A distributed robust optimization method for electric-thermal integrated energy system considering correlation

Abstract

The present application relates to a distributed robust optimization method for an electric-thermal integrated energy system considering correlation. The method includes: by combining two uncertain parameters, namely, the output of renewable energy units and the ambient temperature, considering the correlation of the outputs of different renewable energy units, as well as the correlation between the outputs of renewable energy units and the ambient temperature, a fuzzy set containing multiple probability distribution information is constructed; an auxiliary variable is introduced to replace the square term in the fuzzy set to obtain an extended fuzzy set; on the basis of the extended fuzzy set, a two-stage distributed robust optimization scheduling model for the electric-thermal integrated energy system is constructed in the day-ahead and day-intraday periods; an affine strategy and the second-order cone duality theory are used to equivalently transform the two-stage distributed robust optimization scheduling model for the electric-thermal integrated energy system in the day-ahead and day-intraday periods into a deterministic second-order cone programming model; the second-order cone programming model is solved to obtain the optimal scheduling decision for the electric-thermal integrated energy system, thereby improving the reliability and safety of the scheduling decision for the electric-thermal integrated energy system.

Description

Technical Field

[0001] The present application relates to the field of integrated energy control technology, and in particular to a distributed robust optimization method for an electric-thermal integrated energy system taking correlation into consideration. Background Art

[0002] Due to the "heat-to-electricity" operation mode of cogeneration units and the restriction relationship between electricity and heat, it is difficult to get rid of the current dilemma of renewable energy consumption by only tapping the regulation potential of the power system. The electric-thermal integrated energy system can release the adjustable potential of cogeneration units and improve the consumption rate of renewable energy through the coordinated dispatch of the power system and the thermal system.

[0003] With the large-scale and continuous grid connection of renewable energy units, the randomness and uncontrollability of their output pose a serious threat to the safe and stable operation of the electric and thermal integrated energy system. In recent years, distributed robust optimization has gradually been applied as a new uncertainty processing method. This method combines the advantages of stochastic optimization and robust optimization, which can avoid the problem of insufficient optimality caused by stochastic optimization's over-reliance on precise probability distribution, and overcome the defect of overly conservative optimization results caused by robust optimization's neglect of probability distribution information.

[0004] Existing studies usually take into account the uncertainty of renewable energy unit output and load in the electric-thermal integrated energy system, but ignore the uncertainty of ambient temperature. In fact, the user's heat consumption is closely related to the ambient temperature, and the uncertainty of ambient temperature will also affect the operation of the electric-thermal integrated energy system. Therefore, the reliability of the dispatch decision of the electric-thermal integrated energy system obtained by only considering the uncertainty of renewable energy output in the optimization problem is low. Summary of the invention

[0005] Based on this, it is necessary to provide a robust optimization method for the distribution of electric and thermal integrated energy systems taking into account correlation, which can improve the reliability of scheduling decisions of the electric and thermal integrated energy systems in response to the above technical problems.

[0006] A robust optimization method for distribution of an electric-thermal integrated energy system considering correlation, the method comprising:

[0007] Step 1: Combining the two uncertain parameters of renewable energy unit output and ambient temperature, considering the correlation between the output of different renewable energy units and the correlation between the output of renewable energy units and ambient temperature, a fuzzy set containing multiple probability distribution information is constructed;

[0008] Step 2: Introduce auxiliary variables to replace the square terms in the fuzzy set to obtain the extended fuzzy set;

[0009] Step 3: Based on the extended fuzzy set, a two-stage distributed robust optimization scheduling model of the electric-thermal integrated energy system is constructed;

[0010] Step 4: Using the affine strategy and the second-order cone duality theory, the day-ahead and day-intraday two-stage distributed robust optimization scheduling model of the electric-thermal integrated energy system is equivalently transformed into a deterministic second-order cone programming model;

[0011] Step 5: Solve the second-order cone programming model to obtain the optimal scheduling decision of the electric and thermal integrated energy system.

[0012] In one embodiment, the fuzzy set containing the correlation between the output of the renewable energy unit and the ambient temperature is:

[0013]

[0014]

[0015] Where: F is a fuzzy set; P is a probability; R is all possible situations of uncertain parameters; P(R) is all possible probability distributions of uncertain parameters; and are the prediction errors of the output of renewable energy units e and f during period t respectively; is the prediction error of the ambient temperature during period t; W is and The uncertain set E p It means taking the expected value; and They are and The variance of for The variance of for and The covariance of for and The covariance of and They are The upper and lower limits of and They are upper and lower limits.

[0016] In one embodiment, the extended fuzzy set G is:

[0017]

[0018]

[0019] Where: G is the extended fuzzy set; is the auxiliary variable introduced; is the corresponding extended uncertainty set; and They are and upper limit.

[0020] In one embodiment, the day-ahead and intraday two-stage distributed robust optimization scheduling model of the electric-thermal integrated energy system includes a day-ahead stage model and an intraday stage model;

[0021] The objective function of the day-ahead model is:

[0022]

[0023] Where: x represents the pre-dispatch variable in the day-ahead stage; w represents the prediction error of the output of renewable energy units and ambient temperature, which is a random variable; sup represents the supremum; Q(x,w) represents the adjustment cost of the electric-thermal integrated energy system under the given day-ahead pre-dispatch variable and the prediction error of the output of renewable energy units and ambient temperature, which is the objective function in the intra-day stage; and are the unit generation, upper reserve and lower reserve costs of CHP unit e respectively; is the power output of cogeneration unit e during period t; and are the upper and lower reserve capacities of the CHP unit e during period t;

