Cost function generation device, processing device, cost function generation method, and cost function generation program

Abstract

This cost function generation device comprises: a parameter information acquisition unit that acquires parameter information including N (an integer of 1 or more) as a parameter; and a function generation unit that generates, on the basis of the parameter information, a cost function used for calculating a generator start / stop schedule of a plurality of generators over a plurality of consecutive time frames by quadratic unconstrained binary optimization and including a plurality of binary variables. The cost function includes a power generation amount for each time frame and for each generator. The plurality of binary variables include N first binary variables for each time frame and for each generator. The power generation amount is expressed using any of 2 to the Nth power patterns of the N first binary variables.

Description

Cost function generation device, processing device, cost function generation method, and cost function generation program CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application is based on U.S. Provisional Patent Application No. 63 / 589832 filed on October 12, 2023 and Japanese Patent Application No. 2024-70246 filed on April 24, 2024, the contents of which are incorporated herein by reference.

[0002] The present disclosure relates to a cost function generation device, a processing device, a cost function generation method, and a cost function generation program.

[0003] The unit commitment problem (UCP) is a model for optimizing generators in a power grid. The UCP is sometimes formulated as a quadratic unconstrained binary optimization (QUBO) (see, for example, Non-Patent Document 1).

[0004] Akshay Sukumar Ajagekar, "QUANTUM COMPUTING FOR PROCESS SYSTEMS OPTIMIZATION AND DATA ANALYTICS," A Thesis [Retrieved October 2, 2023], Internet <URL: https: / / hdl.handle.net / 1813 / 70302> F. Glover, G. Kochenberger, Y. Du, A Tutorial on Formulating and Using QUBO Models, arXiv e-prints (2018) [Retrieved October 6, 2023], Internet <URL: https: / / arxiv.org / abs / 1811.11538>

[0005] In the method described in Non-Patent Document 1, the amount of power generated by a generator is expressed using one of N+1 patterns using N+1 binary variables. This requires many binary variables and increases the calculation cost, which is undesirable. Therefore, an object of the present disclosure is to provide a cost function generation device, a processing device, a cost function generation method, and a cost function generation program that are capable of expressing the amount of power generated using a small number of binary variables.

[0006] A cost function generation device according to one aspect of the present invention comprises a parameter information acquisition unit that acquires parameter information including N (an integer greater than or equal to 1) as a parameter, and a function generation unit that generates a cost function including a plurality of binary variables based on the parameter information, the cost function being a cost function for calculating a generator start-up / shutdown schedule for a plurality of generators over a plurality of consecutive time frames by quadratic unconstrained binary optimization, wherein the cost function includes the amount of power generation for each of the time frames and for each of the generators, the plurality of binary variables including N first binary variables for each of the time frames and for each of the generators, and the amount of power generation is expressed using one of 2 to the power of N patterns using the N first binary variables.

[0007] In this way, by using a configuration in which 2^N powers of power generation are represented by N first binary variables, the power generation amounts can be represented by a small number of binary variables.

[0008] In the above aspect, the parameter information includes H and U as the parameters, and the plurality of binary variables are a i t,t as a second binary variable, and the cost function includes the following equation (1) as a first constraint term: H and U are the time frame and the number of generators, respectively; t and i are the indexes of the time frame and the generator, respectively; a i t,t indicates one of the on and off states of the generator with index i in the time frame with index t, k is an index, and z ik tmay be the first binary variable.

[0009] According to this aspect, the second binary variable a i t,t When indicates ON, (1-a i t,t ) becomes zero, so Σ k=1 N z ik t On the other hand, the second binary variable a i t,t When indicates OFF, (1-a i t,t ) is 1, so Σ k=1 N z ik t is reflected in the cost function. Therefore, in the optimization process, Σ k=1 N z ik t can be optimized so that it is close to zero. This allows the first binary variable z ik t and a second binary variable a i t,t can be obtained.

[0010] In the above aspect, the parameter information is H, U, L t , P max,i and P min,i as the parameters, and the plurality of binary variables include a i t,t as a second binary variable, and the cost function includes the following equation (2) as a second constraint term: H and U are the time frame and the number of generators, respectively; t and i are the indexes of the time frame and the generator, respectively; a i t,t indicates one of the on and off states of the generator with index i in the time frame with index t, k is an index, and z ik t is the first binary variable, and L tis the power demand in the time frame of index t, and P max,i and P min,i may be the maximum and minimum power generation of the generator with index i, respectively.

[0011] According to this aspect, in each time frame, the total amount of power generated by the plurality of generators and the power demand L t The first binary variable z ik t This allows optimizing the first binary variable z ik t and a second binary variable a i t,t can be obtained.

[0012] In the above aspect, the parameter information is H, U, L t , P max,i , R t and F as the parameters, and the plurality of binary variables are i t,t and ψ k t as second and third binary variables, respectively, and the cost function includes the following equation (3) as a third constraint term: H and U are the time frame and the number of generators, respectively; t and i are the indexes of the time frame and the generator, respectively; a i t,t indicates either the on or off state of the generator with index i in the time frame with index t, F is an integer equal to or greater than 1, k is an index, and L t is the power demand in the time frame of index t, and P max,i is the maximum power generation of the generator with index i, and R t may be the operating reserve in the time frame of index t.

[0013] Σ i=0 U-1 P max,i a it,t is Σ i=0 U-1 P max,i Therefore, in each time frame, Σ i=0 U-1 P max,i a i t,t L t +R t In this case, the third binary variable ψ becomes close to zero. k t Therefore, in the optimization process, the second binary variable a is adjusted so that Q3 is close to zero at each time frame. i t,t and a third binary variable ψ k t This allows optimizing the second binary variable a i t,t and a third binary variable ψ k t can be obtained.

[0014] In the above aspect, the parameter information is H, U, P max,i , P min,i , P up,i , P down,i and F as the parameters, and the plurality of binary variables include a i t,t and χ i,k t as second and fourth binary variables, respectively, and the cost function includes the following equation (4) as a fourth constraint term: H and U are the time frame and the number of generators, respectively; t and i are the indexes of the time frame and the generator, respectively; a i t,t indicates either the on or off state of the generator with index i in the time frame with index t, F is an integer equal to or greater than 1, k is an index, and z ik t is the first binary variable, and P max,i and P min,iare the maximum and minimum power generation amounts of the generator with index i, respectively, and P up,i and P down,i may be the power generation increase limit value and the power generation decrease limit value of the generator with index i, respectively.

[0015] The power generation increase limit P is calculated from the increase in the power generation amount of the generator with index i from the time frame with index t-1 to the time frame with index t. up,i It is preferable that the value obtained by subtracting P is equal to or less than zero. up,i +P down,i )・Σ k=1 F 2 -k χ i,k t is equal to or greater than zero (P up,i +P down,i ) is a positive real number equal to or less than . Therefore, in the optimization process, for each time frame and each generator, the power generation increase limit value P up,i The first binary variable z is set so that the value obtained by subtracting ik t , the second binary variable a i t,t and a fourth binary variable χ i,k t This allows optimizing the first binary variable z ik t , the second binary variable a i t,t and a fourth binary variable χ i,k t can be obtained.

