An on-the-fly power spot market least purchase cost function fitting method suitable for quantum computing

Abstract

The application discloses a power spot market minimum power purchase cost function fitting method suitable for quantum calculation, belongs to the cross field of power system optimization and quantum calculation, and comprises the following steps: constructing a security constrained unit commitment optimization model based on power system parameters; constructing a training sample set of unit start state and minimum power purchase cost based on the security constrained unit commitment optimization model; fitting an explicit function relationship between the minimum power purchase cost and the unit start state by adopting a kernel function enhanced elastic net regression algorithm based on the training sample set; converting the explicit function relationship into a quadratic unconstrained binary optimization model suitable for quantum calculation, and solving the quadratic unconstrained binary optimization model, so that the power spot market minimum power purchase cost function fitting suitable for quantum calculation is realized. The application solves the calculation efficiency bottleneck of the existing method in the power spot market clearing and the difficulty in explicit expression of a target function in quantum calculation adaptation.

Description

Technical Field

[0001] This invention belongs to the interdisciplinary field of power system optimization and quantum computing, and specifically relates to a method for fitting the minimum electricity purchase cost function in the spot market that is adapted to quantum computing. Background Technology

[0002] With the advancement of the electricity spot market, market clearing demands the solution of large-scale MILP problems, and computational time constraints hinder real-time decision-making. Traditional solvers (such as Gurobi) can guarantee optimality, but their long computation time makes them unsuitable for the real-time requirements of the market. Dedicated quantum computers show potential advantages in combinatorial optimization problems, but their hardware primarily supports QUBO models. Existing methods attempt to directly express the MILP objective function as an explicit function of binary variables (such as unit start-up and shutdown states), but face two major challenges:

[0003] 1. The relationship between the minimum electricity purchase cost C and the unit start-up and shutdown state U (binary vector) is a discontinuous piecewise affine function, which traditional linear regression (such as Lasso) cannot accurately fit.

[0004] 2. Solution space explosion: The combination space of U is 2n (n is the number of units), which makes exhaustive sampling impossible.

[0005] Therefore, there is an urgent need for a method that can accurately fit the C-U mapping relationship and realize the transformation of MILP to QUBO, laying the foundation for the application of quantum computing in the clearing of the electricity spot market. This invention aims to prove that the C-U function relationship can be explicitly fitted and transformed into a QUBO model, laying the foundation for the implementation of quantum computing. Summary of the Invention

[0006] To address the aforementioned shortcomings in existing technologies, this invention provides a quantum computing-adapted method for fitting the minimum electricity purchase cost function in the electricity spot market. This method solves the computational efficiency bottleneck in the clearing of the electricity spot market and addresses the challenge of explicit expression of the objective function in quantum computing adaptation.

[0007] To achieve the aforementioned objectives, the technical solution adopted by this invention is as follows: a method for fitting a minimum electricity purchase cost function in the spot market that is adapted to quantum computing, comprising the following steps:

[0008] S1: Construct a safety-constrained unit combination optimization model based on power system parameters;

[0009] S2: Based on the aforementioned safety-constrained unit combination optimization model, construct a training sample set of unit start-up states and minimum power purchase cost;

[0010] S3: Based on the training sample set, the kernel-enhanced elastic network regression algorithm is used to fit the explicit functional relationship between the minimum power purchase cost and the unit's operating status;

[0011] S4: Transform the explicit functional relationship into a quadratic unconstrained binary optimization model adapted to quantum computing, and solve it to achieve the fitting of the minimum electricity purchase cost function for spot electricity adapted to quantum computing.

[0012] Furthermore, the unit combination optimization model in S1 is a spot market clearing MILP model, which includes an objective function, unit physical constraints, and grid security constraints;

[0013] The objective function is:

[0014]

[0015] in, For the unit During the period active power, , and This is the coal consumption coefficient. This indicates the unit's start-up and shutdown status. and These are the start-up and shutdown cost coefficients, respectively. and These are the start and stop event indicator variables, respectively;

[0016] The physical constraints of the unit include upper and lower limits of output, minimum operating time, ramp rate, and start / stop logic constraints.

[0017] The power grid security constraints include node power balance constraints and DC power flow constraints.

[0018] Furthermore, step S2 includes the following sub-steps:

[0019] S21: Obtain the suboptimal solution corresponding to the MILP model using the Gurobi solver. Sample, of which, This is the unit start-up and shutdown state vector. The minimum electricity purchase cost corresponding to the unit start-up and shutdown state vector;

[0020] S22: Within the feasible region satisfying the unit's physical constraints, uniformly generate supplementary samples of the unit's start-up and shutdown state vectors. Calculate the corresponding minimum electricity purchase cost by solving the economic dispatch problem with fixed unit start-up and shutdown state vectors, thus obtaining the training sample set. Among them, the economic scheduling problem is a quadratic programming problem, which is transformed into a linear programming problem through piecewise linearization.

