Data-driven spot market electricity price risk assessment system

Abstract

The present invention discloses a spot market electricity price risk assessment system based on data-driven, including a data acquisition module, a unit output and transmission line flow calculation module, a sample identification module, a first electricity price calculation module, and a second electricity price calculation module; the present invention constructs a GP substitution model of the DC-OPF problem to identify key information for LMP calculation. By solving a set of linear equations, a model-data hybrid EPRA method is proposed. The method significantly improves the efficiency of EPRA without affecting the accuracy of EPRA.

Description

Technical Field

[0001] The present invention relates to the field of power market, and in particular to a data-driven spot market electricity price risk assessment system. Background Art

[0002] To reduce pollution and greenhouse gas emissions, high penetration of renewable energy has become one of the basic characteristics of smart grids. With the development of renewable energy and the adoption of the marginal point price (LMP) method, the spot market is full of uncertainties caused by load and renewable energy fluctuations. The above uncertainties lead to sharp fluctuations in electricity prices, bringing serious operational and planning risks to electricity market participants.

[0003] Compared with the uncertainty in electricity production and use, electricity prices are more volatile and more difficult to predict. Therefore, electricity price risk assessment (EPRA) is crucial for market participants. Reliable assessment methods are the basis for spot market operation and risk control. Current research focuses on the risks caused by electricity price fluctuations, and analyzes price risks in the electricity market based on methods such as Monte Carlo simulation and mean-variance model. For EPRA, the expected value and standard deviation of LMP need to be evaluated to support market risk control of independent system operators (ISOs). Usually, LMP can be obtained based on the DC optimal power flow (DC-OPF) model, which is derived from the Lagrange multipliers of power balance constraints and transmission constraints, including energy components and congestion components. Probabilistic optimal power flow (POPF) can comprehensively consider various uncertainties in the spot market, thus becoming an effective tool for evaluating LMP in deregulated electricity markets.

[0004] In order to solve the POPF problem, there are two main computational methods in existing research, namely model-based methods and data-based methods. Model-based methods can be roughly divided into analytical methods and simulation methods. Typical analytical methods, such as point estimation methods, construct representative samples based on the probability density function (PDF) of uncertain variables. EPRA results can be obtained based on the OPF solution of representative samples, which is computationally effective but requires complex mathematical derivations and strict assumptions. Typical simulation methods include Monte Carlo simulation, which solves the OPF model for a large number of randomly generated samples to obtain EPRA results. The results of this method are reliable, but there is a huge computational burden.

[0005] In recent years, data-driven machine learning methods have been widely used in POPF calculations, providing a new approach to achieve high-precision and high-efficiency EPRA. The core idea of ​​the data-driven method is to construct a data-driven alternative model to establish a functional mapping relationship between the input system operating state of the OPF problem and the output OPF solution, thereby greatly improving the computational efficiency of the POPF problem. Existing literature proposes a deep neural network (DNN) method for solving the optimal power flow problem based on historical data and offline simulation. However, the existing data-driven methods applicable to POPF problems still have a technical gap for EPRA problems. First, discrete Lagrange multipliers are required to calculate LMP, which is not available in existing POPF data-driven methods. Second, deep learning requires a large number of training samples, which does not match the current practice of the spot market. Third, there are inherent learning errors in the data-driven POPF results, which may cause the EPRA results to be unreliable. In summary, it is urgent to study a data-driven assessment device for spot market electricity price risk that takes into account both calculation accuracy and speed. Summary of the invention

[0006] The purpose of the present invention is to provide a data-driven spot market electricity price risk assessment system, including a data acquisition module, a unit output and transmission line flow calculation module, a sample identification module, a first electricity price calculation module, and a second electricity price calculation module.

[0007] The data acquisition module acquires the power system operation data and inputs it into the unit output and transmission line flow calculation module and the sample identification module.

[0008] The unit output and transmission line power flow calculation module stores a DC-OPF Gaussian process substitution model.

[0009] The unit output and transmission line flow calculation module inputs the power system operation data into the DC-OPF Gaussian process substitution model to obtain the unit output and transmission line flow, thereby identifying marginal units and blocked transmission lines.

[0010] The unit output and transmission line power flow calculation module transmits the unit output, transmission line power flow, marginal units and blocked transmission lines to the sample identification module.

[0011] The sample identification module stores sample verification criteria.

[0012] The sample identification module verifies the power system operation data, unit output and transmission line flow according to the sample verification criteria. If the verification is passed, the unit output, transmission line flow, marginal unit and blocked transmission line are input into the first electricity price calculation module; otherwise, the unit output, transmission line flow, marginal unit and blocked transmission line are input into the second electricity price calculation module.

[0013] The first electricity price calculation module stores a first electricity price calculation model.

[0014] If the first electricity price calculation module receives the unit output, transmission line flow, marginal unit and blocked transmission line, the unit output, transmission line flow, marginal unit and blocked transmission line are input into the first electricity price calculation model to calculate the node electricity price LMP.

[0015] The second electricity price calculation module stores a second electricity price calculation model.

[0016] If the second electricity price calculation module receives the unit output, transmission line flow, marginal unit and blocked transmission line, the unit output, transmission line flow, marginal unit and blocked transmission line are input into the second electricity price calculation model to calculate the node electricity price LMP.

[0017] Furthermore, the power system operation data includes power system topology and load data.

[0018] Further, the DC-OPF Gaussian process substitution model is as follows:

[0019]

[0020] Where y is the output, including power generation and transmission line flow. c(·) is the relevant cost function. A and B are the corresponding matrices for vectors x and y, respectively. b is the coefficient; Ω is the output set.

[0021] Furthermore, the output of the DC-OPF Gaussian process substitution model f(x)=[f(x1),f(x2),…,f(x n )] follows the following distribution:

[0022]

[0023] Where x=[x1,x2,…,x n ] is the input set.

[0024]

[0025] Where X = [x1, x2, …, x n ] Tis a matrix of n×p dimensions. m(·) represents the mean function, and C(·,·) represents the covariance function.

