JP5168048B2 - Secondary planning problem calculation device, program for secondary planning problem calculation device, tidal current plan calculation device, generator output value calculation device, and portfolio optimization device - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To solve the problem that when variables are set to a value close to upper and lower limit values when repeatedly performing an arithmetic operation by using a Newton method in order to obtain the optimal solution of a secondary plan problem, the calculation is made unstable, and convergence is time consuming, and solutions can not be obtained with no convergence. <P>SOLUTION: This secondary plan program calculation device is provided with: an initialization means for calculating the initial values of control variables and variables as the Lagrangian multiplier group of the constraint equation group of upper limit constraint or lower limit constraint of the control variables, and for storing the initial values in a variable storage means; a mismatch quantity calculation means for calculating mismatch quantity as the optimal condition separation quantity of a secondary plan problem; a correction quantity calculation means for calculating the correction direction and correction quantity of variables so that the mismatch quantity can be decreased; a fixed variable setting means for setting a fixed flag in the variable storage means corresponding to the control variables whose correction quantity is equal to or less than a first threshold or the slack variables of the control variables; a variable correction means for updating the numerical values of the variable storage means based on the correction direction and correction quantity about the variables which have no fixed flag; and a repetition means for the output of the value of the control variables stored in the variable storage means by making convergence decision. <P>COPYRIGHT: (C)2010,JPO&amp;INPIT

Description

  The present invention relates to a calculation device for calculating an optimal solution of a quadratic programming problem and a program for the calculation device. The present invention also relates to a calculation device that handles tidal current calculation, generator output value formulation, and portfolio optimization as a two-dimensional planning problem.

  A practically effective mathematical programming method for solving a large-scale quadratic programming problem with a conventional two-dimensional programming problem calculator is an interior point method. The interior point method is an iterative method that obtains an optimal solution while repeatedly generating a sequence of operation points leading to an optimal solution by using information on the operation points in the executable region.

  As a method of converging the iterative processing faster, there is a method of using an active set that is a set of constraint equations that are established as equalities among constraint equations (for example, Patent Document 1).

Japanese Patent Laid-Open No. 2004-280792

  In a conventional two-dimensional programming problem calculation apparatus, when iterative calculation is performed using Newton's method to obtain an optimal solution of a quadratic programming problem, it is necessary to solve a linear equation for each calculation. However, when the variables are close to the upper and lower limit values, the calculation becomes unstable, and it takes time for convergence, or there is a problem that a solution cannot be obtained without convergence.

  The present invention has been made to solve the above problem, and provides a quadratic programming problem calculation apparatus that realizes stable calculation even when a variable is close to the upper and lower limit values, and a program for this apparatus. The purpose is to do.

  The secondary programming problem calculation apparatus according to the present invention includes a problem storage means for storing secondary programming problem information representing a secondary programming problem having a constraint equation group including a constraint equation of an upper limit constraint or a lower limit constraint of a control variable; An initializing means for obtaining an initial value of a variable that is a Lagrange multiplier group of the control variable and the constraint equation group, and storing the initial value in a variable storage means; a variable stored in the variable storage means; A mismatch amount calculating means for calculating a mismatch amount that is a deviation amount when substituting into the optimality condition of the problem, a correction amount calculating means for determining a correction direction and a correction amount of the variable so that the mismatch amount is reduced, and Fixed variable setting means for setting a fixed flag in the variable storage means corresponding to the control variable having a correction amount equal to or less than a first threshold value or the slack variable of the control variable; and the fixed flag Variable correction means for updating the numerical value of the variable storage means according to the correction direction and correction amount for the variable that does not have, and the mismatch amount value obtained by the variable stored in the variable storage means is a second threshold value If larger, the correction amount calculation means, the fixed variable setting means and the variable correction means are repeated, and if the mismatch amount value is less than or equal to a second threshold value, it is determined that convergence has occurred and the variable storage means Repeating means for outputting the stored value of the control variable.

  According to the present invention, by fixing the control variable when the control variable takes a value close to the upper and lower limit values, it becomes possible to eliminate the calculation that causes the instability and obtain an optimum solution more stably.

Embodiment 1 FIG.
FIG. 1 is a configuration diagram showing the configuration of the first embodiment of the secondary planning problem calculation apparatus. Hereinafter, in this figure, the secondary programming problem calculation device stores problem information storing secondary planning problem information representing a secondary programming problem having a constraint equation group including constraint equations for upper limit constraints or lower limit constraints of control variables. 101, an initializing unit 102 that obtains an initial value of a variable that is a Lagrangian multiplier of a control variable and a constraint expression group, and stores the initial value in the variable storage unit 103; and a variable stored in the variable storage unit 103 is a quadratic program. A mismatch amount calculation unit 104 that calculates a mismatch amount that is a deviation amount when substituted for the optimality condition of the problem, a correction amount calculation unit 105 that calculates a correction direction and a correction amount of a variable so as to reduce the mismatch amount, and a correction A fixed variable setting means 107 for setting a fixed flag in the variable storage means 103 corresponding to a control variable whose amount is equal to or less than the first threshold value or a slack variable of the control variable; The variable correction means 108 for updating the numerical value of the variable storage means 103 with the correction direction and the correction amount for a variable that does not have a parameter, and the mismatch amount value obtained by the variable stored in the variable storage means 103 is greater than the second threshold value In this case, the correction amount calculation unit 105, the fixed variable setting unit 107, and the variable correction unit 108 are repeated. When the mismatch amount value is equal to or smaller than the second threshold value, the convergence is determined and stored in the variable storage unit 103. And repeating means 112 for outputting the value of the control variable.

  Next, the operation of the secondary planning problem calculation apparatus will be described. First, the initializing means 102 obtains initial values of variables that are Lagrange multipliers of control variables and constraint expression groups from the quadratic programming problem information stored in the problem storage means 101, and sets the initial values of the variables as variable storage means. 103. Next, the mismatch amount calculation means 104 is the amount of deviation from the optimum value when the variable stored in the variable storage means 103 is substituted for the optimality condition of the quadratic programming problem stored in the problem storage means 101, that is, the deviation amount. Calculate the amount of mismatch. The correction amount calculation means 105 calculates the variable correction direction and the correction amount so that the mismatch amount decreases, and stores it in the correction amount storage means 106. The fixed variable setting unit 107 examines a control variable or slack variable whose correction amount stored in the correction amount storage unit 106 is equal to or less than the first threshold value, and sets a fixed flag in the variable storage unit 103 corresponding to the variable. The variable correction means 108 changes the variable value of the variable storage means 103 according to the correction direction and the correction amount for the variables having no fixed flag in the variable storage means 103. If the mismatch amount value obtained from the variable stored in the variable storage unit 103 is less than or equal to the second threshold value, the repetition unit 112 determines that the value has converged and the value of the control variable stored in the variable storage unit 103. Is output. If the convergence is not determined, the correction amount calculation unit 105, the fixed variable setting unit 107, and the variable correction unit 108 are sequentially activated to repeat the process for determining the convergence.

  FIG. 2 is a block diagram showing the hardware of the quadratic planning problem optimizing apparatus. FIG. 3 is an explanatory diagram of means realized by each hardware device of the optimization device for the secondary planning problem. In the figure, the hardware of the optimization device for the secondary planning problem is composed of an input device 1, a hard disk drive (external storage device) 2, a main storage device 3, a central processing unit 4, and an output device 5.

  FIG. 4 is a block diagram of the secondary planning problem calculation apparatus. In the following, description will be made using components in the block diagram. A problem (secondary plan problem information) of the evaluation function f (x), the equality constraint h (x), and the upper and lower limit values (xmin, xmax) of the control variable x is input to the input device 1 by the problem input means 1a. Is done. The input problem (secondary plan problem information) is stored by the problem storage unit 101 realized by the external storage device 2. The output device 5 includes a result output means 5a that outputs the value of the control variable x stored by the variable storage means 103 realized by the external storage device 2.

  The external storage device 2 stores the evaluation function f (x), the equality constraint h (x), and the upper and lower limit values (xmin, xmax) of the control variable input by the problem input unit 1a of the input device 1 in the corresponding storage memory. The input problem storage means 2a is realized. Further, a value obtained by linearly converting the value of the control variable x stored in the variable storage unit 103 of the main storage device 3 after the calculation according to the upper and lower limit values of the control variable stored in the input problem storage unit 1a is obtained. The control variable storage means 2b which memorize | stores in an applicable memory is implement | achieved. The external storage device 2 stores a program describing a procedure for executing the secondary planning problem calculation device on the computer. By reading this and executing it by the central processing unit 4, the computer can function as a secondary planning problem calculation device.

  The main storage device 3 uses the evaluation function f (x) and the equation constraint h (x) stored by the input problem storage means 1a of the external storage device 2 as the upper and lower limit values (xmin, xmax) of the control variable. The problem storage means 3a for storing the data converted on the basis of the value in the corresponding storage memory is realized. In addition, a variable storage that stores the values of the control variable x, the slack variable s, the Lagrange multiplier λx for the lower limit constraint of the control variable, the Lagrange multiplier λs for the lower limit constraint of the slack variable, and the Lagrange multiplier λh for the equality constraint in the corresponding storage memory. Means (103) 3b is realized. Further, the fixed setting storage means 3c for storing a flag indicating that the control variable x or the slack variable s is fixed in the corresponding storage memory is realized. Further, the convergence parameter storage means 3d for storing the value of the convergence parameter μ to be converged in the convergence calculation in the corresponding storage memory is realized.

  Further, the value of the mismatch amount e representing the amount of deviation from the KKT (Karush-Kuhn-Tucker) condition indicating that all constraint equations are satisfied and the differential value of the evaluation function with respect to the control variable is 0 is stored in the corresponding storage memory. The mismatch amount storage means 3e is realized. Here, the KKT condition is one of the optimality conditions for the quadratic programming problem. The correction direction and correction amount Δx of the control variable x, the correction direction and correction amount Δs of the slack variable s, the correction direction and correction amount Δλx of the Lagrange multiplier λx with respect to the lower limit constraint of the control variable, and the lower limit constraint of the slack variable The correction direction and correction amount storage means 3f for storing the values of the correction direction and correction amount Δλs of the Lagrange multiplier λs and the correction direction and correction amount Δλh of the Lagrange multiplier λh for the above equality constraints in the corresponding storage memory is realized. . Further, the correction equation storage means 3g for storing the correction equation that needs to be calculated in the calculation of the correction direction and the correction amount 3f in the corresponding storage memory is realized. Further, the fixed setting change presence / absence storage means 3h for storing in the corresponding storage memory whether or not the fixed setting storage means 3c has been rewritten to a value different from the previously stored fixed setting value is realized.

  The central processing unit 4 realizes the following means. The evaluation function f (x), the equation constraint h (x), the control variable x, the slack variable s of the control variable x, the Lagrange multiplier λx for the lower limit constraint of the control variable x, and the lower limit constraint of the slack variable s Lagrangian multiplier λs for Eq., Lagrange multiplier λh for equality constraint h (x), convergence parameter μ, the control variable and the fixed setting of the slack variable are determined and stored by the variable storage means of the main memory. The initialization means 4a is realized.

  In addition, a mismatch amount calculation unit 4b that calculates a mismatch amount e that represents the amount of deviation from the KKT condition and stores it in the mismatch amount storage unit 3e of the main storage device is realized. Further, an optimization process end determination means 4c for determining whether or not to end the process of the secondary planning problem calculation apparatus is realized. In addition, the control variable x, slack variable s, and control variable stored in the variable storage unit 103 of the main storage device 3 are decreased so that the mismatch amount e stored in the mismatch amount storage unit 3e of the main storage device 3 decreases. The correction direction and the correction amount are calculated for the Lagrange multiplier λx for the lower limit constraint of x, the Lagrange multiplier λs for the lower limit constraint of the slack variable s of the control variable x, and the Lagrange multiplier λh for the equation constraint h (x), respectively. The correction direction and correction amount calculation means 4d stored by the correction direction and correction amount storage means of the main storage device is realized.

