A two-stage monthly unit commitment and maintenance plan optimization method considering social carbon emission factors and short-term benefits

Abstract

The present invention proposes a two-stage monthly unit commitment and maintenance plan joint optimization method considering social carbon emission factors and short-term benefits. The historical wind speed data of multiple wind farms are used to fit the double-peak Weibull distribution function of the hourly wind speed of the corresponding wind farms respectively, and multiple wind farms for generating the required wind speed scenarios are modeled to generate wind speed scenarios with spatio-temporal tail correlation, and typical scenarios are obtained. The final monthly load forecasting results are obtained by expanding the BiLSTM load forecasting model considering socio-economic factors and environmental protection factors. Then, a two-stage monthly unit commitment and maintenance plan joint optimization model considering social carbon emission factors and short-term benefits is established with the first-stage objective and the second-stage objective, and the optimal solution of the model is obtained. The rationality of the proposed method is verified by comparing this method with the conventional models that do not consider social carbon emission factors, do not consider day-ahead unit commitment, and do not consider maintenance plans.

Description

Technical Field

[0001] The present invention belongs to the field of new energy optimal scheduling, and particularly relates to a two-stage monthly unit commitment and maintenance plan optimization method considering social carbon emission factors and short-term benefits. Background Art

[0002] Unit commitment is widely regarded as a crucial part of power system optimal scheduling. Further considering the social factor of carbon emission in unit commitment can reduce carbon emissions and achieve the optimal economic and environmental benefits. Among the unit commitments on multiple time scales, the medium- and long-term monthly unit commitment has a larger optimization space and a longer time scale than the short-term unit commitment. It can avoid frequent unit start-stop, thus achieving better optimization effects, further reducing carbon emissions, and promoting the consumption of new energy. In order to reduce carbon emissions and promote the further consumption of new energy, the reasonable joint optimization of monthly unit commitment and unit maintenance considering social carbon emission factors and short-term unit commitment benefits greatly affects the consumption of new energy and is of great significance in ensuring the reliable and economic operation of the power system.

[0003] Although the existing traditional monthly unit commitment methods partially consider the joint optimization of monthly unit commitment and day-ahead unit commitment, they are not well considered for the scenario of large-scale and high-proportion new energy access. In particular, they do not fully consider the impact of social carbon emission factors at the monthly time level, nor do they comprehensively consider the mutual influence with the maintenance plan. Most of them conduct joint optimization scheduling of monthly unit commitment and short-term unit commitment after the maintenance plan is determined, reducing the optimization space, ignoring the impact of social carbon emission factors, and not considering comprehensively enough, resulting in a large deviation between the optimization results of monthly unit commitment and the actual situation, increasing the economic cost and environmental cost. Summary of the Invention

[0004] To solve the deficiencies in the above background art, the present invention proposes a two-stage monthly unit commitment and maintenance plan optimization method considering social carbon emission factors and short-term benefits.

[0005] The specific technical solution of the present invention is a two-stage monthly unit commitment and maintenance plan optimization method considering social carbon emission factors and short-term benefits, which specifically includes the following steps:

[0006] Step 1: Use the historical wind speed data of multiple wind farms to respectively fit the double-peak Weibull distribution function of the hourly wind speed of the corresponding wind farms. Model the spatio-temporal correlation of multiple wind farms to obtain the wind speed scenarios of spatio-temporal tail correlation, and then reduce them through the synchronous back substitution reduction method to obtain typical scenarios.

[0007] Step 2: Through data preprocessing and normalization of the historical data of the load and related social, weather and other characteristics, then using MI mutual information for feature selection, and inputting the selected key features into the BiLSTM load prediction model for training, finally predicting the monthly load time series.

[0008] Step 3: Taking the monthly unit start-stop cost and maintenance cost as the monthly cost target, and taking the daily unit start-stop cost, daily unit operation coal consumption cost, carbon emission environmental penalty cost and wind abandonment cost as the daily cost target, establish a joint optimization scheduling model for the two-stage monthly unit combination and maintenance plan considering social carbon emission factors and short-term benefits, where the objective function of the first stage is the lowest monthly cost, and the objective function of the second stage is the lowest daily cost. Then, through the Benders decomposition algorithm, the joint optimization scheduling problem of the two-stage monthly unit combination and maintenance plan considering social carbon emission factors and short-term benefits is split into master and sub-problems and iteratively solved to obtain its optimal solution, specifically including:

[0009] The objective function of the joint optimization scheduling model for the two-stage monthly unit combination and maintenance plan considering social carbon emission factors and short-term benefits mainly includes the first-stage monthly cost target and the second-stage daily cost target, which can be specifically expressed by the mathematical model as:

[0010] F = F M + F D1 + F D2 (9)

[0011]

[0012]

[0013] Among them, F M is the monthly cost, F D = F D1 + F D2 is the daily cost, the monthly cost F M includes the monthly unit start-stop cost and maintenance plan cost, and the daily cost F D = F D1 + F D2 includes the daily unit start-stop cost, daily unit operation coal consumption cost, carbon emission environmental penalty cost and wind abandonment cost; is the daily coal consumption cost of thermal power units, is the carbon emission environmental penalty cost; a i 、b i 、c i are the characteristic coefficients of the coal consumption cost of thermal power unit i; λ c and λ s are the cost coefficients corresponding to CO2 and SO2 gas emissions respectively; and are the CO2 and SO2 gas emission coefficients of thermal power unit i, respectively; is the fuel consumption of thermal power unit i at the t-th time period on the d-th day; β i is the coal consumption per unit power generation of thermal power unit i; D represents 30h per month (D = 30), T represents 24h per day (T = 24), I represents the number of thermal power units, Y i M is a flag determining whether the thermal power unit is a monthly unit, Y i D is a flag determining whether the thermal power unit is a daily unit, is the start-stop state of thermal power unit i belonging to the monthly unit combination at the t-th time period on the d-th day; is the start-stop state of thermal power unit i belonging to the daily unit combination at the t-th time period on the d-th day under scenario s; S is the total number of scenarios of the analyzed wind farm; I s,i,d,t is the start-stop state of thermal power unit i finally determined to be subordinate at the t-th time period on the d-th day under scenario s; is the planned output of thermal power unit i at the t-th time period on the d-th day under scenario s. F i (·) is the power generation cost characteristic function of thermal power unit i; F envs,i,t (·) is the environmental penalty function for CO2 and SO2 gas emissions, SUC i is the start-stop cost of the i-th thermal power unit; N is the total number of maintenance items, W n,d is the cost of starting maintenance of the n-th maintenance item on the d-th day, τ n,d is the start-maintenance state of the n-th maintenance item in the i-th maintenance time period, 1 indicates starting maintenance, 0 indicates not the start-maintenance time period; λ w is the curtailment penalty, is the curtailment power.