[0024] The cogeneration unit constraints of the day-ahead model are:

[0025]

[0026]

[0027]

[0028]

[0029]

[0030] Where: and are the maximum and minimum electrical outputs of the combined heat and power unit e, respectively; is the power output of the cogeneration unit e during period t-1; and are the upper and lower reserve capacities of the CHP unit e during period t-1, respectively; and are the maximum upward and downward ramp rates of CHP unit e, respectively;

[0031] The energy hub constraint of the day-ahead model is:

[0032]

[0033]

[0034] Where: is the output of renewable energy unit e during period t; is the input electrical power of heat pump e during period t; and are the electrical and thermal outputs of energy hub e during period t, respectively; is the heat-to-power ratio of the combined heat and power unit e; COP e HP is the electric-to-heat conversion efficiency of the heat pump e;

[0035] The power system constraints of the day-ahead model are:

[0036]

[0037]

[0038]

[0039] Where: is the set of power grid branches with the head end node j; and are respectively the active output power and reactive output power of the power supply at the grid node j during period t; P ij,t and Q ij,t are the active and reactive transmission powers of the power grid branch ij during period t; P jl,t and Q jl,t are the active and reactive transmission powers of the power grid branch jl in period t respectively; and are the active and reactive loads at the grid node j during period t; V i,t and V j,t are the voltage amplitudes at grid nodes i and j during period t; r ij and x ij are the resistance and reactance of the grid branch ij respectively; V 0 is the rated voltage amplitude;

[0040] The thermal system constraints of the day-ahead model are:

[0041]

[0042]

[0043]

[0044]

[0045]

[0046]

[0047] Where: and are the sets of heating network pipelines connected to the heating network node n at the beginning and end of the pipelines respectively; and are the heat source output and heat load at the heating network node n during period t; c P is the specific heat capacity of water; and are the hot water mass flow rates of the heat source and heat load at the node n of the heating network during period t, respectively; and are the inlet and outlet temperatures of hot water at node n of the heating network during period t, respectively; and are the equivalent heat capacity and heat loss coefficient of the building at the heating network node n, respectively; and are the indoor temperatures of the building at node n of the heating network at time periods t and t-1 respectively; T t A is the ambient temperature during period t; and are the starting and ending temperatures of hot water in the heating network pipe p during period t; p is the heat transfer coefficient of the heating network pipe p; L p is the length of the heat network pipeline p; m p,t is the hot water mass flow rate of the heating network pipe p during period t; is the mixed temperature of hot water at node n of the heating network during period t; e is a natural constant;

[0048] The objective function of the intraday stage model is:

[0049]

[0050] In the formula, y represents the intraday stage adjustment variable; is the power output adjustment of the cogeneration unit e during period t; is the cost of wind and solar power abandonment of renewable energy unit e; is the amount of wind and solar power abandoned by renewable energy unit e during period t; is the load shedding cost at grid node i; is the load shedding amount at the grid node i during period t;

[0051] The constraint on the adjustment amount of the cogeneration unit in the intraday stage model is:

[0052]

[0053] The constraint on the energy hub adjustment amount of the intraday stage model is:

[0054]

[0055]

[0056]

[0057] Where: is the input power adjustment of heat pump e during period t; and are the electrical and thermal output adjustments of energy hub e during period t, respectively;

[0058] The constraints on the power system adjustment amount of the intraday stage model are:

[0059]

[0060]

[0061]

[0062]

[0063] Where: and are respectively the active and reactive output power adjustments of the power source at the grid node j during period t; and are the active and reactive transmission power adjustments of the power grid branch ij during period t respectively; and are respectively the active and reactive transmission power adjustments of the power grid branch jl in period t; is the load shedding amount at the grid node j during period t; and are the voltage amplitude adjustment values ​​at the grid nodes i and j during period t respectively;

[0064] The constraint on the thermal system adjustment of the intraday stage model is:

[0065]

[0066]

[0067]

[0068]

[0069]

[0070]

[0071] Where: and are the heat source output and heat load adjustment at the heating network node n during period t respectively; and are the inlet and outlet temperature adjustments of hot water at node n of the heating network during period t, respectively; and are the indoor temperature adjustment of the building at the heating network node n at time periods t and t-1 respectively; and are the temperature adjustment values ​​of the hot water start and end of the heat network pipe p during time period t; It is the mixed temperature adjustment of hot water at node n of the heating network during period t.

[0072] In one embodiment, the step of using the affine strategy and the second-order cone duality theory to equivalently transform the day-ahead and intra-day two-stage distributed robust optimization scheduling model of the electric-thermal integrated energy system into a deterministic second-order cone programming model includes:

[0073] Introducing the affine strategy to limit the intraday adjustment variables to uncertain variables and auxiliary variables The linear affine function of is:

[0074]

[0075] Where: y m,t Uniform form of the variables adjusted for intraday period; and is the linear coefficient of the linear affine function, is the decision variable;

[0076] Represent the day-ahead phase model, intraday phase model, extended fuzzy sets and linear affine functions in matrix / vector form;

[0077] The matrix / vector form of the day-ahead model is:

[0078]

[0079] Ax≤b (39)

[0080] Where: A is the coefficient matrix of the day-ahead model; b and c are the vectors of the day-ahead model; the superscript T indicates transposition;

[0081] The matrix / vector form of the intraday stage model is:

[0082]

[0083] Ex+Ιy+Mw≤h (41)

[0084] Where: E, I and M are the coefficient matrices of the intraday stage model; d and h are the vectors of the intraday stage model;

[0085] The matrix / vector form of the extended fuzzy set is:

[0086]

[0087]