[0021] Furthermore, step S3 includes the following sub-steps:

[0022] S31: Apply a kernel function mapping to the unit start-up and shutdown state vector, mapping it to a high-dimensional feature space. The mapped feature vector... The format is:

[0023]

[0024] in, The first state vector of the unit start-up and shutdown state One portion, , Number of generating units;

[0025] S32: By optimizing the objective function through regularization, the function parameters are solved to achieve an explicit function fit between the minimum electricity purchase cost and the unit's operating state. The optimization objective is:

[0026]

[0027] in, This is a constant offset. Let be a coefficient vector, representing the weight of each feature in relation to the cost. Let this be the minimum electricity purchase cost value corresponding to the k-th sample in the training sample set. The unit start-up and shutdown state vector for the k-th sample The mapped feature vector, This is the transpose of the matrix. and For regularization parameters, This represents the number of training samples.

[0028] Furthermore, in step S4, the explicit functional relationship is transformed into a quadratic unconstrained binary optimization model adapted for quantum computing, as shown in the following formula:

[0029]

[0030] in, It is a symmetric coefficient matrix. It is a vector of linear terms;

[0031] The construction process of the quadratic unconstrained binary optimization model is as follows: the fitting function is obtained through Taylor expansion. Approximately a quadratic polynomial Ignore the constant term The objective function is then obtained.

[0032] A quantum computing-adapted system for fitting the minimum electricity purchase cost function in the electricity spot market includes:

[0033] Model building module: Used to build a safety-constrained unit combination optimization model;

[0034] Sample generation module: used to obtain a training sample set of unit start-up status and minimum power purchase cost;

[0035] Function Fitting Module: Used to fit the explicit functional relationship between minimum electricity purchase cost and unit operating status using a kernel-enhanced elastic network regression algorithm;

[0036] Model transformation module: used to transform the explicit functional relationship into a quadratic unconstrained binary optimization model adapted for quantum computing, and to solve it.

[0037] An electronic device, comprising:

[0038] Memory, used to store computer programs;

[0039] A processor is used to execute the computer program to implement the above-described method for fitting the minimum electricity purchase cost function in the spot market of electricity, adapted to quantum computing.

[0040] The beneficial effects of this invention are:

[0041] (1) This invention breaks through the bottleneck of the compatibility between mixed integer programming and quantum computing, and for the first time realizes the explicit transformation of the MILP problem in the clearing of the electricity spot market into the QUBO model. By constructing an explicit functional mapping relationship between the start-up and shutdown states of the generating units (binary variables) and the optimal electricity purchase cost, the quantum computing compatibility problem caused by the coupling of continuous and discrete variables in the traditional MILP model is solved, providing theoretical support for the application of quantum computing in the real-time electricity market.

[0042] (2) This invention accurately fits the discontinuous cost function relationship and innovatively proposes a kernel-enhanced elastic network regression algorithm. By using radial basis functions or quadratic polynomial kernels, binary variables are mapped to a high-dimensional feature space, and parameters are optimized by regularized cross-validation. This method accurately captures the discontinuous piecewise affine characteristics between electricity purchase cost and unit status.

[0043] (3) The present invention realizes the lightweight encoding of quantum solvable models. By Taylor expansion, the fitting function is explicitly transformed into the QUBO standard form. The generated model can be directly solved efficiently by quantum annealing or quantum approximation optimization algorithm.

[0044] (4) The present invention enhances engineering applicability and system compatibility. The end-to-end function fitting system constructed supports the fully automated processing from MILP modeling, sample generation, function fitting to QUBO conversion. It is compatible with existing power market optimization modules (such as unit constraints and grid security constraints), and significantly reduces the threshold for the implementation of quantum computing in the power system. Attached Figure Description

[0045] Figure 1 This is a flowchart of a method for fitting a minimum electricity purchase cost function in the spot electricity market that is adapted to quantum computing, according to the present invention.

[0046] Figure 2 This is a histogram of the prediction error distribution.

[0047] Figure 3 This is a histogram of the relative error distribution.

[0048] Figure 4 A scatter plot showing the predicted cost versus the actual cost.