[0026] The DC-OPF Gaussian process substitution model has the following distribution of Y:

[0027]

[0028] In the formula, σ 2 and I n are the noise variance and the n-dimensional identity matrix respectively. Y refers to the output of the DC-OPF Gaussian process surrogate model.

[0029] The sample set (X) of the DC-OPF Gaussian process surrogate model t ,,Y t ) is as follows:

[0030]

[0031] In the formula, is the identity matrix;

[0032] Parameter Y and Initial Y t The joint distribution of |X is as follows

[0033]

[0034] In the formula, parameter C 11 =C(X,X)+σ 2 I n , initial C 12 =C(X,X t ), parameter C 21 =C(X t ,X), initial C 22 =C(X t ,X t )+σ 2 I nt .

[0035] The output Y of the DC-OPF Gaussian process surrogate model t The expected value of is as follows:

[0036]

[0037] Where μ is the expected value.

[0038] Furthermore, the DC-OPF Gaussian process substitution model is trained by historical power system operation data.

[0039] The training steps of the DC-OPF Gaussian process substitution model include:

[0040] 1) Obtain a training sample set D = (X, Y). Each row of the sample set X is an I-dimensional uncertainty input vector, including the load demand D of all buses. i The output matrix Y consists of I G +I L Output variable columns. G The elements of the column output variable are the unit output P corresponding to each input vector x. L The elements of the column output variable are the transmission line power flows PF corresponding to each input vector x.

[0041] 2) Use the square exponential covariance kernel function to construct the GP substitution model, that is:

[0042]

[0043] In the formula, C SE (x k ,x * ) is the output of the GP substitution model; τ, l are the parameters of the GP substitution model; x k 、x * It is the input of GP substitution model;

[0044] 3) Rewrite formula (8) as follows:

[0045] Y|X,ξ~N(m(X),C SE (X,X)+σ 2 I). (9)

[0046] Where ξ=(τ,l) is a hyperparameter.

[0047] 4) Based on the maximum likelihood estimation, we get:

[0048]

[0049] In the formula, is the estimated value of hyperparameter and standard deviation;

[0050] Among them, the maximum likelihood estimate logP(Y|X,ξ,σ) is as follows:

[0051]

[0052] Furthermore, the output power of marginal unit i satisfies the following formula:

[0053] P min,i +ε g,i ≤P i ≤P max,i -ε g,i (12)

[0054] Where Pi is the output power of the generator; P max,i and P min,i are the upper and lower limits of the generator output power respectively; g,i is the marginal unit relaxation factor;

[0055] Transmission power of blocked transmission line l Satisfy the following formula:

[0056] (PF l ≥F l -ε PF,l or PF l ≤-F l +ε PF,l ) (13)

[0057] In the formula, F l is the upper limit of the transmission power of line l; D i is the generator load demand; PTDF li is the power transfer distribution factor from node i to line l; ε PF,l is the relaxation factor for the blocked transmission line.

[0058] Further, the sample identification module verifies the power system operation data, unit output and transmission line flow according to the sample verification criteria, including:

[0059] 1) Determine whether the power system operation data, unit output and transmission line flow satisfy the following formula. If so, the verification is passed. If not, proceed to step 2).

[0060] N MG +1=N CL (14)

[0061] Where N MG 、N CL is the number of marginal generators and the number of blocked transmission lines;

[0062] 2) Determine whether the power system operation data unit output and transmission line flow satisfy the following formula. If so, the verification is successful; if not, the verification fails.

[0063]

[0064] Where, mean(LMP i ) is the average value of LMP at node i. p is the ratio threshold. LMP i is the electricity price at node i.

[0065] Furthermore, the first electricity price calculation model is used to calculate the marginal node electricity price LMP.

[0066] Among them, the electricity price LMP of node i i As shown below:

[0067]

[0068] Where L is the Lagrangian function. PTDF li is the power transfer distribution factor from node i to line l. and are the Lagrange multipliers for the upper and lower limits of the power flow of the line, respectively. i is the load demand of the generator. λ is the Lagrange multiplier of the power balance constraint. L is a collection of transmission lines.

[0069] Among them, the Lagrangian function L is as follows:

[0070]

[0071] In the formula, I G is the set of generator nodes. i is the production cost of the generator. i is the output power of the generator. i is the node. PTDF li is the power transfer distribution factor from node i to line l. is the transmission power of line l. i is the load demand of the generator. λ is the corresponding Lagrange multiplier. and are the Lagrange multipliers for the upper and lower constraints of the line power flow, respectively. and are the Lagrange multipliers for the upper and lower limits of the generator output. max,i , P min,i are the upper and lower limits of the output power respectively. I is the set of system nodes. L is a collection of transmission lines.

[0072] Further, the steps of calculating the node electricity price LMP include:

[0073] 1) When node i is not a marginal unit, according to the KKT condition, the following relationship is established:

[0074]

[0075] When node i is a marginal unit, according to the KKT condition, the following relationship is established:

[0076]

[0077] In the formula, the parameters I MG and NMG are the set and number of marginal units respectively.

[0078] 2) Establish the matrix form of equation (19), namely:

[0079]

[0080] 3) Rewrite formula (20) according to the transmission line constraint information to obtain:

[0081]

[0082] In the formula, is the Lagrange multiplier of the line power flow constraint;

[0083] Among them, the number of blocked transmission lines N CL As shown below:

[0084] N CL =L-(L+1-N MG )=N MG -1 (22)

[0085] 4) Formula (21) is solved according to the marginal unit nodes and blocked transmission lines to obtain the power transfer distribution factor from node i to line l.

[0086] 5) Input the power transfer distribution factor from node i to line l into formula (16) to calculate the electricity price LMP.

[0087] Furthermore, the second electricity price calculation model includes a general DC-OPF model.

[0088] The objective function of the general DC-OPF model is as follows:

[0089]

[0090] In the formula, c i is the production cost of the generator. i is the output power of the generator. G is the total number of nodes. i is a node.

