A multi-objective optimization scheduling method for integrated energy systems considering uncertainty

Abstract

This invention presents a multi-objective optimization scheduling method for integrated energy systems that considers uncertainty. Belonging to the field of integrated energy systems and their operation scheduling, it addresses the problem that existing methods fail to consider the potential risks to system operation and reduced control flexibility caused by uncertainty. This invention provides a multi-objective optimization scheduling method for integrated energy systems that considers uncertainty. Based on historical data of the integrated energy system, the probability density function of each energy source's output is calculated using the Edgeworth method; the cumulative distribution function of distributed energy source output and the quantiles corresponding to given probability values ​​are calculated; based on the confidence interval of uncertainty, the probability density function and cumulative distribution function of distributed energy sources are obtained; and multi-objective optimization is performed using the confidence interval as a constraint to calculate the output strategy of each distributed energy source. This method not only mitigates the impact of source-side uncertainty on the system but also ensures the system's operational economy, environmental friendliness, and stability, providing a foundation for flexible control.

Description

Technical Field

[0001] This invention belongs to the field of integrated energy systems and their operation and scheduling, and specifically relates to a multi-objective optimization scheduling method for integrated energy systems that takes into account uncertainties. Background Technology

[0002] The integration of a high proportion of renewable energy into integrated energy systems has led to a diversification of distributed generation units. However, the uncertainties inherent in renewable energy cannot be ignored. Once integrated, these uncertainties are transmitted into the integrated energy system, impacting its overall economic efficiency and environmental friendliness. Common multi-objective optimization methods only consider economic and environmental objectives, neglecting uncertainties arising during system operation. They also fail to quantify the impact of power supply fluctuations on the optimization results. As integrated energy systems become more diversified and complex, the uncertainties brought by high proportions of distributed and renewable energy sources are transmitted and accumulated during system power supply, posing significant challenges to the system's safe operation and flexible control. Furthermore, the degradation and evolution of system structures and equipment measurement errors also increase the system's inherent uncertainty. Therefore, adding an uncertainty dimension to the analysis is crucial for integrated energy systems. Summary of the Invention

[0003] To address the problem that existing methods fail to consider the potential risks to system operation and reduced control flexibility caused by uncertainty, this invention provides a multi-objective optimization scheduling method for integrated energy systems that considers uncertainty. Based on the Edgeworth expansion method and drawing on Taylor expansion techniques, the probability density function of random variables is expanded into a power series consisting of normally distributed random variables and higher-order correction terms. At each order, the cumulative difference between the actual random variable and the normally distributed random variable is introduced for correction. Furthermore, the Edgeworth expansion exhibits better convergence, which is helpful in analyzing the uncertainties of complex integrated energy systems.

[0004] The technical solution adopted in this invention is as follows: A multi-objective optimization scheduling method for a comprehensive energy system considering uncertainties, comprising the following steps:

[0005] S1, based on the historical data of distributed energy output connected to the integrated energy system, calculates the probability density function of each energy output using the Edgeworth method, which is used to analyze the uncertainty distribution of energy processing;

[0006] S2, based on the Edgeworth series expansion method, expand the cumulative distribution function of distributed energy output in the integrated energy system and the quantile corresponding to the given probability value, so that each energy output can be treated as a random variable by the Edgeworth series expansion method, and its probability density function can be expanded into a power series composed of normal random variables and higher-order correction terms of random variables.

[0007] S3. Calculate the confidence interval of the output uncertainty of distributed energy based on the confidence interval of the maximum posterior density, so as to obtain the probability density function and cumulative distribution function of distributed energy.

[0008] S4. Using the confidence interval calculated in step S3 as a constraint, the MOEA / D algorithm is used for multi-objective optimization to calculate the output strategy of each distributed energy source, which can achieve multi-objective optimal scheduling.

[0009] The purpose of this invention is to provide a multi-objective optimization scheduling method for integrated energy systems that considers uncertainty. Based on historical data of the distributed energy sources included in the integrated energy system, the method uses the Edgeworth series expansion to treat the output of each energy source as a random variable, expanding its probability density function into a power series composed of normally distributed random variables and higher-order correction terms. A correction method is used at each order to introduce the cumulative difference between the actual random variables and the normally distributed random variables. The probability density function and cumulative distribution function of the distributed energy sources are calculated, and then the corresponding confidence intervals for the distributed energy sources are calculated, thereby quantifying the uncertainty on the source side of the integrated energy system. Considering the system's economic and environmental benefits, multi-objective optimization scheduling is performed to mitigate the impact of distributed energy uncertainty on the integrated energy system, while simultaneously ensuring the system's economic and environmental performance.