[0014] Introduce the start-up cost decision variables of each thermal power unit at each time period under monthly and daily decisions and and linearly segmentize The corresponding objective function can be simplified as:

[0015]

[0016] The corresponding constraint conditions generated after linearization:

[0017]

[0018]

[0019]

[0020] Finally, the above model is split into master and sub-problems through the Benders decomposition algorithm and iteratively solved to obtain its optimal solution.

[0021] In the above joint optimal scheduling model of two-stage monthly unit commitment and maintenance plan considering social carbon emission factors and short-term benefits, the implementation of Step 1 includes:

[0022] 1) According to the conclusion that at the same time of each day in the same quarter in the relevant literature, there is the same probability distribution characteristic, the wind speed v of the same hour every day within a month is set i to conform to the same probability distribution. The historical wind speed data of multiple wind farms are used to respectively fit the distribution function of the hourly wind speed described by the double-peak (seven-parameter) Weibull distribution function. The expression of the double-peak Weibull distribution function is as follows:

[0023]

[0024]

[0025]

[0026] In the formula: are two single-peak Weibull distributions included in the double-peak Weibull distribution of the w-th wind farm at the i-th time period. w represents the corresponding wind farm, w = 1, 2, 3,..., W, and i represents the corresponding time period in a day, i = 1, 2, 3,..., 24; are respectively the shape parameter, location parameter, and scale parameter of the wind speed probability density function (PDF) of the w-th wind farm at the i-th time period, and r i w is the percentage of the single-peak Weibull distribution

[0027] Step1: Statistically analyze the wind speed data of 24 hours per day corresponding to this month in recent years. Select the wind speed data of 6 years. Calculate according to 30 days per month. According to the monthly statistics, 60×3 = 180 data can be obtained for each hour to fit the wind speed probability density function to obtain the corresponding double-peak Weibull distribution function.

[0028] Step2: According to the Copula theory, the tCopula function is used to model the spatial tail correlation of each wind farm. Considering the random variables V of the wind speeds of each wind farm at the i-th time period i 1 ,..., V i W , denotes the marginal probability distribution function of denotes Marginal probability density function. The joint probability distribution function F of the wind speeds of each wind farm in the i-th period is represented by the Copula function C and a Copula density function c i and the joint probability density function f i , specifically expressed as:

[0029]

[0030]

[0031] Step3: The C-vine structure is adopted to model the tail time correlation. The C-vine structure is used to simulate the 24-hour wind speed random variables of each wind farm. Based on the C-vine structure, the 24-hour joint density of the k-th wind farm can be expressed as:

[0032]

[0033] The parameters of the C-vine structure can be solved by Sequential Estimation (SE). The historical data of wind speed is used for the maximum likelihood estimation of the parameters of the first layer, and the parameters of the remaining layers are estimated by the pseudo-observations generated by the conditional distribution function.

[0034] 2) According to the spatial joint probability distribution function of different wind farms at each time node, in the first step, W-dimensional temporary samples with spatial correlation are generated, and each sample follows a uniform distribution. Then, based on the sampling method of the C-vine structure, according to the time joint probability distribution function of each wind farm, the above-generated temporary samples are used to further generate the final wind speed scenarios with spatio-temporal tail correlation. The steps to generate the final wind speed scenarios are as follows:

[0035] ① Initialize the reference variable of wind farm w, and let w = 1;

[0036] ② Let denote Z w the i-th column, denote the realization of the hourly wind speed variable of the w-th wind farm at time i in the standard space;

[0037] ③ Let Solve the equation using the bisection method to obtain i.e.,

[0038] ④ When t > 2, can be obtained by iterative solution ;

[0039] ⑤ Substitute into V i wObtained by the inverse distribution function Convert the realization of the standard space into the original space. Denote the wind speed scenario of the w-th wind farm, w = w + 1;

[0040] ⑥ Repeat steps ②, ③, ④, and ⑤ until w = W to obtain the final wind speed scenarios.

[0041] After generating a number of the above final wind speed time series samples, consider the operating physical characteristics of the wind turbines to generate their corresponding wind power scenarios, and then use the synchronous back substitution reduction method to reduce the generated wind power scenarios to obtain the most representative scenarios.

[0042] In the above joint optimal scheduling model of two-stage monthly unit commitment and maintenance planning considering social carbon emission factors and short-term benefits, the implementation of step 2 includes:

[0043] 1) Select relevant features affecting the load

[0044] Mainly select meteorological factors, holiday calendar index factors, social and economic factors, and environmental protection factors that have a greater impact on the power load and incorporate them into the power load prediction feature library. The relevant feature variables are temperature, working day, dew point, weekend, precipitation, holiday, air pressure, season, weather, population, AQI.