[0091] The constraints of the general DC-OPF model are as follows:

[0092]

[0093]

[0094]

[0095]

[0096] Where PTDF li is the power transfer distribution factor from node i to line l. is the transmission power of line l. i is the load demand of the generator. λ is the corresponding Lagrange multiplier. and are the Lagrange multipliers for the upper and lower constraints of the line power flow, respectively. and are the Lagrange multipliers for the upper and lower limits of the generator output. max,i , P min,i are the upper and lower limits of the output power respectively.

[0097] It is worth noting that the present invention first proposes a data-driven EPRA framework, including a Gaussian process substitution model for DC optimal power flow problems and a model-data dual-driven electricity price calculation method. Then, in order to ensure the accuracy of the EPRA algorithm, an adaptability criterion based on the Karush-Kuhn-Tucker (KKT) condition and a secondary verification process are proposed to distinguish GP learning error samples. Finally, the calculation results on the IEEE benchmark system show that this method can obtain EPRA results that are exactly the same as Monte Carlo simulations, while significantly improving the calculation efficiency.

[0098] The technical effect of the present invention is unquestionable. The present invention aims at the problem that the input-output mapping relationship of the LMP problem is complex, resulting in high calculation cost, long solution time, and difficulty in popularization and application in actual engineering. A data-driven EPRA calculation device based on physical models and historical data is proposed. Compared with the existing model-based and data-based methods, the present invention has the following advantages: 1) It ensures that EPRA has no precision loss, and the EPRA results obtained by the present invention are exactly the same as the traditional Monte Carlo method; 2) The number of training samples required for learning LMP is significantly reduced due to the introduction of Gaussian process; 3) The use of Gaussian process direct mapping replaces a large number of time-consuming POPF calculation processes, thereby improving the calculation efficiency of EPRA. In order to reduce the scale of the EPRA problem and improve the calculation speed, the present invention proposes a data-driven framework. At the same time, since it is difficult to directly learn LMP, the present invention constructs a GP replacement model for the DC-OPF problem to identify the key information of the LMP calculation. By solving a set of linear equations, a model-data hybrid EPRA method is proposed. This method significantly improves the efficiency of EPRA without affecting the accuracy of EPRA. 4) The present invention establishes a model-based adaptability criterion and performs a secondary verification of EPRA to determine inaccurately calculated samples. Before using GP to identify the marginal units and blocked transmission lines of the samples, the physical model information is first used to distinguish samples with learning errors, thereby ensuring the accuracy of EPRA. 5) The present invention can be widely used in the risk assessment of electricity prices in the power market, and is particularly suitable for analysis situations where there is high uncertainty in the power system, providing technical support for the rapid calculation of electricity price risk assessment. BRIEF DESCRIPTION OF THE DRAWINGS

[0099] Figure 1 This is a flow chart of the data-driven framework of the present invention;

[0100] Figure 2 It is a relationship diagram between DC-OPF and GP of the present invention;

[0101] Figure 3 Comparison of EPRA mean error for IEEE 30-bus system;

[0102] Figure 4 Comparison of EPRA standard deviation errors for IEEE 30-bus systems;

[0103] Figure 5 Comparison of EPRA mean error for IEEE 118-bus system;

[0104] Figure 6 Comparison of EPRA standard deviation errors for IEEE 118-bus systems. DETAILED DESCRIPTION

[0105] The present invention is further described below in conjunction with the embodiments, but it should not be understood that the above subject matter of the present invention is limited to the following embodiments. Without departing from the above technical ideas of the present invention, various substitutions and changes are made according to the common technical knowledge and customary means in the art, which should all be included in the protection scope of the present invention.

[0106] Embodiment 1:

[0107] See also Figure 1 to Figure 2 The data-driven spot market electricity price risk assessment system includes a data acquisition module, a unit output and transmission line flow calculation module, a sample identification module, a first electricity price calculation module, and a second electricity price calculation module.

[0108] The data acquisition module acquires the power system operation data and inputs it into the unit output and transmission line flow calculation module and the sample identification module.

[0109] The unit output and transmission line power flow calculation module stores a DC-OPF Gaussian process substitution model.

[0110] The unit output and transmission line flow calculation module inputs the power system operation data into the DC-OPF Gaussian process substitution model to obtain the unit output and transmission line flow, thereby identifying marginal units and blocked transmission lines.

[0111] The unit output and transmission line power flow calculation module transmits the unit output, transmission line power flow, marginal units and blocked transmission lines to the sample identification module.

[0112] The sample identification module stores sample verification criteria.

[0113] The sample identification module verifies the power system operation data, unit output and transmission line flow according to the sample verification criteria. If the verification is passed, the unit output, transmission line flow, marginal unit and blocked transmission line are input into the first electricity price calculation module; otherwise, the unit output, transmission line flow, marginal unit and blocked transmission line are input into the second electricity price calculation module.

[0114] The first electricity price calculation module stores a first electricity price calculation model.

[0115] If the first electricity price calculation module receives the unit output, transmission line flow, marginal unit and blocked transmission line, the unit output, transmission line flow, marginal unit and blocked transmission line are input into the first electricity price calculation model to calculate the node electricity price LMP.

[0116] The second electricity price calculation module stores a second electricity price calculation model.

[0117] If the second electricity price calculation module receives the unit output, transmission line flow, marginal unit and blocked transmission line, the unit output, transmission line flow, marginal unit and blocked transmission line are input into the second electricity price calculation model to calculate the node electricity price LMP.

[0118] The power system operation data includes power system topology and load data.

[0119] The DC-OPF Gaussian process alternative model is as follows:

[0120]

[0121] Where y is the output set, including power generation and transmission line flow. c(·) is the relevant cost function. A and B are the corresponding matrices for vectors x and y, respectively. b is the coefficient; Ω is the set of y.

[0122] The output of the DC-OPF Gaussian process substitution model is f(x)=[f(x1),f(x2),…,f(x n )] follows the following distribution:

[0123]

[0124] Where x=[x1,x2,…,x n ] is the input set.