[0016] In the above aspect, the parameter information is H, U, P max,i , P min,i , P up,i , P down,i and F as the parameters, and the plurality of binary variables are i t,t and φ i,k tas a second binary variable and a fifth binary variable, respectively, and the cost function includes the following equation (5) as a fifth constraint term: H and U are the time frame and the number of generators, respectively; t and i are the indexes of the time frame and the generator, respectively; a i t,t indicates either the on or off state of the generator with index i in the time frame with index t, F is an integer equal to or greater than 1, k is an index, and z ik t is the first binary variable, and P max,i and P min,i are the maximum and minimum power generation amounts of the generator with index i, respectively, and P up,i and P down,i may be the power generation increase limit value and the power generation decrease limit value of the generator with index i, respectively.

[0017] The power generation increase of the generator with index i from the time frame of index t-1 to the time frame of index t is subject to the power generation decrease limit value P down,i It is preferable that the value obtained by adding P up,i +P down,i )・Σ k=1 F 2 -k φ i,k t is equal to or greater than zero (P up,i +P down,i ) is a positive real number equal to or less than . Therefore, in the optimization process, for each time frame and each generator, the power generation decrease limit value P down,i The first binary variable z is calculated so that the value of ik t , the second binary variable a i t and a fifth binary variable φ i,k t This allows optimizing the first binary variable z ikt , the second binary variable a i t and a fifth binary variable φ i,k t can be obtained.

[0018] In the above aspect, the parameter information includes H, U, and T min,on,i , T on,i -1 and G as the parameters, and the plurality of binary variables are i t,t2 and η i,j t as a sixth binary variable and a seventh binary variable, respectively, and the cost function includes the following equation (6) as a sixth constraint term: H and U are the time frame and the number of generators, respectively; t and t2 are the indexes of the time frame; i is the index of the generator; and a i t,t2 indicates the product of the on or off state of the generator with index i in each of the time frames after the time frame with index t2 and before the time frame with index t, G is an integer equal to or greater than 1, j is an index, and T min,on,i is the minimum start-up time of the generator with index i, and T on,i -1 may be the continuous running period of the generator with index i in the time frame with index zero.

[0019] From the time frame with index t-1 to the time frame with index t, in order to satisfy the minimum start-up time constraint for the generator with index i, (a i t-1,t-1 -a i t,t ) (T on,i t-1 -T min,on,i ) is preferably an integer greater than or equal to zero. j=0 G-1 2 j η i,j tis an integer equal to or greater than zero. Therefore, in the optimization process, for each time frame and each generator, (a i t-1,t-1 -a i t,t ) (T on,i t-1 -T min,on,i ) is greater than or equal to zero. i t,t and η i,j t This allows optimizing the sixth binary variable a i t,t2 and the seventh binary variable η i,j t can be obtained.

[0020] In the above aspect, the cost function includes the following equation (7) as a seventh constraint term: t1 is the index of the time frame, i t1,t1 indicates either the on or off state of the generator with index i in the time frame with index t1, and a i t1-1,t2 indicates the product of the on or off state of the generator with index i in each of the time frames after the time frame with index t2 and before the time frame with index t1-1, and a i t1,t2 may denote the product of the on or off states of the generator with index i in each of the time frames after the time frame with index t2 and before the time frame with index t1.

[0021] According to this aspect, a i t1,t2 ≠ a i t1,t1 ・a i t1-1,t2 In the case of [a i t1,t1 ・a i t1-1,t2 -2 (a i t1,t1 +a i t1-1,t2 ) a i t1,t2 +3ai t1,t2 ] gives 1 or 3, a i t1,t2 = a i t1,t1 ・a i t1-1,t2 In the case of [a i t1,t1 ・a i t1-1,t2 -2 (a i t1,t1 +a i t1-1,t2 ) a i t1,t2 +3a i t1,t2 ] gives zero. Therefore, in the optimization process, in each time frame and each generator, a i t1,t2 = a i t1,t1 ・a i t1-1,t2 A valid sixth binary variable a that satisfies i t1,t2 , a i t1,t1 and a i t1-1,t2 can be obtained.

[0022] In the above aspect, the parameter information is max,i and P min,i as the parameters, and the plurality of binary variables include a i t,t as a second binary variable, and the power generation amount is expressed by the following equation (8): t and i are the indexes of the time frame and the generator, respectively; i t,t indicates one of the on and off states of the generator with index i at the time frame with index t, k is an index, and z ik t is the first binary variable, and P max,i and P min,i may be the maximum and minimum power generation of the generator with index i, respectively.

[0023] According to this aspect, 2 N powers of power generation can be expressed by N first binary variables.

[0024] In the above aspect, the parameter information includes H, U, and T min,off,i , T off,i -1 and G as the parameters, and the plurality of binary variables are b i t,t2 and γ i,j t as eighth and ninth binary variables, respectively, and the cost function includes the following equation (9) as an eighth constraint term: H and U are the time frame and the number of generators, respectively; t and t2 are the indexes of the time frame; i is the index of the generator; b i t,t2 indicates the product of the on or off state of the generator with index i in each of the time frames after the time frame with index t2 and before the time frame with index t, G is an integer equal to or greater than 1, j is an index, and T min,off,i is the minimum stop time of the generator with index i, and T off,i -1 may be the continuous stop duration of the generator with index i in the time frame with index zero.

[0025] In order to satisfy the minimum outage time constraint for the generator with index i from the time frame with index t-1 to the time frame with index t, (b i t-1,t-1 -b i t,t ) (T off,i t-1 -T min,off,i ) is preferably an integer greater than or equal to zero. j=0 G-1 2 j gamma i,j t is an integer equal to or greater than zero. Therefore, in the optimization process, for each time frame and each generator, (b i t-1,t-1 -b it,t ) (T off,i t-1 -T min,off,i ) is greater than or equal to zero. i t,t and γ i,j t This allows optimizing the eighth binary variable b i t,t2 and the ninth binary variable γ i,j t can be obtained.

[0026] In the above aspect, the cost function includes the following equation (10) as a ninth constraint term: t1 is the index of the time frame, and b i t1,t1 indicates either the off or on state of the generator with index i in the time frame with index t1, and b i t1-1,t2 indicates the product of the off or on state of the generator with index i in each of the time frames after the time frame with index t2 and before the time frame with index t1-1, and b i t1,t2 may denote the product of the off or on states of the generator with index i in each of the time frames after the time frame with index t2 and before the time frame with index t1.