[0088] Where: v is the vector form of auxiliary variables; J is the coefficient matrix of the extended fuzzy set; σ, w, and is the vector of extended fuzzy sets;

[0089] The matrix / vector form of the linear affine function is:

[0090] y=Y w w+Y v v (44)

[0091] Where: Y w and Y v is the coefficient matrix of the linear affine function;

[0092] According to the definition of the extended fuzzy set G, the supremum problem in the objective function of the day-ahead model is expressed as a semi-infinite optimization problem. The expression of the semi-infinite optimization problem is:

[0093]

[0094]

[0095]

[0096]

[0097] f(w,v)≥0 (49)

[0098] Where: f(w,v) is the joint probability density function of w and v; df(w,v) is the differential of f(w,v); α, β and γ are the dual variables of the corresponding constraints;

[0099] By applying the strong duality theory, the above semi-infinite optimization problem is transformed into a finite-dimensional dual problem. The expression of the finite-dimensional dual problem is:

[0100] minα+γ Tσ (50)

[0101] γ≥0 (51)

[0102]

[0103] For formula (52) as a robust constraint, first, substitute formula (44) for the linear affine function into formula (52), and according to the extended fuzzy set expressed in matrix / vector form According to the definition of , formula (52) can be rewritten as the expression for the worst case:

[0104]

[0105] w≥w:δ (54)

[0106]

[0107] 2Jw=τ:η (56)

[0108] v-1=ψ:κ (57)

[0109] v+1=ζ:π (58)

[0110]

[0111]

[0112] Where: τ, ψ and ζ are the introduced auxiliary variables; δ, ε, η, κ, π, θ and ρ are the dual variables of the corresponding constraint formula;

[0113] Secondly, by applying the second-order cone duality theory, the worst case expressions (53)-(60) are rewritten as the dual problem, which is expressed as:

[0114]

[0115]

[0116]

[0117]

[0118] δ≤0,ε≥0,ρ≥0 (65)

[0119] For formula (41) which is also a robust constraint, first, the linear affine function (44) is substituted into formula (41), and then the extended fuzzy set expressed in matrix / vector form is According to the definition of , formula (41) can be rewritten as the expression for the worst case:

[0120]

[0121] w≥w:δ k (67)

[0122]

[0123] 2Jw=τ:η k (69)

[0124] v-1=ψ:κ k (70)

[0125] v+1=ζ:π k (71)

[0126]

[0127]

[0128] Where: (·) k represents the kth row of the matrix / vector; τ k , k and k is the auxiliary variable introduced; δ k , ε k , η k , κ k , π k ,θ k and ρ k is the dual variable of the corresponding constraint;

[0129] Secondly, by applying the second-order cone duality theory, the worst case expressions (66)-(73) are rewritten as the dual problem, which is expressed as:

[0130]

[0131]

[0132]

[0133]

[0134] δ k ≤0,ε k ≥0,ρ k ≥0 (78).

[0135] In one embodiment, the step of solving the second-order cone programming model to obtain an optimal scheduling decision for the electric-thermal integrated energy system includes:

[0136] The second-order cone programming model is written in GAMS or Python general modeling software, and the CPLEX or MOSEK solver in the general modeling software is used to solve the written second-order cone programming model to obtain the optimal scheduling decision of the electric-thermal integrated energy system.

[0137] The above-mentioned robust optimization method for the electric-thermal integrated energy system considering correlation describes the probability distribution of uncertain parameters by incorporating two uncertain parameters, namely, the output of renewable energy units and ambient temperature, and their correlation into fuzzy sets, making the description of the true probability distribution of the output of renewable energy units and ambient temperature more accurate, which helps to exclude extreme probability distributions that are unlikely to occur, thereby improving the reliability of scheduling decisions for the electric-thermal integrated energy system. Furthermore, by considering the uncertainty of ambient temperature in the optimization scheduling model, the optimization decision of the electric-thermal integrated energy system can effectively prevent the ambient temperature deviation that may occur the next day, thereby improving the safety of the electric-thermal integrated energy system. BRIEF DESCRIPTION OF THE DRAWINGS

[0138] Figure 1 A schematic flow chart of a method for optimizing the distribution of electric and thermal integrated energy systems taking into account correlation in one embodiment;

[0139] Figure 2 This is the network topology diagram of Bali's electric and thermal integrated energy system;

[0140] Figure 3 This is the energy hub structure diagram;

[0141] Figure 4 It is the output of renewable energy units, ambient temperature and electrical load diagram;

[0142] Figure 5 This is a comparison chart of the total cost of the electric-thermal integrated energy system under different optimization schemes. DETAILED DESCRIPTION

[0143] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0144] In one embodiment, Figure 1 As shown, a distributed robust optimization method for an electric-thermal integrated energy system considering correlation is provided, and the method is applied to a terminal as an example for explanation, including the following steps:

[0145] Step S1: Combining the two uncertain parameters of renewable energy unit output and ambient temperature, considering the correlation between the outputs of different renewable energy units, and the correlation between the outputs of renewable energy units and ambient temperature, a fuzzy set containing multiple probability distribution information is constructed.

[0146] Step S2: Introduce auxiliary variables to replace the square terms in the fuzzy set to obtain the extended fuzzy set.

[0147] Step S3: Based on the extended fuzzy set, a two-stage day-ahead and intraday distributed robust optimization scheduling model for the electric-thermal integrated energy system is constructed.

[0148] Step S4: Using the affine strategy and the second-order cone duality theory, the day-ahead and day-intraday two-stage distributed robust optimization scheduling model of the electric-thermal integrated energy system is equivalently transformed into a deterministic second-order cone programming model.

