Adaptive optimization method for collaborative operation of multi-community integrated energy system

Abstract

The application discloses a kind of self-adapting optimization methods for the collaborative operation of multi-community integrated energy system, comprising: establishing the feasible region of safe operation of power transformer, for evaluating the load capacity of oil-immersed transformer;Establish a rolling optimization scheduling model of multi-community integrated energy system, with the minimum total operation cost of the system as the objective function, and impose community operation constraints;Using an improved adaptive ADMM algorithm based on spectral penalty factor to distribute the rolling optimization scheduling model for iterative optimization, to obtain the optimal scheduling strategy.The method of the present application provides a fast distributed collaborative optimization method with higher safety and new energy consumption rate for the operation of multi-community integrated energy system, and can protect the privacy and security of each subject.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of integrated energy systems, in particular to an adaptive optimization method for coordinated operation of multi-community integrated energy systems. BACKGROUND

[0002] In recent years, with the rapid growth of distributed energy resources such as photovoltaic and wind power generation, the energy system has been rapidly transformed, gradually shifting to a distributed system based on renewable energy. In this system, users are directly involved in the production, consumption, conversion and trading of energy. Therefore, community integrated energy systems have attracted increasing attention and are considered a key to the success of energy transformation. Due to the limitations of space, scale and function of a single community integrated energy system, it is worth studying the coordinated energy management of multi-community integrated energy systems. In order to realize the coordinated operation of communities with different configurations and preferences, establishing an energy sharing mechanism in a multi-community integrated energy system is an effective way to promote the use of renewable energy resources and further reduce community peak power demand and system operating costs.

[0003] There have been some research reports on the coordinated optimization and scheduling of multi-community integrated energy systems. However, most of the current research ignores the importance of power transformer load capacity. Many of the premises for the coordinated optimization of multi-community integrated energy systems are based on the assumption that grid-transmitted electrical energy is seemingly endless. However, with the continued growth of power demand and the widespread access of distributed energy resources, the risk of power transformer overload is increasingly prominent. As a core infrastructure in the distribution network, long-term operation of power transformers in an overloaded state can accelerate their aging process, not only shortening their service life, but also causing significant economic losses. Therefore, taking practical and effective measures to prevent power transformer overload is of great practical significance to ensure the safe and stable operation of the power grid.

[0004] Currently, the main methods for optimizing and scheduling multi-community integrated energy systems are centralized and distributed. Centralized optimization requires the transmission of various data from all communities in the system to the control center for unified scheduling, which results in a huge amount of communication and computation, and also damages the data privacy of participants. Therefore, most scholars use distributed algorithms for research, in which each interest subject only interacts with other subjects to perform autonomous optimization, ensuring the privacy and security of each subject. However, the distributed algorithm is an iterative optimization process, and its convergence speed is affected by the initial value selection of the algorithm parameters. SUMMARY

[0005] The purpose of the present application is to overcome the deficiencies and shortcomings of the prior art, and to provide an adaptive optimization method for collaborative operation of a multi-community integrated energy system, which can achieve the safety and economy of the overall system operation while taking into account the privacy and interests of each community.

[0006] To achieve the above-mentioned purpose, the technical solution provided by the present application is: an adaptive optimization method for collaborative operation of a multi-community integrated energy system, comprising the following steps:

[0007] 1) Establish a feasible region for safe operation of a power transformer, which is used to evaluate the load capacity of the power transformer;

[0008] 2) Establish a rolling optimization scheduling model for the multi-community integrated energy system, with the minimum total operating cost of the system as the objective function, and impose community operation constraints, including combined heat and power unit operation constraints, electric boiler operation constraints, gas boiler operation constraints, electric energy storage operation constraints, thermal energy storage operation constraints, translatable load constraints, energy sharing constraints, power transformer operation constraints, and energy balance constraints; wherein the operation constraints of the power transformer are set based on the feasible region of the power transformer determined in step 1) to ensure safe operation of the power transformer;

[0009] 3) Use an improved adaptive ADMM algorithm to perform distributed iterative optimization on the rolling optimization scheduling model to obtain an optimal scheduling strategy; wherein ADMM is the Alternating Direction Method of Multipliers, and the specific improvement in the improved adaptive ADMM algorithm is: an adaptive spectral penalty factor is proposed, i.e., an update method for the penalty factor, which automatically selects the appropriate value according to the current state to effectively reduce the influence of the selection and initial value of the penalty factor on the algorithm and speed up the optimization process of ADMM.