[0045] 2) Data preprocessing

[0046] Data cleaning: Perform data cleaning on the load data (hourly level) and relevant feature quantities for the previous several years, including several steps such as missing value imputation, noise removal, outlier detection, and data smoothing. Then apply min-max data normalization to scale the historical load values and social, weather, and date holiday features to the range of 0 to 1. Specifically, it is expressed as follows:

[0047]

[0048] 3) Feature selection

[0049] Use the MI feature selection method to calculate the mutual information for each feature. X and Y are set as two random variables, X is the relevant feature quantity affecting the load, and Y is the load prediction quantity. The joint probability density function of X and Y is set as μ X,Y , and their marginal density functions are μ X (x) and μ Y (y). Since both the load-related feature quantity and the predicted load quantity X and Y are discrete values, MI is expressed as:

[0050]

[0051] 4) Load prediction model

[0052] Considering that the load is non - stationary and fluctuating, a bidirectional long short - term memory neural network (BiLSTM) is used to predict the load. The selected relevant key feature quantities are input into the BiLSTM prediction model for training, and finally the monthly load time series is obtained by predicting the load.

[0053] The advantages of the present invention are as follows:

[0054] The method proposed in the present invention comprehensively considers the relevant impacts of social carbon emission factors, jointly optimizes the monthly unit commitment and maintenance plan, groups the monthly units and daily units, considers the impact of the day - ahead unit commitment, expands the optimization space, obtains the best economic and environmental benefits, and makes the subsequent day - ahead unit commitment decision more reasonable. At the same time, in the optimization process, the uncertainty of a high - proportion wind farm is reasonably characterized by typical scenarios, and the impact of social factors is also considered in the load prediction process, improving the accuracy of monthly load prediction. Compared with the monthly unit commitment model that does not consider social factors, short - term benefits and maintenance plans, the decision - making strategy is more reasonable and economic, achieving a win - win situation for both economy and environment, responding to the carbon emission reduction goal and promoting the consumption of new - energy wind power.

[0055] The present invention provides a more reliable decision - making strategy for monthly unit commitment optimization scheduling by establishing a joint optimization scheduling model for two - stage monthly unit commitment and maintenance plan considering social carbon emission factors and short - term benefits, which is more conducive to the further reasonable consumption of new energy and responds to the dual - carbon goal. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 is the flowchart of the method of the present invention;

[0057] Figure 2 is the schematic diagram of the LSTM structure;

[0058] Figure 3 is the schematic diagram of the unit commitment result of the present invention;

[0059] Figure 4 is the schematic diagram of the output results of each station after optimization of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0060] To facilitate the understanding and implementation of the present invention by those of ordinary skill in the art, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the embodiments described herein are only for the purpose of illustrating and explaining the present invention, and are not used to limit the present invention.

[0061] The following will introduce the implementation manner of the present invention, specifically as follows: Figures 1 to 4 will introduce the implementation manner of the present invention, specifically as follows:

[0062] Step 1: Use the historical wind speed data of multiple wind farms to fit the bimodal Weibull distribution function of the hourly wind speed for each corresponding wind farm. Model the spatio-temporal correlation of multiple wind farms to obtain the wind speed scenarios of spatio-temporal tail correlation, and then reduce them through the synchronous back-substitution reduction method to obtain typical scenarios.

[0063] Step 2: Conduct data preprocessing and normalization on the historical data of the load and related social, weather and other characteristics, then use MI mutual information for feature selection, and input the selected key features into the BiLSTM load prediction model for training, and finally predict the monthly load time series.

[0064] Step 3: Take the monthly unit start-stop cost and maintenance cost as the monthly cost target, and take the daily unit start-stop cost, daily unit operation coal consumption cost, carbon emission environmental penalty cost and wind curtailment cost as the daily cost target, and establish a joint optimization scheduling model for the two-stage monthly unit commitment and maintenance plan considering the short-term benefits of social carbon emission factors. The objective function of the first stage is to minimize the monthly cost, and the objective function of the second stage is to minimize the daily cost. Then, through the Benders decomposition algorithm, the joint optimization scheduling problem of the two-stage monthly unit commitment and maintenance plan considering social carbon emission factors and short-term benefits is split into master and sub-problems for iterative solution to obtain its optimal solution.

[0065] The above steps constitute a joint optimization method for the two-stage monthly unit commitment and maintenance plan considering social carbon emission factors and short-term benefits. The block diagram is as Figure 1 shown. Use the historical wind speed data of the wind farm to fit the bimodal Weibull distribution function of the hourly wind speed and model its spatio-temporal correlation to obtain the wind speed scenarios of spatio-temporal tail correlation, and then reduce them through the synchronous back-substitution reduction method to obtain typical scenarios. Obtain the final monthly load prediction result through load prediction considering social factors. Then, taking the monthly cost target as the first-stage target and the daily cost as the second-stage target, establish a joint optimization model for the two-stage monthly unit commitment and maintenance plan considering social carbon emission factors and short-term benefits, and solve the master and sub-problems iteratively through the Benders decomposition algorithm to obtain the optimal solution of the model.