[0027] According to this aspect, b i t1,t2 ≠ b i t1,t1 ・b i t1-1,t2 In the case of [b i t1,t1 ・b i t1-1,t2 -2 (b i t1,t1 +b i t1-1,t2 ) b i t1,t2 +3b i t1,t2 ] gives 1 or 3, and b i t1,t2 = b i t1,t1・b i t1-1,t2 In the case of [b i t1,t1 ・b i t1-1,t2 -2 (b i t1,t1 +b i t1-1,t2 ) b i t1,t2 +3b i t1,t2 ] gives zero. Therefore, in the optimization process, in each time frame and each generator, b i t1,t2 = b i t1,t1 ・b i t1-1,t2 The eighth valid binary variable b i t1,t2 , b i t1,t1 and b i t1-1,t2 can be obtained.

[0028] In the above aspect, the plurality of binary variables are i t,t as a tenth binary variable, and the cost function includes the following equation (11) as a tenth constraint term: a i t,t indicates either the on or off state of the generator with index i in the time frame with index t, and b i t,t may indicate either the on or off state of the generator with index i in the time frame with index t.

[0029] According to this aspect, a i t,t and b i t,t When both are 1 or zero, [a i t,t +b i t,t -1] 2 gives 1, and a i t,t and b i t,tWhen one of the two is 1 and the other is zero, then [a i t,t +b i t,t -1] 2 Therefore, in the process of optimization, in each time frame and in each generator, a valid second binary variable a is a complementary logic variable, one of which is 1 and the other of which is 0. i t,t and the tenth binary variable b i t,t can be obtained.

[0030] A processing device according to another aspect of the present invention includes the cost function generation device described above, and a quantum computer unit that optimizes the plurality of binary variables so as to reduce a cost based on the cost function.

[0031] In this way, by using N first binary variables to represent 2^N powers of power generation, it is possible to represent the power generation amounts with fewer binary variables. Furthermore, by generating a cost function that represents the classical generation costs and constraints in UCP in a format suitable for optimization by a quantum computer unit and optimizing multiple binary variables by the quantum computer unit, it is possible to efficiently determine a generator start / stop schedule that satisfies the constraints and keeps costs down.

[0032] A cost function generation method according to another aspect of the present invention is a cost function generation method in a cost function generation device, comprising: acquiring parameter information including N (an integer greater than or equal to 1) as a parameter; and generating a cost function including a plurality of binary variables based on the parameter information, the cost function being for calculating a generator start-up / shutdown schedule for a plurality of generators over a plurality of consecutive time frames by quadratic unconstrained binary optimization, wherein the cost function includes the amount of power generation for each of the time frames and for each of the generators, the plurality of binary variables including N first binary variables for each of the time frames and for each of the generators, and the amount of power generation is expressed using one of 2 to the power of N patterns using the N first binary variables.

[0033] In this way, by using a configuration in which 2^N powers of power generation are represented by N first binary variables, the power generation amounts can be represented by a small number of binary variables.

[0034] A processing device according to another aspect of the present invention includes a quantum computer unit that optimizes the plurality of binary variables so as to reduce a cost based on the cost function generated by the above-described cost function generation method.

[0035] In this way, by using N first binary variables to represent 2^N powers of power generation, it is possible to represent the power generation amounts with fewer binary variables. Furthermore, by generating a cost function that represents the classical generation costs and constraints in UCP in a format suitable for optimization by a quantum computer unit and optimizing multiple binary variables by the quantum computer unit, it is possible to efficiently determine a generator start / stop schedule that satisfies the constraints and keeps costs down.

[0036] A cost function generation program according to another aspect of the present invention is a cost function generation program used in a cost function generation device, which causes a computer to function as: a parameter information acquisition unit that acquires parameter information including N (an integer greater than or equal to 1) as a parameter; and a function generation unit that generates a cost function including a plurality of binary variables based on the parameter information, the cost function being a cost function for calculating a generator start-up / shutdown schedule for a plurality of generators over a plurality of consecutive time frames by quadratic unconstrained binary optimization, wherein the cost function includes the amount of power generation for each of the time frames and for each of the generators, the plurality of binary variables including N first binary variables for each of the time frames and for each of the generators, and the amount of power generation is expressed using one of 2 to the power of N patterns using the N first binary variables.

[0037] In this way, by using a configuration in which 2^N powers of power generation are represented by N first binary variables, the power generation amounts can be represented by a small number of binary variables.

[0038] According to the present disclosure, it is possible to provide a cost function generation device, a processing device, a cost function generation method, and a cost function generation program that are capable of expressing the amount of power generation using a small number of binary variables.

[0039] It is a diagram for explaining a generator start-up / shutdown schedule according to an embodiment of the present disclosure. It is a diagram showing the configuration of a processing device according to an embodiment of the present disclosure. It is a flowchart defining an operation procedure when a processing device according to an embodiment of the present disclosure performs cost calculation processing.

[0040] DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS The present invention will be described with reference to the accompanying drawings, in which the same reference numerals denote the same or similar components.

[0041] 1 is a diagram for explaining a generator start-up / shutdown schedule according to an embodiment of the present disclosure. As shown in FIG. 1, the generator start-up / shutdown schedule is a schedule of power to be supplied by a plurality of generators over a plurality of consecutive time frames, i.e., a schedule of the amount of power generated by each generator for each time frame.

[0042] In FIG. 1, for example, a schedule from 1:00 to 10:00 is shown. The unit and number of time blocks are 1 hour and 10, respectively. The number of generators is 5. Note that the unit of time block may be shorter or longer than 1 hour. The number of time blocks may be 2 to 9 or 11 or more. The number of generators may be 2 to 4 or 6 or more.

[0043] 2 is a diagram illustrating a configuration of a processing device according to an embodiment of the present disclosure. As illustrated in FIG. 2, the processing device 101 includes a cost function generation device 11 and a quantum computer unit 41. The cost function generation device 11 includes a parameter information acquisition unit 31 and a function generation unit 32.

[0044] The parameter information acquisition unit 31 acquires parameter information. The parameter information is generated by, for example, an administrator who manages the generator start / stop schedule. The parameter information includes, for example, N, F, H, U, A i , B i , C i , L t , Rt , P max,i , P min,i , P up,i , P down,i , T min,on,i , T min,off,i , C start,i , C shut,i , T on,i -1 and T off,i -1 as a parameter.

[0045] N and F are, for example, integers equal to or greater than 1. H and U are the number of time frames and generators, respectively, and are, for example, integers equal to or greater than 1.

[0046] A i , B i and C i is a parameter for calculating the power generation cost of the power generator with index i, and is a real number equal to or greater than zero.

[0047] L t and R t are the power demand and the operating reserve at the time frame of index t, respectively, and are real numbers equal to or greater than zero.

[0048] P max,i and P min,i are the maximum and minimum power generation amounts of the generator with index i, respectively, and are real numbers equal to or greater than zero.

[0049] P up,i and P down,i are the power generation increase limit value and power generation decrease limit value of the generator with index i, respectively, and are real numbers equal to or greater than zero. min,on,i and T min,off,i are the minimum start-up time and minimum shutdown time of the generator with index i, respectively, and are integers equal to or greater than zero.

[0050] C start,i and C shut,i are the start-up cost and shutdown cost of the generator with index i, respectively, and are real numbers greater than or equal to zero.