[0010] Further, the feasible region of the power transformer refers to all possible load ranges that meet all current and temperature restrictions, i.e., C&T restrictions, i.e., the power transformer can safely operate within the feasible region; wherein the construction process of the feasible region is as follows:

[0011] 1) Convert the C&T restrictions to an equivalent maximum steady-state load, establish a relationship between the maximum steady-state load and the ambient temperature, and the method is as follows: given an ambient temperature and an initial value of a steady-state load, calculate the hot spot temperature HST and the top oil temperature TOT under the steady-state load according to the IEC60076 standard, and gradually increase the load until HST and TOT reach the C&T restrictions;

[0012] 2) According to the relationship between the maximum steady-state load and the ambient temperature established above, the HST and TOT temperature limit values are converted into the corresponding maximum load values at each ambient temperature, and the minimum value among the current, HST and TOT limit values is taken as the maximum load for safe operation of the power transformer at the ambient temperature;

[0013] 3) According to the predicted air temperature curve in the scheduling period, the C&T limit value of the power transformer is selected, and the maximum load for safe operation corresponding to each temperature is obtained, and the region below the maximum load is the feasible region for safe operation of the power transformer.

[0014] Further, a rolling optimization scheduling model of the multi-community integrated energy system is established, specifically including:

[0015] 1) Taking the minimum total operation cost of the multi-community integrated energy system as the objective function, i.e., the sum of the operation costs of each community is minimum, which includes the purchase cost of electricity and natural gas, and the objective function expression is as follows:

[0016]

[0017] In the formula, F is the total operation cost of the system, i is the community number, t is the scheduling time, represents the set of all community integrated energy systems, represents the set of scheduling times, v e,t , v g,t are the purchase electricity price and purchase gas price at t, respectively, G i,t are the purchase electricity power and purchase gas power of community i at t; considering the volatility of renewable energy production and the uncertainty of load, a rolling time domain optimization method is adopted, i.e., at t, according to the actual data at the current t, the predicted values of renewable energy production and load demand at the remaining time, only the decision at the current t is executed, and for the next time t+1, the scheduling time range moves forward by one hour, and the optimal solution at the next time will be obtained according to the new predicted data;

[0018] 2) Apply community operation constraints, including combined heat and power unit operation constraints, electric boiler operation constraints, gas boiler operation constraints, electric energy storage operation constraints, thermal energy storage operation constraints, translatable load constraints, energy sharing constraints, power transformer operation constraints and energy balance constraints;

[0019] The combined heat and power unit operation constraint is:

[0020]

[0021]

[0022]

[0023]

[0024] wherein, is the natural gas power consumed by the cogeneration unit of community i at time t, and are the power generation and heat generation of the cogeneration unit of community i at time t, respectively, is the power generation of the cogeneration unit of community i at time t+1, and are the power generation and heat generation efficiency of the cogeneration unit of community i, respectively, ΔP i CHP is the hourly ramping rate upper limit of the cogeneration unit of community i, and P i CHP are the upper and lower limits of the cogeneration unit of community i, respectively;

[0025] The operation constraints of the electric boiler are:

[0026]

[0027]

[0028]

[0029] wherein, is the power consumed by the electric boiler of community i at time t, is the power consumed by the electric boiler of community i at time t+1, ΔP i EB is the hourly ramping rate upper limit of the electric boiler of community i, and P i EB are the upper and lower limits of the electric boiler of community i, respectively, is the heat generation of the electric boiler of community i at time t, is the heat generation efficiency of the electric boiler of community i;

[0030] The operation constraints of the gas boiler are:

[0031]

[0032]

[0033] wherein, is the natural gas power consumed by the gas boiler of community i at time t, is the heat generation of the gas boiler of community i at time t, is the heat generation efficiency of the gas boiler of community i, and are the upper and lower limits of the thermal power output of the gas boiler in community i, respectively;