[0010] Further, step S1 includes the following steps:

[0011] Step S1.1: Organize historical data on the output of distributed energy sources (including renewable energy sources in the system) within the integrated energy system;

[0012] Step S1.2: Taking the output of each distributed energy source as a random variable x, and using the Edgeworth series expansion method, approximate the probability distribution function of the random variable through the standard normal distribution function, specifically:

[0013] If we treat the output of each distributed energy source as a random variable and denote it as x, then the standard form of the formula for calculating y is as follows:

[0014]

[0015] In the formula, μ is the mean of x; σ is the standard deviation; and y is the standard form of x.

[0016] Calculate the cumulant generating function K x (t), for the cumulant generating function K x (t) By taking the nth derivative at t=0, we can obtain the nth cumulant k of the random variable x. n , represented as:

[0017]

[0018]

[0019] In the formula: k n The symbol represents the nth-order cumulant of x; t is the cumulant generating function K. x The variable (t);

[0020] Let f(x) be the probability density function of the random variable x. Then the Edgeworth expansion of f(x) is:

[0021]

[0022] In the formula, Let x be a normal distribution; s is the analytical correction order based on the normal distribution, taking the value of a natural number; σ s S is σ raised to the power of s. m+2 For k m+2 The cumulative amount after semi-normalization; k m The symbol for the m-th order cumulant of x; He s+2p It is a Hermite polynomial;

[0023] k m To find a solution that satisfies the following Diophantine equation:

[0024]

[0025]

[0026] At the same time, S m+2 satisfy:

[0027]

[0028] S m+2 For k m+2 The cumulative amount after semi-normalization; σ 2m+2 It is σ raised to the power of 2m+2.

[0029] Furthermore, step 2 includes the following steps:

[0030] Step S2.1: Based on the probability density function f(x) obtained in step S1.2, perform integration calculation. Then, the cumulative distribution function F(x) of the historical energy data of Bucherer is expressed as:

[0031]

[0032] Step S2.2 involves inverting the cumulative distribution function obtained in step S2.1 and numerically calculating the quantiles corresponding to a given cumulative probability value. This process is repeated to approximate the quantile values ​​corresponding to the given cumulative probability value with a given precision, ultimately obtaining the maximum posterior density confidence interval. This step is a general algorithm and lays the groundwork for step 3.

[0033] Furthermore, step S3 specifically includes:

[0034] The confidence interval for the output uncertainty of distributed energy sources is calculated based on the maximum a posteriori density confidence interval. When the setpoint of the distributed energy source in the actual system is θ, given any θ1, θ2 and confidence level 1-α, the maximum a posteriori density confidence interval [θ] corresponding to x is calculated. L ,θ U ] is represented as:

[0035]

[0036] In the formula, the statistic θ L and θ U The confidence interval is divided into a lower limit and an upper limit; P(θ) is the probability; P(θ) L ≤θ≤θ U |x) is the cumulative distribution function curve in the interval [θ]. L ,θ U The area enclosed by the x-axis and the x-axis.

[0037] Further, step S4 includes the following steps:

[0038] Step S4.1: Taking the economic efficiency and environmental friendliness of the integrated energy system as optimization objectives, and using the confidence interval as the output constraint of distributed energy resources, a multi-objective optimization scheduling model is constructed. The optimization objectives of the scheduling strategy are the economic efficiency and environmental friendliness of system operation, which respectively refer to minimizing the system operation cost and pollutant emissions. The constraints include unit operation constraints and confidence interval constraints corresponding to output uncertainty. The general form of the multi-objective optimization model can then be expressed as:

[0039]

[0040] In the formula, obj1 is the economic objective function; obj2 is the environmental objective function; x represents the output of each distributed energy source; H(x) and G(x) refer to all the equality constraints and inequality constraints in the operation of the distributed energy units, respectively, among which the inequality constraint condition includes the constraint that the unit output is within the confidence interval.

[0041] Step S4.2: The MOEA / D algorithm is used to decompose the multi-objective optimization into multiple sub-problems, and a weight vector for the optimization objective is constructed. The optimization objective of the function is to achieve the best state of operational economy and environmental protection. N uniformly distributed weight vectors are constructed, and the weight vectors are represented as follows:

[0042]

[0043] In the formula, and These are the weights corresponding to obj1 and obj2, respectively, where j = 1, 2, ..., N, and N is the number of weight vectors. Each subproblem consists of a uniformly distributed weight vector. The larger j is, the smaller the weight of obj1 and the larger the weight of obj2.