[0125]

[0126] Where X = [x1, x2, …, x n ] T is a matrix of n×p dimensions. m(·) represents the mean function, and C(·,·) represents the covariance function.

[0127] The DC-OPF Gaussian process substitution model has the following distribution of Y:

[0128]

[0129] In the formula, σ 2 and I n are the noise variance and the n-dimensional identity matrix respectively. Y refers to the output of the DC-OPF Gaussian process surrogate model.

[0130] The sample set (X) of the DC-OPF Gaussian process surrogate model t ,,Y t ) is as follows:

[0131]

[0132] In the formula, is the identity matrix;

[0133] Parameter Y and Initial Y t The joint distribution of |X is as follows

[0134]

[0135] In the formula, parameter C 11 =C(X,X)+σ 2 I n , initial C 12 =C(X,X t ), parameter C 21 =C(X t ,X), initial C 22 =C(X t ,X t )+σ 2 I nt .

[0136] The output Y of the DC-OPF Gaussian process surrogate model t The expected value of is as follows:

[0137]

[0138] Where μ is the expected value.

[0139] The DC-OPF Gaussian process substitution model is trained by historical power system operation data.

[0140] The training steps of the DC-OPF Gaussian process substitution model include:

[0141] 1) Obtain a training sample set D = (X, Y). Each row of the sample set X is an I-dimensional uncertainty input vector, including the load demand D of all buses. i The output matrix Y consists of I G +I L Output variable columns. G The elements of the column output variable are the unit output P corresponding to each input vector x. L The elements of the column output variable are the transmission line power flows PF corresponding to each input vector x.

[0142] 2) Use the square exponential covariance kernel function to construct the GP substitution model, that is:

[0143]

[0144] In the formula, C SE (x k ,x * ) is the output of the GP substitution model; τ, l are the parameters of the GP substitution model; xk 、x * It is the input of GP substitution model;

[0145] 3) Rewrite formula (8) as follows:

[0146] Y|X,ξ~N(m(X),C SE (X,X)+σ 2 I). (9)

[0147] Where ξ=(τ,l) is a hyperparameter.

[0148] 4) Based on the maximum likelihood estimation, we get:

[0149]

[0150] In the formula, is the estimated value of hyperparameter and standard deviation;

[0151] Among them, the maximum likelihood estimate logP(Y|X,ξ,σ) is as follows:

[0152]

[0153] The output power of marginal unit i satisfies the following formula:

[0154] P min,i +ε g,i ≤P i ≤P max,i -ε g,i (12)

[0155] Where P i is the output power of the generator; P max,i and P min,i are the upper and lower limits of the generator output power respectively; g,i is the marginal unit relaxation factor;

[0156] Transmission power of blocked transmission line l Satisfy the following formula:

[0157] (PF l ≥F l -ε PF,l or PF l ≤-F l +ε PF,l ) (13)

[0158] In the formula, F l is the upper limit of the transmission power of line l; D i is the generator load demand; PTDF li is the power transfer distribution factor from node i to line l; ε PF,lis the relaxation factor for the blocked transmission line.

[0159] The steps of the sample identification module verifying the power system operation data, unit output and transmission line flow according to the sample verification criteria include:

[0160] 1) Determine whether the power system operation data, unit output and transmission line flow satisfy the following formula. If so, the verification is passed. If not, proceed to step 2).

[0161] N MG +1=N CL (14)

[0162] Where N MG 、N CL is the number of marginal generators and the number of blocked transmission lines;

[0163] 2) Determine whether the power system operation data unit output and transmission line flow satisfy the following formula. If so, the verification is passed. If not, the verification fails. Specifically, the correctness of this LMP calculation is determined by the statistical value of the previous LMP.

[0164]

[0165] Where, mean(LMP i ) is the average value of LMP at node i. p is the ratio threshold. LMP i is the electricity price at node i.

[0166] The first electricity price calculation model is used to calculate the marginal node electricity price LMP.

[0167] Among them, the electricity price LMP of node i i As shown below:

[0168]

[0169] Where L is the Lagrangian function. PTDF li is the power transfer distribution factor from node i to line l. and are the Lagrange multipliers for the upper and lower limits of the power flow of the line, respectively. i is the load demand of the generator. λ is the Lagrange multiplier of the power balance constraint. L is a collection of transmission lines.

[0170] Among them, the Lagrangian function L is as follows:

[0171]

[0172] In the formula, I Gis the set of generator nodes. i is the production cost of the generator. i is the output power of the generator. i is the node. PTDF li is the power transfer distribution factor from node i to line l. is the transmission power of line l. i is the load demand of the generator. λ is the corresponding Lagrange multiplier. and are the Lagrange multipliers for the upper and lower constraints of the line power flow, respectively. and are the Lagrange multipliers for the upper and lower limits of the generator output. max,i , P min,i are the upper and lower limits of the output power respectively. I is the set of system nodes. L is a collection of transmission lines;

[0173] The steps to calculate the node electricity price LMP include:

[0174] 1) When node i is not a marginal unit, according to the KKT condition, the following relationship is established:

[0175]

[0176] When node i is a marginal unit, according to the KKT condition, the following relationship is established:

[0177]

[0178] In the formula, the parameters I MG and N MG are the set and number of marginal units respectively.

[0179] 2) Establish the matrix form of equation (19), namely:

[0180]

[0181] 3) Rewrite formula (20) according to the transmission line constraint information to obtain:

[0182]

[0183] In the formula, is the Lagrange multiplier of the line power flow constraint;

[0184] Among them, the number of blocked transmission lines N CL As shown below:

[0185] N CL =L-(L+1-N MG )=NMG -1 (22)

[0186] 4) Formula (21) is solved according to the marginal unit nodes and blocked transmission lines to obtain the power transfer distribution factor from node i to line l.

[0187] 5) Input the power transfer distribution factor from node i to line l into formula (16) to calculate the electricity price LMP.