[0066] Specifically, in Step 1, according to the conclusion in relevant literature that the same moment of each day in the same quarter has the same probability distribution characteristics, set the wind speed v i of the same hour of each day within a month to conform to the same probability distribution, and use the historical wind speed data of multiple wind farms to respectively fit the distribution function of the hourly wind speed described by the bimodal (seven-parameter) Weibull distribution function. The expression of the bimodal Weibull distribution function is as follows:

[0067]

[0068]

[0069]

[0070]

[0071]

[0072]

[0073] where: are two single-peak Weibull distributions included in the double-peak Weibull distribution for the \(w\)th wind farm at the \(i\)th time period, and \(F\) i w (\(v\) i ) is the corresponding cumulative distribution function, \(w\) represents the corresponding wind farm, \(w = 1, 2, 3, \cdots, W\), and \(i\) represents the corresponding time period in a day, \(i = 1, 2, 3, \cdots, 24\); are the shape parameter, location parameter, and scale parameter of the wind speed probability density function (PDF) for the \(w\)th wind farm at the \(i\)th time period, respectively, and \(r\) i w is the percentage of the single-peak Weibull distribution, and its obtaining method is as follows:

[0074] Step1: Statistically analyze the wind speed data for 24 hours of each day corresponding to this month in recent years. Select 6 years of wind speed data, calculate each month as 30 days, and according to the monthly statistics, 60×3 = 180 data can be obtained for each hour to fit the wind speed probability density function. For each wind farm to be analyzed, the historical data can be expressed as \(v\) history =\{v1, v2, \cdots, v 24×d \}, where \(d\) represents the number of observation days. Arrange the historical data of each day in a row to obtain a matrix, where each column represents the expression form of the wind speed random variable for each hour.

[0075]

[0076] Step2: According to the processed historical data recorded and statistically analyzed for each wind farm, use the maximum likelihood estimation (MLE) to fit the parameters of the double-peak Weibull distribution function of the wind speed for each hour of the month to be analyzed.

[0077] Step3: According to the Copula theory, several one-dimensional marginal probability distribution functions can be connected into a joint probability distribution function through the Copula function to model the spatial tail correlation of each wind farm. Considering the random variables \(V\) of the wind speeds of each wind farm at the \(i\)th time period i 1 , \cdots, \(V\) i W , denote the marginal probability distribution function of denote the marginal probability density function. According to Sklar's theorem, there is a Copula function C and a Copula density function c, then the joint probability distribution function F i and the joint probability density function f i of the wind speeds of each wind farm at time period i satisfy (3) and (4), and can be expressed as:

[0078]

[0079]

[0080] Since the wind speed has a symmetric upper and lower tail correlation relationship, the tCopula function is more reasonable than other Copula functions in modeling the tail correlation structure of the wind speed. Therefore, the tCopula is used to fit the joint probability distribution function of the wind speed, and the parameters are estimated through historical data to maximize the log-likelihood function. In Copula theory, the tail correlation coefficient of two random variables can be calculated by equations (25) and (26).

[0081]

[0082]

[0083] Step4: Since Copula theory is difficult to handle high-dimensional situations, the C-vine structure is used to model the tail time correlation. When modeling the time tail correlation of each wind farm, the joint probability distribution contains 24 random variables representing the wind speed per hour. The C-vine structure is used to simulate the 24-hour wind speed random variables of each wind farm. Based on the vine-copula structure, the joint density function can be decomposed into an independent part and a conditional part of correlation. Therefore, based on the C-vine structure, the 24h joint density of the k-th wind farm can be expressed as:

[0084]

[0085] The parameters of the C-vine structure can be solved by Sequential Estimation (SE). The historical data of the wind speed is used for the maximum likelihood estimation of the parameters of the first layer, and the parameters of the remaining layers are estimated by the pseudo-observations generated by the conditional distribution function.

[0086] 2) According to the spatial joint probability distribution function of different wind farms at each time node, in the first step, W-dimensional temporary samples with spatial correlation are generated, and each sample follows a uniform distribution. The steps to generate the temporary samples are as follows:

[0087] ① Initialize the time variable i and set i = 1;

[0088] ② Generate the sampling matrix S i ∈R M×W , because the wind speed has symmetric fat - tail characteristics, use the Latin Hypercube Sampling method (LHS) to formulate the tail correlation coefficients of the wind speed in equations (28) and (29). M represents the number of scenarios;

[0089]

[0090]

[0091] λ up and λ lo represent the upper and lower tail correlation coefficients, F -1 (x) and G -1 (y) are the inverse functions of F(x) and G(y) respectively.

[0092] ③ Let w = 1;

[0093] ④ Substitute the w - th column of S i into the corresponding marginal probability distribution function F i w w (·) to obtain which follows U(0,1), w = w + 1;

[0094] ⑤ Repeat ④ until w = W;

[0095] ⑥ Let the matrix Z w represent the temporary sample of the w - th wind farm, and fill into the i - th column of Z w , i = i + 1;

[0096] ⑦ Repeat ②, ③, ④, ⑤ and ⑥ until i = 24, and finally obtain the complete temporary sample matrix Z w .

[0097] 3) Sampling method based on the C - vine structure. According to the time - joint probability distribution function of each wind farm, use the above - generated temporary samples to further generate the final wind speed scenarios with spatio - temporal tail correlations. The steps to generate the final wind speed scenarios are as follows:

[0098] ① Initialize the reference variable of wind farm w and set w = 1;

[0099] ② Let represent the i - th column of Z w , represent the realization of the hourly wind speed variable of the w - th wind farm at time i in the standard space;

[0100] ③ Let Solve the equation using the bisection method to obtain That is

[0101] ④ When t > 2, It can be solved iteratively to obtain;

[0102] ⑤ Substitute into the inverse distribution function of V i w to obtain Convert the realization of the standard space to the original space. Denote the wind speed scenario of the w-th wind farm, w = w + 1;

[0103] ⑥ Repeat ②, ③, ④, and ⑤ until w = W to obtain the final wind speed scenarios.

[0104] 4) Scenario reduction

[0105] Considering the computational efficiency and to be more in line with the actual wind power generation situation, after generating a number of the above-mentioned final wind speed time series samples, the relevant wind power scenarios should be generated according to the operating physical characteristics of the analyzed wind turbines first, and then the redundant wind power scenarios should be reduced to a reasonable and most representative number of scenarios using scenario reduction techniques.

[0106] The expression between the output power of the wind turbine and the relevant wind speed at a certain hub height is approximated by a piecewise function as shown below:

[0107]

[0108] In the formula, P rated is the rated output power of the fan; v CI , v rated , v CO are the cut-in wind speed, cut-out wind speed, and rated wind speed of the fan respectively.