[0044] Step S4.3: Construct the Chebyshev aggregation function to transform the multi-objective optimization problem into a single-objective optimization problem, and solve for the Pareto front corresponding to the original optimization problem;

[0045] The single-objective optimization function is constructed using the Chebyshev aggregation method, and is expressed as:

[0046]

[0047] In the formula, x is a vector consisting of all independent variables in the j-th subproblem; This is the weight vector corresponding to the economic objective function and the environmental objective function; obj i,min Let obj be the reference point for the minimum value of the i-th optimization objective component. i,min ∈{obj 1,min ,obj 2,min};

[0048] Each time a new solution is generated, that is, the solutions near the current subproblem are replaced based on the Chebyshev aggregation function, the Pareto front of the original optimization problem is finally obtained;

[0049] Step S4.4: The TOPSIS method is used to make decisions on the Pareto solution set obtained in step S4.3, and the optimal compromise solution that satisfies multiple optimization objectives is selected, which corresponds to the output of each distributed energy source.

[0050] Furthermore, in step S4.1, each distributed energy unit must satisfy the balance between electrical power and thermal power, expressed as:

[0051] P c =P b (26)

[0052]

[0053] In the formula, P c For purchased power, Pb This refers to the electrical power consumption of the electric boiler. Total output of all distributed units; Q s (t+1) and Q s (t) represents the amount of heat stored in the thermal storage tank at times t+1 and t; Q b Q represents the heating capacity of the electric boiler. dis The power that outputs thermal energy to the thermal storage tank; μ dis The efficiency of the thermal energy output from the thermal storage tank; Q ch The power of inputting thermal energy into the thermal storage tank; μ ch The efficiency of inputting thermal energy into the thermal storage tank; Δt is the time interval between time t+1 and time t;

[0054] Considering uncertainties, the unit output constraints are constructed from the confidence interval calculated in step S3, and expressed as follows:

[0055]

[0056] In the formula Q s,L Q s,U The values ​​of θ are respectively L θ U The values ​​are equal;

[0057] In summary, the operating cost of this implementation case is the cost of purchased electricity, and the economic objective function is expressed as:

[0058] obj1=min(ΣC P (t)P c (t)·Δt) (29)

[0059] In the formula, C P and P c These are the price and power of purchased electricity, respectively.

[0060] Environmental performance indicators consider SO2 and NO x For the four types of pollutants, namely, H, CO, CO2, and CO2, the environmental protection objective function can be expressed as:

[0061]

[0062] In the formula, PS d PN d PY d PC d These are the SO2 and NO corresponding to each distributed energy source. x Emissions of CO and CO2; d is the energy unit number; D is the total energy consumption.

[0063] Furthermore, the specific process of step S4.4 is as follows:

[0064] Suppose that the Pareto front obtained in step S4.3 has l solution sets, and the number of weight vectors is the same as the number of solution sets, i.e., l = N. Each subproblem corresponds to a set of solution sets. Then the solution sets and the two optimization objectives can form a decision matrix X = (x ji ) l×2 , where x ji The calculation steps of the TOPSIS method are as follows: Let j be the value of the j-th solution set under the ith optimization objective.

[0065] Calculate the weighted normalized decision matrix Y = (y ji ) l×2 And the positive and negative ideal solutions Y+ and Y-:

[0066]

[0067]

[0068] Regarding economic and environmental objectives:

[0069]

[0070] In the formula, y ji Let j be the value of the j-th element in the weighted normalized decision matrix under the i-th optimization objective. This represents the solution that minimizes cost under the economic objective function. This represents the solution that minimizes emissions under the environmental objective function. This represents the solution that maximizes cost under the economic objective function. This represents the solution that maximizes emissions under the environmental protection objective function.

[0071] Calculate the Euclidean distance between different solution sets and the positive and negative ideal solutions. and The calculation is as follows:

[0072]

[0073]

[0074] Calculate the closeness of each solution set to the ideal solution. The calculation is as follows:

[0075]

[0076] Based on the calculation results, By sorting the data in descending order and selecting the maximum value as the optimal compromise solution, the optimal scheduling strategy for the output of each distributed energy source can be obtained.