[0051] T on,i -1 and T off,i -1are the continuous start-up period and continuous stop period of the generator with index i in the time frame with index zero, and are integers equal to or greater than zero.

[0052] The classical variables in UCP are p i t , T on,i t and d i t There is. i t is the power generation amount of the generator with index i in the time frame with index t, and is a real number greater than or equal to zero. on,i t is the continuous running period of the generator with index i in the time frame with index t, and is an integer equal to or greater than zero. i t represents either the on or off state of the generator with index i in the time frame with index t, and has a value of zero or one. In this embodiment, when the generator is on or off, d i t have a value of one or zero, respectively.

[0053] The classical production cost in UCP is, for example, Σ t=0 H-1 Σ i=0 U-1 {A i ・d i t +B i ・p i t +C i ・(p i t ) 2} is given by

[0054] The classical startup costs in UCP are, for example, Σ t=0 H-1 Σ i=0 U-1 C start,i ・d i t · (1-d i t-1 ) is given by

[0055] The classical shutdown cost in UCP is, for example, Σ t=0 H-1 Σ i=0 U-1 C shut,i · (1-d i t )・d i t-1 is given by

[0056] Classical constraints in UCP include, for example, upper and lower limit constraints on generator output, supply and demand balance constraints, operating reserve constraints, power generation increase constraints, power generation decrease constraints, minimum generator start-up time constraints, start-up time equations, minimum generator shutdown time constraints, and shutdown time equations.

[0057] The upper and lower limits of the generator output are, for example, P min,i ・d i t ≦p i t ≦P max,i ・d i t is given by

[0058] The supply and demand balance constraint is, for example, Σ i=0 U-1 ・p i t =L t The operating reserve constraint is given by, for example, Σ i=0 U-1 P max,i ・d i t ≧L t +R t is given by

[0059] The power generation increase constraint is, for example, p i t -p i t-1 ≦P up,i The power generation reduction constraint is given by, for example, -P down,i ≦p i t -p i t-1 is given by

[0060] The minimum start-up time constraint for the generator is (d i t-1 -d it ) (T on,i t-1 -T min,on,i ) ≧0. The activation time equation is, for example, T on,i t =T on,i t-1 ・d i t +d i t is given by

[0061] The minimum downtime constraint for the generator is (d i t -d i t-1 ) (T off,i t-1 -T min,off,i ) ≥ 0. The stopping time equation is, for example, T off,i t =T off,i t-1 · (1-d i t ) + (1-d i t ) is given by

[0062] The function generator 32 generates a cost function Cqubo including multiple binary variables based on the parameter information. The cost function Cqubo is a function for calculating a generator start / stop schedule for multiple generators over multiple consecutive time frames by quadratic unconstrained binary optimization. The cost function Cqubo is expressed, for example, by Equation (12).

[0063] where i is the index. Q and Q i is a variable. In particular, the variable Q is a cost term that represents the classical production cost, start-up cost, and shut-down cost in UCP by a binary variable.

[0064] Variable Q i is a constraint term that represents each classical constraint in UCP by a binary variable. i is a large positive number to penalize.

[0065] Specifically, the variable Q1 is a constraint term that represents the upper and lower limit constraints of the classical generator output in UCP using binary variables.

[0066] The variable Q2 is a constraint term that represents a classical supply-demand balance constraint in the UCP using a binary variable. The variable Q3 is a constraint term that represents a classical operating reserve constraint in the UCP using a binary variable.

[0067] The variables Q4 and Q5 are constraint terms that represent the classical power generation increase constraint and power generation decrease constraint in UCP by binary variables, respectively.

[0068] The variable Q6 is a function of the classical minimum wake-up time constraint and wake-up time equation in UCP, expressed as a sixth binary variable a i t,t2 and the seventh binary variable η i,j t The variable Q7 is a constraint term expressed by the sixth binary variable a i t,t2 is a constraint to ensure that the

[0069] The variable Q8 represents the classical minimum stopping time constraint and stopping time equation in UCP as an eighth binary variable b i t,t2 and the ninth binary variable γ i,j t The variable Q is the eighth binary variable b used for the variable Q. i t,t2 is a constraint to ensure that the

[0070] Variable Q 10 is the second binary variable a used for variable Q6 i t,t and the tenth binary variable b used for variable Q i t,t is a constraint to ensure that and are complementary logic variables.

[0071] (Variable Q0) The cost function Cqubo is the power generation amount p i t Specifically, the variable Q0 is expressed by equation (13).

[0072] where t and i are the time frame and generator indexes, respectively. The range of index t is tε[0, H−1]. The range of index i is iε[0, U−1].

[0073] The power generation amount p of generator i at time frame t i t is expressed by equation (8). ik t is a first binary variable. A binary variable represents either zero or one. k is an index. The range of index k is kε[1, N]. The precision of the power generation amount of generator i is determined by N.

[0074] a i t,t is a second binary variable that represents either the on or off state of the generator with index i (hereinafter sometimes referred to as generator i) in the time frame with index t (hereinafter sometimes referred to as time frame t). i t,t The relationship between the classical variables in UCP is a i t,t = d i t That is, when generator i is on or off in time frame t, a i t,t have a value of one or zero, respectively.

[0075] Power generation amount p i t is expressed using one of 2 N patterns. k=1 N 2 -k z ik t represents a positive decimal with an accuracy of 1 / Nth power of 2. i t (P max,i -P min,i ) multiplied by the decimal point.

[0076] The startup cost when generator i starts operation is C start,i ・ai t,t · (1-a i t-1,t-1 ) is expressed as start,i ・a i t,t · (1-a i t-1,t-1 ) is C when generator i is off at time frame t-1 and on at time frame t immediately after time frame t-1. start,i Give.

[0077] The shutdown cost when generator i stops operating is C shut,i · (1-a i t,t ) a i t-1,t-1 It is expressed as follows. shut,i · (1-a i t,t ) a i t-1,t-1 is C when generator i is on at time frame t-1 and off at time frame t immediately after time frame t-1. shut,i Give.

[0078] (Variable Q1) The cost function Cqubo is the second binary variable a of the first generator in the first time frame. i t,t indicates off, the N first binary variables z ik t The variable Q1 (an example of the "first constraint term") indicates the sum of

[0079] Specifically, the variable Q1 is expressed by the following equation (1): i t,t When indicates ON, (1-a i t,t ) becomes zero, so Σ k=1 N z ik t Regardless of the value, it is not reflected in the cost function Cqubo.

[0080] On the other hand, the second binary variable a i t,tWhen indicates OFF, (1-a i t,t ) is 1, so Σ k=1 N z ik t is reflected in the cost function Cqubo. Therefore, in the optimization process, Σ k=1 N z ik t is optimized to be close to zero. For example, Σ k=1 N z ik t When is zero, Σ k=1 N 2 -k z ik t is zero, so from equation (8), the power generation amount p of the generator i at time frame t is i t becomes zero.