[0049] Figure 5 A histogram comparing the distribution of actual costs and predicted costs. Detailed Implementation

[0050] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0051] like Figure 1 As shown, a method for fitting the minimum electricity purchase cost function in the spot electricity market, adapted to quantum computing, includes the following steps:

[0052] This embodiment uses a standard IEEE 30-node system as the test object to verify the effectiveness of the method of the present invention. The system parameters are as follows:

[0053] Unit parameters: 6 generator sets, capacity range pu, coal consumption coefficient tons / (pu)², minimum operating / downtime is 2 hours, uphill / downhill ramp rate pu / h, startup cost / time, shutdown cost / Second-rate.

[0054] Line parameters: 41 lines, reactance values PU, limited edition pu.

[0055] Load data: 24-hour load curves for 30 nodes, with a total load peak of 2.83 pu (T17-T19 period) and a valley of 1.98 pu (T3 period).

[0056] Note: All parameters have been normalized. Coal consumption cost is calculated based on a coal price of $100 / ton (i.e., coal consumption cost = .

[0057] S1: Construct a safety-constrained unit combination optimization model based on power system parameters;

[0058] The unit combination optimization model in S1 is a spot market clearing MILP model, which includes an objective function, unit physical constraints, and grid security constraints.

[0059] The objective function is to minimize the electricity purchase cost (including coal consumption cost and start-up and shutdown cost):

[0060]

[0061] in, For the unit During the period active power, , and This is the coal consumption coefficient. This indicates the unit's start-up and shutdown status. and These are the start-up and shutdown cost coefficients, respectively. and These are the start and stop event indicator variables, respectively;

[0062] The physical constraints of the unit include upper and lower limits of output, minimum operating time, ramp rate, and start / stop logic constraints.

[0063] Output upper and lower limit constraints (taking unit 1 as an example):

[0064]

[0065] in, For Unit 1 during the time period Start-stop status, For Unit 1 during the time period The active power;

[0066] Minimum runtime constraint:

[0067]

[0068] Slope rate constraint:

[0069]

[0070]

[0071] in, For the unit During the period active power, For the unit During the period Start-stop status, For the unit Maximum output and The ramp rate during normal operation;

[0072] Start / stop logic constraints:

[0073]

[0074]

[0075]

[0076]

[0077] The power grid security constraints include node power balance constraints and DC power flow constraints;

[0078] Node power balance constraints:

[0079]

[0080] in, For nodes Time period The load, , For the nodal admittance matrix elements, For the line reactance connecting nodes n and m, and The node voltage phase angle is denoted as .

[0081] DC power flow constraints:

[0082]

[0083] in, For the line The maximum trend limit, and These represent the voltage phase angles at the nodes at both ends of the line during time period t. Let be the reactance value (pu) of line l.

[0084] S2: Based on the aforementioned safety-constrained unit combination optimization model, construct a training sample set of unit start-up states and minimum power purchase cost;

[0085] S2 includes the following sub-steps:

[0086] S21: Obtain the suboptimal solution corresponding to the MILP model using the Gurobi solver. Sample, of which, This is the unit start-up and shutdown state vector. The minimum electricity purchase cost corresponding to the unit start-up and shutdown state vector;

[0087] S22: Within the feasible region satisfying the unit's physical constraints, uniformly generate supplementary samples of the unit's start-up and shutdown state vectors. Calculate the corresponding minimum electricity purchase cost by solving the economic dispatch problem with fixed unit start-up and shutdown state vectors, thus obtaining the training sample set. Among them, the economic scheduling problem is a quadratic programming problem, which is transformed into a linear programming problem through piecewise linearization.

[0088] In this embodiment, a joint sampling strategy is used to generate 5500 sets. The sample is as follows:

[0089] Gurobi Solution Pool Sampling: The Gurobi 9.5 solver was used to solve the MILP model of S1. By setting the SolutionPoolCapacity=5000 parameter, up to 5000 optimal and suboptimal solutions were obtained, along with the corresponding unit start-stop state vector U (a binary vector of 6 units × 24 time periods) and minimum power purchase cost C. The samples cover typical scenarios of peak, flat, and off-peak loads to ensure solution diversity.

[0090] Latin hypercube supplementary sampling: Within the feasible region satisfying the unit's physical constraints, supplementary samples of U are uniformly generated, and the corresponding C value is calculated by solving the economic dispatch problem with a fixed U. The economic dispatch problem is a quadratic programming problem with the objective of minimizing coal consumption cost after fixing U, and its feasibility is verified through the following steps: 1) Checking the minimum operating / downtime constraints based on the state machine model (e.g., continuous unit operation requires ≥2 hours); 2) For feasible U, solving the economic dispatch (ED) problem (quadratic programming) with a fixed U, and calculating the corresponding C value. The ED problem aims to minimize coal consumption cost, with constraints similar to those in S1 regarding unit output, ramp-up, and grid safety.