[0077] The beneficial effects of this invention are as follows: This invention combines historical data of distributed energy output to obtain the uncertainty fluctuation range of each unit, and uses the quantified uncertainty as the operating constraint of the unit. Combined with the MOEA / D algorithm, it realizes the optimal output strategy of the integrated energy system in terms of both economy and environmental protection. This not only mitigates the impact of source-side uncertainty on the system, but also ensures the economic, environmental and stability operation of the system, providing a foundation for flexible regulation. Attached Figure Description

[0078] Figure 1 This is a flowchart of the present invention;

[0079] Figure 2 This is a schematic diagram of the integrated energy system structure. Detailed Implementation

[0080] The technical solutions of the embodiments of the present invention will be explained and described below with reference to the accompanying drawings. However, the following embodiments are only preferred embodiments of the present invention and not all of them. Other embodiments obtained by those skilled in the art based on the embodiments in the implementation methods without creative effort are all within the protection scope of the present invention.

[0081] This embodiment considers the multi-objective optimization scheduling method for integrated energy systems that takes into account uncertainties, such as... Figure 1 As shown, it includes the following steps:

[0082] S1, based on the historical data of distributed energy output connected to the integrated energy system, calculates the probability density function of each energy output using the Edgeworth method, which is used to analyze the uncertainty distribution of energy processing;

[0083] Step S1.1: Organize historical data on the output of distributed energy sources (including renewable energy sources in the system) within the integrated energy system;

[0084] Step S1.2: Taking the output of each distributed energy source as a random variable x, and using the Edgeworth series expansion method, approximate the probability distribution function of the random variable through the standard normal distribution function, specifically:

[0085] If we treat the output of each distributed energy source as a random variable and denote it as x, then the standard formula for calculating x is as follows:

[0086]

[0087] In the formula, μ is the mean of x; σ is the standard deviation; and y is the standard form of x.

[0088] Calculate the cumulant generating function K x (t), for the cumulant generating function K x(t) By taking the nth derivative at t=0, we can obtain the nth cumulant k of the random variable x. n , represented as:

[0089]

[0090]

[0091] In the formula: k n The symbol represents the nth-order cumulant of x; t is the cumulant generating function K. x The variable (t);

[0092] Let f(x) be the probability density function of the random variable x. Then the Edgeworth expansion of f(x) is:

[0093]

[0094] In the formula, Let x be a normal distribution; s is the analytical correction order based on the normal distribution, taking the value of a natural number; σ s S is σ raised to the power of s. m+2 For k m+2 The cumulative amount after semi-normalization; k m The symbol for the m-th order cumulant of x; He s+2p It is a Hermite polynomial;

[0095] k m To find a solution that satisfies the following Diophantine equation:

[0096]

[0097]

[0098] At the same time, S m+2 satisfy:

[0099]

[0100] S n For k n The cumulative amount after semi-normalization; σ 2m+2 It is σ raised to the power of 2m+2;

[0101] Hermite polynomial form and the first 6 terms are represented as follows:

[0102]

[0103] He0(x)=1

[0104] He1(x)=x

[0105] He2(x)=x2 -1

[0106] He3(x)=x 3 -3x

[0107] He4(x)=x 4 -6x 2 +3

[0108] He5(x)=x 5 -10x 3 +15x

[0109] He6(x)=x 6 -15x 4 +45x 2 -15;

[0110] S2, based on the Edgeworth series expansion method, expands the cumulative distribution function of distributed energy output in the integrated energy system and the quantiles corresponding to given probability values, so that each energy output can be treated as a random variable through the Edgeworth series expansion method, and its probability density function can be expanded into a power series composed of normal random variables and higher-order correction terms of random variables; specifically:

[0111] Step S2.1: Based on the probability density function f(x) obtained in step S1.2, perform integration calculation. Then, the cumulative distribution function F(x) of the historical energy data of Bucherer is expressed as:

[0112]

[0113] Step S2.2 involves inverting the cumulative distribution function obtained in step S2.1 and numerically calculating the quantiles corresponding to a given cumulative probability value. This process is repeated to approximate the quantile values ​​corresponding to the given cumulative probability value with a given precision, ultimately obtaining the maximum posterior density confidence interval. This step is a general algorithm and lays the groundwork for step 3.

[0114] S3. Calculate the confidence interval of the output uncertainty of distributed energy based on the confidence interval of the maximum posterior density, so as to obtain the probability density function and cumulative distribution function of distributed energy.