[0034] The electrical energy storage operation constraints are:

[0035]

[0036]

[0037]

[0038]

[0039]

[0040] wherein, and are the minimum and maximum allowed capacities of the electrical energy storage in community i, respectively, is the energy of the electrical energy storage in community i at time t, c is the self-discharge rate of the electrical energy storage in community i, is the energy variation of the electrical energy storage in community i over the period τ, and are the charging and discharging power of the electrical energy storage in community i at time t, respectively, and are the charging and discharging efficiency of the electrical energy storage in community i, respectively, and ΔT is the control period, and are the initial and target capacities of the electrical energy storage in community i, respectively, is the Boolean variable corresponding to the electrical energy storage in community i at time t, and are the upper limits of the charging and discharging power of the electrical energy storage in community i, respectively;

[0041] The thermal energy storage operation constraints are:

[0042]

[0043]

[0044]

[0045]

[0046]

[0047] wherein, and are the minimum and maximum allowed capacities of the thermal energy storage in community i, respectively, is the energy of the thermal energy storage in community i at time t,​c Energy of community i thermal storage at time t, Self-discharging rate of community i thermal storage, Energy change of community i thermal storage in period τ, and Charging and discharging power of community i thermal storage at time t, and Charging and discharging efficiency of community i thermal storage, ΔT is a control period, and Initial capacity and target capacity of community i thermal storage, Boolean variable corresponding to community i thermal storage at time t, and Upper limit of charging and discharging power of community i thermal storage;

[0048] The translatable load constraint is:

[0049]

[0050]

[0051]

[0052]

[0053] In the formula, and Translatable electric and thermal load of community i at time t, and Total demand of translatable electric and thermal load of community i in an optimization time domain, and Upper limit of translatable electric and thermal load power of community i, Ω e,i and Ω h,i Translatable electric and thermal load schedulable time set of community i;

[0054] The energy sharing constraint is:

[0055]

[0056]

[0057] In the formula, Electric power shared by community i to other communities at time t, Indicates that community i purchases power from other communities, Indicates that community i sells power to other communities, and P i sharerespectively, are the upper and lower limits of the electrical power that community i can share;

[0058] The power transformer operation constraints are:

[0059]

[0060]

[0061]

[0062] where P t Tr is the transmission power of the power transformer at time t, P t RES is the shared wind or photovoltaic power at time t, and P t Tr respectively, are the upper and lower limits of the electrical power that community i can share; is the upper limit of the electrical power that community i can purchase;

[0063] The energy balance constraints are:

[0064]

[0065]

[0066]

[0067] where, is the electrical power that community i can generate from renewable energy at time t, L e,i,t and L h,i,t are the fixed electrical and thermal loads of community i at time t.

[0068] Further, the improved adaptive ADMM algorithm is used to iteratively optimize the rolling optimization scheduling model in a distributed manner, which specifically includes:

[0069] 1) The energy sharing, power transformer operation and other coupled constraints are decoupled by introducing auxiliary variables, which are represented as:

[0070]

[0071]

[0072] where, and respectively, are the upper and lower limits of the electrical power that community i can share; and corresponding auxiliary variables;

[0073] 2) Convert the rolling optimization scheduling model into a compact form, denoted as:

[0074] min F(P) + D(W)

[0075] s.t. AP = W

[0076] where D is an auxiliary function, D(W) = 0, P is a set of decision variables, which includes W is a set of auxiliary variables, which includes A is a relationship matrix of decision variables and auxiliary variables;

[0077] 3) Establish the augmented Lagrangian equation for the compact form of the above rolling optimization scheduling model as:

[0078]

[0079] where L ρ (P, W, λ) is the augmented Lagrangian equation, λ is the Lagrange multiplier, and ρ is the penalty factor.