[0188] The second electricity price calculation model includes a general DC-OPF model.

[0189] The objective function of the general DC-OPF model is as follows:

[0190]

[0191] In the formula, c i is the production cost of the generator. i is the output power of the generator. G is the total number of nodes. i is a node.

[0192] The constraints of the general DC-OPF model are as follows:

[0193]

[0194]

[0195]

[0196]

[0197] Where PTDF li is the power transfer distribution factor from node i to line l. is the transmission power of line l. i is the load demand of the generator. λ is the corresponding Lagrange multiplier. and are the Lagrange multipliers for the upper and lower constraints of the line power flow, respectively. and are the Lagrange multipliers for the upper and lower limits of the generator output. max,i , P min,i are the upper and lower limits of the output power respectively.

[0198] Embodiment 2:

[0199] The data-driven spot market electricity price risk assessment system is as follows:

[0200] Establishing a data-driven EPRA calculation framework

[0201] In the spot market, LMP arises from economic dispatch. Specifically, the system operator solves the problem of optimal economic generation that meets variable loads and renewable energy while satisfying generation and transmission constraints. In fact, in the DC-OPF model, there is a linear relationship between LMP and Langrangian multipliers. This relationship depends on marginal units and blocked transmission lines, which can be obtained through the DC-OPF model. Therefore, the present invention proposes a data-driven framework, the core idea of ​​which is to establish a GP alternative model for the DC-OPF problem to identify marginal units and blocked transmission lines, thereby improving the computational efficiency of EPRA. The physical properties of the DC-OPF model are taken into account to ensure the accuracy of the model. First, the LMP formula is studied using the general DC-OPF model and its Karush–Kuhn–Tucker (KKT) conditions. Then, a data-driven method for EPRA is proposed.

[0202] 1) General DC-OPF model

[0203] The general DC-OPF model for economic dispatch is as follows:

[0204] Objective function:

[0205]

[0206] Constraints:

[0207]

[0208]

[0209]

[0210]

[0211] Where: c i is the production cost of the generator; PTDF li is the power transfer distribution factor from node i to line l; is the transmission power of line l, expressed as PF l ;P i and D i are the generator output power and load demand respectively. Please note that in this invention, renewable energy is regarded as a negative load and is included in D i middle.

[0212] The objective function minimizes the actual power supply operation cost. Equation (2) is the system power balance equation, and λ is the corresponding Lagrange multiplier. The constraints in equations (3) and (4) limit the power flow of the transmission line, and and are the Lagrange multipliers for the upper and lower limits of the power flow of the line, respectively. In formula (5), it represents the operating limit of the actual generator power, and are the Lagrange multipliers for the upper and lower limits of the generator output respectively.

[0213] 2) LMP framework

[0214] Based on the KKT condition, we derive the LMP, the Lagrange multiplier λ for the power balance constraint, and the dual multiplier for the line transmission limit and Note that in the following analysis, the saddle point obtained using the KKT condition corresponds to the global optimal solution of the OPF model.

[0215] In order to obtain the LMP, the Lagrangian function of the DC-OPF model (1)-(5) is expressed as LF as follows:

[0216]

[0217] Then, the LMP of the load at node i is obtained according to the Lagrangian function in equation (6), as follows:

[0218]

[0219] According to the KKT condition, the following relationship for generator i can be obtained:

[0220]

[0221] For marginal units, Formula (8) can be expressed as:

[0222]

[0223] Where: I MG and N MG are the set and number of marginal units respectively. Then, the matrix form of the above equation is analyzed. The matrix form of formula (9) is:

[0224]

[0225] In formula (10), there is N MG equations and (L+1) unknown variables, there is no unique solution. To solve these equations, we must first determine (L+1-N MG ) variables. Therefore, the transmission line constraint information is introduced. Note that for an unblocked transmission line, η l =0.

[0226] Therefore, blocking the transmission line NCL The number is:

[0227] N CL =L-(L+1-N MG )=N MG -1. (11)

[0228] Then formula (10) can be rewritten as:

[0229]

[0230] Based on the above discussion, if the marginal units and blocked transmission lines are known, the LMP can be calculated by solving a set of linear equations in equation (12). Therefore, the identification of marginal units and blocked transmission lines is the key to EPRA.

[0231] 3) Data-driven framework

[0232] The EPRA framework proposed in this invention is as follows Figure 1 The three steps are described as follows:

[0233] Step 1: Identify marginal units and blocked transmission lines. Power system operation data (such as D i ) are collected from historical data or through Monte Carlo simulation and input into the trained DC-OPF Gaussian process surrogate model. For each sample, the DC-OPF output (e.g., unit output and transmission line power flow) is immediately available. Marginal units and blocked transmission lines can then be identified quickly and with high accuracy.

[0234] Step 2: Distinguish the error samples. For the DC-OPF problem, if the number of blocked transmission lines N CL is n, then the number of marginal generators N MG is n+1. By using this natural property in the proposed framework, samples with learning errors can be distinguished. Therefore, for each sample with marginal units and blocked transmission lines identified by the GP substitution model, the present invention proposes the following adaptability criteria:

[0235] N MG +1=N CL . (13)

[0236] It is worth pointing out that the proposed adaptability criterion is not strictly complete. Only a very small number of samples meet the adaptability criteria, but there are learning errors. For these samples, due to the change in marginal generation cost, the LMP errors of all nodes will deviate greatly from the actual value. Therefore, a second verification process is proposed based on historical data, as follows:

[0237]

[0238] Where: mean(LMP i ) is the average value of LMP at node i, which can be calculated based on historical data. In the present invention, p is set to 50%.

[0239] Step 3: LMP calculation and EPRA. According to Equation (13), if the sample meets the adaptability criteria, the LMP can be calculated by solving a set of linear equations; otherwise, we should run DC-OPF to obtain the LMP. Then, with all the LMP data in hand, EPRA can be completed by performing statistical analysis on the LMP data.