[0091] S3: Based on the training sample set, the kernel-enhanced elastic network regression algorithm is used to fit the explicit functional relationship between the minimum power purchase cost and the unit's operating status;

[0092] S3 includes the following sub-steps:

[0093] S31: Apply a kernel function mapping to the unit start-up and shutdown state vector, mapping it to a high-dimensional feature space. The mapped feature vector... The format is:

[0094]

[0095] in, The first state vector of the unit start-up and shutdown state One portion, , Number of generating units;

[0096] S32: By optimizing the objective function through regularization, the function parameters are solved to achieve an explicit function fit between the minimum electricity purchase cost and the unit's operating state. The optimization objective is:

[0097]

[0098] in, This is a constant offset. Let be a coefficient vector, representing the weight of each feature in relation to the cost. Let this be the minimum electricity purchase cost value corresponding to the k-th sample in the training sample set. The unit start-up and shutdown state vector for the k-th sample The mapped feature vector, This is the transpose of the matrix. and For regularization parameters, This represents the number of training samples.

[0099] In this embodiment, based on a sample set of 2500 sets, an elastic network regression with kernel function enhancement is used to construct... Explicit functions include the following steps:

[0100] Kernel function mapping: Choosing a quadratic polynomial kernel The original binary vector U (dimension 6×24=144) is mapped to a high-dimensional feature space, and the resulting feature vector is:

[0101]

[0102] It includes linear terms, quadratic cross terms, and constant terms, with dimensions of . .

[0103] Optimize parameters using elastic network regression, with the mapped parameters Given C as input and C as the objective, the function parameters are solved by optimizing the objective through regularization. A random search is used for hyperparameter optimization (10 parameter combinations, 2-fold cross-validation). The optimal parameters are: =0.8334, l1_ratio=0.2911. The fitting results show: mean absolute error (MAE) of the test set = 51,900.11, mean absolute percentage error (MAPE) = 0.85%, and coefficient of determination (R²) = 0.7839, verifying the fitting accuracy. Figure 2-4 As shown.

[0104] S4: Transform the explicit functional relationship into a quadratic unconstrained binary optimization model adapted to quantum computing, and solve it to achieve the fitting of the minimum electricity purchase cost function for spot electricity adapted to quantum computing.

[0105] In step S4, the explicit functional relationship is transformed into a quadratic unconstrained binary optimization model adapted for quantum computing, as shown in the following formula:

[0106]

[0107] in, It is a symmetric coefficient matrix. It is a vector of linear terms;

[0108] The construction process of the quadratic unconstrained binary optimization model is as follows: the fitting function is obtained through Taylor expansion. Approximately a quadratic polynomial Ignore the constant term The objective function is then obtained.

[0109] In this embodiment, the fitting function is transformed into a quantum-solvable quadratic unconstrained binary optimization model. The fitting function after quadratic polynomial kernel mapping can be expressed as:

[0110]

[0111] in, For constant terms, The coefficients are linear. The coefficient of the quadratic term ( U is the unit start-up and shutdown state vector, and its components are... , The components of the U vector represent binary variables indicating the start-up and shutdown status of the generator unit.

[0112] Ignore constant terms Due to the square term ( In a binary variable, it equals Therefore, we can combine the square terms into the linear terms in the quadratic function, ultimately obtaining a quantum solvable model:

[0113]

[0114] This model can be directly solved using a quantum annealer (such as D-WaveAdvantage) or a quantum approximate optimization algorithm (QAOA). The MAE (mean squared error) between the predicted and actual costs is 51900.11 (MAPE = 0.85%). Figure 5 As shown, the fitting accuracy was verified.

[0115] This invention also discloses a quantum computing-adapted system for fitting the minimum electricity purchase cost function in the spot electricity market, comprising:

[0116] Model building module: Used to build a safety-constrained unit combination optimization model;

[0117] Sample generation module: used to obtain a training sample set of unit start-up status and minimum power purchase cost;

[0118] Function Fitting Module: Used to fit the explicit functional relationship between minimum electricity purchase cost and unit operating status using a kernel-enhanced elastic network regression algorithm;

[0119] Model transformation module: used to transform the explicit functional relationship into a quadratic unconstrained binary optimization model adapted for quantum computing, and to solve it.

[0120] The present invention also discloses an electronic device, comprising:

[0121] Memory, used to store computer programs;

[0122] A processor is used to execute the computer program to implement the above-described method for fitting the minimum electricity purchase cost function in the spot market of electricity, adapted to quantum computing.