[0149] Step S5: Solve the second-order cone programming model to obtain the optimal scheduling decision of the electric-thermal integrated energy system.

[0150] Among them, the electric-thermal integrated energy system can be dispatched according to the optimized dispatching decision of the electric-thermal integrated energy system.

[0151] The above-mentioned distributed robust optimization method for the electric-thermal integrated energy system considering correlation, by combining the two uncertain parameters of renewable energy unit output and ambient temperature, considers the correlation of the output of different renewable energy units, as well as the correlation of the output of renewable energy units and ambient temperature, and constructs a fuzzy set containing multiple probability distribution information, so that the description of the real probability distribution of renewable energy unit output and ambient temperature is more accurate, which helps to exclude the extreme probability distribution that is impossible to occur; introduces auxiliary variables to replace the square terms in the fuzzy set to obtain the extended fuzzy set; on the basis of the extended fuzzy set, constructs a two-stage distributed robust optimization scheduling model of the electric-thermal integrated energy system from day one to day one, and considers the uncertainty of ambient temperature in the optimization scheduling model, so that the optimization decision of the electric-thermal integrated energy system can effectively prevent the ambient temperature deviation that may occur the next day; adopts the affine strategy and the second-order cone duality theory to equivalently transform the two-stage distributed robust optimization scheduling model of the electric-thermal integrated energy system from day one to day one into a deterministic second-order cone programming model; solves the second-order cone programming model to obtain the optimal scheduling decision of the electric-thermal integrated energy system, which improves the reliability and safety of the scheduling decision of the electric-thermal integrated energy system.

[0152] In one embodiment, the fuzzy set containing the correlation between the output of the renewable energy unit and the ambient temperature is:

[0153]

[0154]

[0155] Where: F is a fuzzy set; P is a probability; R is all possible situations of uncertain parameters; P(R) is all possible probability distributions of uncertain parameters; and are the prediction errors of the output of renewable energy units e and f during period t respectively; is the prediction error of the ambient temperature during period t; W is and The uncertain set E p It means taking the expected value; and They are and The variance of for The variance of for and The covariance of for and The covariance of and They are The upper and lower limits of and They are upper and lower limits.

[0156] In one embodiment, the expanded fuzzy set G is:

[0157]

[0158]

[0159] Where: G is the extended fuzzy set; is the auxiliary variable introduced; is the corresponding extended uncertainty set; and They are and upper limit.

[0160] In one embodiment, the day-ahead and intraday two-stage robust optimization scheduling model for the electric-thermal integrated energy system includes a day-ahead stage model and an intraday stage model.

[0161] Among them, in the day-ahead stage, the dispatcher determines the pre-dispatch decision of the electric-thermal integrated energy system, including the benchmark operating point and adjustable reserve capacity, based on the predicted values ​​of the output of renewable energy units and ambient temperature. In the intraday stage, the dispatcher adjusts the dispatch decision of the electric-thermal integrated energy system based on the predicted errors of the output of renewable energy units and ambient temperature to smooth the fluctuations of the output of renewable energy units and ambient temperature.

[0162] The objective function of the day-ahead model is:

[0163]

[0164] Where: x represents the pre-dispatch variable in the day-ahead stage; w represents the prediction error of the output of renewable energy units and ambient temperature, which is a random variable; sup represents the supremum; Q(x,w) represents the adjustment cost of the electric-thermal integrated energy system under the given day-ahead pre-dispatch variable and the prediction error of the output of renewable energy units and ambient temperature, which is the objective function in the intra-day stage; and are the unit generation, upper reserve and lower reserve costs of CHP unit e respectively; is the power output of cogeneration unit e during period t; and are the upper and lower reserve capacities of the CHP unit e during period t;

[0165] The cogeneration unit constraints of the day-ahead model are:

[0166]

[0167]

[0168]

[0169]

[0170]

[0171] Where: and are the maximum and minimum electrical outputs of the combined heat and power unit e, respectively; is the power output of the cogeneration unit e during period t-1; and are the upper and lower reserve capacities of the CHP unit e during period t-1, respectively; and are the maximum upward and downward ramp rates of CHP unit e, respectively;

[0172] The energy hub constraint of the day-ahead model is:

[0173]

[0174]

[0175] Where: is the output of renewable energy unit e during period t; is the input electrical power of heat pump e during period t; and are the electrical and thermal outputs of energy hub e during period t, respectively; is the heat-to-power ratio of the combined heat and power unit e; COP eHP is the electric-to-heat conversion efficiency of the heat pump e;

[0176] The power system constraints of the day-ahead model are:

[0177]

[0178]

[0179] V j,t =V i,t -(P ij,t r ij +Q ij,t x ij ) / V 0 (15)

[0180] Where: is the set of power grid branches with the head end node j; and are respectively the active output power and reactive output power of the power supply at the grid node j during period t; P ij,t and Q ij,t are the active and reactive transmission powers of the power grid branch ij during period t; P jl,t and Q jl,t are the active and reactive transmission powers of the power grid branch jl in period t respectively; and are the active and reactive loads at the grid node j during period t; V i,t and V j,t are the voltage amplitudes at grid nodes i and j during period t; r ij and x ij are the resistance and reactance of the grid branch ij respectively; V 0 is the rated voltage amplitude;

[0181] The thermal system constraints of the day-ahead model are:

[0182]

[0183]

[0184]

[0185]

[0186]

[0187]