[0240] DC-OPF Gaussian process substitution model

[0241] The basic idea of ​​the DC-OPF Gaussian process substitution model is to use GP to replace the time-consuming optimization process of DC-OPF, such as Figure 2 The complex DC-OPF features can be expressed by the mapping relationship f:D i →P i ,PF l .

[0242] 1) Gaussian process regression method

[0243] Gaussian process is a widely used data-driven method that has good adaptability to complex problems with small samples, nonlinearity, and high dimensions. In nonparametric statistics, the regularity of relationships can be assumed without concentrating the data in an easily described class. This characteristic enables GP to predict function values ​​inside and outside the input domain with a smaller sample size.

[0244] The present invention introduces GP to solve the regression problem. f(·) represents the regression function, that is, the output of the GP substitution model. Its corresponding p-dimensional input vector is represented as x. For the GP regression problem, the set of training sample input x is represented as [x1, x2, …, x n ]. Therefore, the corresponding output f(x) can be expressed as [f(x1),f(x2),…,f(x n )]. The Gaussian process model output f(x) follows a joint multivariate normal distribution as follows:

[0245]

[0246] Where: m(·) represents the mean function, C(·,·) represents the covariance function. Then, equation (15) can be rewritten as

[0247]

[0248] Where: X is an n×p dimensional matrix, representing [x1,x2,…,x n ]T Then, considering the presence of independent and identically distributed noise in the model output f(x), the realization Y can be expressed as:

[0249]

[0250] Where: 2 and I n are the noise variance and the n-dimensional identity matrix, respectively. Note that in practical applications of GP output, the noise is always taken into account.

[0251] In order to infer the noisy GP regression output from the above sample set (X, Y), a Bayesian inference framework is introduced. The Bayesian posterior distribution of the model output can be inferred from the Bayesian prior distribution y(x)|x and the likelihood estimate. For the test sample input set X t ,,Y t The Bayesian prior distribution of can be expressed as:

[0252]

[0253] Combine the training sample sets (X, Y), Y and Y t The joint distribution of |X can be expressed as:

[0254]

[0255] Where: C 11 =C(X,X)+σ 2 I n , C 12 =C(X,X t ), C 21 =C(X t ,X),C 22 =C(X t ,X t )+σ 2 I nt .

[0256] Then, according to the rules of conditional Gaussian distribution, from the training sample set (X, Y) and the test sample input set X t Infer Y t The Bayesian posterior distribution of . It follows a Gaussian distribution Σ(X t )). Y t The expected value of can be expressed as:

[0257]

[0258] So far, the general form of GP regression has been derived. Formula (20) can be used as an alternative model to the complex DC-OPF model.

[0259] 2) GP substitution model of DC-OPF

[0260] The basic DC-OPF model introduced in Section 1 can be further expressed as the following linear programming (LP) problem:

[0261]

[0262] Where: y is the output set, including power generation and transmission line flow, which is the key variable to determine marginal units and blocked transmission lines, c(·) is the relevant cost function. A and B are the corresponding matrices of vectors x and y, respectively. For random x, the DC-OPF in (21) can be converted to a POPF problem.

[0263] In this device, a GP replacement model is proposed for the DC-OPF problem, which improves the effectiveness of POPF at a lower computational cost. It specifically includes the following modules:

[0264] Module 1: Training sample generation module. To construct the GP surrogate model described in (20), for the DC-OPF problem, the training sample set D = (X, Y) can be obtained from the historical operation data of the system operator or by running a Monte Carlo simulation. In the Monte Carlo simulation, the uncertainty vector ω is sampled and the DC-OPF output is calculated for a large number of samples. Here, each row of X is an I-dimensional uncertainty input vector, including the load demands D of all buses. i The output matrix Y contains I G +I L The output variable list is the unit output P and the transmission line power flow PF corresponding to each input vector x.

[0265] Module 2: Gaussian process surrogate model. Based on the training data set D = [X, Y], we choose the squared exponential (SE) covariance kernel function to construct the GP surrogate model, namely:

[0266]

[0267] The hyperparameter ξ = (τ, l) can be calculated using the Gaussian maximum likelihood estimation method, which is optimal under the Gaussian assumption and easy to implement. Equation (17) with the hyperparameter can be rewritten as:

[0268] Y|X,ξ~N(m(X),C SE (X,X)+σ 2 I). (23)

[0269] Based on the maximum likelihood estimation, we can get:

[0270]

[0271] The maximum likelihood estimate can be expressed as:

[0272]

[0273] Using a gradient-based optimization algorithm, the hyperparameters can be deduced while fully building the GP surrogate model of DC-OPF.

[0274] Module 3: EPRA key information identification module. For the output of the GP alternative model (such as P and PF), learning errors are inevitable. In order to identify the key information of EPRA (such as marginal units and blocked lines) and address the impact of learning errors, the relaxation factor ε is introduced. Then, the marginal units and blocked transmission lines can be identified according to the following inequality:

[0275] Marginal unit i:

[0276] P min,i +ε g,i ≤P i ≤P max,i -ε g,i ; (26)

[0277] Blocking transmission line l:

[0278] (PF l ≥F l -ε PF,l or PF l ≤-F l +ε PF,l ). (27)

[0279] After obtaining the marginal units and blocked transmission lines for each sample, EPRA can be quickly calculated without loss of accuracy based on the framework proposed in Section 2.

[0280] Embodiment 3:

[0281] In this embodiment, the IEEE 30-node system and the IEEE 118-node system are used to illustrate the implementation plan, and the following methods are compared:

[0282] M0: Monte Carlo simulation (benchmark);

[0283] M1: SAE neural network based method;

[0284] M2: SDAE neural network based method;

[0285] M3: A stacked extreme learning machine based approach;

[0286] M4: Gaussian process based method;

[0287] M5: The method proposed by the device of the present invention.

[0288] The hyperparameter settings of each data-driven method are shown in Table 1. The learning error of M1~M5 is calculated as follows:

[0289]

[0290] Where: Г and p are the output of the data-driven method and its dimension; K represents the number of detection samples, and mean(Г) is the mean of Г.