[0109] Use the synchronous back substitution reduction method to reduce the generated wind power scenarios, and the specific implementation is as follows:

[0110] ① Determine which scenarios need to be reduced. Eliminate scenario w s* , which meets the requirements of the following formula

[0111]

[0112] ② Change the total number of scenarios: n S = n S -1, and then select the scenario closest to the eliminated scenario w s* ​

[0113]

[0114] ③Change and eliminate scenario w s* The closest scenario Probability of:

[0115]

[0116] ④If the total number of remaining scenarios n S is still greater than the required number of scenarios, repeat the reduction algorithm in ① until the number of remaining scenarios meets the requirements.

[0117] In the above joint optimal scheduling model of two-stage monthly unit commitment and maintenance plan considering social carbon emission factors and short-term benefits, the implementation of step 2 includes:

[0118] 1) Select relevant features affecting the load

[0119] Mainly select meteorological factors, holiday calendar index factors, socio-economic factors and environmental protection factors that have a greater impact on the power load and incorporate them into the power load forecasting feature library. The relevant feature variables are temperature, working day, dew point, weekend, precipitation, holiday, air pressure, season, weather, population, AQI.

[0120] 2) Data preprocessing

[0121] Data cleaning: Clean the load data (hourly) and related feature quantities for the previous several years, including several steps such as missing value imputation, noise removal, outlier detection and data smoothing.

[0122] Data standardization: Apply min-max data standardization to scale the historical load values and social, weather and date holiday features to the range of 0 to 1. Specifically expressed as follows:

[0123]

[0124] 3) Feature selection

[0125] If there are C features affecting the power load, the specific steps to calculate the mutual information of each feature are as follows:

[0126] X and Y are set as two random variables, X is the relevant feature quantity affecting the load, and Y is the load prediction quantity. The joint probability density function of X and Y is set as μ X,Y , and their marginal density functions are μ X (x) and μ Y (y), specifically expressed as:

[0127] μX (x) = ∫μ X,Y (x, y)dy (35)

[0128] μ Y (y) = ∫μ X,Y (x, y)dx (36)

[0129] H(y) is the marginal entropy, and the uncertainty in Y can be obtained as:

[0130] H(y) = -∫μ Y (y) log μ Y (y)dy (37)

[0131] If Y is obtained indirectly from X, then H(Y|X) is the conditional entropy, and the uncertainty of Y can be expressed as:

[0132] H(X|Y) = -∫μ X (x) ∫μ Y (y|X = x) log μ Y (y|X = x)dydx (38)

[0133] If considered jointly, H(X,Y) is the joint entropy, and the uncertainty about (X,Y) can be expressed as:

[0134] H(X,Y) = -∫μ X,Y (x,y) log μ X,Y (x,y)dxdy (39)

[0135] The MI between X and Y is calculated as:

[0136] M(X,Y) = H(Y) - H(Y|X) (40)

[0137] Since Y is the load prediction output in the load prediction problem, then MI can appropriately calculate the importance of X to the model Y, where Y = X + H and H is the prediction range. MI can be further expressed as:

[0138] M(X,Y) = H(X) + H(Y) - H(X,Y) (41)

[0139] Specifically, it can be expressed as:

[0140]

[0141] Since both the load-related feature quantity and the predicted load quantity X and Y are discrete values, MI is expressed as:

[0142]

[0143] Finally, the most critical relevant feature quantity is selected according to the MI value.

[0144] 4) Load forecasting model

[0145] Considering the non - stationarity and volatility of the load, a Bidirectional Long Short - Term Memory Neural Network (BiLSTM) is used to forecast the load. BiLSTM is applied to detect the long - term and short - term memory properties of the load. The selected relevant key feature quantities are input into the BiLSTM prediction model for training, and finally the monthly load time series is obtained by forecasting the load. There are mainly three gate mechanisms inside LSTM, which are specifically described as follows:

[0146] ① Forget gate. In this stage, the input information passed in from the previous node is selectively forgotten.

[0147] ② Input gate. In this stage, the input of this stage is selectively "remembered" to determine whether to add the new input information to the cell state. It mainly selectively remembers the input.

[0148] ③ Output gate. In this stage, it will determine which will be regarded as the output of the current state.

[0149] In the above - mentioned joint optimal scheduling model of two - stage monthly unit commitment and maintenance plan considering social - type carbon emission factors and short - term benefits, the implementation of step 3 includes:

[0150] 1) The objective function of the joint optimal scheduling model of two - stage monthly unit commitment and maintenance plan considering social - type carbon emission factors and short - term benefits mainly includes the monthly cost target in the first stage and the daily cost target in the second stage, which can be specifically expressed by the mathematical model as:

[0151] F = F M + F D1 + F D2 (44)

[0152]

[0153]