[0115] The confidence interval for the output uncertainty of distributed energy sources is calculated based on the maximum a posteriori density confidence interval. When the setpoint of the distributed energy source in the actual system is θ, given any θ1, θ2 and confidence level 1-α, the maximum a posteriori density confidence interval [θ] corresponding to x is calculated. L ,θ U ] is represented as:

[0116]

[0117] In the formula, the statistic θL and θ U The confidence interval is divided into a lower limit and an upper limit; P(θ) is the probability; P(θ) L ≤θ≤θ U |x) is the cumulative distribution function curve in the interval [θ]. L ,θ U The area enclosed by the x-axis and the x-axis;

[0118] S4, using the confidence interval calculated in step S3 as a constraint, employs the MOEA / D algorithm for multi-objective optimization, calculating the output strategy of each distributed energy source, which can achieve multi-objective optimal scheduling, specifically:

[0119] Step S4.1: Taking the economic efficiency and environmental friendliness of the integrated energy system as optimization objectives, and using the confidence interval as the output constraint of distributed energy resources, a multi-objective optimization scheduling model is constructed. The optimization objectives of the scheduling strategy are the economic efficiency and environmental friendliness of system operation, which respectively refer to minimizing the system operation cost and pollutant emissions. The constraints include unit operation constraints and confidence interval constraints corresponding to output uncertainty. The general form of the multi-objective optimization model can then be expressed as:

[0120]

[0121] In the formula, obj1 is the economic objective function; obj2 is the environmental objective function; x represents the output of each distributed energy source; H(x) and G(x) refer to all the equality constraints and inequality constraints in the operation of the distributed energy units, respectively, among which the inequality constraint condition includes the constraint that the unit output is within the confidence interval.

[0122] The integrated energy system in this implementation case includes an electric boiler, a thermal storage tank, a photovoltaic unit, and a heat pump. A schematic diagram of the system structure is shown below. Figure 2 The user-side thermal energy requires electric boilers and thermal storage tanks, which are jointly supplied by photovoltaic and heat pump units. The electric boilers are powered by auxiliary power from the external power grid. All equality and inequality constraints in the operation of the above distributed energy units are expanded as follows.

[0123] The equality and inequality constraints for electric boilers are expressed as follows:

[0124] Q b (t)=η b P b (t) (19)

[0125] P b min ≤P b (t)≤P b max (20)

[0126] In the formula, Q bThe heating power of the electric boiler; η b For electrothermal conversion efficiency; P b P b max P b min These represent the power consumption of the electric boiler and its maximum and minimum values.

[0127] The equality and inequality constraints of the thermal storage tank are expressed as follows:

[0128] Q s (t+1)=(1-γ s )Q s (t)+δ s Q ch Δtμ ch -(1-δ s )Q dis Δt / μ dis (twenty one)

[0129] In the formula, Q s (t+1) and Q s (t) represents the heat storage capacity of the thermal storage tank at time t+1 and time t; γ s δ is the self-heating coefficient of the thermal storage tank; s δ represents a 0 / 1 variable indicating the working state of the thermal storage tank. If the thermal storage tank is in the heat storage state, δ s =1, if the thermal storage tank is in a heat release state, δ s =0; Q ch Q dis These represent the power of the thermal energy input and output of the thermal storage tank, respectively; μ ch μ dis These represent the efficiency of the thermal energy input and output of the thermal storage tank, respectively.

[0130] The operating constraints of the thermal storage tank can be expressed as:

[0131]

[0132] In the formula, and These are the upper and lower limits of the heat storage capacity of the thermal storage tank; These are the maximum heat storage capacity and maximum heat release capacity of the thermal storage equipment, respectively.

[0133] The output power of a photovoltaic unit is expressed as:

[0134]

[0135] In the formula, P pv P represents the real-time power generation of the photovoltaic unit. pv,u Rated power of the photovoltaic unit; η pvThe performance coefficient of the photovoltaic unit; RI and RI ref These are the hourly average solar radiation intensity and the solar radiation intensity under standard conditions (usually taken as 1000W / m2), respectively. The power temperature coefficient of a photovoltaic (PV) unit is typically taken as -0.35% / ℃; T pv and T pv,ref These are the temperature of the photovoltaic cell and the temperature of the photovoltaic cell under standard test conditions, respectively, typically taken as 25℃.