[0081] (Variable Q2) The cost function Cqubo is the power generation amount p of multiple generators in the second time frame. i t The sum of the electricity demand in the second time frame L t The variable Q2 (an example of a "second constraint term") has a value according to the magnitude of the difference between

[0082] Specifically, the variable Q2 is expressed by the following equation (2): In this embodiment, the variable Q2 is the power generation amount p i t The sum of the electricity demand in the second time frame L t The square of the difference between

[0083] During the optimization process, the power generation amount p i t The total of the electricity demand L t The first binary variable z ik t and a second binary variable a i t,t is optimized.

[0084] (Variable Q3) The plurality of binary variables are a plurality of third binary variables ψ for representing positive real terms for each time frame. k t In particular, a plurality of third binary variables ψ k t are F third binary variables ψ for each time frame k t and expresses a first decimal number equal to or greater than zero using any of 2 F patterns. The first decimal number equal to or greater than zero can be expressed, for example, as follows: k=1 F 2 -k ψ k t and represents a positive decimal number with an accuracy of 1 / Fth power of 2.

[0085] The cost function Cqubo includes a variable Q3 (an example of a "third constraint term") whose value corresponds to the magnitude of the difference between the value obtained by subtracting the second sum from the first sum and the real term. Specifically, the variable Q3 is expressed by equation (3).

[0086] Here, the first sum is the sum of the second binary variable a i t,t The maximum power generation capacity P of the generator is on. max,i The sum of Σ i=0 U-1 P max,i a i t,t The second total is the power demand L in the third time frame. t and operating reserve R t The real term is the value obtained by subtracting the second sum from the third sum and multiplying the result by the first decimal point of the third time frame that is equal to or greater than zero. The third sum is the maximum power generation capacity P of the multiple generators. max,i The sum of Σ i=0 U-1 P max,i is.

[0087] In this embodiment, the variable Q3 reflects the square of the difference between the value obtained by subtracting the second total from the first total in the third time frame and the value obtained by multiplying the value obtained by subtracting the second total from the third total by a first decimal greater than or equal to zero.

[0088] The first sum, i.e., Σ i=0U-1 P max,i a i t,t is the third sum, i.e., Σ i=0 U-1 P max,i Therefore, when the first sum is equal to or greater than the second sum in each time frame, the difference approaches zero. k t Therefore, in the optimization process, the second binary variable a is adjusted so that the difference approaches zero at each time frame. i t,t and a third binary variable ψ k t is optimized.

[0089] (Variable Q4) A plurality of binary variables are provided, including a plurality of fourth binary variables χ for representing a second decimal point of zero or more for each time frame and each generator. i,k t In particular, a plurality of fourth binary variables χ i,k t is the F fourth binary variables χ for each time frame and each generator. i,k t and a second decimal number equal to or greater than zero is represented using one of 2 F patterns. The second decimal number equal to or greater than zero can be represented, for example, by Σ k=1 F 2 -k χ i,k t and represents a decimal number greater than or equal to zero with an accuracy of 1 in the Fth power of 2.

[0090] The cost function Cqubo is calculated by subtracting the power generation increase limit P from the fourth total. up,i The fourth constraint term includes a variable Q4 (an example of a "fourth constraint term") whose value corresponds to the magnitude of the sum of the value obtained by subtracting ∑ ∑ ∑ b ...

[0091] Here, the fourth total is the power generation amount of the second generator in the fourth time frame minus the power generation amount of the second generator in the time frame immediately before the fourth time frame, that is, (P max,i -P min,i ) {Σ k=1N 2 -k (z ik t -z ik t-1 )+P min,i (a i t,t -a i t-1,t-1 ) In other words, the fourth total is the increase in the amount of power generated by the second generator from the time frame immediately before the fourth time frame to the fourth time frame. The positive predetermined value is, for example, the power generation increase limit value P up,i and power generation reduction limit P down,i The sum of P up,i +P down,i is.

[0092] In this embodiment, the variable Q4 is the fourth total power generation increase limit value P up,i The value obtained by subtracting this and the power generation increase limit P up,i and power generation reduction limit P down,i The sum of is multiplied by the second decimal point greater than or equal to zero of the second generator in the fourth time frame, and the square of the sum of is reflected.

[0093] The power generation increase limit P is calculated from the increase in the power generation amount of the second generator from the time frame immediately before the fourth time frame to the fourth time frame. up,i It is preferable that the value obtained by subtracting P is equal to or less than zero. up,i +P down,i )・Σ k=1 F 2 -k χ i,k t is equal to or greater than zero (P up,i +P down,i ) is a positive real number equal to or less than 0. Therefore, in the optimization process, for each time frame and each generator, the power generation increase limit value P up,i The first binary variable z is set so that the value obtained by subtracting ik t , the second binary variable a i t,t and a fourth binary variable χ i,k t is optimized.

[0094] (Variable Q5) The plurality of binary variables are a plurality of fifth binary variables φ for representing a third decimal point of zero or more for each time frame and each generator. i,k t In particular, a plurality of fifth binary variables φ i,k t are F fifth binary variables φ for each time frame and each generator. i,k t and a third decimal number equal to or greater than zero is represented using one of 2 F patterns. A third decimal number equal to or greater than zero is, for example, Σ k=1 F 2 -k φ i,k t and represents a decimal number greater than or equal to zero with an accuracy of 1 in the Fth power of 2.

[0095] The cost function Cqubo is the fourth total power generation reduction limit value P down,i and the product of the third decimal point, which is equal to or greater than zero, of the second generator in the fourth time frame and a positive predetermined value. Specifically, the variable Q5 is expressed by equation (5). Here, the positive predetermined value is, for example, the power generation amount increase limit value P up,i and power generation reduction limit P down,i The sum of P up,i +P down,i is.

[0096] In this embodiment, the variable Q5 is the fourth total power generation reduction limit value P down,i The power generation increase limit P up,i and power generation reduction limit P down,i The sum of is multiplied by the third decimal point greater than or equal to zero of the second generator in the fourth time frame, and the square of the difference is reflected.

[0097] The increase in the amount of power generated by the second generator from the time frame immediately before the fourth time frame to the fourth time frame is subject to the power generation reduction limit P down,i It is preferable that the value obtained by adding P up,i +P down,i )・Σ k=1 F 2 -k φ i,kt is equal to or greater than zero (P up,i +P down,i ) is a positive real number equal to or less than 0. Therefore, in the optimization process, for each time frame and each generator, the power generation reduction limit value P down,i The first binary variable z is calculated so that the value of ik t , the second binary variable a i t,t and a fifth binary variable φ i,k t is optimized.

[0098] (Variable Q6) The plurality of binary variables are a plurality of sixth binary variables a for each end time frame, for each start time frame before the end time frame, and for each generator. i t1,t2 where t2≦t1. The sixth binary variable a i t1,t2 There are U H(H+1) / 2 second binary variables a i t1,t1 is the sixth binary variable a when t2=t1 i t1,t2 is.