[0154] Among them, F M is the monthly cost, F D = F D1 + F D2 is the daily cost. The monthly cost F M includes the monthly unit start - stop cost and maintenance plan cost. The daily cost F D = F D1 + F D2 includes the daily unit start - stop cost, the daily unit operation coal consumption cost, the carbon emission environmental penalty cost and the wind curtailment cost; is the daily coal consumption cost of thermal power units, is the environmental penalty cost for carbon emissions; a i , b i , c i are the characteristic coefficients of the operating coal consumption cost of thermal power unit i; λ c and λ s are the cost coefficients corresponding to the emissions of CO2 and SO2 gases respectively; and are the CO2 and SO2 gas emission coefficients of thermal power unit i respectively; is the fuel consumption of thermal power unit i at the t-th time period on the d-th day; β i is the coal consumption per unit power generation of thermal power unit i; D represents 30 days per month (D = 30), T represents 24 hours per day (T = 24), I represents the number of thermal power units, Y i M is the flag determining whether the thermal power unit is a monthly unit, Y i D is the flag determining whether the thermal power unit is a daily unit, is the start-stop state of thermal power unit i belonging to the monthly unit combination at the t-th time period on the d-th day; is the start-stop state of thermal power unit i belonging to the daily unit combination at the t-th time period on the d-th day in scenario s; S is the total number of scenarios of the analyzed wind farm; I s,i,d,t is the start-stop state of thermal power unit i finally determined to be subordinate at the t-th time period on the d-th day in scenario s; is the planned output of thermal power unit i at the t-th time period on the d-th day in scenario s. F i (·) is the power generation cost characteristic function of thermal power unit i; F envs,i,t (·) is the environmental penalty function for the emissions of CO2 and SO2 gases, SUC i is the start-stop cost of the i-th thermal power unit; N is the total number of maintenance items, W n,d is the cost of starting the maintenance of the n-th maintenance item on the d-th day, τ n,d is the start state of the n-th maintenance item in the i-th maintenance period, 1 means starting maintenance, 0 means not in the starting maintenance period; λ w is the penalty for wind curtailment, is the wind curtailment power.

[0155] 2) The specific relevant constraint conditions are as follows:

[0156] 1. Single-unit constraint:

[0157] ① Output upper and lower limit constraints of thermal power unit:

[0158]

[0159] In the formula, is the lower limit of the output of thermal power unit i; is the upper limit of the output of thermal power unit i.

[0160] ② Ramp rate constraint of thermal power unit:

[0161]

[0162]

[0163] In the formula, RU i is the upward ramp rate of thermal power unit i; RD i is the downward ramp rate of thermal power unit i; T0 is the duration of each studied scheduling period.

[0164] ③ Consecutive start-stop constraint of thermal power unit:

[0165]

[0166]

[0167]

[0168]

[0169] In the formula, T i on and T i off are the minimum consecutive start-stop times of thermal power unit i.

[0170] ④ Constraint on the total number of starts of each thermal power unit in the monthly unit:

[0171]

[0172] In the formula, is the maximum required total number of starts of monthly thermal power unit i.

[0173] ⑤ Monthly contract power constraint:

[0174]

[0175]

[0176] In the formula, Q i is the contract power allocated to the thermal power unit per month; Q sum is the total power demand for that month; is the maximum value of the wind power for that month, expressed as follows:

[0177]

[0178] In the formula, Indicates the specific monthly predicted power generation of wind power for the next month.

[0179] ⑥ Optimization cycle constraint for start-stop of single ownership relationship between monthly and daily thermal power units:

[0180] Each thermal power unit can only be selected in either monthly or daily operation:

[0181] Y i M +Y i D =1 (58)

[0182] When thermal power unit i belongs to the monthly unit, it can be scheduled to start up in the monthly unit combination:

[0183]

[0184] When thermal power unit i belongs to the daily unit, it can be scheduled to start up in the daily unit combination:

[0185]

[0186] If the unit is not scheduled to start up within the month, it automatically belongs to the daily unit, that is, at least one period in the monthly unit is in the startup state:

[0187]

[0188] Final start-stop plan constraint for thermal power unit i:

[0189]

[0190] ⑦ Carbon emission constraint:

[0191]

[0192]

[0193] In the formula, are the power generation emission coefficients of thermal power unit i respectively; is the total carbon emission of all thermal power units, C MAX is the maximum carbon emission limit.

[0194] 2. System constraints:

[0195] ① Power balance constraint:

[0196]

[0197]

[0198] In the formula, The load \(l_d\) at the \(t\)-th period of the \(d\)-th day The output power of wind farm \(j\) at the \(t\)-th period of the \(d\)-th day under scenario \(s\) The actual power generation capacity of wind farm \(j\) at the \(t\)-th period of the \(d\)-th day under scenario \(s\).

[0199] ② Spinning reserve constraint:

[0200]

[0201]

[0202]

[0203] In the formula, \(T\) R Is the time interval of the corresponding spinning reserve ramp And Are the conventional system's traditional up and down spinning reserve requirements at the \(t\)-th period of the \(d\)-th day Is the rated capacity of wind farm \(j\); \(\alpha\) up And \(\alpha\) down Are the positive and negative spinning reserve demand coefficients of wind power output respectively.

[0204] ③ DC power flow security constraint of the line:

[0205]

[0206] In the formula, Is the upper limit of the transmission capacity of line \(l\); \(D\) l,i And \(D\) l,j Are the generator power distribution factors of thermal power unit \(i\) or wind farm \(j\) for line \(l\).

[0207] 3. Maintenance plan constraint:

[0208] ① Maintenance status constraint:

[0209]

[0210]

[0211] In the formula, \(y\) n,d Is the maintenance status of maintenance item \(n\) on the \(d\)-th day. If it is in the maintenance status, it is 1, otherwise it is 0; \(M\) Cn Is the duration of maintenance item \(n\).

[0212] ② Earliest and latest start time constraints for maintenance:

[0213]

[0214]

[0215] Where D n,min is the earliest start time of maintenance item n; D n,max is the latest start time of maintenance item n.

[0216] ③ Sequential maintenance constraint:

[0217]

[0218]

[0219] Where n1 is the maintenance item number; M Ds is the time interval that maintenance item n1 needs to be ahead of item n.

[0220] ⑤ Mutually exclusive maintenance constraint:

[0221]

[0222] ⑥ Simultaneous maintenance constraint:

[0223]

[0224] ⑦ Maintenance resource constraint:

[0225]

[0226] Where S d is the upper limit of maintenance items carried out at the same time.