[0136] Photovoltaic units complete the electro-thermal conversion through an external heat pump, where the operating constraints of the heat pump can be expressed as:

[0137] Q h (t)=cop h ·P pv (t) (24)

[0138] 0≤Q h (t)≤Q h,u (25)

[0139] In the formula, Q h Provides heating power for the heat pump; cop h Q is the coefficient of performance (COP) of the heat pump. h,u This refers to the rated power of the heat pump.

[0140] In summary, each distributed energy unit must satisfy the balance between electrical power and thermal power, expressed as:

[0141] P c =P b (26)

[0142]

[0143] In the formula, P c For purchased power, Total output of all distributed units; Q s (t+1) and Q s (t) represents the amount of heat stored in the thermal storage tank at times t+1 and t; Q b Q represents the heating capacity of the electric boiler. dis The power that outputs thermal energy to the thermal storage tank; μ dis The efficiency of the thermal energy output from the thermal storage tank; Q ch The power of inputting thermal energy into the thermal storage tank; μ ch The efficiency of inputting thermal energy into the thermal storage tank; Δt is the time interval between time t+1 and time t;

[0144] Considering uncertainties, the unit output constraints are constructed from the confidence interval calculated in step S3, and are expressed as follows:

[0145]

[0146] In the formula Q s,L Q s,U The values ​​of θ are respectively L θ U The values ​​are equal;

[0147] In summary, the operating cost of this implementation case is the cost of purchased electricity, and the economic objective function is expressed as:

[0148] obj1=min(∑C P (t)P c (t)·Δt) (29)

[0149] In the formula, C P and P c These are the price and power of purchased electricity, respectively.

[0150] Environmental performance indicators consider SO2 and NO x For the four types of pollutants, namely, H, CO, CO2, and CO2, the environmental protection objective function can be expressed as:

[0151]

[0152] In the formula, PS d PN d PY d PC d These are the SO2 and NO corresponding to each distributed energy source. x Emissions of CO and CO2; d is the energy unit number; D is the total energy consumption.

[0153] Step S4.2: The MOEA / D algorithm is used to decompose the multi-objective optimization into multiple sub-problems, and a weight vector for the optimization objective is constructed. The optimization objective of the function is to achieve the best state of operational economy and environmental protection. N uniformly distributed weight vectors are constructed, and the weight vectors are represented as follows:

[0154]

[0155] In the formula, and These are the weights corresponding to obj1 and obj2, respectively, where j = 1, 2, ..., N, and N is the number of weight vectors. Each subproblem consists of a uniformly distributed weight vector, and j represents the j-th subproblem. The larger j is, the smaller the weight of obj1 and the larger the weight of obj2.

[0156] Step S4.3: Construct the Chebyshev aggregation function to transform the multi-objective optimization problem into a single-objective optimization problem, and solve for the Pareto front corresponding to the original optimization problem;

[0157] The single-objective optimization function is constructed using the Chebyshev aggregation method, and is expressed as:

[0158]

[0159] In the formula, x is a vector consisting of all independent variables in the j-th subproblem; This is the weight vector corresponding to the economic objective function and the environmental objective function; obj i,min Let obj be the reference point for the minimum value of the i-th optimization objective component. i,min ∈{obj 1,min ,obj 2,min};

[0160] Each time a new solution is generated, that is, the solutions near the current subproblem are replaced based on the Chebyshev aggregation function, the Pareto front of the original optimization problem is finally obtained;

[0161] Step S4.4: The TOPSIS method is used to make decisions on the Pareto solution set obtained in step S4.3, and the optimal compromise solution that satisfies multiple optimization objectives is selected, which corresponds to the output of each distributed energy source.

[0162] Suppose that the Pareto front obtained in step S4.3 has l solution sets, and the weight vector is the same as the number of solution sets, i.e., l = N. Each subproblem corresponds to a set of solution sets. Then the solution sets and the two optimization objectives can form a decision matrix X = (x ji ) l×2 , where x ji The calculation steps of the TOPSIS method are as follows: Let j be the value of the j-th solution set under the ith optimization objective.

[0163] Calculate the weighted normalized decision matrix Y = (y ji ) l×2 And calculate the positive and negative ideal solutions Y+ and Y-:

[0164]

[0165]

[0166] Regarding economic and environmental objectives:

[0167]

[0168] In the formula, y ji Let j be the value of the j-th element in the weighted normalized decision matrix under the i-th optimization objective. This represents the solution that minimizes cost under the economic objective function. This represents the solution that minimizes emissions under the environmental objective function. This represents the solution that maximizes cost under the economic objective function. This represents the solution that maximizes emissions under the environmental protection objective function.