[0080] Further, the improved adaptive ADMM algorithm is used to perform distributed iterative optimization on the rolling optimization scheduling model, including the following steps:

[0081] 1) Each community's energy management system independently and in parallel solves its own autonomous optimization sub-problem, denoted as:

[0082]

[0083] where k represents the current iteration number, P i,k+1 is a set of decision variables of community i in the k+1 iteration, P i is a set of decision variables of community i, ρ k is a penalty factor in the k iteration, W i,k is a set of auxiliary variables corresponding to community i in the k iteration, λ k is a Lagrange multiplier in the k iteration;

[0084] 2) According to the optimization results of each community, the power transformer updates the auxiliary variables, denoted as:

[0085]

[0086] where P k+1 is a set of decision variables of all communities in the k+1 iteration, W k+1 is a set of auxiliary variables of all communities in the k+1 iteration;

[0087] 3) The coordinator coordinates the operation of the community and the power transformer based on the updated information of the two, and iteratively solves the Lagrange multiplier, denoted as:

[0088] λ k+1 = λ k + ρ k (AP k+1 -W k+1 )

[0089] wherein λ k+1 is the Lagrange multiplier of the k+1 iteration;

[0090] 4) Calculate the adaptive spectral penalty factor value ρ k+1 of the next iteration;

[0091] 5) Determine whether the optimization result meets the condition. If the original residual and the dual residual of the optimization result are less than the set threshold value, respectively, it is determined that the optimal scheduling strategy is reached at this time, and the optimization result is output. If the optimization result does not meet the condition, the iteration number is increased by one, and steps 1)-4) are repeated until the condition is met.

[0092] Further, the adaptive spectral penalty factor calculation process is:

[0093]

[0094]

[0095]

[0096]

[0097]

[0098]

[0099] Δλ k = λ k - λ k0

[0100]

[0101]

[0102]

[0103]

[0104]

[0105]

[0106]

[0107] wherein, is the auxiliary Lagrange multiplier of the k+1th iteration, k0 denotes the iteration number before k, is the difference of the auxiliary Lagrange multiplier at the k0th iteration and the kth iteration, is the dual function of F, is the approximate linear value of the differential of the function at the kth iteration, and are the local curvature estimations of the function at the kth iteration based on the steepest gradient and the minimum gradient, respectively, a k is the local curvature estimation of the function at the kth iteration by integrating the steepest gradient and the minimum gradient, Δλ k is the difference of the Lagrange multiplier at the k0th iteration and the kth iteration, is the dual function of D, is the approximate linear value of the differential of the function at the kth iteration, and are the local curvature estimations of the function at the kth iteration based on the steepest gradient and the minimum gradient, respectively, β k is the local curvature estimation of the function at the kth iteration by integrating the steepest gradient and the minimum gradient, and are the criteria for measuring the reliability of a k and β k at the kth iteration, ∈ lim is the step length threshold.

[0108] Further, the optimization result is judged whether it satisfies the condition, wherein the condition is:

[0109] ||r k ||2=||AP k -W k ||2≤∈ tol

[0110] ||d k ||2=||ρ k A T (W k -W k-1 )||2≤∈ tol

[0111] wherein, r k and dk are the original residual and dual residual of the kth iteration, respectively, A T is the transpose of matrix A, W k-1 is the set of auxiliary variables corresponding to all communities of the k-1th iteration, ∈ tol is the convergence criterion.

[0112] Compared with the prior art, the present application has the following advantages and beneficial effects:

[0113] 1. The present application establishes the feasible region of the power transformer, which can be used as a reference for safe operation to prevent the power transformer from being overloaded.

[0114] 2. The present application can coordinate the energy sharing among communities, improve the renewable energy consumption of the multi-community integrated energy system, and reduce the total operation cost of the system.

[0115] 3. The present application considers the safe operation of the power transformer, which can effectively avoid the problem of power transformer overload.

[0116] 4. The adaptive ADMM algorithm based on the spectral penalty factor proposed in the present application can adaptively adjust the penalty factor with the iteration process and calculation, accelerate the convergence speed of distributed optimization, improve the calculation efficiency, effectively avoid the problem of initial value selection, and improve the robustness of the algorithm. BRIEF DESCRIPTION OF DRAWINGS

[0117] Figure 1 is the flowchart of the present application.

[0118] Figure 2 is the topology diagram of the multi-community integrated energy system.