[0099] Sixth binary variable a i t1,t2 represents the product of the on / off states of the generator in each time frame after the start time frame and before the end time frame. i t1,t2 is defined by equation (14) when the time frame index satisfies 0≦t2≦t1<H.

[0100] Further, the plurality of binary variables include a plurality of seventh binary variables η for representing first integers equal to or greater than zero for each time frame and each generator at the index t. i,j t In particular, a plurality of seventh binary variables η i,j t is the G seventh binary variables η for each time frame and each generator. i,j tand expresses a first integer greater than or equal to zero using any of 2 to the power of G patterns. The first integer is, for example, Σ j=0 G-1 2 j η i,j t and represents integers greater than or equal to zero with precision to the Gth power of 2.

[0101] The cost function Cqubo includes a variable Q6 (an example of a "sixth constraint term") having a value corresponding to the magnitude of the difference between the startup time constraint evaluation formula for the third generator in the fifth time frame and a first integer equal to or greater than zero for the third generator in the fifth time frame. Specifically, the variable Q6 is expressed by equation (6).

[0102] Here, the minimum start-up time constraint evaluation formula for the generator i when the index t is zero is expressed as follows: i t1,t2 This can be expressed as in equation (15).

[0103] Here, the negative index t of a variable (e.g., a i -1,-1 ) is specified by the initial condition of the problem. Equation (15) is the minimum start-up time constraint of a classical generator in UCP, i.e., (d i t-1 -d i t ) (T on,i t-1 -T min,on,i ) ≧0, the left side of the sixth binary variable a i t1,t2 It is expressed by an equation including:

[0104] In this embodiment, the variable Q6 is determined by the minimum activation time constraint evaluation formula (15), which is an integer, and the first integer when the index t is zero, that is, Σ j=0 G-1 2 j η i,j 0 When the value given by the minimum start-up time constraint evaluation formula (15) is equal to or greater than zero, that is, when the minimum start-up time constraint for the generator i is satisfied when the index t is zero, the difference is zero.i,0 0 ~η i,G-1 0 Therefore, in the optimization process, in the time frame where the index t is zero and in each generator, the sixth binary variable a is set so that the difference becomes zero. i 0,0 and G seventh binary variables η i,0 0 ~η i,G-1 0 is optimized.

[0105] The start-up time equation above, T on,i t =T on,i t-1 ・d i t +d i t is the sixth binary variable a i t,t2 and T on,i -1 This can be expressed as in equation (15).

[0106] The minimum startup time constraint evaluation formula for the generator i when the index t is 1 or greater is the sixth binary variable a i t1,t2 and equation (16) can be expressed as equation (17).

[0107] Equation (17) is the minimum start-up time constraint of the classical generator in UCP, i.e., (d i t-1 -d i t ) (T on,i t-1 -T min,on,i ) ≧0, the left side of the sixth binary variable a i t1,t2 and is expressed by equation (16).

[0108] The variable Q6 is the minimum activation time constraint evaluation formula (17), which is an integer, and the first integer when the index t is 1 or more, that is, Σ j=0 G-1 2 j η i,j tWhen the value given by the minimum start-up time constraint evaluation formula (17) is equal to or greater than zero, that is, when the minimum start-up time constraint for the generator i is satisfied when the index t is equal to or greater than 1, the difference becomes zero. i,0 t ~η i,G-1 t Therefore, in the optimization process, for each time frame and each generator with an index t of 1 or more, the sixth binary variable a i t,t2 and G seventh binary variables η i,0 t ~η i,G-1 t is optimized.

[0109] That is, the variable Q6 is the minimum start-up time constraint of the classical generator in UCP, i.e., (d i t-1 -d i t ) (T on,i t-1 -T min,on,i ) ≧0 as the sixth binary variable a i t1,t2 and the seventh binary variable η i,j t It is expressed by an equation including:

[0110] (Variable Q7) The cost function Cqubo is a function of a plurality of sixth binary variables a i t1,t2 The seventh constraint term includes a variable Q7 (an example of a "seventh constraint term") having Rosenberg's formula (Non-Patent Document 2) to evaluate whether the seventh constraint term is valid. Specifically, the variable Q7 is expressed by formula (7). Here, Rosenberg's formula is expressed by formula (18).

[0111] When y, x1, x2∈{0, 1}, Rosenberg's formula (18) gives eight patterns of values ​​shown in Table 1. When the combination of y, x1, and x2 satisfies the equation y = x1 x2, Rosenberg's formula (18) gives zero. On the other hand, when the combination of y, x1, and x2 satisfies the equation y = x1 x2, Rosenberg's formula (18) gives 1 or 3. In other words, Rosenberg's formula (18) is a quadratic penalty cost function that imposes a penalty when the equation y = x1 x2 does not hold when y, x1, x2∈{0, 1}.

[0112] Sixth binary variable a i t1,t2 is expressed as two sixth binary variables a i t1,t1 and a i t1-1,t2 It is required that the formula (19) holds true at any indexes t1 and t2.

[0113] The variable Q in equation (7) is obtained by fitting equation (19) to Rosenberg's formula (18) and summing it with respect to the indices t1, t2, and i. ７ where 0≦t2<t1<H and 0≦i<U.

[0114] (Variable Q8) The multiple binary variables are multiple eighth binary variables b for each end time frame, each start time frame before the end time frame, and each generator. i t1,t2 where t2≦t1. The eighth binary variable b i t1,t2 There are U·H(H+1) / 2 of these.

[0115] Binary variable b i t1,t1 is the eighth binary variable b when t2 = t1 i t1,t2 (Hereinafter, the tenth binary variable b i t1,t1 It is sometimes called "b". it1,t1 represents either the off or on state of generator i at time frame t1. i t1,t1 The relationship between the classical variables in UCP is b i t1,t1 = (1-d i t1 ) That is, b i t1,t1 is a i t1,t1 Specifically, when generator i is on or off in time frame t1, b i t1,t1 has a value of zero or one, respectively.

[0116] 8th binary variable b i t1,t2 indicates the product of the off or on state of the generator in each time frame after the start time frame and before the end time frame. i t1,t2 is defined by equation (20) when the time frame index satisfies 0≦t2≦t1<H.

[0117] Further, the plurality of binary variables include a plurality of ninth binary variables γ for representing second integers equal to or greater than zero for each time frame and each generator at the index t. i,j t In particular, the plurality of ninth binary variables γ i,j t is the G ninth binary variable γ for each time frame and each generator. i,j t and expresses a second integer greater than or equal to zero using any of 2 to the power of G patterns. The second integer is, for example, Σ j=0 G-1 2 j gamma i,j t and represents integers greater than or equal to zero with precision to the Gth power of 2.

[0118] The cost function Cqubo includes a variable Q8 (an example of an "eighth constraint term") having a value corresponding to the magnitude of the difference between the shutdown time constraint evaluation formula for the fourth generator in the sixth time frame and a second integer equal to or greater than zero for the fourth generator in the sixth time frame. Specifically, the variable Q8 is expressed by equation (9).