[0169] Calculate the Euclidean distance between different solution sets and the positive and negative ideal solutions. and The calculation is as follows:

[0170]

[0171]

[0172] Calculate the closeness of each solution set to the ideal solution. The calculation is as follows:

[0173]

[0174] Based on the calculation results, By sorting the data in descending order and selecting the maximum value as the optimal compromise solution, the optimal scheduling strategy for the output of each distributed energy source can be obtained.

[0175] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Those skilled in the art should understand that the present invention includes, but is not limited to, the contents described in the accompanying drawings and the specific embodiments above. Any modifications that do not depart from the functional and structural principles of the present invention will be included within the scope of the claims.

Claims

1.A method for multi-objective optimization scheduling of integrated energy systems considering uncertainty, characterized in that, Comprising the following steps: S1, according to the distributed energy output history data of the integrated energy system, through Edgeworth The method calculates the probability density function of each energy output, which is used for analyzing the uncertainty distribution of energy processing; including the following steps: Step S1.1, collate the historical data of the distributed energy output contained in the integrated energy system; Step S1.2, taking the output of each distributed energy as a random variable x , in combination Edgeworth with the series expansion method, the probability distribution function of the random variable is approximated by the standard normal distribution function, specifically: The output of each distributed energy is taken as a random variable and denoted as x Then x The standard form y calculation formula of is as follows: （1） wherein μ is the mean; x is the mean; σ is the standard deviation, y is the standard form; x is the standard form; Cumulant generating function K x ( t ), the cumulant generating function K x ( t ) evaluated at t = 0, i.e. n , gives the x th cumulant of the random variable x n k n , denoted by （2） （3） In the formula: k n denotes x the sign of the n cumulant of order k; t is the cumulant generating function K x of the variable t ​ Recall f ( x ) that the probability density function of a random variable x is denoted by f ( x ) Edgeworth The expansion of Edgeworth is given by （4） In the formula, for The normal distribution; s This is the analytical correction order based on the normal distribution, and its value is a natural number; σ s for σ of s Power of 1 S m+2 for k m+2 The cumulative amount after semi-normalization; k m express x of m The symbol for the cumulant; for Hermite Polynomial; k m To satisfy the solution of the Diophantine equation: （5） （6） At the same time, S m+2 satisfies: （7） S m+2 is k m+2 half-normalized cumulants; σ 2m+2 is σ 2m+2 S2, based on Edgeworth The series expansion method is used to expand the cumulative distribution function of the distributed energy output in the comprehensive energy system and the quantile corresponding to a given probability value, so as to obtain the quantile of the distributed energy output in the comprehensive energy system by Edgeworth The series expansion method takes each energy output as a random variable, and expands the probability density function of the random variable into a power series composed of a normal random variable and a high-order correction term of the random variable. S3, calculate the confidence interval of the distributed energy output uncertainty according to the maximum posterior density confidence interval, to obtain the distributed energy probability density function and the cumulative distribution function; S4, using the confidence interval calculated in step S3 as a constraint, a multi-objective optimization is performed using the MOEA / D algorithm to calculate the output strategy of each distributed energy, which can realize multi-objective optimization scheduling. 2.The method of claim 1, wherein, Step 2 comprises the following steps: Step S2.1, the cumulative distribution function of the building energy historical data is represented as: f x F x ​​​​ （8） Step S2.2, based on the cumulative distribution function obtained in step S2.1, the inverse is calculated, and the quantile corresponding to the given cumulative probability value is calculated by numerical method, and the quantile value corresponding to the given cumulative distribution probability value is continuously approximated under the given precision, to obtain the maximum posterior density confidence interval. 3.The method of claim 2, wherein, Step S3 is specifically: A credible interval of the distributed energy output uncertainty is calculated according to a maximum posterior density credible interval, when a set value of the distributed energy in an actual system is θ , θ 1, θ 2 and a confidence level is 1- α - x A corresponding maximum posterior density credible interval θ L , θ U is expressed as: （9） where the statistic and The lower and upper limits of the confidence interval are The probability The area under the cumulative distribution function curve in the interval and x axis. 4.The method of claim 3, wherein, Step S4 comprises the following steps: Step S4.1, taking the economy and environmental protection of the integrated energy system as the optimization objective, and taking the confidence interval as the distributed energy output constraint, a multi-objective optimization scheduling model is constructed; the optimization objective of the scheduling strategy is the economy and environmental protection of the system operation, which respectively means the minimum cost and pollutant emission of the