[0188] Where: and are the sets of heating network pipelines connected to the heating network node n at the beginning and end of the pipelines respectively; and are the heat source output and heat load at the heating network node n during period t; c P is the specific heat capacity of water; and are the hot water mass flow rates of the heat source and heat load at the node n of the heating network during period t, respectively; and are the inlet and outlet temperatures of hot water at node n of the heating network during period t, respectively; and are the equivalent heat capacity and heat loss coefficient of the building at the heating network node n, respectively; and are the indoor temperatures of the building at node n of the heating network at time periods t and t-1 respectively; T t A is the ambient temperature during period t; and are the starting and ending temperatures of hot water in the heating network pipe p during period t; p is the heat transfer coefficient of the heating network pipe p; L p is the length of the heat network pipeline p; m p,t is the hot water mass flow rate of the heating network pipe p during period t; is the mixed temperature of hot water at node n of the heating network during period t; e is a natural constant;

[0189] The objective function of the intraday stage model is:

[0190]

[0191] In the formula, y represents the intraday stage adjustment variable; is the power output adjustment of the cogeneration unit e during period t; is the cost of wind and solar power abandonment of renewable energy unit e; is the amount of wind and solar power abandoned by renewable energy unit e during period t; is the load shedding cost at grid node i; is the load shedding amount at the grid node i during period t;

[0192] The constraint on the adjustment amount of the cogeneration unit in the intraday stage model is:

[0193]

[0194] The constraint of the energy hub adjustment amount of the intraday stage model is:

[0195]

[0196]

[0197]

[0198] Where: is the input power adjustment of heat pump e during period t; and are the electrical and thermal output adjustments of energy hub e during period t, respectively;

[0199] The constraints on the power system adjustment of the intraday stage model are:

[0200]

[0201]

[0202]

[0203]

[0204] Where: and are respectively the active and reactive output power adjustments of the power source at the grid node j during period t; and are the active and reactive transmission power adjustments of the power grid branch ij during period t respectively; and are respectively the active and reactive transmission power adjustments of the power grid branch jl in period t; is the load shedding amount at the grid node j during period t; and are the voltage amplitude adjustment values ​​at the grid nodes i and j during period t respectively;

[0205] The constraint on the thermal system adjustment of the intraday stage model is:

[0206]

[0207]

[0208]

[0209]

[0210]

[0211]

[0212] Where: and are the heat source output and heat load adjustment at the heating network node n during period t respectively; and are the inlet and outlet temperature adjustments of hot water at node n of the heating network during period t, respectively; and are the indoor temperature adjustment of the building at the heating network node n at time periods t and t-1 respectively; and are the temperature adjustment values ​​of the hot water start and end of the heat network pipe p during period t; It is the mixed temperature adjustment of hot water at node n of the heating network during period t.

[0213] In one embodiment, the steps of equivalently converting the day-ahead and intraday two-stage distributed robust optimization scheduling model of the electric-thermal integrated energy system into a deterministic second-order cone programming model by using an affine strategy and second-order cone duality theory include:

[0214] Introducing the affine strategy to limit the intraday adjustment variables to uncertain variables and auxiliary variables The linear affine function of is:

[0215]

[0216] Where: y m,t The uniform form of the variables is adjusted for the intraday period; and is the linear coefficient of the linear affine function, is the decision variable;

[0217] Represent the day-ahead phase model, intraday phase model, extended fuzzy sets and linear affine functions in matrix / vector form;

[0218] The matrix / vector form of the day-ahead model is:

[0219]

[0220] Ax≤b (39)

[0221] Where: A is the coefficient matrix of the day-ahead model; b and c are the vectors of the day-ahead model; the superscript T indicates transposition;

[0222] The matrix / vector form of the intraday stage model is:

[0223]

[0224] Ex+Ιy+Mw≤h (41)

[0225] Where: E, I and M are the coefficient matrices of the intraday stage model; d and h are the vectors of the intraday stage model;

[0226] The matrix / vector form of the extended fuzzy set is:

[0227]

[0228]

[0229] Where: v is the vector form of auxiliary variables; J is the coefficient matrix of the extended fuzzy set; σ, w, and is the vector of extended fuzzy sets;

[0230] The matrix / vector form of a linear affine function is:

[0231] y=Y w w+Y v v (44)

[0232] Where: Y w and Y v is the coefficient matrix of the linear affine function;

[0233] According to the definition of the extended fuzzy set G, the supremum problem in the objective function of the day-ahead model is expressed as a semi-infinite optimization problem. The expression of the semi-infinite optimization problem is:

[0234]

[0235]

[0236]

[0237]

[0238] f(w,v)≥0 (49)

[0239] Where: f(w,v) is the joint probability density function of w and v; df(w,v) is the differential of f(w,v); α, β and γ are the dual variables of the corresponding constraints;

[0240] Applying the strong duality theory, the above semi-infinite optimization problem is transformed into a finite-dimensional dual problem. The expression of the finite-dimensional dual problem is:

[0241] minα+γ T σ (50)

[0242] γ≥0 (51)

[0243]

[0244] For formula (52) as a robust constraint, first, substitute formula (44) for the linear affine function into formula (52), and according to the extended fuzzy set expressed in matrix / vector form According to the definition of , formula (52) can be rewritten as the expression for the worst case:

[0245]

[0246] w≥w:δ (54)

[0247]

[0248] 2Jw=τ:η (56)

[0249] v-1=ψ:κ (57)

[0250] v+1=ζ:π (58)

[0251]

[0252]

[0253] Where: τ, ψ and ζ are the introduced auxiliary variables; δ, ε, η, κ, π, θ and ρ are the dual variables of the corresponding constraint formula;

[0254] Secondly, by applying the second-order cone duality theory, the worst case expressions (53)-(60) are rewritten as the dual problem, which is expressed as:

[0255]

[0256]

[0257]

[0258]

[0259] δ≤0,ε≥0,ρ≥0 (65)

[0260] For formula (41) which is also a robust constraint, first, the linear affine function (44) is substituted into formula (41), and then the extended fuzzy set expressed in matrix / vector form is According to the definition of , formula (41) can be rewritten as the expression for the worst case:

[0261]

[0262] w≥w:δ k (67)

[0263]

[0264] 2Jw=τ:η k (69)

[0265] v-1=ψ:κk (70)

[0266] v+1=ζ:π k (71)

[0267]

[0268]

[0269] Where: (·) k represents the kth row of the matrix / vector; τ k , k and k is the auxiliary variable introduced; δ k , ε k , η k , κ k , π k ,θ k and ρ k is the dual variable of the corresponding constraint;

[0270] Secondly, by applying the second-order cone duality theory, the worst case expressions (66)-(73) are rewritten as the dual problem, which is expressed as:

[0271]

[0272]

[0273]

[0274]

[0275] δ k ≤0,ε k ≥0,ρ k ≥0 (78).

[0276] In one embodiment, the steps of solving the second-order cone programming model to obtain an optimal scheduling decision for the electric-thermal integrated energy system include:

[0277] A second-order cone programming model is written in GAMS or Python general modeling software, and the CPLEX or MOSEK solver in the general modeling software is used to solve the written second-order cone programming model to obtain the optimal scheduling decision of the electric-thermal integrated energy system.

[0278] The above-mentioned robust optimization method for the electric-thermal integrated energy system considering correlation describes the probability distribution of uncertain parameters by incorporating two uncertain parameters, namely, the output of renewable energy units and ambient temperature, and their correlation into fuzzy sets, making the description of the true probability distribution of the output of renewable energy units and ambient temperature more accurate, which helps to exclude extreme probability distributions that are unlikely to occur, thereby improving the reliability of scheduling decisions for the electric-thermal integrated energy system. Furthermore, by considering the uncertainty of ambient temperature in the optimization scheduling model, the optimization decision of the electric-thermal integrated energy system can effectively prevent the ambient temperature deviation that may occur the next day, thereby improving the safety of the electric-thermal integrated energy system.

[0279] In one embodiment, the actual Bali electric and thermal integrated energy system is used as an example, and its network topology is as follows: Figure 2 As shown in Figure 1, the system is composed of a 9-node power system (①…⑨) and a 32-node thermal system (1…32) coupled. The three energy hubs (energy hub 1, energy hub 2, and energy hub 3) are connected to nodes ①, ⑨, and ⑥ of the power system and nodes 31, 1, and 32 of the thermal system, respectively. The structure of the energy hub is as follows: Figure 3 As shown in Figure 1, the renewable energy units in energy hub 1 are wind turbines, and the renewable energy units in energy hubs 2 and 3 are photovoltaic units. The predicted values ​​of renewable energy unit output, ambient temperature and electrical load are shown in Figure 1. Figure 4 The parameters of the cogeneration unit are shown in Table 1. The MOSEK solver of GAMS software is used to solve the second-order cone programming model, and the convergence accuracy of MOSEK is set to 0.001.

[0280] Table 1 Parameters of the cogeneration unit

[0281]

[0282] In order to illustrate the advantages of the robust optimization method for the electric-thermal integrated energy system considering correlation of the present invention, which incorporates two uncertain parameters, the output of renewable energy units and the ambient temperature, and their correlation in the fuzzy set, the following four schemes are designed:

[0283] Solution 1: No probability distribution information is considered;

[0284] Option 2: Consider the output of renewable energy units and the expected ambient temperature;

[0285] Option 3: Consider the expectation and variance of renewable energy unit output and ambient temperature;

[0286] Scheme 4: Consider the expectation, variance and covariance of renewable energy unit output and ambient temperature.

[0287] Solve the distributed blue bar optimization model corresponding to the above four schemes, and the total cost of the electric and thermal integrated energy system is obtained as follows: Figure 5 As shown. It can be seen that as more probability distribution information is considered (from Scheme 1 to Scheme 4), the total cost of the electric-thermal integrated energy system continues to decrease. When all the probability distribution information considered is included (corresponding to Scheme 4), the total cost of the electric-thermal integrated energy system reaches the minimum value of $781.33, which is 25.44% lower than that of Scheme 1. This is because the distributed robust optimization method can learn the true probability distribution of uncertain parameters from the probability distribution information. When more probability distribution information is included in the fuzzy set, the amount of information obtained about the true probability distribution of the output of renewable energy units and the ambient temperature is also more, and the fuzzy set is also reduced to the surrounding of the true probability distribution. This shows that by incorporating more probability distribution information, the fuzziness of uncertain parameters can be reduced, thereby accurately reducing the fuzzy set, thereby reducing the conservatism of the optimization results and improving the reliability of the scheduling decision of the electric-thermal integrated energy system.

[0288] In order to illustrate the advantage of considering the uncertainty of ambient temperature in the optimization model of the distributed robust optimization method of the electric and thermal integrated energy system considering the correlation of the present invention, a comparative analysis is conducted with the method that only considers the uncertainty of the output of renewable energy units. It can be seen that when the uncertainty of ambient temperature is considered, the pre-dispatch cost of the cogeneration unit on the day before is higher. This is because, in order to prevent the possible deviation of ambient temperature on the next day, the dispatcher chooses to increase the pre-output of the cogeneration unit. This pre-dispatch strategy can well cope with all possible ambient temperature fluctuations, which is manifested as the daily load shedding cost corresponding to this strategy is 0. In contrast, when the uncertainty of ambient temperature is not considered, although the pre-dispatch cost of the cogeneration unit on the day before is small, when the fluctuation of ambient temperature is large, it will lead to the occurrence of load shedding, which will cause the electric and thermal integrated energy system to suffer severe load shedding penalties, which is manifested as the daily load shedding cost corresponding to this strategy is as high as $130.70. The high load shedding penalty makes the total system cost of this strategy higher, which is 8.77% higher than when the uncertainty of ambient temperature is considered. This example shows that considering the uncertainty of ambient temperature can help prevent ambient temperature deviations the next day, thereby improving the economy and safety of the electric-thermal integrated energy system.