[0291] Table 1 Hyperparameter settings of data-driven methods

[0292]

[0293] (1) IEEE 30-bus system simulation analysis

[0294] 1) Learning performance of DCOPF and LMP

[0295] First, we prove that the evaluation of LMP in the EPRA problem is more complex than that of the OPF problem, and it is difficult to directly use existing data-driven methods to learn well. Table 2 compares the learning performance of LMP learned by M1-M4 and DC-OPF output. For M1-M3, the number of training samples is set to 10,000; for M4 and M5, the number of training samples is set to 200; for all methods, the number of test samples is set to 10,000.

[0296] Table 2 Comparison of average errors between LMP and DC-OPF in IEEE 30-bus system

[0297]

[0298] The results show that directly learning LMP is difficult for data-driven methods due to its discontinuity. In addition, the DC-OPF problem is relatively simple, making the DC-OPF learning output method more reasonable.

[0299] 2) Computational efficiency of the proposed method

[0300] To demonstrate the benefits achieved by the proposed method, we compare the LMP computation time and error of M1-M5 in the IEEE 30-node system, as shown in Table 3. For the proposed method (M5), the number of training and testing samples is the same as that of M4.

[0301] Table 3 Comparison of average LMP errors of IEEE 30-bus system

[0302]

[0303] The following conclusions can be drawn:

[0304] 1. Among the above EPRA methods, the proposed device (M5) has the highest accuracy, which is exactly the same as the baseline method. This framework filters out the learning error of GP through the identification process and model-based adaptive criteria.

[0305] 2. Compared with M0, the test time is shortened by 59.34%. The results show that this method significantly improves the computational efficiency of LMP without losing accuracy.

[0306] 3. For M1~M4, learning errors in data-driven methods are inevitable even if the training sample size is large.

[0307] 4. Compared with the M1-M3 method, the training sample size of the M5 method is much smaller than that of the M1-M3 method, which meets the requirements of current industrial practice.

[0308] The errors of EPRA results were compared, such as Figure 3-4 As shown. For the method and apparatus proposed in the present invention, the EPRA results of the mean and standard deviation are very accurate. However, for M1 to M4, the estimated results of the mean are relatively accurate, while the standard deviation is far from the actual value of M0, so an accurate EPRA cannot be obtained. In particular, Figure 4 As shown, in certain specific nodes (e.g., node 8 and node 24), the errors are quite large. This may cause false information to be transmitted to ISO and market participants, resulting in serious market risks.

[0309] (2) IEEE118 node system simulation analysis

[0310] Taking the IEEE 118-node system as an example, the scalability of this method is verified. The learning error is shown in Table 4, and the EPRA evaluation results are shown in Figure 5-6 The test sample number is set to be the same as that of the IEEE 30-node system.

[0311] Table 4 Comparison of average LMP errors of IEEE 118-node system

[0312]

[0313]

[0314] The results show that the device can ensure the accuracy of EPRA in a practical scale system while improving the calculation speed. In addition, at 72 to 110 nodes, the statistical moments (i.e., mean and standard deviation) are far from the actual values, indicating that EPRA cannot be achieved through data-driven direct learning. In summary, the data-driven EPRA calculation device proposed in the present invention can improve the calculation efficiency of EPRA without loss of accuracy. Therefore, the present invention can provide technical support for the rapid calculation of EPRA.

Claims

1. A data-driven spot market electricity price risk assessment system, characterized by: It includes a data acquisition module, a unit output and transmission line flow calculation module, a sample identification module, a first electricity price calculation module, and a second electricity price calculation module; The data acquisition module acquires the power system operation data and inputs it into the unit output and transmission line flow calculation module and the sample identification module; The unit output and transmission line power flow calculation module stores a DC-OPF Gaussian process substitution model; The unit output and transmission line power flow calculation module inputs the power system operation data into the DC-OPF Gaussian process substitution model to obtain the unit output and transmission line power flow, thereby identifying marginal units and blocked transmission lines; The unit output and transmission line power flow calculation module transmits the unit output, transmission line power flow, marginal units and blocked transmission lines to the sample identification module; The sample identification module stores sample verification criteria; The sample identification module verifies the power system operation data, unit output and transmission line flow according to the sample verification criteria. If the verification is passed, the unit output, transmission line flow, marginal unit and blocked transmission line are input into the first electricity price calculation module; otherwise, the unit output, transmission line flow, marginal unit and blocked transmission line are input into the second electricity price calculation module; The first electricity price calculation module stores a first electricity price calculation model; If the first electricity price calculation module receives the unit output, the transmission line flow, the marginal unit and the blocked transmission line, the unit output, the transmission line flow, the marginal unit and the blocked transmission line are input into the first electricity price calculation model to calculate the node electricity price LMP; The second electricity price calculation module stores a second electricity price calculation model; If the second electricity price calculation module receives the unit output, transmission line flow, marginal unit and blocked transmission line, the unit output, transmission line flow, marginal unit and blocked transmission line are input into the second electricity price calculation model to calculate the node electricity price LMP.

2. The data-driven spot market electricity price risk assessment system according to claim 1, characterized in that: The power system operation data includes power system topology and load data.

3. The data-driven spot market electricity price risk assessment system according to claim 1, characterized in that: The DC-OPF Gaussian process alternative model is as follows: Where y is the output, including power generation and transmission line flow; c(·) is the relevant cost function; A and B are the corresponding matrices of vectors x and y, respectively; b is the coefficient; and Ω is the output set.