[0119] Here, the minimum stop time constraint evaluation formula for the generator i when the index t is zero is the eighth binary variable b i t1,t2 This can be expressed as equation (21) by:

[0120] Equation (21) is the minimum outage time constraint of classical generators in UCP, i.e., (d i t -d i t-1 ) (T off,i t-1 -T min,off,i ) ≧0 is set as the eighth binary variable b i t1,t2 It is expressed by an equation including:

[0121] In this embodiment, the variable Q is a function of the minimum stopping time constraint evaluation formula (21), which is an integer, and the second integer when the index t is zero, i.e., Σ j=0 G-1 2 j gamma i,j 0 When the value given by the minimum stop time constraint evaluation formula (21) is equal to or greater than zero, that is, when the minimum stop time constraint for the generator i is satisfied when the index t is zero, the difference is zero. i,0 0 ~γ i,G-1 0 Therefore, in the optimization process, in the time frame where the index t is zero and in each generator, the eighth binary variable b i 0,0 and G ninth binary variables γ i,0 0 ~γ i,G-1 0 is optimized.

[0122] The stopping time equation above, T off,i t =T off,i t-1 · (1-d i t ) + (1-d i t ) is the eighth binary variable b i t,t2 and T off,i -1 This can be expressed as equation (22) by:

[0123] The minimum stop time constraint evaluation formula for the generator i when the index t is 1 or more is the eighth binary variable b i t,t2 and can be expressed as equation (23) using equation (22).

[0124] Equation (23) is the minimum outage time constraint of classical generators in UCP, i.e., (d i t -d i t-1 ) (T off,i t-1 -T min,off,i ) ≧0 is set as the eighth binary variable b i t,t2 and is expressed by equation (22).

[0125] The variable Q is a function of the minimum stopping time constraint evaluation formula (23), which is an integer, and the second integer when the index t is 1 or greater, i.e., Σ j=0 G-1 2 j gamma i,j t When the value given by the minimum stop time constraint evaluation formula (23) is equal to or greater than zero, that is, when the minimum stop time constraint for the generator i is satisfied when the index t is equal to or greater than 1, the difference becomes zero. i,0 t ~γ i,G-1 t Therefore, in the optimization process, for the time frames where the index t is 1 or more and for each generator, the eighth binary variable bi t,t2 and G ninth binary variables γ i,0 t ~γ i,G-1 t is optimized.

[0126] That is, the variable Q is the minimum stop time constraint of the classical generator in UCP, i.e., (d i t -d i t-1 ) (T off,i t-1 -T min,off,i ) ≧0 as the eighth binary variable b i t1,t2 and the ninth binary variable γ i,j t It is expressed by an equation including:

[0127] (Variable Q9) The cost function Cqubo is a function of multiple eighth binary variables b i t1,t2 The variable Q (an example of a "ninth constraint term") is included, which has Rosenberg's formula (18) to evaluate whether the variable Q is valid. Specifically, the variable Q is expressed by the formula (10).

[0128] 8th binary variable b i t1,t2 is expressed as two sixth binary variables b i t1,t1 and b i t1-1,t2 It is required that the formula (24) holds true at any indexes t1 and t2.

[0129] The variable Q in equation (10) is obtained by fitting equation (24) to the Rosenberg formula and summing it with respect to the indices t1, t2, and i. ９ where 0≦t2<t1<H and 0≦i<U.

[0130] (variable Q 10 The cost function C is calculated for the generator i by the second binary variable a i t,tand the tenth binary variable b at the time frame of index t i t,t and a variable Q having a value obtained by subtracting 1 from the sum of 10 (an example of the "tenth constraint term").

[0131] In this embodiment, the variable Q 10 is the second binary variable a at the time frame of index t for generator i i t,t and the tenth binary variable b at the time frame of index t i t,t The square of the sum of and minus 1 is reflected. 10 is expressed by equation (11).

[0132] b i t1,t1 But, a i t1,t1 If a is the inverse of i t,t +b i t,t -1 becomes zero. On the other hand, b i t1,t1 But, a i t1,t1 If it is not the inverse of i t,t +b i t,t -1 becomes 1 or -1. Therefore, in the optimization process, in each time frame and each generator, a i t,t +b i t,t The second binary variable a is set so that -1 becomes zero. i t,t and the tenth binary variable b i t,t is optimized. This optimizes the second binary variable a i t,t and the tenth binary variable b i t,t It can be guaranteed that and are complementary logic variables.

[0133] [Cost Calculation Processing] FIG. 3 is a flowchart defining an operation procedure when a processing device according to an embodiment of the present disclosure performs cost calculation processing.

[0134] The processing device 101 includes a computer, and a processing unit such as a CPU in the computer reads out from a memory (not shown) and executes a program including some or all of the steps in the flowcharts shown below. The computer program can be installed externally. The computer program is distributed in a state stored on a recording medium.

[0135] As shown in FIG. 3, first, the parameter information acquisition unit 31 in the processing device 101 acquires parameter information (step S102).

[0136] Next, the function generating unit 32 generates a cost function Cqubo expressed by equation (12) based on the parameter information (step S104).

[0137] Next, the quantum computer unit 41 optimizes a plurality of binary variables so as to reduce the cost based on the cost function Cqubo (step S106).

[0138] The above-described embodiments are intended to facilitate understanding of the present invention and are not intended to limit the present invention. The elements of the embodiments, as well as their arrangement, materials, conditions, shapes, sizes, etc., are not limited to those illustrated and can be modified as appropriate. Furthermore, configurations shown in different embodiments can be partially substituted or combined with each other.

[0139] 11... Cost function generating device 31... Parameter information acquiring unit 32... Function generating unit 41... Quantum computer unit 101... Processing device

Claims

1. A cost function generating device comprising: a parameter information acquiring unit that acquires parameter information including N (an integer greater than or equal to 1) as a parameter; and a function generating unit that generates a cost function including a plurality of binary variables based on the parameter information, the cost function being a cost function for calculating a generator start-up and shutdown schedule for a plurality of generators over a plurality of consecutive time frames by binary optimization without quadratic constraints, the cost function including the amount of power generation for each of the time frames and for each of the generators, the plurality of binary variables including N first binary variables for each of the time frames and for each of the generators, and the amount of power generation being expressed using one of 2 to the power of N patterns using the N first binary variables.

2. The parameter information includes H and U as the parameters, and the plurality of binary variables are a i t,t as a second binary variable, and the cost function includes the following equation (1) as a first constraint term: H and U are the time frame and the number of generators, respectively; t and i are the time frame and the generator index, respectively; a i t,t indicates one of the on and off states of the generator with index i in the time frame with index t, k is an index, and z ik t The cost function generator of claim 1 , wherein: x is the first binary variable.

