrix factor corresponding to the part of W is calculated. First number 5
As described above, the matrix L is decomposed into two matrices L _P and L _W.

[0032]

[Equation 5]

Here, L _P is a matrix corresponding to the busbars included in _P1 to P3, which is the same as L, and the other columns are matrices in which only one diagonal element is 1, and L _W is conversely included in W. The column corresponding to the bus is the same as L, and the other columns have only diagonal elements of 1
Is the matrix of. Similarly, the matrix U is decomposed into two matrices U _W and U _{P as shown} in Equation 6.

[0034]

[Equation 6]

From Equation 6 and Equation 1, Equation 2, Equation 5, and Equation 6, Equation 7 is obtained.

[0036]

[Equation 7]

Here, when equation 8 is set, W _B becomes an inverse matrix factor for W.

[0038]

[Equation 8]

The part of multiplying the inverse matrix of L _P corresponds to the forward substitution calculation of _{P1 to} P3, and the part of multiplying the inverse matrix of U _P corresponds to the backward substitution calculation of _{P1 to} P3.

Since the result of the product of the inverse matrix of L _P and I has already been obtained by the forward substitution calculation (step 51), multiplication of this with the inverse matrix factor W _B corresponds to forward and backward substitution of W. You will be able to calculate. Here, the fact that the product of the matrix and the vector can be calculated independently for each row of the matrix is used, and is calculated in parallel by the node processor 16 for each row. As can be seen from the equation (8), W _B is an identity matrix except for the part corresponding to W (the inverse matrix of U _Wd , the inverse matrix of L _Wd ), and therefore only the row of this part needs to be calculated. The calculated result is written in the shared memory 18 as needed. Note that W _B is calculated by the host processor 15 when performing LU decomposition.

In general, when the inverse matrix is obtained, the number of non-zero elements increases, so the number of operations increases in the calculation using the inverse matrix factor. However, in this case, the W portion is the trunk portion of the divided path graph, and the number of non-zero elements has already increased due to fill-in, so the number of operations does not increase much even if the inverse matrix is taken.

By the method described above, the parts for solving simultaneous linear equations can be efficiently parallelized, and transient stability calculation can be performed at high speed.

Although a simple system has been described in the above description, parallel calculation can of course be performed by the same method even when the number of nodes or the number of generators is large or the number of node processors is large. Basically, focusing on the decomposition path graph, the branch and leaf parts may be calculated by forward and backward substitution, and the trunk part may be calculated by the inverse matrix factor.

Next, the case where the sparse vector method is applied will be described.

In the transient stability calculation, the circuit equations are usually calculated for all the buses, but only the generator bus value is required for the calculation of the differential equation in the vector V, and the constant impedance in the vector I. Considering that the value of the load bus becomes 0, considerable calculation can be omitted. In this way, a method of paying attention to the sparsity of the vectors V and I and omitting unnecessary operations is called a sparse vector method (reference, W. Tinney, et al., “Sparse Vec
tor Methods ”, IEEE Trans. on Power Apparatus and
Systems, Vol.104, No.2, pp.295 (1985-2)).

Even when this method is applied, parallelization can be performed in exactly the same manner. For example, in the case of the system of FIG. 3, the decomposition path graph is simple as shown in FIG. 6, but can be parallelized by the same idea. In particular, when the number of nodes appearing in the decomposition path graph is reduced, the effect of further improving the parallelization efficiency can be expected.

Next, a case where the present invention is applied to a stabilization control device for a power system will be described with reference to FIG. When an abnormality such as an accident occurs in the electric power system, the operation information of the protection relay and the circuit breaker is input online via the data input unit 11, and the simulator 12 performs the simulation based on the input. The simulator 12 has a host processor and a plurality of node processors as in FIG. The result of the simulation is sent to the control device 71, the control device 71 determines a control strategy based on the result, and sends an operation command to the control device in the power system.

Since the simulation can be performed at high speed by using the present invention, if a sufficiently high speed processor is prepared,
For example, before a generator goes out of step, it can be predicted by simulation and countermeasures can be taken. Further, the prediction of the result for the control measure can be performed at high speed by using the simulator 12.

As described above, by applying the present invention to the system stabilization control device, it is possible to predict the behavior with respect to an accident faster than real time, and reflect it in the control policy to perform accurate stabilization control. .

Further, since the center of the present invention is a method for solving simultaneous linear equations at high speed, any method other than power system simulation can be applied as long as the simultaneous linear equations need to be solved at high speed. is there.

[0051]

According to the present invention, when solving simultaneous linear equations, it is possible to efficiently perform parallel calculation without duplicating the same calculation between the processors, so that the phenomenon of the power system can be simulated at high speed. Also, by applying the sparse vector method, unnecessary processing can be omitted, and there is an effect that simulation can be performed at higher speed. In addition, simulation is performed based on the online information, and the result is reflected in the control policy, so that there is an effect that the system can be stabilized accurately.

[Brief description of drawings]

FIG. 1 is a configuration diagram when the present invention is applied to an online stability monitoring device of a power system.

FIG. 2 is a block diagram showing a procedure of transient stability calculation.

FIG. 3 is a system diagram showing an example of a power system.

FIG. 4 is a diagram showing a decomposition path graph.

FIG. 5 is a block diagram showing a procedure for solving simultaneous linear equations.

FIG. 6 is a diagram showing a decomposition path graph when a sparse vector method is used.

FIG. 7 is a configuration diagram when the present invention is applied to a stabilization control device of a power system.

[Explanation of symbols]

11 ... Data input section, 12 ... Simulator, 15 ... Host processor, 16 ... Node processor, 18 ... Shared memory.

Claims (3)

[Claims] 1. A power system simulation apparatus in which a plurality of processors solve an equation describing a phenomenon of a power system for simulation, and when the plurality of processors solve simultaneous simultaneous linear equations by forward-backward substitution calculation A power system simulation device characterized in that a part of the backward substitution calculation is replaced with calculation by an inverse matrix factor. 2. The power system simulation device according to claim 1, wherein forward / backward substitution calculation for elements not included in the constant vector of the simultaneous linear equations and not corresponding to the generator bus is omitted. 3. The power system simulation apparatus according to claim 1, further comprising input means for taking in online information of the power system, and performing simulation based on the online information input from the input means.