4. The data-driven spot market electricity price risk assessment system according to claim 3 is characterized in that: The output of the DC-OPF Gaussian process substitution model is f(x)=[f(x1),f(x2),…,f(x n )] follows the following distribution: Where x=[x1,x2,…,x n ] is the input set; m(·) represents the mean function, C(·,·) represents the covariance function; Where X = [x1, x2, …, x n ] T is a matrix of dimension n×p; The DC-OPF Gaussian process substitution model has the following distribution of Y: In the formula, σ 2 and I n are the noise variance and the n-dimensional identity matrix respectively; Y refers to the output of the DC-OPF Gaussian process surrogate model; The sample set (X) of the DC-OPF Gaussian process surrogate model t , Y t ) is as follows: In the formula, is the identity matrix; Parameter Y and Initial Y t The joint distribution of |X is as follows In the formula, parameter C 11 =C(X,X)+σ 2 I n , initial C 12 =C(X,X t ), parameter C 21 =C(X t ,X), initial C 22 =C(X t ,X t )+σ 2 I nt ; The output Y of the DC-OPF Gaussian process surrogate model t The expected value of is as follows: Where μ is the expected value.

5. The data-driven spot market electricity price risk assessment system according to claim 3, characterized in that: The DC-OPF Gaussian process substitution model is trained by historical power system operation data; The training steps of the DC-OPF Gaussian process substitution model include: 1) Obtain a training sample set D = (X, Y); each row of the sample set X is an I-dimensional uncertainty input vector, including the load demand D of all buses i ; The output matrix Y includes I G +I L Output variable column; I G The elements of the column output variable are the unit output P corresponding to each input vector x; L The elements of the column output variable are the transmission line power flow PF corresponding to each input vector x; 2) Use the square exponential covariance kernel function to construct the GP substitution model, that is: In the formula, C SE (x k ,x * ) is the output of the GP substitution model; τ, l are the parameters of the GP substitution model; x k 、x * It is the input of GP substitution model; 3) Rewrite formula (8) as follows: Y|X,ξ~N(m(X),C SE (X,X)+σ 2 (9) Where ξ=(τ,l) is a hyperparameter; 4) Based on the maximum likelihood estimation, we get: In the formula, is the estimated value of hyperparameter and standard deviation; Among them, the maximum likelihood estimate logP(Y|X,ξ,σ) is as follows:

6. The data-driven spot market electricity price risk assessment system according to claim 3, characterized in that: The output power of marginal unit i satisfies the following formula: P min,i +e g,i ≤P i ≤P max,i -e g,i (12) Where P i is the output power of the generator; P max,i and P min,i are the upper and lower limits of the generator’s output power respectively; ε g,i is the marginal unit relaxation factor; Transmission power of blocked transmission line l Satisfy the following formula: (PF l ≥F l -e PF,l or PF l ≤-F l +e PF,l ) (13) In the formula, F l is the upper limit of the transmission power of line l; D i is the generator load demand; PTDF li is the power transfer distribution factor from node i to line l; ε PF,l is the relaxation factor for the blocked transmission line.

7. The data-driven spot market electricity price risk assessment system according to claim 1, characterized in that: The steps of the sample identification module verifying the power system operation data, unit output and transmission line flow according to the sample verification criteria include: 1) Determine whether the following formula is true. If true, the verification is successful. If not, proceed to step 2); N MG +1=N CL (14) Where N MG 、N CL is the number of marginal generators and the number of blocked transmission lines; 2) Determine whether the power system operation data unit output and transmission line flow satisfy the following formula. If so, the verification is passed; if not, the verification fails; Where, mean(LMP i ) is the average price of electricity at node i; p is the proportional threshold; LMP i is the electricity price at node i.

8. The data-driven spot market electricity price risk assessment system according to claim 1, characterized in that: The first electricity price calculation model is used to calculate the marginal node electricity price LMP; Among them, the electricity price LMP of node i i As shown below: Where L is the Lagrangian function; PTDF li is the power transfer distribution factor from node i to line l; and are the Lagrange multipliers for the upper and lower limits of the power flow of the line respectively; D i is the load demand of the generator; λ is the Lagrange multiplier of the power balance constraint; I L is a collection of transmission lines; Among them, the Lagrangian function L is as follows: In the formula, I G is the set of generator nodes; c i is the production cost of the generator; P i is the output power of the generator; i is the node; PTDF li is the power transfer distribution factor from node i to line l; is the transmission power of line l; D i is the load demand of the generator; λ is the corresponding Lagrange multiplier; and are the Lagrange multipliers for the upper and lower constraints of the line power flow, respectively; and are the Lagrange multipliers for the upper and lower limits of the generator output respectively; P max,i , P min,i are the upper and lower limits of the output power respectively; I is the set of system nodes; I L A collection of transmission lines.

9. The data-driven spot market electricity price risk assessment system according to claim 8, characterized in that: The steps to calculate the node electricity price LMP include: 1) When node i is not a marginal unit, according to the KKT condition, the following relationship is established: When node i is a marginal unit, according to the KKT condition, the following relationship is established: In the formula, the parameters I MG and N MG are the set and number of marginal units respectively; 2) Establish the matrix form of equation (19), namely: 3) Rewrite formula (20) according to the transmission line constraint information to obtain: In the formula, is the Lagrange multiplier of the line power flow constraint; Among them, the number of blocked transmission lines N CL As shown below: 4) Solve formula (21) according to the marginal unit nodes and blocked transmission lines to obtain the power transfer distribution factor from node i to line l; 5) Input the power transfer distribution factor from node i to line l into formula (16) to calculate the electricity price LMP.

10. The data-driven spot market electricity price risk assessment system according to claim 1, characterized in that: The second electricity price calculation model includes a general DC-OPF model; The objective function of the general DC-OPF model is as follows: In the formula, c i is the production cost of the generator; P i is the output power of the generator; I G is the total number of nodes; i is the node; The constraints of the general DC-OPF model are as follows: Where PTDF li is the power transfer distribution factor from node i to line l; is the transmission power of line l; D i is the load demand of the generator; λ is the corresponding Lagrange multiplier; and are the Lagrange multipliers for the upper and lower constraints of the line power flow, respectively; and are the Lagrange multipliers for the upper and lower limits of the generator output respectively; P max,i , P min,i are the upper and lower limits of the output power respectively.

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