[0227] ⑧ Correlation constraint between thermal power unit maintenance plan and monthly unit commitment:

[0228]

[0229] Where A i,n is an element in the correlation matrix A IN ={A i,n} between thermal power unit i and maintenance item n, indicating that A i,n =1 when maintenance item n includes maintenance of thermal power unit i, otherwise A i,n =0; B d,d1,t is an element of the correlation matrix representing the corresponding relationship between the time period index variable t of each hour of the unit commitment every day and the time period index variable d of the maintenance plan every day of, indicating that the time period index variable d and d1 of the maintenance plan are related to the index variable t of each hour of the unit commitment period every day, and B d,d1,t =0 means not related. Specifically, it is expressed as follows:

[0230]

[0231] 3) The objective function and constraint conditions of the above two-stage monthly unit commitment and maintenance scheduling joint optimization model considering social carbon emission factors and short-term benefits are quite complex mixed-integer nonlinear programming problems (MINLP), which are difficult to solve directly. Considering the relationship constraints among existing variables, decision variables can be linearly represented by other variables, and then the non-linear terms can be approximated by linear terms.

[0232] Due to the constraint of Equation (58), Equation (62) can be expressed as:

[0233]

[0234] Combining Equations (59) and (60), it can be further simplified to:

[0235]

[0236] The upper and lower limits of the output of thermal power units can be expressed as:

[0237]

[0238] The associated constraints between the maintenance schedule of thermal power units and the monthly unit commitment can be expressed as:

[0239]

[0240] Introduce the start-up cost decision variables for each thermal power unit at each time period under monthly and daily decisions and and linearly segmentize , the corresponding objective function can be simplified to:

[0241]

[0242] The corresponding constraint conditions generated after linearization:

[0243]

[0244]

[0245]

[0246] The Benders decomposition algorithm is used to iteratively solve the master problem and sub-problem of the above model to obtain the optimal solution of the model.

[0247] To verify the reliability and effectiveness of this method, under the condition that other conditions are the same, this method is used to optimize the monthly unit commitment to obtain the monthly start-up and shutdown plan and related maintenance plans, and compare them with the conventional model that does not consider social carbon emissions factors, does not consider the day-ahead unit commitment, and does not consider the maintenance plan model. The method proposed in this paper considers more comprehensive factors, expands the optimization space, takes into account the relevant impacts of the maintenance plan and the day-ahead unit commitment on the monthly unit commitment, and finally obtains a more reasonable and practical optimization decision-making strategy, with lower comprehensive costs for both economy and environment, responding to the dual-carbon goal.

[0248] The specific implementation cases described in this paper are only examples to illustrate the spirit of the present invention. Those skilled in the art to which the present invention pertains can make various modifications or supplements to the described specific implementation cases or use similar ways to substitute them, but will not deviate from the spirit of the present invention or exceed the scope defined by the appended claims.

Claims

1. A two-stage monthly unit commitment and maintenance schedule optimization method considering social carbon emission factors and short-term benefits, characterized in that, Specifically, it includes the following steps: Step 1: Use the historical wind speed data of multiple wind farms to fit the double-peak Weibull distribution function of the hourly wind speed of the corresponding wind farms respectively; model the spatio-temporal correlation of multiple wind farms to obtain the wind speed scenarios of spatio-temporal tail correlation, and then reduce them through the synchronous back substitution reduction method to obtain typical scenarios; Step 2: Through data preprocessing and normalization of the historical data of the load and relevant social and weather characteristics, then use MI mutual information for feature selection, and input the selected key features into the BiLSTM load prediction model for training, and finally predict the monthly load time series; Step 3: Take the monthly unit start-stop cost and maintenance cost as the monthly cost target, and take the daily unit start-stop cost, daily unit operation coal consumption cost, carbon emission environmental penalty cost and wind abandonment cost as the daily cost target, and establish a joint optimization scheduling model for the two-stage monthly unit combination and maintenance plan considering the short-term benefits of social carbon emission factors, where the objective function of the first stage is the lowest monthly cost, and the objective function of the second stage is the lowest daily cost; then use the Benders decomposition algorithm to split the joint optimization scheduling problem of the two-stage monthly unit combination and maintenance plan considering social carbon emission factors and short-term benefits into master and sub-problems for iterative solution to obtain its optimal solution, specifically including: The objective function of the joint optimization scheduling model for the two-stage monthly unit combination and maintenance plan considering social carbon emission factors and short-term benefits mainly includes the first-stage monthly cost target and the second-stage daily cost target, which can be specifically expressed by a mathematical model as: F = F M + F D1 + F D2 (9) Among them, F M is the monthly cost, and F D = F D1 + F D2 is the daily cost. The monthly cost F M includes the monthly unit start-stop cost and maintenance plan cost. The daily cost F D = F D1 + F D2 includes the daily unit start-stop cost, daily unit operation coal consumption cost, carbon emission environmental penalty cost, and wind curtailment cost; is the daily coal consumption cost of the thermal power unit, is the carbon emission environmental penalty cost; a i , b i , c i are the coal consumption cost characteristic coefficients of thermal power unit i; λ c and λ s are the cost coefficients corresponding to CO2 and SO2 gas emissions respectively; and are the CO2 and SO2 gas emission coefficients of thermal power unit i respectively; is the fuel consumption of thermal power unit i at the t-th time period on the d-th day; β i is the unit coal consumption for power generation of thermal power unit i; D represents 30h per month, T represents 24h per day, I represents the number of thermal power units, and Y i M is a flag determining whether the thermal power unit is a monthly unit, and Y i D is a flag determining whether the thermal power unit is a daily unit, is the start-stop state of thermal power unit i belonging to the monthly unit combination at the t-th time period on the d-th day; is the start-stop state of thermal power unit i belonging to the daily unit combination in scenario s at the t-th time period on the d-th day; S is the total number of scenarios of the wind farm being analyzed; I s,i,d,t is the start-stop state of thermal power unit i finally determined to be subordinate in scenario s at the t-th time period on the d-th day; is the planned output of thermal power unit i in scenario s at the t-th time period on the d-th day; F i (·) is the power generation cost characteristic function of thermal power unit i; F envs,i,t (·) is the environmental penalty function for CO2 and SO2 gas emissions, and SUC i is the start-stop cost of the i-th thermal power unit; N is the total number of maintenance projects, and W n,d is the cost of starting the n-th maintenance project on the d-th day, and τ n,d is the start state of the n-th maintenance project in the i-th maintenance time period, where 1 indicates starting maintenance and 0 indicates not being the start maintenance time period; λ w is the wind curtailment penalty, is the curtailed wind power; Introduce the start-up cost decision variables for each thermal power unit at each time period under monthly and daily decisions and And linearize it piecewise, and the corresponding objective function can be simplified to: Segmented linearization, the corresponding objective function can be simplified to: The corresponding constraint conditions generated after linearization: Finally, use the Benders decomposition algorithm to split the above model into master and sub-problems for iterative solution to obtain its optimal solution.