  Further, based on the correction direction and the correction amount stored in the correction direction and correction amount storage means 3f of the main storage device 3, the control variable x and the slack variable s are set so that the fixed setting of the storage device is not fixed. Whether or not the control variable x and the slack variable s are fixedly set. When the fixed setting is made, the determination result is stored by the variable fixing storage means of the main storage device and the fixed setting is changed. Variable fixed setting means 4e stored by the fixed setting change presence / absence storage means of the main storage device is realized.

  Further, based on the correction direction and correction amount stored by the correction direction and correction amount storage means of the main storage device and the fixed setting of the control variable stored by the variable fixed setting storage means, the main storage device The control variable x stored by the variable storage means, the slack variable s, the Lagrange multiplier λx for the lower limit constraint of the control variable x, the Lagrange multiplier λs for the lower limit constraint of the slack variable s, and the equality constraint h (x) Each of the Lagrange multipliers λh is updated, and the variable correction means 4f stored by the variable storage means of the main storage device is realized.

  Further, the convergence parameter updating means 4g is realized that updates the convergence parameter μ stored in the main storage device 3 and stores it by the convergence parameter storage means of the storage device. Further, the value of the control variable x stored by the variable storage unit 103 of the main storage device 3 is linearly based on the upper and lower limit values (xmin, xmax) of the control variable stored by the input problem storage unit of the external storage device 2. An end processing unit 4h that converts and stores it by the control variable storage unit (103) of the external storage device 2 is realized.

Here, since inequality constraints can be converted to equality constraints by introducing new variables, generality is not lost even if all constraints are treated as equality constraints. All constraint expressions are described as equality constraints.
gmin <g (x) <gmax
↓
h (x) = 0 (h (x) = g (x) −x ′)
gmin <x ′ <gmax (1)

  The problem input means 1a of the input device 1 inputs the evaluation function f (x), the equation constraint h (x), and the upper and lower limit values (xmin, xmax) of the control variable x from a keyboard, a file, a network, etc. The problem is stored by the problem storage means 2a of the storage device.

The result output means 5a of the output device 5 outputs the value of the control variable x stored by the control variable storage means (103) of the external storage device 2 to a display, file, printer, network, or the like.

  The initialization means 4a of the central processing unit 4 is all for the control variable x, the evaluation function f (x) and the equation constraint h (x) stored in the input problem storage means of the external storage device 2. The coefficient of the evaluation function, the coefficient of the equality constraint, and the value of the constant term are changed so that the control variable x of 0 ≦ x ≦ 1 is stored in the problem storage means of the main memory. At the same time, the initialization means 4a of the central processing unit 4 sets all the values of the control variable x to 0.5, the Lagrange multiplier λx for the lower limit constraint of the control variable x, and the Lagrange for the lower limit constraint of the slack variable s of the control variable x. The value of the multiplier λs is set to 1.0, the value of the Lagrange multiplier λh for the equation constraint h (x) is set to 0 and stored by the variable storage means of the storage device, and the convergence parameter μ is set to 0.5 and the convergence parameter storage of the storage device is stored. The fixed setting of the control variable is set to 0 and stored by the fixed setting storage unit of the storage device.

  Here, the coefficient of the evaluation function and the coefficient of the equality constraint are changed so that the control variable x satisfies 0 ≦ x ≦ 1 in the initialization means, but the present invention can be implemented without performing this operation. It is. However, it is carried out in order to simplify the subsequent arithmetic processing and the description thereof.

  The linear transformation method is as follows.

  However,

Here, x _i is a control variable stored by the input problem storage means (101) of the external storage device 2, and x ′ _i is a control variable stored by the variable storage means (103) of the main storage device 3. is there.

  Here, it is not necessary to consider the constant term in the linear transformation of the evaluation function.

  In the mismatch amount calculation unit 4b of the central processing unit 4, first, the control variable x and its slack variable s approach the lower limit value in the evaluation function f (x) stored by the problem storage unit (101) of the main storage unit 3. Introducing a barrier function that sometimes has a large value, the problems to be addressed are as follows.

Here, log x _i and log s _i are barrier functions. The KKT conditions for the above problem are as follows.

  Next, as shown in Equation 6 below, a deviation amount e from the KKT condition is calculated and stored by the mismatch amount storage means of the main storage device.

The optimization processing end determination means 4c of the central processing unit 4 stores the fixed setting change presence / absence stored by the fixed setting change presence / absence storage means of the main storage device 3, the mismatch amount e stored by the mismatch amount storage means 104, and the convergence parameter storage. If the convergence parameter μ stored by the means satisfies the following condition, it is determined that the process is finished, the CPU finishes the finish processing means, and the repeat process is finished. Further, if any one of the following conditions is not satisfied, the processing is continued.
・ No change in fixed setting ・ All values of mismatch amount e are sufficiently close to 0 ・ The value of convergence parameter μ is sufficiently close to 0

  The correction direction and correction amount calculation means 4d of the central processing unit 4 obtains x, s, λh, λx, λs such that the mismatch amount e stored by the mismatch amount storage means of the main storage device 3 is small. Calculate by linear approximation at each current value. The correction direction and the correction amount are obtained as follows. However, although the correction direction and the correction amount are calculated by performing linear approximation at the current position of each variable here, the correction direction and the correction amount may be calculated by another method.

ここで、以下の式８，９，１０の関係式を用いて、上記の式からｅ_３，ｅ_４を省くことが可能となり、上記の式は式１１に変換することができる。

Here, it is possible to omit e ₃ and e ₄ from the above equations using the following relational expressions 8, 9, and 10, and the above expressions can be converted into Expression 11.

  The correction equation is stored by the correction equation storage means of the main memory according to the equation (11). Here, since the coefficient matrix is a symmetric matrix, the linear equation of Expression 11 can be solved by triangulating the coefficient matrix using the modified Cholesky method and performing forward substitution and backward substitution. Further, the calculated values of Δx and Δλh are stored by the correction direction and correction amount storage means of the main storage device. Further, using the values of Δx and Δλh stored in the main storage device, the values of Δs, Δλx, and Δλs are calculated according to Equations 8, 9, and 10, and the correction direction and correction amount of the main storage device are calculated. Store by storage means. Here, the modified Cholesky method, forward substitution, and backward substitution are used to solve the linear equation, but the linear equation may be solved by other methods.

The variable fixing setting means 4e of the central processing unit 4 includes the control variable x stored by the variable storage means (103) of the main storage device, the slack variable s of the control variable x, and the correction direction and correction amount storage means. When the stored correction direction and correction amount Δx of the control variable x and the correction direction and correction amount Δs of the slack variable s satisfy (x + Δx) <Lx ₁ or (s + Δs) <Ls ₁ If (x + Δx) <Lx ₁ , the fixed setting is set to -1.If (s + Δs) <Ls ₁ , the fixed setting is set to 1. Remember by means. At this time, for all the fixed settings stored by the fixed setting storage means of the main storage device, if none was changed, the fixed setting change presence or absence is 0, if any one is changed, 1 Stored by the fixed setting change presence / absence storage means of the main storage device.

The variable correction means 4f of the central processing unit 4 sets the value of the corresponding slack variable s to Ls ₂ when the fixed setting value stored by the fixed setting storage means of the main storage device 3 is −1. Is stored by the variable storage means. When the fixed setting value stored by the fixed setting storage means of the main storage device 3 is 1, the value of the corresponding control variable x is set to Lx ₂ and stored by the variable storage means of the storage device. When the fixed setting value stored by the fixed setting storage means of the main storage device 3 is 0, the corresponding control variable x, the corresponding slack variable s, the Lagrange multiplier λx for all the control variables x, and all the slacks For Lagrange multipliers λs for variables and Lagrange multipliers λh for all the above equality constraints, the values of x, s, λx, λs, λh stored by the variable storage means of the main memory are updated according to The data is stored by variable storage means of the storage device.

  The end processing means 4h of the central processing unit 4 determines the value of the control variable x stored by the variable storage means of the main storage device based on the upper and lower limit values of the control variable stored by the input problem storage means of the external storage device 2. The result of linear transformation as shown in Expression 13 is stored by the control variable storage means of the external storage device 3. However, when the control variable x is processed without linear conversion in the initialization unit of the central processing unit 4, it is not necessary to perform the linear conversion work here, and the variable is stored by the variable storage unit 103 of the main storage unit 3. The value of the control variable x is stored as it is by the control variable storage means (103) of the external storage device 2.

  Here, x is the value of the control variable stored by the variable storage means 103 of the main storage device 3, and x ′ is the value of the control variable stored by the control variable storage means of the external storage device 2.

  Next, the processing order of the secondary planning problem calculation apparatus according to the present embodiment will be described with reference to the flowchart shown in FIG. In FIG. 5, step S1 shows the process of the problem input means of the input device. In step S2, the process of the initialization means of the central processing unit 4 is shown. Steps S3 to S8 show an iterative optimization calculation processing part for obtaining the value of the control variable that satisfies the KKT condition. Step S3 shows the processing of the mismatch amount calculation means 104 of the central processing unit 4. Step S4 shows the process of the optimization process end determination means of the central processing unit 4. If it is determined that the process is to be continued, the process proceeds to step S5. If it is determined that the process is to be ended, the process proceeds to step S9.

  Step S5 shows the correction direction and correction amount calculation means of the central processing unit 4. Step S6 shows the processing of the variable fixing setting means of the central processing unit 4. In step S7, the process of the variable correction means of the central processing unit 4 is shown. In step S8, the process of the convergence parameter update means of the central processing unit 4 is shown. Step S9 shows the processing of the end processing means of the central processing unit 4. Step S10 shows the result output means of the output device. As described above, the optimal value of the quadratic programming problem is obtained in this way by the above iterative optimization calculation. In the above description, the optimization end determination process or the optimization process end determination is performed after the mismatch amount calculation unit 104. However, the optimization end determination process or the optimization process end determination is not performed only for the first time, and the next and subsequent times. You may make it do. In this case, it can be considered that the mismatch amount is calculated by the convergence determination calculation 109 in the repeating unit 112, the convergence determination is performed 110, and the output 111 is performed. The same applies to the following embodiments.

  An example in which the present invention is applied to the following secondary planning problem is shown.

  Expression 14 is input by the problem input means of the input device 1 and stored in the corresponding location by the input problem storage means of the external storage device 2. The memory image of the external storage device is as follows. When the variable is 7, the evaluation function secondary terms and primary terms are as shown in Table 1, respectively.

  When the number of constraint equations is 3, the second-order terms, first-order terms, and zero-order terms of the constraint equations are as shown in Tables 2, 3, and 4, respectively. The memory image of the upper and lower limit values of the control variable is as shown in Table 5.

  Next, the evaluation function f (x) and the constraint equation h (x) stored by the input problem storage unit of the external storage device 2 are stored by the initialization unit of the central processing unit 4 by the problem storage unit of the main storage unit. Control variable x, slack variable s, Lagrange multiplier λx of control variable x, Lagrange multiplier λs of slack variable, Lagrange multiplier λh of equation constraint, variable fixed setting, fixed setting change presence, convergence parameter μ values are initialized And stored in the corresponding locations by the variable storage means, the fixed setting storage means, the fixed setting change presence / absence storage means, and the convergence parameter storage means of the main storage device. The memory image of the main storage device is as shown in Table 6 below.