3. The parameter information is H, U, L t , P max,i and P min,i The parameters include: i t,t as a second binary variable, and the cost function includes the following equation (2) as a second constraint term: H and U are the time frame and the number of generators, respectively; t and i are the time frame and the generator index, respectively; a i t,t indicates one of the on and off states of the generator with index i in the time frame with index t, k is an index, and z ik t is the first binary variable, and L t is the power demand in the time frame of index t, and P max,i and P min,i The cost function generating device according to claim 1 , wherein i,j ...

4. The parameter information is H, U, L t , P max,i , R t and F as the parameters, and the plurality of binary variables include a i t,t and ψ k t as second and third binary variables, respectively; and the cost function includes the following equation (3) as a third constraint term: H and U are the time frame and the number of generators, respectively; t and i are the time frame and the generator index, respectively; a i t,t indicates one of the on and off states of the generator with index i in the time frame with index t, F is an integer equal to or greater than 1, k is an index, and L t is the power demand in the time frame of index t, and P max,i is the maximum power generation of the generator with index i, and R t The cost function generating device according to claim 1 , wherein x is the operating reserve in the time frame of index t.

5. The parameter information is H, U, P max,i , P min,i , P up,i , P down,i and F as the parameters, and the plurality of binary variables include a i t,t and χ i,k t as second and fourth binary variables, respectively; and the cost function includes the following equation (4) as a fourth constraint term: H and U are the time frame and the number of generators, respectively; t and i are the time frame and the generator index, respectively; a i t,t indicates one of the on and off states of the generator with index i in the time frame with index t, F is an integer equal to or greater than 1, k is an index, and z ik t is the first binary variable, max,i and P min,i are the maximum and minimum power generation of the generator of index i, respectively; P up,i and P down,i The cost function generating device according to claim 1 , wherein i,j ...

6. The parameter information is H, U, P max,i , P min,i , P up,i , P down,i and F as the parameters, and the plurality of binary variables include a i t,t and φ i,k t as a second binary variable and a fifth binary variable, respectively; and the cost function includes the following equation (5) as a fifth constraint term: H and U are the time frame and the number of generators, respectively; t and i are the time frame and the generator index, respectively; a i t,t indicates one of the on and off states of the generator with index i in the time frame with index t, F is an integer equal to or greater than 1, k is an index, and z ik t is the first binary variable, max,i and P min,i are the maximum and minimum power generation of the generator of index i, respectively; P up,i and P down,i The cost function generating device according to claim 1 , wherein i,j ...

7. The parameter information is H, U, T min,on,i , T on,i -1 and G as the parameters, and the plurality of binary variables include a i t,t2 and η i,j t as sixth and seventh binary variables, respectively; and the cost function includes the following equation (6) as a sixth constraint term: H and U are the time frame and the number of generators, respectively; t and t2 are the indexes of the time frame; i is the index of the generator; a i t,t2 indicates the product of the on or off state of the generator with index i in each of the time frames from the time frame with index t2 onwards to the time frame with index t, G is an integer equal to or greater than 1, j is an index, and T min,on,i is the minimum start-up time of the generator with index i, T on,i -1 The cost function generating device according to claim 1 , wherein i i is the continuous running period of the generator with index i in the time frame with index zero.

8. The cost function includes the following equation (7) as a seventh constraint term: t1 is the index of the time frame, i t1,t1 indicates one of the on and off states of the generator with index i in the time frame with index t1, i t1-1,t2 indicates the product of the on or off state of the generator with index i in each of the time frames after the time frame with index t2 and before the time frame with index t1-1, and a i t1,t2 The cost function generating device according to claim 7 , wherein i represents a product of on or off states of the generator with index i in each of the time frames after the time frame with index t2 and before the time frame with index t1.

9. The parameter information is max,i and P min,i The parameters include: i t,t as a second binary variable, and the power generation amount is expressed by the following equation (8): t and i are the time frame and generator index, respectively; i t,t indicates one of the on and off states of the generator with index i in the time frame with index t, k is an index, and z ik t is the first binary variable, max,i and P min,i The cost function generating device according to claim 1 , wherein i,j ...

10. The parameter information is H, U, T min,off,i , T off,i -1 and G as the parameters, and the plurality of binary variables are i t,t2 and γ i,j t as an eighth binary variable and a ninth binary variable, respectively; and the cost function includes the following equation (9) as an eighth constraint term: H and U are the time frame and the number of generators, respectively; t and t2 are the indexes of the time frame; i is the index of the generator; b i t,t2 indicates the product of the on or off state of the generator with index i in each of the time frames from the time frame with index t2 onwards to the time frame with index t, G is an integer equal to or greater than 1, j is an index, and T min,off,i is the minimum outage time of the generator with index i, T off,i -1 The cost function generating device according to claim 1 , wherein i i is the continuous outage duration of the generator with index i in the time frame with index zero.

11. The cost function includes the following equation (10) as a ninth constraint term: t1 is the index of the time frame, i t1,t1 indicates one of the off and on states of the generator with index i in the time frame with index t1, and b i t1-1,t2 b indicates the product of the off or on state of the generator with index i in each of the time frames after the time frame with index t2 and before the time frame with index t1-1; i t1,t2 The cost function generating device according to claim 10 , wherein i denotes a product of the off or on state of the generator with index i in each of the time frames after the time frame with index t2 and before the time frame with index t1.

12. The plurality of binary variables are: b i t,t as a tenth binary variable, and the cost function includes the following equation (11) as a tenth constraint term: a i t,t indicates one of the on and off states of the generator with index i in the time frame with index t, and b i t,t The cost function generating device according to claim 7 , wherein i represents one of an on and off state of the generator with index i in the time frame with index t.

13. A processing device comprising: a cost function generating device according to any one of claims 1 to 12; and a quantum computer unit that optimizes the plurality of binary variables so as to reduce a cost based on the cost function.

14. A cost function generating method in a cost function generating device, comprising: acquiring parameter information including N (an integer equal to or greater than 1) as a parameter; and generating a cost function including a plurality of binary variables for calculating a generator start-up and shutdown schedule for a plurality of generators over a plurality of consecutive time frames by quadratic unconstrained binary optimization based on the parameter information, wherein the cost function includes a power generation amount for each of the time frames and for each of the generators, the plurality of binary variables including N first binary variables for each of the time frames and for each of the generators, and the power generation amount is expressed using one of 2 to the power of N patterns using the N first binary variables.

15. A processing device comprising: a quantum computer unit that optimizes the plurality of binary variables so as to reduce a cost based on the cost function generated by the cost function generation method according to claim 14.

16. A cost function generation program used in a cost function generating device, comprising: a parameter information acquisition unit that acquires parameter information including N (an integer equal to or greater than 1) as a parameter; and a function generation unit that generates a cost function including a plurality of binary variables based on the parameter information, the cost function being for calculating a generator start-stop schedule for a plurality of generators over a plurality of consecutive time frames by quadratic unconstrained binary optimization, wherein the cost function includes a power generation amount for each of the time frames and for each of the generators, the plurality of binary variables including N first binary variables for each of the time frames and for each of the generators, and the power generation amount is expressed using one of 2 to the power of N patterns using the N first binary variables.

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