[0289] Table 2 Comparison of system scheduling costs when considering and not considering ambient temperature uncertainty

[0290]

[0291] It should be understood that although Figure 1The steps in the flowchart are shown in sequence as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified in this document, there is no strict order restriction for the execution of these steps, and these steps can be executed in other orders. Moreover, Figure 1 At least part of the steps may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily executed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least part of the sub-steps or stages of other steps.

[0292] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0293] The above-mentioned embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention patent. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the patent of the present application shall be subject to the attached claims.

Claims

1. A robust optimization method for the distribution of electric and thermal integrated energy systems considering correlation. It is characterized in that The method comprises: Step 1: Combining the two uncertain parameters of renewable energy unit output and ambient temperature, considering the correlation between the output of different renewable energy units and the correlation between the output of renewable energy units and ambient temperature, a fuzzy set containing multiple probability distribution information is constructed; Step 2: Introduce auxiliary variables to replace the square terms in the fuzzy set to obtain the extended fuzzy set; Step 3: Based on the extended fuzzy set, a two-stage distributed robust optimization scheduling model of the electric-thermal integrated energy system is constructed; Step 4: Using the affine strategy and the second-order cone duality theory, the day-ahead and day-intraday two-stage distributed robust optimization scheduling model of the electric-thermal integrated energy system is equivalently transformed into a deterministic second-order cone programming model; Step 5: Solve the second-order cone programming model to obtain the optimal scheduling decision of the electric-thermal integrated energy system; The fuzzy set containing multiple probability distribution information is constructed as follows: Where: F is a fuzzy set; P is a probability; R is all possible situations of uncertain parameters; P(R) is all possible probability distributions of uncertain parameters; and are the prediction errors of the output of renewable energy units e and f during period t respectively; is the prediction error of the ambient temperature during period t; W is and The uncertain set E p It means taking the expected value; and They are and The variance of for The variance of for and The covariance of for and The covariance of and They are The upper and lower limits of and They are The upper and lower limits of The extended fuzzy set G is: Where: G is the extended fuzzy set; is the auxiliary variable introduced; is the corresponding extended uncertainty set; and They are and The upper limit of The day-ahead and day-intraday two-stage distributed robust optimization scheduling model for the electric-thermal integrated energy system includes a day-ahead stage model and a day-intraday stage model; The objective function of the day-ahead model is: Where: x represents the pre-dispatch variable in the day-ahead stage; w represents the prediction error of the output of renewable energy units and ambient temperature, which is a random variable; sup represents the supremum; Q(x,w) represents the adjustment cost of the electric-thermal integrated energy system under the given pre-dispatch variable in the day-ahead stage and the prediction error of the output of renewable energy units and ambient temperature, which is the objective function of the intra-day stage model; and are the unit generation, upper reserve and lower reserve costs of the CHP unit, respectively; is the electrical output of the cogeneration unit during period t; and is the upper and lower reserve capacity of the CHP unit during period t; The cogeneration unit constraints of the day-ahead model are: Where: and are the maximum and minimum electrical outputs of the cogeneration unit, respectively; is the electrical output of the cogeneration unit during period t-1; and They are the upper and lower reserve capacities of the cogeneration unit during period t-1, respectively; and are the maximum upward and downward ramp rates of the CHP unit, respectively; The energy hub constraint of the day-ahead model is: Where: is the output of renewable energy units during period t; is the input electrical power of the heat pump during period t; and are the electricity and heat output of the energy hub during period t, respectively; is the heat-to-electricity ratio of the cogeneration unit; is the electric-to-heat conversion efficiency of the heat pump; The power system constraints of the day-ahead model are: V j,t = V i,t - (P ij,t r ij + Q ij,t x ij ) / V 0 (15) Where: is the set of power grid branches with the head end node j; and are respectively the active output power and reactive output power of the power supply at the grid node j during period t; P ij,t and Q ij,t are the active and reactive transmission powers of the power grid branch ij during period t; P jl,t and Q jl,t are the active and reactive transmission powers of the power grid branch jl in period t respectively; and are the active and reactive loads at the grid node j during period t; V i,t and V j,t are the voltage amplitudes at grid nodes i and j during period t; r ij and x ij are the resistance and reactance of the grid branch ij respectively; V 0 is the rated voltage amplitude; The thermal system constraints of the day-ahead model are: Where: and are the sets of heating network pipelines connected to the heating network node n at the beginning and end of the pipelines respectively; and are the heat source output and heat load at the heating network node n during period t; c P is the specific heat capacity of water; and are the hot water mass flow rates of the heat source and heat load at the node n of the heating network during period t, respectively; and are the inlet and outlet temperatures of hot water at node n of the heating network during period t, respectively; and are the equivalent heat capacity and heat loss coefficient of the building at the heating network node n, respectively; and are the indoor temperatures of the building at node n of the heating network at time periods t and t-1 respectively; T t A is the ambient temperature during period t; and are the starting and ending temperatures of hot water in the heating network pipe p during period t; p is the heat transfer coefficient of the heating network pipe p; L p is the length of the heat network pipeline p; m p,t is the hot water mass flow rate of the heating network pipe p during period t; is the mixed temperature of hot water at node n of the heating network during period t; e is a natural constant; The objective function of the intraday stage model is: In the formula, y represents the intraday stage adjustment variable; is the power output adjustment of the cogeneration unit during period t; The cost of curtailing wind and solar power generation for renewable energy units; is the amount of wind and solar power abandoned by renewable energy units during period t; is the load shedding cost at grid node i; is the load shedding amount at the grid node i during period t; The constraint on the adjustment amount of the cogeneration unit in the intraday stage model is: The constraint on the energy hub adjustment amount of the intraday stage model is: Where: is the input electric power adjustment of the heat pump during period t; and are the electrical and thermal output adjustments of the energy hub during period t, respectively; The constraints on the power system adjustment amount of the intraday stage model are: Where: and are respectively the active and reactive output power adjustments of the power source at the grid node j during period t; and are the active and reactive transmission power adjustments of the power grid branch ij during period t respectively; and are respectively the active and reactive transmission power adjustments of the power grid branch jl in period t; is the load shedding amount at the grid node j during period t; and are the voltage amplitude adjustment values ​​at the grid nodes i and j during period t respectively; The constraint on the thermal system adjustment of the intraday stage model is: Where: and are the heat source output and heat load adjustment at the heating network node n during period t respectively; and are the inlet and outlet temperature adjustments of hot water at node n of the heating network during period t, respectively; and are the indoor temperature adjustment of the building at the heating network node n at time periods t and t-1 respectively; and are the temperature adjustment values ​​of the hot water start and end of the heat network pipe p during period t; It is the mixed temperature adjustment of hot water at node n of the heating network during period t.