  Here, since the upper and lower limits of the control variables are all 1 and 0 in the above problem, the evaluation function f (x) stored by the input problem storage means of the external storage device 2 and the constraint equation h ( x) is stored in the problem storage means of the main storage device as it is. Further, in this embodiment, for simplification, the fixed setting is set for each set of the control variable x and the corresponding slack variable s. When the fixed setting is made, the corresponding x, s Although both are fixed, it is not always necessary to fix the control variable x and the slack variable s at the same time.

  Next, the process repeats. By the mismatch amount calculation means of the central processing unit 4, the evaluation function f (x), the equality constraint h (x), the control variable x, the slack variable s, the Lagrange multiplier λx of the control variable x, the Lagrange multiplier λs of the slack variable, The mismatch amount of the KKT condition is calculated based on the Lagrangian multiplier λh of the equality constraint, the variable fixed setting, and the value of the convergence parameter μ, and stored in the variable storage means 103 of the main storage device 3. The memory image of the main storage device 3 is as shown in Table 7 below.

  The end determination is performed by the optimization processing end determination unit of the central processing unit 4, and the fixed setting change presence / absence value stored by the fixed setting change presence / absence storage unit of the main storage device is 0 and the value of the convergence parameter μ is sufficiently 0 If all the mismatches are close to 0, the computation is terminated. At this time, the termination processing means of the central processing unit 2 is executed, and the value of the control variable x stored by the variable storage means of the main storage device is added to the control variable stored by the input problem storage means of the external storage device 2. Linear conversion is performed based on the lower limit value, and the result is stored by the control variable storage means of the external storage device 2 and output to a display, file, printer, network, etc. by the result output means of the output device. The memory image of the HDD is as shown in Table 8 below.

The output image by the result output means of the output device is as follows.
[X] 0.027273, 0.209091, 0.000000, 0.054545, 1.00000, 0.883117, 0.069519

  If the optimization processing end determination means of the central processing unit 4 determines that the processing is to be continued, the control variable is calculated based on the mismatch amount stored by the mismatch amount storage means of the main storage device by the correction direction and correction amount calculation means. x, slack variable s, control variable x Lagrangian multiplier λx, Lagrange multiplier λs of slack variable, Lagrangian multiplier λh of equality constraints and correction amounts Δx, Δs, Δλx, Δλs, Δλh Is stored by the correction direction and correction amount storage means. The memory images of the main storage device are as shown in Tables 9 and 10 below. Since the coefficient matrix of the correction equation is a symmetric matrix, only the following elements need be stored.

In the variable fixing setting means of the central processing unit 4, the control variable x, slack variable s stored by the variable storage means of the main storage device, and the correction direction and correction amount Δx stored by the correction direction and correction amount storage means. , Δs is determined to be fixed when (x + Δx) <Lx ₁ or (s + Δs) <Ls ₁ is satisfied, and fixed when (x + Δx) <Lx ₁ When (s + Δs) <Ls ₁ , the fixed setting is set to 1 and is stored by the fixed setting storage means of the main memory.

  In the variable correction means 108 of the central processing unit 4, the control variable x, the slack variable s, the Lagrange multiplier λx of the control variable, the Lagrange multiplier λs of the slack variable, and the equality constraints stored in the variable storage means 103 of the main storage device 3 are stored. The value of the Lagrange multiplier λh is updated based on the correction direction and correction amount stored by the correction direction and correction amount storage means of the main storage device, and stored by the variable storage means of the main storage device.

  Finally, the convergence parameter update means of the central processing unit 4 updates the convergence parameter μ stored by the convergence parameter storage means of the main storage device and stores it by the convergence parameter storage means of the main storage device. Returning to the processing of the calculation means. This operation is repeated to calculate a solution that satisfies the KKT condition of the quadratic programming problem.

  According to the present embodiment, it is possible to omit an unstable calculation by fixing the control variable when the control variable takes a value close to the upper and lower limit values. In addition, there is an effect that an optimum solution can be obtained at a higher speed by omitting the arithmetic processing related to the control variable or slack variable that is fixedly set.

Embodiment 2. FIG.
In the secondary planning problem calculation apparatus described in the first embodiment, the fixed variables can be released as follows.

  The secondary planning problem calculation apparatus according to the present embodiment includes the problem storage unit 101, the initialization unit 102, the variable storage unit 103, the mismatch amount calculation unit 104, the correction amount calculation unit 105, and the fixed variable setting unit according to the first embodiment. In addition to the variable correction means 108 and the repetition means 112, the following fixing release means 113 is provided. When the correction direction and the correction amount of the control variable having a fixed flag indicate a direction away from the lower limit constraint of the control variable, the fixing release unit 113 releases the fixed flag of the control variable. . Details will be described below.

  When the control variable x and the slack variable s are fixedly set, the central processing unit 4 described above performs a fixed setting release determination and stores it in the fixed setting storage memory of the storage device by the storage unit. Variable fixing release means 2e is provided that stores the fixed setting change presence / absence as 1 when the fixed setting is changed, and stores it in the fixed setting change presence / absence storage memory of the storage device by the storage means.

The variable unfixing means 2e is configured such that the value of the Lagrange multiplier λx for the lower limit constraint of the control variable x, the Lagrange multiplier λs for the lower limit constraint of the slack variable s satisfies one of the following conditions: Judged to be unfixed.
・ Fixed setting is -1 and λx <λs
・ Fixed setting is 1 and λx> λs

According to the present embodiment, an optimal solution can be obtained when a control variable in which the value of the control variable x in the optimal solution is not the upper limit value or the lower limit value of the variable is mistakenly set in the calculation process. By canceling the fixed setting, the optimal solution can be obtained even if the determination of the fixed setting is wrong.

Embodiment 3 FIG.
In the present embodiment, the fixed variable is released by means different from that of the second embodiment.

The secondary planning problem calculation apparatus according to the present embodiment includes the problem storage unit 101, the initialization unit 102, the variable storage unit 103, the mismatch amount calculation unit 104, the correction amount calculation unit 105, and the fixed variable setting unit according to the first embodiment. In addition to the variable correction means 108 and the repetition means 112, the following fixing release means 113 is provided. When the value of 1 in the Lagrange multiplier group is equal to or greater than a predetermined value, the fixing release means 113 releases the corresponding control variable or the fixed flag of the slack variable of the control variable.

  FIG. 6 is an operation flowchart of the secondary planning problem calculation apparatus according to the present embodiment. The difference from the above embodiment is that the variable fixed setting releasing means (113) in step S14 is included. Details will be described below.

  In the quadratic programming problem optimizing apparatus of the first embodiment, the central processing unit 4 calculates the values of Δx and Δs without omitting the calculations related to the control variables x and slack variables s that are fixedly set, and stores the variables. When storing by the means, the fixed setting release determination is performed and the storage means stores in the fixed setting storage memory of the storage device, and when the fixed setting is changed by the release determination, the fixed setting change presence / absence is set to 1 by the storage means. There is provided variable fixation releasing means 2e for storing the fixed setting change presence / absence storage memory of the storage device.

The variable fixation releasing means 2e in the central processing unit 4 has one of the following values: fixed setting, correction amount and correction direction Δx of control variable x, correction amount of slack variable s and correction direction Δs stored in the storage device If the condition is satisfied, it is determined that the fixation is released.
・ Fixed setting is −1 and Δx> 0
・ Fixed setting is 1 and Δs> 0

  According to the present embodiment, even when a control variable that should not be fixed is erroneously set as fixed, the fixed setting can be canceled, and an optimal solution can be obtained even when the determination of the fixed setting is incorrect. become.

Embodiment 4 FIG.
The generator output value calculation apparatus can be configured using the secondary planning problem calculation apparatus of the above embodiment. The generator output value calculation device determines an output planned value that each of the generators should generate in order to minimize the total power generation cost of a plurality of generators connected to the power system. The present embodiment relates to such a generator output value calculation apparatus.

  FIG. 1 is a configuration diagram of a generator output value calculation apparatus. Although it is the same as the said Embodiment 1, although the internal specific process differs, the concept of each means is the same. The generator output value calculation apparatus includes a problem storage unit 101, an initialization unit 102, a mismatch amount calculation unit 104, a correction amount calculation unit 10, a fixed variable setting unit 107, a variable correction unit 108, and a repetition unit 112.

Specifically, the generator output value calculation device includes a constraint expression including a total power generation constraint indicating that the total sum of the generator outputs is the total power input, and the upper and lower limit constraints of the generator output of each generator. Problem storage means for storing quadratic programming problem information expressing a quadratic programming problem having a group, a Lagrange multiplier group for the constraint equation group, an initial value of a variable that is a slack variable of the generator output and the generator output And an initializing means for storing the initial value in the variable storage means, and a mismatch amount which is a deviation amount when the variable stored in the variable storage means is substituted for the optimality condition of the quadratic programming problem. A mismatch amount calculating means for calculating; a correction amount calculating means for obtaining a correction direction and a correction amount of the variable so that the mismatch amount decreases; the generator output having the correction amount equal to or less than a first threshold; Fixed variable setting means for setting a fixed flag in the variable storage means corresponding to a rack variable, and variable correction means for updating a numerical value of the variable storage means with the correction direction and correction amount for the variable not having the fixed flag And when the value of the mismatch amount obtained by the variable stored in the variable storage means is larger than a second threshold value, the correction amount calculation means, the fixed variable setting means and the variable correction means are repeated, and the mismatch When the value of the quantity is equal to or less than the second threshold value, there is provided a repeating means for determining the convergence and outputting the value of the generator output stored in the variable storage means.

  FIG. 2 is a hardware configuration diagram of the present embodiment. As in the first embodiment, each of the above means is realized by each device. FIG. 7 is another hardware configuration diagram of the present embodiment. Details will be described below.

  In the figure, an input device 6, a generator output formulation device 7, and an output device 8 are shown. The input device 6 includes input means. The output device 8 includes a result output means for outputting the value of the generator output as a calculation result.

  The generator output formulation device 7 realizes the following means as condition input means and storage means. Total generated power storage means for storing the total power to be generated by all the generators, power generation output upper and lower limit value storage means for storing the power generation output upper and lower limit values of each generator, and the power generation cost coefficient of each generator The total power generation cost f (x) created from the power generation cost coefficient storage means, the generator cost coefficient stored by the total power generation cost coefficient storage means, and the sum of the generator outputs are stored by the total power generation storage means. The problem of inputting a generator output determination problem consisting of the total generated power constraint h (x) indicating that the total generated power is generated and the generated output upper and lower limit values of each generator stored by the generated output upper and lower limit storage means The input means, the total power generation cost f (x) input by the problem input means, the total generated power restriction h (x), and the generator output upper and lower limit values (xmin, xmax) of each generator are stored. The total power generation cost f (x) and the total power generation constraint h (x) stored in the power problem storage means and the input problem storage means are set to the generator output upper and lower limit values (xmin, xmax) of each generator. And a problem storage means for storing the data converted based on the value of.

  Further, the generator output formulating device 7 includes the generator output x, the slack variable s of the generator output x, the Lagrange multiplier λx for the lower limit constraint of the generator output, the Lagrange multiplier λs for the lower limit constraint of the slack variable, the total generated power Variable storage means 103 is provided for storing each value of the Lagrange multiplier λh for the constraint. Here, the variable storage means 103 includes fixed setting storage means for storing a flag (fixed flag) indicating that the generator output x or the slack variable s is fixed.

  Further, the generator output formulation device 7 includes fixed setting change presence / absence storage means for storing whether or not the fixed setting storage means has been rewritten to a value different from the previously stored fixed setting value.

  Further, the generator output formulating device 7 generates a Lagrange multiplier for the total generation cost f (x), the total generation power constraint h (x), the generator output x, the slack variable s, and the lower limit constraint of the generator output x. λx, Lagrange multiplier λs for the lower limit constraint of the slack variable s, Lagrange multiplier λh for the total generated power constraint h (x), convergence parameter μ, the generator output and the fixed value of the slack variable Initializing means for storing the variable memory means of the main memory is provided.