system operation; the constraint conditions include unit operation constraint and confidence interval constraint corresponding to output uncertainty, then the general form of the multi-objective optimization model can be represented as: （10） In the formula, is an economic objective function; is an environmental objective function; represents the output of each distributed energy source; and respectively refer to all equality constraints and inequality constraints in the distributed energy unit operation, wherein the inequality constraint condition contains the constraint condition that the unit output is within the confidence interval. Step S4.2, using MOEA / D algorithm to decompose multi-objective optimization into multiple sub-problems, and constructing the weight vector of optimization objective; the optimization objective of the function is to achieve the best state of running economy and environmental protection, and a uniformly distributed weight vector is constructed, which is represented as: a uniformly distributed weight vector, which is represented as: （11） wherein and correspond to and corresponding weights, wherein , N is the number of weight vectors, each sub-problem is composed of a uniformly distributed weight vector, j the larger, the smaller the weight of the larger the weight of Step S4.3, construct a Chebyshev aggregation function to convert the multi-objective optimization problem into a single-objective optimization problem, and solve to obtain the Pareto front corresponding to the original optimization problem; A single-objective optimization function is constructed using the Chebyshev aggregation method, which is represented as: （12） In the formula, is the vector composed of all independent variables in the first j sub-problem; is the weight vector corresponding to the operation economy objective function and the environmental protection objective function; is the minimum reference point of the first optimization objective component, ; Each time a new solution is generated, the solutions near the current sub-problem are replaced based on the Chebyshev aggregation function, and finally the Pareto front of the original optimization problem is obtained; Step S4.4, using the TOPSIS method to make decisions on the Pareto solution set obtained in step S4.3, and selecting the optimal compromise solution that meets multiple optimization objectives, i.e., the output of each distributed energy. 5.The method of claim 4, wherein, Each distributed energy unit in step S4.1 needs to meet the balance of electric power and thermal power, which is represented as: （26） （27） wherein is the purchased electric power, is the electric boiler electric power; is the total power of all distributed units; and is the thermal storage tank is the thermal storage tank t is the thermal storage tank; is the electric boiler heating power; is the thermal storage tank output thermal energy power; is the thermal storage tank output thermal energy efficiency; Q ch is the thermal storage tank input thermal energy power; μ ch is the thermal storage tank input thermal energy efficiency; is the is the time interval between and Considering the uncertainty, the confidence interval calculated in step S3 is used to construct the unit output constraint, which is represented as: （28） wherein , the values of θ L , θ U are equal to the values of The operating cost is the cost of purchased electricity, and the economy objective function is represented as: （29） In the formula, and are the price and power of the purchased electricity, respectively; The environmental protection index considers SO2, NO x , CO, and CO2, and the environmental protection target function is expressed as: （30） In the formula, , , , are the emission amounts of SO2, NOx, CO, and CO2 corresponding to each distributed energy, respectively; x d is the energy unit number; and D is the total energy.​ 6.The method of Claim 5, wherein The specific process of step S4.4 is: If there are l solution sets in the Pareto front obtained in step S4.3, the number of weight vectors is consistent with the number of solution sets, i.e. l = N , each sub-problem corresponds to a set of solution sets, and the solution sets and the two optimization objectives can form a decision matrix , where is the value of the j th solution set under the i th optimization objective, and the calculation steps of the TOPSIS method are as follows: Computing a weighted normalized decision matrix and positive and negative ideal solutions , : （13） （14） For the economy objective and the environmental protection objective: （15） In the formula, y ji is the value of the i-th element in the j-th row of the weighted normalized decision matrix under the k-th optimization objective, j i is the value of the i-th element in the j-th row of the weighted normalized decision matrix under the k-th optimization objective, represents the solution corresponding to the minimum cost under the economic objective function, represents the solution corresponding to the minimum emission under the environmental protection objective function, represents the solution corresponding to the maximum cost under the economic objective function, represents the solution corresponding to the maximum emission under the environmental protection objective function.​ Euclidean distances between different solution sets and the positive and negative ideal solutions are calculated and are calculated as follows: （16） （17） calculating the closeness of each solution set to the positive ideal solution is calculated as follows: （18） Based on the calculation results, By sorting the data in descending order and selecting the maximum value as the optimal compromise solution, the optimal scheduling strategy for the output of each distributed energy source can be obtained.

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