2. The method according to claim 1, It is characterized in that The step of using the affine strategy and the second-order cone duality theory to equivalently transform the day-ahead and intraday two-stage distributed robust optimization scheduling model of the electric-thermal integrated energy system into a deterministic second-order cone programming model includes: Introducing the affine strategy to limit the intraday adjustment variables to uncertain variables and auxiliary variables The linear affine function of is: where: y m,t is the unified form of the intra-day stage adjustment variable; and are the linear coefficients of the linear affine function and are decision variables; Represent the day-ahead phase model, intraday phase model, extended fuzzy sets and linear affine functions in matrix / vector form; The matrix / vector form of the day-ahead model is: Ax≤b (39) Where: A is the coefficient matrix of the day-ahead model; b and c are the vectors of the day-ahead model; the superscript T indicates transposition; The matrix / vector form of the intraday stage model is: Ex+Ιy+Mw≤h (41) Where: E, I and M are the coefficient matrices of the intraday stage model; d and h are the vectors of the intraday stage model; The matrix / vector form of the extended fuzzy set is: where \(v\) is the vector form of the auxiliary variable; \(J\) is the coefficient matrix of the extended fuzzy set; \(\sigma\), w , and are the vectors of the extended fuzzy set; The matrix / vector form of the linear affine function is: y=Y w w+Y v v (44) Where: Y w and Y v is the coefficient matrix of the linear affine function; According to the definition of the extended fuzzy set G, the supremum problem in the objective function of the day-ahead model is expressed as a semi-infinite optimization problem. The expression of the semi-infinite optimization problem is: f(w,v)≥0 (49) Where: f(w,v) is the joint probability density function of w and v; df(w,v) is the differential of f(w,v); α, β and γ are the dual variables of the corresponding constraints; By applying the strong duality theory, the above semi-infinite optimization problem is transformed into a finite-dimensional dual problem. The expression of the finite-dimensional dual problem is: minα+γ T p(50) γ≥0 (51) For formula (52) as a robust constraint, first, substitute formula (44) for the linear affine function into formula (52), and according to the extended fuzzy set expressed in matrix / vector form According to the definition of , formula (52) can be rewritten as the expression for the worst case: w≥ w :d (54) 2Jw=τ :η (56) v-1=ψ:κ (57) v+1=ζ:π (58) Where: τ, ψ and ζ are the introduced auxiliary variables; δ, ε, η, κ, π, θ and ρ are the dual variables of the corresponding constraint formula; Secondly, by applying the second-order cone duality theory, the worst case expressions (53)-(60) are rewritten as the dual problem, which is expressed as: δ≤0,ε≥0,ρ≥0 (65) For formula (41) which is also a robust constraint, first, the linear affine function (44) is substituted into formula (41), and then the extended fuzzy set expressed in matrix / vector form is The definition of , formula (41) is rewritten as the expression for the worst case: w≥ w :d k (67) 2Jw=τ :η k (69) v-1=ψ :k k (70) v + 1 = ζ : π k (71) Where: (·) k represents the k-th row of the matrix / vector; τ k , ψ k and ζ k are introduced auxiliary variables; δ k , ε k , η k , κ k , π k , θ k and ρ k are the dual variables of the corresponding constraint equations; Secondly, by applying the second-order cone duality theory, the worst case expressions (66)-(73) are rewritten as the dual problem, which is expressed as: d k ≤0,e k ≥0,ρ k ≥0 (78).

3. The method according to claim 1, It is characterized in that The step of solving the second-order cone programming model to obtain an optimal scheduling decision for the electric-thermal integrated energy system includes: The second-order cone programming model is written in GAMS or Python general modeling software, and the CPLEX or MOSEK solver in the general modeling software is used to solve the written second-order cone programming model to obtain the optimal scheduling decision of the electric-thermal integrated energy system.

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