  Further, the generator output formulation device 7 includes mismatch amount calculation means for calculating a mismatch amount e representing the amount of deviation from the KKT condition (the optimality condition for the quadratic programming problem).

  Further, the generator output formulation device 7 includes an optimization processing end determination unit that determines whether or not to end the processing of the optimization device.

  Further, the generator output formulation device 7 reduces the generator output x, slack variable s, Lagrange multiplier λx with respect to the lower limit constraint of the generator output x, slack of the generator output x so that the mismatch amount e decreases. Correction direction and correction amount calculating means for calculating a correction direction and a correction amount for each of the Lagrange multiplier λs for the lower limit constraint of the variable s and the Lagrange multiplier λh for the total generated power constraint h (x), and the correction direction and correction Based on the quantity, for the generator output x and slack variable s that are set to not fix the above fixed setting, determine whether to set the generator output x and slack variable s fixedly, The variable fixing setting unit stores the determination result by the variable fixing storage unit, and stores the change of the fixed setting by the fixed setting change presence / absence storage unit.

  Further, the generator output formulation device 7 generates the generator output x stored in the variable storage unit based on the correction direction and the correction amount and the fixed setting of the generator output stored in the variable fixed setting storage unit. Updating the Lagrange multiplier λx for the lower limit constraint of the slack variable s, the generator output x, the Lagrange multiplier λs for the lower limit constraint of the slack variable s, and the Lagrange multiplier λh for the total generated power constraint h (x), Variable correction means for storing each of the variable storage means is provided.

  Further, the generator output formulating device 7 includes a convergence parameter updating unit that updates the convergence parameter μ, and the generator output upper and lower limits of the generator output x stored in the input problem storage unit. End processing means for linearly converting the values according to the values (xmin, xmax) and storing them by the generator output storage means is provided.

  The condition input device inputs the output upper and lower limit values of each generator, the power generation cost coefficient of each generator, and the total generated power from a keyboard, a file, a network, etc. Stored by cost coefficient storage means and total generated power storage means.

Next, the total power generation cost f (x) can be calculated from the power generation cost coefficient of each generator stored by the power generation cost coefficient storage means as follows.
Power generation cost coefficient of generator i: a _i , b _i , c _i (14)
Power generation cost of generator i: a _i x _i ² + b _i x _i + c _i (15)

  Further, the total generated power constraint h (x) indicating that the total generated power stored by the total generated power storage means is the sum of the output of each generator can be expressed as follows.

  The total power generation cost, the total generated power constraint, and the upper and lower limit values of each generator output are stored by the input problem storage means, and the calculated value of each generator output x is stored by the generated power storage means.

  Next, with respect to the generator output x, the total power generation cost f (x), and the total power generation constraint h (x), the total power generation cost is set so that all generator outputs x satisfy 0 ≦ x ≦ 1. And the value of the constant of the total generated power constraint and the value of the constant term, all the values of the generator output x are 0.5, the Lagrange multiplier λx and the lower limit of the slack variable s for the lower limit constraint of the generator output x The value of the Lagrange multiplier λs for the constraint is 1.0, the value of the Lagrange multiplier λh for the total generated power constraint h (x) is stored as 0 by the variable storage means, and the fixed setting of the generator is set as 0. And the convergence parameter μ is set to 0.5. Here, in the initialization means, in order to simplify the subsequent calculation processing and the description thereof, the value of the coefficient of the total power generation cost and the coefficient of the total power generation constraint so that the generator output x satisfies 0 ≦ x ≦ 1. However, the present invention can be implemented without performing this operation.

  The linear transformation method is as follows.

  However,

Here, x _i is the generator output stored by the generated power storage means (101) of the external storage device 2, and x ′ _i is the power generation stored by the variable storage means (103) of the main storage device 3. Output.

  Here, it is not necessary to consider the constant term in the linear conversion of the total power generation cost.

  The mismatch amount calculation means 104 first introduces a barrier function that takes a large value when the generator output x and its slack variable s approach the lower limit value in the total power generation cost f (x). It can be expressed as follows.

Here, log x _i and log s _i are barrier functions. The KKT conditions for the above problem are as follows.

  Next, as shown in Equation 21, a deviation amount e from the KKT condition is calculated.

The optimization process end determination means determines that the process ends when the fixed setting change presence / absence, mismatch amount e, and convergence parameter μ stored by the fixed setting change presence / absence storage means satisfy the following conditions, and executes the end processing means: Terminate the iteration process. Further, if any one of the following conditions is not satisfied, the processing is continued.
・ No change in fixed setting ・ All values of mismatch amount e are sufficiently close to 0 ・ The value of convergence parameter μ is sufficiently close to 0

  The correction direction and correction amount calculation means calculates x, s, λh, λx, and λs so as to reduce the mismatch amount e by performing linear approximation on each current value. The correction direction and the correction amount are obtained as follows. However, although the correction direction and the correction amount are calculated by performing linear approximation at the current position of each variable here, the correction direction and the correction amount may be calculated by another method.

Here, using the relational expressions of the following expressions 24, 25, and 26, it is possible to omit e ₃ and e ₄ from the above expressions, and the above expressions can be converted into expressions 27.

  Δx and Δλh are obtained according to Equation 27. Here, since the coefficient matrix is a symmetric matrix, the linear equation of Expression 27 can be solved by triangulating the coefficient matrix using the modified Cholesky method and performing forward substitution and backward substitution. Further, using the values of Δx and Δλh, the values of Δs, Δλx, and Δλs are calculated according to Equation 24, Equation 25, and Equation 26. Here, although the modified Cholesky method, forward substitution, and backward substitution are used for solving the linear equations, the linear equations may be solved by other methods.

The variable fixing setting means 107 includes the generator output x stored in the variable storage means 103, the slack variable s, and the correction direction and correction amount Δx of the generator output x stored in the correction direction and correction amount storage means, slack. When each value of the correction direction and the correction amount Δs of the variable s satisfies (x + Δx) <Lx ₁ or (s + Δs) <Ls ₁ , it is determined that the fixed setting is performed, and (x + Δx) <Lx ₁ In this case, the fixed setting is set to −1, and if (s + Δs) <Ls ₁ , the fixed setting is set to 1 and stored by the fixed setting storage means of the storage device. At this time, with respect to all the fixed settings stored by the fixed setting storage means, the fixed setting change presence / absence is set to 0 if none has been changed, and 1 if any change has been made. Store by storage means.

When the value of the fixed setting stored by the fixed setting storage unit is −1, the variable correction unit sets the value of the corresponding slack variable s to Ls ₂ and stores the value by the variable storage unit. When the fixed setting value stored by the fixed setting storage means is 1, the value of the corresponding generator output x is set to Lx ₂ and stored by the variable storage means. When the fixed setting value stored by the fixed setting storage means is 0, the corresponding generator output x, the corresponding slack variable s, the Lagrange multiplier λx for all the generator outputs x, and all the slack variables The values of x, s, λx, λs, and λh stored by the variable storage unit are updated in accordance with the following expression and stored by the variable storage unit 103 for the Lagrange multiplier λs and the Lagrange multiplier λh for all the total generated power constraints. .

  The end processing means linearly sets the value of the generator output x stored in the variable storage means 103 based on the upper and lower limit values of the generator output stored in the generated power upper and lower limit value storage means as shown in the following Expression 29. The converted result is stored in the generator output storage means. However, in the case where the generator output x is processed without linear conversion in the initialization means, there is no need to perform linear conversion work here, and the value of the generator output x stored by the variable storage means is directly generated. It is stored by the machine output storage means.

  Here, x is a generator output value stored by the variable storage means 103 of the main storage device 3, and x 'is a generator output value stored by the generator output storage means of the external storage device 2. .

  The result output means outputs the output power of each generator stored in the generated power storage means to a display, file, printer, network or the like.

  FIG. 9 is a block configuration diagram of the generator output value calculation apparatus according to the present embodiment. The processing order of the generator output value calculation apparatus of this Embodiment is demonstrated with reference to the flowchart shown in FIG. 9 and FIG. In the figure, step S31 shows processing of the condition input means and corresponds to the input means of FIG. Step S32 shows the processing of the problem input means and corresponds to the input means of FIG. Step S33 shows the processing of the initialization means 102. Steps S34 to S39 show an iterative optimization calculation processing part (112) for obtaining a generator output that satisfies the KKT condition. Further, in step S34, the mismatch amount calculation means 104 is shown. In step S35, the process of the optimization process end determination means is shown. If it is determined that the process is to be continued, the process proceeds to step S36. If it is determined that the process is to be ended, the process proceeds to step S40.

  In step S36, the process of the correction direction and correction amount calculation means 105 is shown. Step S37 shows the process of the variable fixing setting means 107. In step S38, the process of the variable correction means 108 is shown. In step S39, the process of the convergence parameter update unit is shown. Step S40 shows the process of the end processing means. In step S41, a result output means is shown. In this way, the generator output with the minimum power generation cost can be obtained by the above repetitive calculation.

  According to the present embodiment, it is possible to stably obtain a generator output at which the sum of the input total generated power and the output power of all the generators is equal and the power generation cost is minimized, By creating a power generation plan and a fuel procurement plan based on the information, it is possible to operate the power system more economically.

Embodiment 5 FIG.
In the generator output value calculation apparatus described in the fourth embodiment, the fixed variable can be released as follows.

  The generator output value calculation apparatus according to the present embodiment includes the problem storage unit 101, the initialization unit 102, the variable storage unit 103, the mismatch amount calculation unit 104, the correction amount calculation unit 105, and the fixed variable setting unit according to the fourth embodiment. In addition to the variable correction means 108 and the repetition means 112, the following fixing release means 113 is provided. The fixing release means 113 releases the fixing flag of the generator output when the correction direction and the correction amount of the generator output having the fixing flag indicate a direction away from the lower limit constraint of the control variable. It is.

  FIG. 11 is an operation flowchart of the generator output value calculation apparatus according to the present embodiment. In the figure, the difference from the fifth embodiment is that the variable fixed setting releasing means 113 in step S46 is entered. Details will be described below.

  In the generator output value formulation device, the central processing unit 4 determines whether to cancel the fixed setting when the generator output x and the slack variable s are fixedly set, and stores them in the variable fixed setting storage means, and also cancels the release. Variable fixing release means for storing the fixed setting change presence / absence as 1 when the fixed setting is changed by the determination is stored by the fixed setting change presence / absence storage means.

The variable fixing release means 113 determines that the fixed release is made when the value of the Lagrange multiplier λx for the lower limit constraint of the fixed setting, the generator output x, and the Lagrange multiplier λs for the lower limit constraint of the slack variable s satisfy any of the following conditions: .
・ Fixed setting is -1 and λx <λs
・ Fixed setting is 1 and λx> λs

  According to the present embodiment, the calculation ends when a generator output whose most economical generator output value is not the upper limit value or lower limit value of the generator output is mistakenly fixed in the calculation process. By canceling the fixed setting for the problem of disappearance, even if the determination of the fixed setting is wrong, the process can be terminated normally.

Embodiment 6 FIG.
In the present embodiment, the fixed variable is released by means different from that of the fifth embodiment.

  The generator output value formulation device of the present embodiment includes the problem storage unit 101, the initialization unit 102, the variable storage unit 103, the mismatch amount calculation unit 104, the correction amount calculation unit 105, and the fixed variable setting unit of the fourth embodiment. In addition to the variable correction means 108 and the repetition means 112, the following fixing release means 113 is provided. When the value of 1 in the Lagrange multiplier group is greater than or equal to a predetermined value, the fixing release means 113 releases the corresponding generator output or the fixed flag of the slack variable of the generator output.