2. The two-stage monthly unit commitment and maintenance schedule optimization method according to claim 1, characterized in that, The implementation of Step 1 includes: Step 1.1: Set the wind speed v at the same hour every day within a month i To conform to the same probability distribution, the historical wind speed data of multiple wind farms are used to respectively fit the distribution function of the hourly wind speed described by the double-peak Weibull distribution function. The expression of the double-peak Weibull distribution function is as follows: Wherein: are two unimodal Weibull distributions included in the bimodal Weibull distribution of the w-th wind farm at the i-th time period, where w represents the corresponding wind farm, w = 1, 2, 3,..., W, and i represents the corresponding time period in a day, i = 1, 2, 3,..., 24; are respectively the shape parameter, location parameter and scale parameter of the wind speed probability density function (PDF) of the w-th wind farm at the i-th time period, r i w is the percentage of the unimodal Weibull distribution, specifically including: Step 1: Statistically analyze the wind speed data of 24 hours per day corresponding to this month in recent years, select 6 years of wind speed data, calculate 30 days per month, and according to the monthly statistics, 60×3 = 180 data can be obtained for each hour to fit the wind speed probability density function to obtain the corresponding double-peak Weibull distribution function; Step 2: According to the Copula theory, use the t Copula function to model the spatial tail correlation of each wind farm, and consider the random variables \(V\) of the wind speeds of each wind farm at time period \(i\) i 1 ,…, \(V\) i W , denote the marginal probability distribution function of denote the marginal probability density function; the joint probability distribution function \(F\) of the wind speeds of each wind farm at time period \(i\) is represented by the Copula function \(C\) and a Copula density function \(c\) i and the joint probability density function \(f\) i , specifically expressed as: Step 3: Use the C-vine structure to model the tail time correlation. The C-vine structure simulates the 24-hour wind speed random variables of each wind farm. Based on the C-vine structure, the 24h joint density of the kth wind farm can be expressed as: The parameters of the C-vine structure can be solved by Sequential Estimation (SE); the historical data of the wind speed is used for the maximum likelihood estimation of the parameters of the first layer, and the parameters of the remaining layers are estimated by the pseudo-observations generated by the conditional distribution function. Step 1.2: According to the spatial joint probability distribution function of each wind farm at each time node, in the first step, generate W-dimensional temporary samples with spatial correlation, each sample following a uniform distribution. Then, based on the sampling method of the C-vine structure, according to the time joint probability distribution function of each wind farm, use the generated temporary samples to further generate the final wind speed scenarios with spatio-temporal tail correlation. The steps to generate the final wind speed scenarios are as follows: ① Initialize the reference variable of wind farm w, and let w = 1; ②Let represent Z w the i-th column, represent the realization of the hourly wind speed variable for the w-th wind farm in the standard space at time i; ③Let Solve the equation using the bisection method to obtain That is ④When t > 2, it can be obtained by iterative solution ; ⑤ Substitute into V i w and obtain by the inverse distribution function of transform the realization of the standard space into the original space; denote the wind speed scenario of the w-th wind farm, w = w + 1; ⑥ Repeat steps ②, ③, ④, and ⑤ until w = W to obtain the final wind speed scenarios; After generating a number of final wind speed time series samples, consider the operating physical characteristics of wind turbines to generate their corresponding wind power scenarios, and then use the synchronous back substitution reduction method to reduce the generated wind power scenarios to obtain the most representative scenarios.

3. The two-stage monthly unit commitment and maintenance schedule optimization method according to claim 1, characterized in that, The implementation of Step 2 includes: Step 2.1: Select relevant features affecting the load Select meteorological factors, holiday calendar index factors, socio-economic factors, and environmental protection factors that have a greater impact on the electricity load and include them in the electricity load prediction feature library. The relevant feature variables are temperature, working day, dew point, weekend, precipitation, holiday, air pressure, season, weather, population, AQI; Step 2.2: Data preprocessing Data cleaning: Perform data cleaning on the load data and relevant feature quantities of the previous several years, including steps such as missing value imputation, noise removal, outlier detection, and data smoothing; then apply min-max data normalization to scale the historical load values and social, weather, and date holiday features to the range of 0 to 1. Specifically, it is expressed as follows: Step 2.3: Feature selection Using the method of MI feature selection, calculate the mutual information for each feature; X and Y are set as two random variables, where X is the relevant feature quantity affecting the load and Y is the load prediction quantity; the joint probability density function of X and Y is set as μ X,Y , and their marginal density functions are μ X (x) and μ Y (y). Since both the load-related feature quantity and the predicted load quantity X and Y are discrete values, MI is expressed as: Step 2.4: Load prediction model Considering the non-stationarity and volatility of the load, use the bidirectional long short-term memory neural network BiLSTM to predict the load. Input the selected relevant key feature quantities into the BiLSTM prediction model for training, and finally predict the load to obtain the monthly load time series.

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