[0123] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. For example, the kernel function can be replaced by a radial basis function (RBF) (which needs to be approximated to a quadratic form through Taylor expansion), and the number of samples can be adjusted according to the unit size (e.g., 5000 samples for 10 units), all of which fall within the scope of protection of the invention. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the essence of the invention, and these modifications and combinations are still within the scope of protection of the invention.

Claims

1. A method for fitting the minimum electricity purchase cost function in the spot electricity market, adapted to quantum computing, characterized in that, Includes the following steps: S1: Construct a safety-constrained unit combination optimization model based on power system parameters; The unit combination optimization model in S1 is a spot market clearing MILP model, which includes an objective function, unit physical constraints, and grid security constraints. The objective function is: ； in, For the unit During the period active power, , and Coal consumption coefficient, This indicates the unit's start-up and shutdown status. and These are the start-up and shutdown cost coefficients, respectively. and These are the start and stop event indicator variables, respectively; The physical constraints of the unit include upper and lower limits of output, minimum operating time, ramp rate, and start / stop logic constraints. The power grid security constraints include node power balance constraints and DC power flow constraints; S2: Based on the aforementioned safety-constrained unit combination optimization model, construct a training sample set of unit start-up states and minimum power purchase cost; S3: Based on the training sample set, the kernel-enhanced elastic network regression algorithm is used to fit the explicit functional relationship between the minimum power purchase cost and the unit's operating status; S3 includes the following sub-steps: S31: Apply a kernel function mapping to the unit start-up and shutdown state vector, mapping it to a high-dimensional feature space. The mapped feature vector... The format is: ； in, The first state vector of the unit start-up and shutdown state One portion, , Number of generating units; S32: By optimizing the objective function through regularization, the function parameters are solved to achieve an explicit function fit between the minimum electricity purchase cost and the unit's operating state. The optimization objective is: ； in, This is a constant offset. Let be a coefficient vector, representing the weight of each feature in relation to the cost. Let this be the minimum electricity purchase cost value corresponding to the k-th sample in the training sample set. The unit start-up and shutdown state vector for the k-th sample The mapped feature vector, This is the transpose of the matrix. and For regularization parameters, This represents the number of training samples; S4: Transform the explicit functional relationship into a quadratic unconstrained binary optimization model adapted to quantum computing, and solve it to achieve the fitting of the minimum electricity purchase cost function for electricity spot market adapted to quantum computing. In step S4, the explicit functional relationship is transformed into a quadratic unconstrained binary optimization model adapted for quantum computing, as shown in the following formula: ； in, It is a symmetric coefficient matrix. This is the unit start-up and shutdown state vector. A vector of linear terms; The construction process of the quadratic unconstrained binary optimization model is as follows: the fitting function is obtained through Taylor expansion. Approximately a quadratic polynomial Ignore the constant term The objective function is then obtained.

2. The method for fitting the minimum electricity purchase cost function in the spot electricity market adapted to quantum computing as described in claim 1, characterized in that, S2 includes the following sub-steps: S21: Obtain the suboptimal solution corresponding to the MILP model using the Gurobi solver. Sample, of which, This is the unit start-up and shutdown state vector. The minimum electricity purchase cost corresponding to the unit start-up and shutdown state vector; S22: Within the feasible region satisfying the unit's physical constraints, uniformly generate supplementary samples of the unit's start-up and shutdown state vectors. Calculate the corresponding minimum electricity purchase cost by solving the economic dispatch problem with fixed unit start-up and shutdown state vectors, thus obtaining the training sample set. Among them, the economic scheduling problem is a quadratic programming problem, which is transformed into a linear programming problem through piecewise linearization.

3. A system for fitting a quantum computing-adapted method for the minimum electricity purchase cost function in the spot electricity market, as described in any one of claims 1-2, characterized in that, include: Model building module: Used to build a safety-constrained unit combination optimization model; Sample generation module: used to obtain a training sample set of unit start-up status and minimum power purchase cost; Function Fitting Module: Used to fit the explicit functional relationship between minimum electricity purchase cost and unit operating status using a kernel-enhanced elastic network regression algorithm; Model transformation module: used to transform the explicit functional relationship into a quadratic unconstrained binary optimization model adapted for quantum computing, and to solve it.

4. An electronic device, characterized in that, include: Memory, used to store computer programs; A processor for executing the computer program to implement the method for fitting the minimum electricity purchase cost function in the spot electricity market using quantum computing as described in any one of claims 1-2.

Images