  FIG. 11 is an operation flowchart of the generator output value calculation apparatus according to the present embodiment. In the figure, the difference from the fifth embodiment is that the variable fixed setting releasing means 113 in step S46 is entered. Details will be described below.

  In the generator output value calculation device, when the values of Δx and Δs are calculated without omitting the calculation related to the generator output x and slack variable s that are fixedly set, the fixed setting release determination is performed by the fixed variable setting storage means. A variable fixing release unit is provided that stores the fixed setting change presence / absence as 1 when the fixed setting is changed by the release determination and stores the fixed setting change presence / absence as 1.

The variable fixing release means determines that the fixed release occurs when the fixed setting, the correction amount and correction direction Δx of the generator output x, and the correction amount and correction direction Δs of the slack variable s satisfy any of the following conditions: .
・ Fixed setting is −1 and Δx> 0
・ Fixed setting is 1 and Δs> 0

  According to the present embodiment, the calculation ends when a generator output whose most economical generator output value is not the upper limit value or lower limit value of the generator output is mistakenly fixed in the calculation process. By canceling the fixed setting for the problem of disappearance, even if the determination of the fixed setting is wrong, the process can be terminated normally.

Embodiment 7 FIG.
A tidal current calculation device can be configured using the secondary planning problem calculation device of the first embodiment. The tidal current calculation device determines each generator output plan value that minimizes the total power generation cost when generating necessary power while satisfying the tidal current constraints in a plurality of generators and transmission lines connected to the power system. is there. The present embodiment relates to such a tidal current calculation device.

  FIG. 1 is a configuration diagram of a tidal current calculation apparatus. Although it is the same as the said Embodiment 1, although the internal specific process differs, the concept of each means is the same. The generator output value calculation apparatus includes a problem storage unit 101, an initialization unit 102, a mismatch amount calculation unit 104, a correction amount calculation unit 10, a fixed variable setting unit 107, a variable correction unit 108, and a repetition unit 112.

Specifically, the power flow calculation device includes a power flow equation for each power generator, a power load, a voltage, an electric energy, a reactance for each power transmission line, and a power flow equation to be satisfied by a bus phase angle for each power generator. Problem storage means 101 for storing secondary planning problem information expressing a secondary programming problem having a constraint equation group including upper and lower limit constraint equations for output, the generator output, slack variables of the generator output, and the constraint equation Variable storage means 103 for storing the value of a variable that is a Lagrange multiplier group for the above, initialization means 102 for obtaining the initial value of the variable and storing the initial value in the variable storage means, and storage in the variable storage means A mismatch amount calculation means 104 for calculating a mismatch amount that is a deviation amount when the variable is substituted into the optimality condition of the quadratic programming problem;
Correction amount calculation means 105 for obtaining the correction direction and correction amount of the variable so that the mismatch amount decreases, and the variable storage means corresponding to the generator output and slack variable whose correction amount is equal to or less than a first threshold. Fixed variable setting means 107 that sets a fixed flag, variable correction means 108 that updates the numerical value of the variable storage means according to the correction direction and the correction amount for the variable that does not have the fixed flag, and stored in the variable storage means If the value of the mismatch amount obtained by the calculated variable is larger than a second threshold value, the correction amount calculation means, the fixed variable setting means, and the variable correction means are repeated, and the mismatch amount value is set to the second threshold value. In the following cases, it is provided with repeating means 112 that determines that the output has converged and outputs the value of the generator output stored in the variable storage means.

  FIG. 2 is a hardware configuration diagram of the present embodiment. As in the first embodiment, each of the above means is realized by each device. FIG. 12 is another hardware configuration diagram of the present embodiment. Details will be described below.

  In the figure, an input device 9, an optimum power flow calculation device 10, and an output device 11 are shown. The input device 9 includes input means. The output device 11 includes a result output unit that outputs a value of the generator output as a calculation result.

  The optimum power flow calculation device 10 determines each generator output plan value that minimizes the total power generation cost when generating necessary power while satisfying the power flow constraints in a plurality of power generators and transmission lines connected to the power system. .

  The electric power system which is the object of the present embodiment, each bus voltage is equal to the voltage phase angle of the corresponding bus, the resistance value between each bus is equal to the reactance value between the corresponding buses, and the current injected into each bus Is approximated by a DC network equal to the active power supplied to or consumed by the corresponding bus.

  The optimum power flow calculation device 10 includes condition input means, total power load storage means for storing all power loads, power generation output upper and lower limit value storage means for storing the power generation output upper and lower limit values of each generator, Phase angle storage means for storing the bus phase angle, power generation cost coefficient storage means for storing the power generation cost coefficient of each generator, resistance value storage means for storing the resistance value of each power transmission line, and reactance of each power transmission line Reactance storage means for storing, and rated capacity storage means for storing the rated capacity of each power transmission line.

  Further, the total power generation cost f (x) created from the generator cost coefficient stored by the total power generation cost coefficient storage means, the generator output, the total power load, the generator output, the reactance, and the phase angle are satisfied. The power flow equation, the phase angle, the reactance, the total constraint h (x) that summarizes the rated capacity constraints to be satisfied by the rated capacity, and the power generation output of each generator stored by the power generation output upper and lower limit value storage means Problem input means for inputting a generator output determination problem consisting of upper and lower limit values, the total power generation cost f (x) input by the problem input means, the total constraint h (x), and the generator output of each generator Input problem storage means for storing upper and lower limit values (xmin, xmax) is provided.

  Further, the total power generation cost f (x) and the total constraint h (x) stored by the input problem storage means are based on the generator output upper and lower limit values (xmin, xmax) of each generator. Problem storage means for storing the converted data is provided.

  Further, the generator output x, the slack variable s of the generator output x, the Lagrange multiplier λx for the lower limit constraint of the generator output, the Lagrange multiplier λs for the lower limit constraint of the slack variable, and the Lagrange multiplier λh for all constraints Variable storage means for storing is provided.

  Further, there is provided a fixed setting storing means for storing a flag indicating that the generator output x or the slack variable s is fixed. The fixed setting storage means stores fixed setting change presence / absence storage means for storing whether or not the value has been rewritten to a value different from the previously stored fixed setting value.

  Further, the total power generation cost f (x), the total constraint h (x), the generator output x, the slack variable s, the Lagrange multiplier λx for the lower limit constraint of the generator output x, and the lower limit constraint for the slack variable s. The Lagrangian multiplier λs, the Lagrange multiplier λh for all the constraints h (x), the convergence parameter μ, the generator output and the fixed setting of the slack variable thereof are determined and stored by the variable storage means 103 of the main storage device 3. Initialization means is provided.

  In addition, a mismatch amount calculation means for calculating a mismatch amount e representing the amount of deviation from the KKT condition is provided.

  In addition, an optimization process end determination unit that determines whether to end the process of the optimization apparatus is provided. Further, the Lagrange multiplier λx for the lower limit constraint of the generator output x, the slack variable s, the lower limit constraint of the generator output x, and the Lagrange multiplier for the lower limit constraint of the slack variable s of the generator output x so that the mismatch amount e is reduced. A correction direction and correction amount calculating means for calculating a correction direction and a correction amount for each of λs and a Lagrange multiplier λh for all the constraints h (x) is provided.

  Further, based on the correction direction and the correction amount, it is determined whether or not the generator output x and the slack variable s are fixedly set for the generator output x and the slack variable s that are set not to be fixed. When the fixed setting is performed, the determination result is stored in the variable fixed storage unit and the variable fixed setting unit stores the change in the fixed setting by the fixed setting change presence / absence storage unit.

  Further, the generator output x, the slack variable s, the power generation stored in the variable storage means based on the correction direction and the correction amount and the fixed setting of the generator output stored in the variable fixation setting storage means. A variable modification in which the Lagrange multiplier λx for the lower limit constraint of the machine output x, the Lagrange multiplier λs for the lower limit constraint of the slack variable s, and the Lagrange multiplier λh for the entire constraint h (x) are updated and stored by the variable storage means, respectively. Means.

  Further, a convergence parameter updating means for updating the convergence parameter μ is provided. Also, a termination process for linearly converting the value of the generator output x in accordance with the generator output upper and lower limit values (xmin, xmax) of each generator stored by the input problem storage means and storing the value by the generator output storage means. Means.

  The condition input device inputs the output upper and lower limit values of each generator, the power generation cost coefficient of each generator, and the total power load from the keyboard, file, network, etc. The data is stored by the storage means and the total power load storage means.

The total power generation cost f (x) can be calculated as follows from the power generation cost coefficient of each generator stored by the power generation cost coefficient storage means.
Power generation cost coefficient of generator i: a _i , b _i , c _i (30)
Power generation cost of generator i: a _i x _i ² + b _i x _i + c _i (31)

The power flow equation to be satisfied by the generator output (x ^P ), the total power load (L), the reactance (X), and the phase angle (x ^θ ) can be expressed as follows.

  The rated capacity constraint to be satisfied by the phase angle, the reactance, and the rated capacity can be expressed as follows.

  The total power generation cost, all the constraints, and the upper and lower limit values of each generator output are stored by the input problem storage means, and the calculated values of each generator output x are stored by the generated power storage means.

  For the generator output x, the total power generation cost f (x) and the total constraint h (x), the coefficient of the total power generation cost and the total constraint so that all the generator outputs x satisfy 0 ≦ x ≦ 1. And the values of the generator output x are all 0.5, the Lagrange multiplier λx for the lower limit constraint of the generator output x, and the Lagrange multiplier λs for the lower limit constraint of the slack variable s Is stored in the variable storage means as 1.0, the value of the Lagrange multiplier λh for all the constraints h (x) is set to 0, the fixed setting of the generator is set as 0 and stored in the variable fixed setting storage means, and the convergence parameter μ is set to 0. .5. Here, in order to simplify the subsequent calculation process and its explanation, the value of the coefficient of the total power generation cost and the coefficient of all constraints are changed so that the generator output x satisfies 0 ≦ x ≦ 1 in the initialization means. However, the present invention can be implemented without performing this operation.

  The linear transformation method is as follows.

  However,

Here, x _i is the generator output stored by the generated power storage means (101) of the external storage device 2, and x ′ _i is the power generation stored by the variable storage means (103) of the main storage device 3. Output.

  Here, it is not necessary to consider the constant term in the linear conversion of the total power generation cost.

  The mismatch amount calculation means 104 first introduces a barrier function that takes a large value when the generator output x and its slack variable s approach the lower limit value in the total power generation cost f (x). It can be expressed as follows.

Here, log x _i and log s _i are barrier functions. The KKT conditions for the above problem are as follows.

  Next, as shown in Expression 38, a deviation amount e from the KKT condition is calculated.

The optimization process end determination means determines that the process ends when the fixed setting change presence / absence, mismatch amount e, and convergence parameter μ stored by the fixed setting change presence / absence storage means satisfy the following conditions, and executes the end processing means: Terminate the iteration process. Further, if any one of the following conditions is not satisfied, the processing is continued.
・ No change in fixed setting ・ All values of mismatch amount e are sufficiently close to 0 ・ The value of convergence parameter μ is sufficiently close to 0

  The correction direction and correction amount calculation means calculates x, s, λh, λx, and λs so as to reduce the mismatch amount e by performing linear approximation on each current value. The correction direction and the correction amount are obtained as follows. However, although the correction direction and the correction amount are calculated by performing linear approximation at the current position of each variable here, the correction direction and the correction amount may be calculated by another method.

Here, it becomes possible to omit e ₃ and e ₄ from the above formula using the relational formulas of the following formulas 40, 41, and 42, and the above formula can be converted into formula 43.

  Δx and Δλh are obtained according to Equation 43. Here, since the coefficient matrix is a symmetric matrix, the linear equation of Expression 43 can be solved by triangulating the coefficient matrix using the modified Cholesky method and performing forward substitution and backward substitution. Further, using the values of Δx and Δλh, the values of Δs, Δλx, and Δλs are calculated according to the formulas a, b, and c. Here, although the modified Cholesky method, forward substitution, and backward substitution are used for solving the linear equations, the linear equations may be solved by other methods.

The variable fixing setting means includes the generator output x, slack variable s stored by the variable storage means, and the correction direction and correction amount Δx of the generator output x stored by the correction direction and correction amount storage means, slack variable. When each value of the correction direction and correction amount Δs of s satisfies (x + Δx) <Lx ₁ or (s + Δs) <Ls ₁ , it is determined that the fixed setting is made, and fixed setting is made when (x + Δx) <Lx ₁ Is set to −1, and (s + Δs) <Ls ₁ , the fixed setting is set to 1 and is stored by the fixed setting storage means of the storage device. At this time, with respect to all the fixed settings stored by the fixed setting storage means, the fixed setting change presence / absence is set to 0 if none has been changed, and 1 if any change has been made. Store by storage means.

When the fixed setting value stored by the fixed setting storage means is −1, the variable correction means 108 sets the value of the corresponding slack variable s to Ls ₂ and stores it by the variable storage means. When the fixed setting value stored by the fixed setting storage means is 1, the value of the corresponding generator output x is set to Lx ₂ and stored by the variable storage means. Further, when the fixed setting value stored by the fixed setting storage means is 0, the corresponding generator output x, the corresponding slack variable s, the Lagrange multiplier λx for all the generator outputs x, and all the slack variables The values of x, s, λx, λs, and λh stored by the variable storage unit are updated in accordance with the following equation for the Lagrange multiplier λs and the Lagrange multiplier λh for all the above-described constraints, and stored by the variable storage unit.

  The termination processing means linearly changes the value of the generator output x stored by the variable storage means based on the upper and lower limit values of the generator output stored by the generated power upper and lower limit value storage means as shown in the following Expression 45. The converted result is stored in the generator output storage means. However, in the case where the generator output x is processed without linear conversion in the initialization means, there is no need to perform linear conversion work here, and the value of the generator output x stored by the variable storage means is directly generated. It is stored by the machine output storage means.

  Here, x is a generator output value stored by the variable storage means 103 of the main storage device 3, and x 'is a generator output value stored by the generator output storage means of the external storage device 2. .

  The result output means outputs the output power of each generator stored in the generated power storage means to a display, file, printer, network or the like.

  FIG. 14 is a block configuration diagram of the tidal current calculation apparatus according to the present embodiment. The processing sequence of the power flow calculation apparatus according to the present embodiment will be described with reference to FIG. 14 and the flowchart shown in FIG. In the figure, step S31 shows processing of the condition input means, and is included in the input means of FIG. Step S32 shows the processing of the problem input means and is included in the input means of FIG. Step S33 shows the processing of the initialization means 102. Steps S34 to S39 show an iterative optimization calculation processing part (112) for obtaining a generator output that satisfies the KKT condition. Further, in step S34, the mismatch amount calculation means 104 is shown. In step S35, the process of the optimization process end determination means is shown. If it is determined that the process is to be continued, the process proceeds to step S36. If it is determined that the process is to be ended, the process proceeds to step S40.

  In step S36, the process of the correction direction and correction amount calculation means 105 is shown. Step S37 shows the process of the variable fixing setting means 107. In step S38, the process of the variable correction means 108 is shown. In step S39, the process of the convergence parameter update unit is shown. Step S40 shows the process of the end processing means. In step S41, a result output means is shown. In this way, an optimal generator output can be obtained by the above-described repetitive calculation.

  In the present embodiment, the power transmission line is a model of only resistance and reactance, but expansion such as considering the capacitance to ground of each power transmission line is also possible. Similarly, expansion such as considering power loss is also possible.

  According to the present embodiment, the generator output that satisfies the tidal current restrictions, the total sum of the input total generated power and the output power of all the generators is equal, the restrictions on the rated capacity of each transmission line are observed, and the power generation cost is minimized. Can be obtained stably, and by creating a power generation plan, a fuel procurement plan, etc. based on the information, a more economical power system can be operated.

  In this embodiment, an apparatus for determining the output of each generator for the purpose of economic load distribution is shown, but the present invention is an apparatus for determining an unknown variable that optimizes the evaluation function so as to satisfy the conditions of the power system. Applicable.

Embodiment 8 FIG.
In the tidal current calculation apparatus described in the seventh embodiment, the fixed variables can be released as follows.

  The tidal current calculation apparatus according to the present embodiment includes the problem storage unit 101, the initialization unit 102, the variable storage unit 103, the mismatch amount calculation unit 104, the correction amount calculation unit 105, the fixed variable setting unit 107, the variable of the seventh embodiment. In addition to the correcting means 108 and the repeating means 112, the following fixing release means 113 is provided. When the correction direction and the correction amount of the generator output having the fixed flag indicate a direction away from the lower limit constraint of the generator output, the fixing release unit 113 releases the fixed flag of the generator output. Is. Details will be described below.

  In the optimum power flow calculation device, when the generator output x and slack variable s are fixedly set, the central processing unit 4 performs release determination of the fixed setting and stores it by the variable fixed setting storage means. Variable fixing release means for storing the fixed setting change presence / absence as 1 when the fixed setting is changed is stored by the fixed setting change presence / absence storage means.

The variable fixing release means determines that the fixed release occurs when the value of the Lagrange multiplier λx for the lower limit constraint of the fixed setting, the generator output x, and the Lagrange multiplier λs for the lower limit constraint of the slack variable s satisfy any of the following conditions: .
・ Fixed setting is -1 and λx <λs
・ Fixed setting is 1 and λx> λs

  According to the present embodiment, the calculation ends when a generator output whose most economical generator output value is not the upper limit value or lower limit value of the generator output is mistakenly fixed in the calculation process. By canceling the fixed setting for the problem of disappearance, even if the determination of the fixed setting is wrong, the process can be terminated normally.

  In this embodiment, an apparatus for determining the output of each generator for the purpose of economic load distribution is shown, but the present invention is an apparatus for determining an unknown variable that optimizes the evaluation function so as to satisfy the conditions of the power system. Applicable.

Embodiment 9 FIG.
In the present embodiment, the fixed variable is released by means different from that of the eighth embodiment.

  The tidal current calculation apparatus according to the present embodiment includes the problem storage unit 101, the initialization unit 102, the variable storage unit 103, the mismatch amount calculation unit 104, the correction amount calculation unit 105, the fixed variable setting unit 107, the variable of the seventh embodiment. In addition to the correcting means 108 and the repeating means 112, the following fixing release means 113 is provided. When the value of 1 in the Lagrange multiplier group is greater than or equal to a predetermined value, the fixing release means 113 releases the corresponding generator output or the fixed flag of the slack variable of the generator output. Details will be described below.

  In the power flow calculation device, when the central processing unit 4 calculates the values of Δx and Δs without omitting the calculation related to the generator output x and slack variable s that are fixedly set, the fixed processing is performed by determining whether to cancel the fixed setting. In addition to storing by the storage unit, a variable fixed release unit that stores the fixed setting change presence / absence as 1 when the fixed setting is changed by the release determination is stored.

The variable fixing release means 113 determines that the fixed release is made when the fixed setting, the correction amount and correction direction Δx of the generator output x, and the correction amount and correction direction Δs of the slack variable s satisfy any of the following conditions: To do.
・ Fixed setting is −1 and Δx> 0
・ Fixed setting is 1 and Δs> 0

  According to the present embodiment, the calculation ends when a generator output whose most economical generator output value is not the upper limit value or lower limit value of the generator output is mistakenly fixed in the calculation process. By canceling the fixed setting for the problem of disappearance, even if the determination of the fixed setting is wrong, the process can be terminated normally.

  In this embodiment, an apparatus for determining the output of each generator for the purpose of economic load distribution is shown, but the present invention is an apparatus for determining an unknown variable that optimizes the evaluation function so as to satisfy the conditions of the power system. Applicable.

Embodiment 10 FIG.
The portfolio optimization apparatus can be configured using the secondary planning problem calculation apparatus of the first embodiment. The portfolio optimizing device formulates an investment ratio for the purpose of minimizing risk while expecting a certain gain when investing in an asset including uncertainty. The present embodiment relates to such a portfolio optimization device.

  FIG. 1 is a configuration diagram of a portfolio optimization device. Although it is the same as the said Embodiment 1, although the internal specific process differs, the concept of each means is the same. The generator output value calculation apparatus includes a problem storage unit 101, an initialization unit 102, a mismatch amount calculation unit 104, a correction amount calculation unit 10, a fixed variable setting unit 107, a variable correction unit 108, and a repetition unit 112.

Specifically, the portfolio optimization device includes a constraint equation indicating that a sum of investment ratios for each asset is a constant value, an equation constraint equation indicating that the expected return value of each asset is an expected rate of return, or Problem storage means 101 for storing secondary planning problem information expressing a secondary programming problem having a constraint expression group including a constraint expression group including an inequality constraint expression and a constraint expression representing the upper and lower limits of the investment ratio, and a Lagrange multiplier for the constraint expression group A group, the investment ratio and an initial value of a variable which is a slack variable of the investment ratio, an initializing means 102 for storing the initial value in the variable storage means 103, and a variable stored in the variable storage means as the 2 A mismatch amount calculation means 104 for calculating a mismatch amount which is a deviation amount when substituted for the optimality condition of the next programming problem, and a method of correcting the variable so that the mismatch amount is reduced A and correction calculation means 105 for obtaining the correction amount, a fixed variable setting means 107 for setting a fixed flag to the variable storage unit in which the correction amount corresponding to the slack variable of the investment ratio or the investment ratio below the first threshold value The variable correction means 108 for updating the numerical value of the variable storage means with the correction direction and the correction amount for the variable that does not have the fixed flag, and the mismatch amount obtained by the variable stored in the variable storage means. When the value is larger than the second threshold value, the correction amount calculation means, the fixed variable setting means and the variable correction means are repeated, and when the mismatch amount value is less than or equal to the second threshold value, it is determined that the value is converged. And repetition means 112 for outputting the value of the investment ratio stored in the variable storage means.

  FIG. 2 is a hardware configuration diagram of the present embodiment. As in the first embodiment, each of the above means is realized by each device. FIG. 15 is another hardware configuration diagram of the present embodiment. FIG. 16 is an explanatory diagram of means realized by each hardware device of the portfolio optimization device according to the present embodiment. Details will be described below.

  In the figure, an input device 12, a portfolio optimization device 13, and an output device 14 are shown. The input device 12 includes input means. The output device 11 includes result output means for outputting the value of the investment ratio of the calculation result.

  The portfolio optimizing apparatus has condition input means and the following means. The portfolio optimization device includes an investment ratio storage means for storing the investment ratio of each asset, an investment ratio upper and lower limit storage means for storing the upper and lower limit values of each asset, and an expected value of the return of each asset. Expected value storage means for storing, distributed storage means for storing the variance of the return rate of each asset, and expected return rate storage means for storing the expected return rate to be secured.

  Further, the portfolio optimizing device is configured to obtain the total asset return ratio f (x) created from the variance of each asset return stored by the distributed storage means storage means, and the return of each asset stored by the expected value storage means. Constraint that indicates that the expected value is the same as the expected rate of return stored by the expected rate of return storage unit, and that the sum of the investment ratios stored by the investment rate storage unit is a constant value And a problem input means for inputting a portfolio optimization problem consisting of all constraints h (x) including and the investment ratio upper and lower limit values of each asset stored by the investment ratio storage means.

  Further, the portfolio optimization apparatus stores the total asset return ratio f (x), the total constraint h (x), and the investment ratio upper and lower limit values (xmin, xmax) input by the problem input unit. Input problem storage means is provided.

  Further, the portfolio optimizing device uses the investment ratio upper and lower limit values (xmin, xmax) as the total asset return ratio f (x) and the total constraint h (x) stored by the input problem storage means. Problem storage means for storing the data converted based on the above.

  In addition, the portfolio optimization device includes the investment ratio x, the slack variable s of the investment ratio x, the Lagrange multiplier λx for the lower limit constraint of the investment ratio, the Lagrange multiplier λs for the lower limit constraint of the slack variable, and the Lagrange multiplier λh for all constraints. Variable storage means 103 is stored.

  In addition, the portfolio optimizing apparatus includes a fixed setting storage unit that stores a flag indicating that the investment ratio x or the slack variable s is fixed. Further, a fixed setting change presence / absence storage means for storing whether or not the fixed setting storage means has been rewritten to a value different from the previously stored fixed setting value is also provided.

  In addition, the portfolio optimization apparatus includes the return on total assets f (x), the total constraint h (x), the investment ratio x, the slack variable s, the Lagrange multiplier λx for the lower limit constraint of the investment ratio x, the slack Lagrangian multiplier λs for the lower limit constraint of variable s, Lagrange multiplier λh for all constraints h (x), convergence parameter μ, the investment ratio, and fixed setting of the slack variable, and the variable storage of the main memory Initialization means for storing by means.

  Further, the portfolio optimizing device includes a mismatch amount calculating means for calculating a mismatch amount e representing the amount of deviation from the KKT condition.

  The portfolio optimizing device further includes an optimization processing end determination unit that determines whether or not to end the processing of the optimizing device.

  Further, the portfolio optimization device reduces the investment ratio x, the slack variable s, the Lagrange multiplier λx to the lower limit constraint of the investment ratio x, and the lower limit constraint of the slack variable s of the investment ratio x so that the mismatch amount e decreases. Correction direction and correction amount calculating means for calculating a correction direction and a correction amount for each of the Lagrange multiplier λs with respect to and the Lagrange multiplier λh with respect to all the constraints h (x).

  In addition, the portfolio optimization device sets the investment ratio x and the slack variable s fixedly for the investment ratio x and the slack variable s that are not set to be fixed based on the correction direction and the correction amount. If the fixed setting is determined, the variable fixing storage unit stores the determination result by the variable fixing storage unit, and stores the change of the fixed setting by the fixed setting change presence / absence storage unit.

  Further, the portfolio optimizing device is configured to determine the investment ratio x, the slack variable stored by the variable storage unit based on the fixed direction and the correction amount and the fixed setting of the investment ratio stored by the variable fixed setting storage unit. s, Lagrange multiplier λx for the lower limit constraint of the investment ratio x, Lagrange multiplier λs for the lower limit constraint of the slack variable s, and Lagrange multiplier λh for the entire constraint h (x), respectively, and stored by the variable storage means Variable correcting means is provided.

  Further, the portfolio optimizing device includes a convergence parameter updating unit that updates the convergence parameter μ.

  The portfolio optimizing device linearly converts the value of the investment ratio x according to the investment ratio upper and lower limit values (xmin, xmax) of each generator stored by the input problem storage means, and stores it by the investment ratio storage means. And a termination processing means.

  The condition input device inputs the upper and lower limits of the investment ratio of each asset, the expected return value of each asset, the return ratio of each asset, and the expected return to be secured from the keyboard, file, network, etc. The data is stored by upper / lower limit value storage means, expected value storage means, distributed storage means, and expected rate of return storage means. Here, the rate of return, its expected value, and variance are not clearly understood, but are assumed here.

The total asset return ratio variance can be calculated as follows from the revenue variance of each asset stored by the variance storage means.
Dispersion of asset i: σ _i (46)
Variance when investing in asset i and asset j: σ _ij (47)
The total asset return can be calculated by the following equation 48.

  A rate of return securing constraint indicating that the expected return value of each asset stored by the expected value storage unit is the same as the expected return rate stored by the expected return rate storage unit, and stored by the investment ratio storage unit The constraint indicating that the sum of the investment ratios is a constant value can be expressed as follows. That is, the entire constraint h (x) is expressed by the following expression 49.

  Here, b represents the expected rate of return.

  The total asset return ratio, all the constraints, and the upper and lower limits of the investment ratio are stored by the input problem storage means, and the calculated value of the investment ratio x of each resource is stored by the investment ratio storage means.

  Coefficient of total asset return and all constraints so that all investment ratios x satisfy 0 ≦ x ≦ 1 for the above investment ratio x, total asset revenue variance f (x) and all constraints h (x) And the value of the investment ratio x are all 0.5, the value of the Lagrange multiplier λx for the lower limit constraint of the investment ratio x and the value of the Lagrange multiplier λs for the lower limit constraint of the slack variable s is 1.0. , The value of the Lagrangian multiplier λh for all the constraints h (x) is stored by the variable storage means as 0, the fixed setting of the asset is stored as 0 by the variable fixed setting storage means, and the convergence parameter μ is 0.5. To do. Here, in the initialization means, in order to simplify the subsequent calculation process and the description thereof, the value of the coefficient of total asset return and the coefficient of all restrictions are changed so that the investment ratio x satisfies 0 ≦ x ≦ 1. However, the present invention can be implemented without performing this operation.

  The linear transformation method is as follows.

  However,

Here, x _i is an investment ratio stored by the investment ratio storage means of the external storage device 2, and x ′ _i is an investment ratio stored by the variable storage means (103) of the main storage device 3.

  Here, it is not necessary to consider a constant term in the linear transformation of the total asset return.

  The mismatch amount calculation means 104 first introduces a barrier function that takes a large value when the investment ratio x and its slack variable s approach the lower limit value in the total asset return variance f (x). It can be expressed as follows.

Here, log x _i and log s _i are barrier functions. The KKT conditions for the above problem are as follows.

  Next, as shown in Expression 54, a deviation amount e from the KKT condition is calculated.

The optimization process end determination means determines that the process ends when the fixed setting change presence / absence, mismatch amount e, and convergence parameter μ stored by the fixed setting change presence / absence storage means satisfy the following conditions, and executes the end processing means: Terminate the iteration process. Further, if any one of the following conditions is not satisfied, the processing is continued.
・ No change in fixed setting ・ All values of mismatch amount e are close enough to 0 ・ The value of convergence parameter μ is close enough to 0

  The correction direction and correction amount calculation means calculates x, s, λh, λx, and λs so as to reduce the mismatch amount e by performing linear approximation on each current value. The correction direction and the correction amount are obtained as follows. However, although the correction direction and the correction amount are calculated by performing linear approximation at the current position of each variable here, the correction direction and the correction amount may be calculated by another method.

Here, using the relational expressions of the following expressions 56, 57, and 58, e ₃ and e ₄ can be omitted from the above expressions, and the above expressions can be converted into expressions 59.

  Δx and Δλh are obtained according to Equation 59. Here, since the coefficient matrix is a symmetric matrix, the linear equation of Equation 59 can be solved by triangulating the coefficient matrix using the modified Cholesky method and performing forward substitution and backward substitution. Also, using the values of Δx and Δλh, the values of Δs, Δλx, and Δλs are calculated according to Equation 56, Equation 57, and Equation 58. Here, the modified Cholesky method, forward substitution, and backward substitution are used for solving the linear equation, but the linear equation may be solved by other methods.

The variable fixed setting means includes the investment ratio x, slack variable s stored by the variable storage means, and the correction direction and correction amount Δx of the investment ratio x stored by the correction direction and correction amount storage means, and the slack variable s. When the values of the correction direction and the correction amount Δs satisfy (x + Δx) <Lx ₁ or (s + Δs) <Ls ₁ , it is determined that the fixed setting is made. Further, when (x + Δx) <Lx ₁ , the fixed setting is set to −1, and when (s + Δs) <Ls ₁ , the fixed setting is set to 1 and is stored by the fixed setting storage unit of the storage device. At this time, with respect to all the fixed settings stored by the fixed setting storage means, the fixed setting change presence / absence is set to 0 if none has been changed, and 1 if any change has been made. Store by storage means.

When the fixed setting value stored by the fixed setting storage means is −1, the variable correction means 108 sets the value of the corresponding slack variable s to Ls ₂ and stores it by the variable storage means. When the fixed setting value stored by the fixed setting storage means is 1, the value of the corresponding investment ratio x is set to Lx ₂ and stored by the variable storage means. If the fixed setting value stored by the fixed setting storage means is 0, the corresponding investment ratio x, the corresponding slack variable s, the Lagrange multiplier λx for all the investment ratios x, and the Lagrange multiplier for all the slack variables The values of x, s, λx, λs, and λh stored by the variable storage unit are updated according to the following expression for the Lagrange multiplier λh for λs and all the above constraints, and stored by the variable storage unit.

  The termination processing means linearly transforms the value of the investment ratio x stored by the variable storage means as shown in Equation 61 based on the upper and lower limit values of the investment ratio stored by the generated power upper and lower limit value storage means. Stored by the investment ratio storage means. However, when the initialization means processes the investment ratio x without performing linear conversion, it is not necessary to perform linear conversion work here, and the value of the investment ratio x stored by the variable storage means is stored as it is. It will be memorized by means.

  Here, x is an investment ratio value stored by the variable storage means 103 of the main storage device 3, and x ′ is an investment ratio value stored by the investment ratio storage means of the external storage device 2.

  The result output means outputs the investment ratio stored in the investment ratio storage means to a display, file, printer, network or the like.

  FIG. 17 shows a block configuration diagram of the portfolio optimizing apparatus of the present embodiment. The processing order of the portfolio optimizing device according to the present embodiment will be described with reference to FIG. 17 and the flowchart shown in FIG. In the flowchart shown in the figure, step S31 indicates processing of the condition input means, and is included in the input means of FIG. Step S32 shows the process of the problem input means and is included in the input means of FIG. Step S33 shows the process 102 of the initialization means. Steps S34 to S39 show an iterative optimization calculation processing part (112) for obtaining an investment ratio that satisfies the KKT condition. In step S34, the process 104 of the mismatch amount calculation means is shown. Further, in step S35, the process of the optimization process end determination means (optimization process end determination in FIG. 17) is shown. If it is determined that the process is to be continued, the process proceeds to step S36. Proceed to

  In step S36, the process of the correction direction and correction amount calculation means 105 is shown. Step S37 shows the process of the variable fixing setting means 107. In step S38, the process of the variable correction means 108 is shown. In step S39, the process of the convergence parameter update unit is shown. Step S40 shows the process of the end processing means. In step S41, a result output means is shown. In this way, an optimal profit ratio can be obtained by the above-described repetitive calculation.

  According to the present embodiment, it becomes possible to stably obtain an investment ratio that minimizes the variance of the return while ensuring the expected return, and creating an investment plan based on the information, etc. By avoiding risk, etc., more efficient risk management becomes possible.

Embodiment 11 FIG.
In the portfolio optimizing device described in the tenth embodiment, the fixed variables can be released as follows.

  The portfolio optimization apparatus according to the present embodiment includes a problem storage unit 101, an initialization unit 102, a variable storage unit 103, a mismatch amount calculation unit 104, a correction amount calculation unit 105, a fixed variable setting unit 107, In addition to the variable correction means 108 and the repetition means 112, the following fixing release means 113 is provided. The fixed release means 113 releases the fixed flag of the investment ratio when the correction direction and the correction amount of the investment ratio having the fixed flag indicate a direction away from the lower limit constraint of the investment ratio. .

  FIG. 11 is an operation flowchart of the portfolio optimizing apparatus according to the present embodiment. In the figure, the difference from the tenth embodiment is that the variable fixed setting releasing means 113 in step S46 is entered. Details will be described below.

  In the portfolio optimizing device of the present embodiment, the central processing unit 4 determines whether to cancel the fixed setting when the investment ratio x and the slack variable s are fixedly set, and stores them by the variable fixed setting storage unit. Variable fixing cancellation means for storing the fixed setting change presence / absence as 1 when the fixed setting is changed by the release determination is stored by the fixed setting change presence / absence storage means.

The variable fixing release means determines that the fixed release is made when the values of the Lagrange multiplier λx for the fixed setting, the lower limit constraint of the investment ratio x, and the Lagrange multiplier λs for the lower limit constraint of the slack variable s satisfy one of the following conditions.
・ Fixed setting is -1 and λx <λs
・ Fixed setting is 1 and λx> λs

  According to the present embodiment, the problem that the calculation does not end when an asset whose investment ratio that reduces the risk most is not the upper limit value or the lower limit value of the investment ratio is mistakenly set in the calculation process, By canceling the fixed setting, even if the determination of the fixed setting is wrong, the process can be normally terminated.

Embodiment 12 FIG.
In the present embodiment, the fixed variable is released by means different from that of the eleventh embodiment.

  The portfolio optimization apparatus according to the present embodiment includes a problem storage unit 101, an initialization unit 102, a variable storage unit 103, a mismatch amount calculation unit 104, a correction amount calculation unit 105, a fixed variable setting unit 107, In addition to the variable correction means 108 and the repetition means 112, the following fixing release means 113 is provided. When the value of 1 in the Lagrange multiplier group is equal to or greater than a predetermined value, the fixed release unit 113 releases the corresponding investment ratio or the fixed flag of the slack variable of the investment ratio.

  FIG. 11 is an operation flowchart of the portfolio optimizing apparatus according to the present embodiment. In the figure, the difference from the tenth embodiment is that the variable fixed setting releasing means 113 in step S46 is entered. Details will be described below.

  In the portfolio optimizing device according to the present embodiment, the central processing means 4 determines whether to cancel the fixed setting when calculating the values of Δx and Δs without omitting the calculation regarding the fixed investment ratio x and slack variable s. Variable fixing setting storage means, and when the fixed setting is changed by the release determination, variable fixing release means for storing the fixed setting change presence / absence as 1 is stored.

The variable fixation release means determines that the fixed release is made when the fixed setting, the correction amount and the correction direction Δx of the investment ratio x, and the correction amount and the correction direction Δs of the slack variable s satisfy any of the following conditions.
・ Fixed setting is −1 and Δx> 0
・ Fixed setting is 1 and Δs> 0

  According to the present embodiment, the problem that the calculation does not end when an asset whose investment ratio that reduces the risk most is not the upper limit value or the lower limit value of the investment ratio is mistakenly set in the calculation process, By canceling the fixed setting, even if the determination of the fixed setting is wrong, the process can be normally terminated.

It is a block diagram of the secondary planning problem calculation apparatus of Embodiment 1 of this invention. It is a hardware block diagram of the secondary planning problem calculation apparatus of Embodiment 1 of this invention. It is explanatory drawing of the means implement | achieved by each apparatus of the hardware of the secondary planning problem calculation apparatus of Embodiment 1 of this invention. It is a block block diagram of the secondary planning problem calculation apparatus of Embodiment 1 of this invention. It is an operation | movement flowchart of Embodiment 1 of this invention. It is an operation | movement flowchart of the optimization apparatus of Embodiment 2 and 3 of this invention. It is a block diagram of the generator output formulation apparatus of Embodiment 4 of this invention. It is a block diagram of each apparatus which comprises the generator output formulation apparatus of Embodiment 4 of this invention. It is a block block diagram of the generator output formulation apparatus of Embodiment 4 of this invention. It is an operation | movement flowchart of the generator output formulation apparatus of Embodiment 4 of this invention. It is an operation | movement flowchart of the generator output formulation apparatus of Embodiment 4 of this invention. It is a block diagram of the tidal current calculation apparatus of Embodiment 7 of this invention. It is a block diagram of each apparatus which comprises the tidal current calculation apparatus of Embodiment 7 of this invention. It is a block block diagram of the tidal current calculation apparatus of Embodiment 7 of this invention. It is a block diagram of the portfolio optimization apparatus of Embodiment 10 of this invention. It is a block diagram of each apparatus which comprises the portfolio optimization apparatus of Embodiment 10 of this invention. It is a block block diagram of the portfolio optimization apparatus of Embodiment 10 of this invention.

Explanation of symbols

  1 input device, 2 external storage device (HDD), 3 main storage device, 4 central processing unit (CPU), 5 output device, 6 input device, 7 generator output formulating device, 8 output device, 9 input device, 10 optimal Power flow calculation device, 11 output device, 12 input device, 13 portfolio optimization device, 14 output device, 101 problem storage means, 102 initialization means, 103 variable storage means, 104 mismatch amount calculation means, 105 correction amount calculation means, 107 Fixed variable setting means, 108 variable correction means, 112 repetition means, 113 fixed variable release means.

Claims (7)

Problem storage means for storing quadratic programming problem information expressing a quadratic programming problem having a constraint equation group including a constraint equation of an upper limit constraint or a lower limit constraint of a control variable;
Initialization means for obtaining an initial value of a variable which is a Lagrange multiplier group of the control variable and the constraint equation group and storing the initial value in a variable storage means;
A mismatch amount calculating means for calculating a mismatch amount that is a deviation amount when the variable stored in the variable storage means is substituted into the optimality condition of the quadratic programming problem;
A correction amount calculating means for determining a correction direction and a correction amount of the variable so that the mismatch amount decreases;
Fixed variable setting means for setting a fixed flag in the variable storage means corresponding to the control variable or the slack variable of the control variable whose correction amount is a first threshold value or less;
Variable correction means for updating the value of the variable storage means according to the correction direction and the correction amount for the variable not having the fixed flag;
If the value of the mismatch amount obtained from the variable stored in the variable storage means is greater than a second threshold value, the correction amount calculation means, the fixed variable setting means, and the variable correction means are repeated, and the mismatch amount A secondary planning problem calculation device comprising: a repeating means for determining that the value of the control variable is converged and outputting the value of the control variable stored in the variable storage means. 2. A fixing release means for releasing the fixed flag of the control variable when the correction direction and the correction amount of the control variable having the fixed flag indicate a direction away from the lower limit constraint. The two-dimensional linear programming problem calculation apparatus described. The fixed release means for releasing a fixed flag of a corresponding control variable or a slack variable of the control variable when a value of 1 in a Lagrange multiplier group is equal to or greater than a predetermined value. Two-dimensional linear programming problem calculator. Problem storage means for storing quadratic programming problem information expressing a quadratic programming problem having a constraint equation group including a constraint equation of an upper limit constraint or a lower limit constraint of a control variable;
Initialization means for obtaining an initial value of a variable which is a Lagrange multiplier group of the control variable and the constraint equation group and storing the initial value in a variable storage means;
A mismatch amount calculating means for calculating a mismatch amount that is a deviation amount when the variable stored in the variable storage means is substituted into the optimality condition of the quadratic programming problem;
A correction amount calculating means for determining a correction direction and a correction amount of the variable so that the mismatch amount decreases;
Fixed variable setting means for setting a fixed flag in the variable storage means corresponding to the control variable or the slack variable of the control variable whose correction amount is a first threshold value or less;
Variable correction means for updating the value of the variable storage means according to the correction direction and the correction amount for the variable not having the fixed flag;
If the value of the mismatch amount obtained from the variable stored in the variable storage means is greater than a second threshold value, the correction amount calculation means, the fixed variable setting means, and the variable correction means are repeated, and the mismatch amount If the value of is less than or equal to the second threshold value, a program for a two-dimensional linear programming problem calculation apparatus that causes a computer to function as a repetition unit that determines convergence and outputs the value of the control variable stored in the variable storage unit . A quadratic program representing a quadratic programming problem having a total power generation constraint indicating that the sum of the generator outputs is the input total generated power and a constraint equation group including upper and lower limit constraints of the generator output of each generator. Problem storage means for storing problem information;
Initializing means for obtaining an initial value of a variable which is a slack variable of a Lagrange multiplier group for the constraint equation group, the generator output and the generator output, and storing the initial value in a variable storage means; and the variable storage means A mismatch amount calculation means for calculating a mismatch amount which is a deviation amount when the stored variable is substituted into the optimality condition of the quadratic programming problem;
A correction amount calculating means for determining a correction direction and a correction amount of the variable so that the mismatch amount decreases;
Fixed variable setting means for setting a fixed flag in the variable storage means corresponding to the generator output and the slack variable whose correction amount is equal to or less than a first threshold;
Variable correction means for updating the numerical value of the variable storage means according to the correction direction and the correction amount for the variable not having the fixed flag;
When the value of the mismatch amount obtained by the variable stored in the variable storage means is larger than a second threshold value, the correction amount calculation means, the fixed variable setting means, and the variable correction means are repeated, and the mismatch amount A generator output value formulation device comprising: a repeating unit that determines that the value is equal to or less than a second threshold value and outputs the value of the generator output stored in the variable storage unit. Constraint equation including generator output for each generator, power load, voltage, electric energy, reactance for each transmission line, power flow equation to be satisfied by bus phase angle for each generator, and upper and lower limit constraint equations for the generator output Problem storage means for storing secondary planning problem information expressing a secondary planning problem having a group;
Variable storage means for storing the generator output, slack variables of the generator output, values of variables that are Lagrange multipliers for the constraint equation;
Initialization means for obtaining an initial value of the variable and storing the initial value in the variable storage means;
A mismatch amount calculating means for calculating a mismatch amount that is a deviation amount when the variable stored in the variable storage means is substituted into the optimality condition of the quadratic programming problem;
A correction amount calculating means for determining a correction direction and a correction amount of the variable so that the mismatch amount decreases;
Fixed variable setting means for setting a fixed flag in the variable storage means corresponding to the generator output and the slack variable whose correction amount is equal to or less than a first threshold;
Variable correction means for updating the numerical value of the variable storage means according to the correction direction and the correction amount for the variable not having the fixed flag;
If the value of the mismatch amount obtained from the variable stored in the variable storage means is greater than a second threshold value, the correction amount calculation means, the fixed variable setting means, and the variable correction means are repeated, and the mismatch amount A tidal current calculation device comprising: a repeating unit that determines that the value is equal to or less than a second threshold value and outputs the value of the generator output stored in the variable storage unit. Constraint expression indicating that the sum of the investment ratios for each asset is a constant value, equality constraint expression or inequality constraint expression indicating that the expected return of each asset is the expected return, and upper and lower limits of the investment ratio Problem storage means for storing secondary programming problem information expressing a secondary programming problem having a constraint equation group including a constraint equation representing
An initializing means for obtaining an initial value of a variable that is a Lagrange multiplier group for the constraint formula group, the investment ratio and a slack variable of the investment ratio, and storing the initial value in a variable storage means;
A mismatch amount calculating means for calculating a mismatch amount that is a deviation amount when the variable stored in the variable storage means is substituted into the optimality condition of the quadratic programming problem;
A correction amount calculating means for determining a correction direction and a correction amount of the variable so that the mismatch amount decreases;
Fixed variable setting means for setting a fixed flag in the variable storage means corresponding to the investment ratio or the slack variable of the investment ratio with the correction amount equal to or less than a first threshold;
Variable correction means for updating the numerical value of the variable storage means according to the correction direction and the correction amount for the variable not having the fixed flag;
If the value of the mismatch amount obtained from the variable stored in the variable storage means is greater than a second threshold value, the correction amount calculation means, the fixed variable setting means, and the variable correction means are repeated, and the mismatch amount A portfolio optimizing apparatus comprising: a repeating unit that determines that the value is equal to or less than a second threshold value and outputs the value of the investment ratio stored in the variable storage unit.

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