[0119] Figure 3 is the relationship diagram between the maximum steady-state load of the power transformer and the ambient temperature.

[0120] Figure 4 is the feasible region diagram of the power transformer.

[0121] Figure 5 is the power curve diagram of the power transformer.

[0122] Figure 6 is the iteration number diagram of the present application based on the ADMM, RBADMM and adaptive ADMM algorithms within the scheduling period.

[0123] Figure 7 is the iteration number curve diagram of the present application based on the ADMM, RBADMM and adaptive ADMM algorithms under different initial penalty parameter values. DETAILED DESCRIPTION

[0124] The application will be described in further detail below with reference to the embodiments and drawings, but the embodiments of the application are not limited thereto.

[0125] With reference to Figure 1 The embodiment provides an adaptive optimization method for collaborative operation of a multi-community integrated energy system.

[0126] 1. Establishing a feasible region of safe operation of a power transformer, which is used for evaluating load capacity of the power transformer.

[0127] 2. According to a topological graph of the multi-community integrated energy system, as shown in Figure 2 a rolling optimization scheduling model of the multi-community integrated energy system is established, a total operation cost of the system is taken as an objective function, community operation constraint conditions are applied, including operation constraint conditions of a combined heat and power unit, operation constraint conditions of an electric boiler, operation constraint conditions of a gas boiler, operation constraint conditions of an electric energy storage, operation constraint conditions of a thermal energy storage, a translatable load constraint condition, an energy sharing constraint condition, operation constraint conditions of a power transformer and an energy balance constraint condition.

[0128] 3. Using an improved adaptive ADMM algorithm, the rolling optimization scheduling model is subjected to distributed iterative optimization in a scheduling cycle of 24 hours within one day, and an optimal scheduling strategy is obtained.

[0129] In the embodiment of the application, the construction process of the feasible region of the power transformer is as follows:

[0130] 1) The C&T limit is converted into an equivalent maximum steady-state load, a relationship between the maximum steady-state load and the ambient temperature is established, and the method is as follows: given an ambient temperature and an initial value, the hot spot temperature HST and the top oil temperature TOT under the steady-state load are calculated according to the IEC60076 standard, and the load is gradually increased until HST and TOT reach the C&T limit.

[0131] 2) According to the relationship between the maximum steady-state load and the ambient temperature established above, the relationship is as shown in Figure 3 The HST and TOT temperature limit values are converted into the corresponding maximum load values under each ambient temperature, and the minimum value among the current, HST and TOT limit values is taken as the maximum load of the safe operation of the power transformer under the ambient temperature.

[0132] 3) According to the predicted air temperature curve in the scheduling cycle, the C&T limit value of the power transformer is selected, the maximum load of the safe operation corresponding to each temperature is obtained, and the region below the maximum load is the feasible region of the safe operation of the power transformer, as shown in Figure 4 .

[0133] The rolling optimization scheduling model of the multi-community integrated energy system specifically includes:

[0134] 1) The total operating cost of the multi-community integrated energy system is taken as the objective function, that is, the sum of the operating costs of each community is minimized, including the purchase cost of electricity and natural gas, and the objective function expression is as follows:

[0135]

[0136] In the formula, F is the total operating cost of the system, i is the community number, t is the scheduling time, represents the set of all community integrated energy systems, represents the set of scheduling times, v e,t , v g,t are the purchase electricity price and purchase gas price at t, G i,t are the purchase electricity power and purchase gas power of community i at t; considering the volatility of renewable energy output and the uncertainty of load, a rolling time domain optimization method is adopted, that is, at t, the optimal solution is obtained according to the actual data at t, the predicted values of renewable energy output and load demand at the remaining time, only the decision at t is executed, and for the next time t+1, the scheduling time range moves forward by one hour, and the optimal solution at the next time will be obtained according to the new predicted data;

[0137] 2) Community operation constraints are applied, including combined heat and power unit operation constraints, electric boiler operation constraints, gas boiler operation constraints, electric energy storage operation constraints, thermal energy storage operation constraints, translatable load constraints, energy sharing constraints, power transformer operation constraints and energy balance constraints;

[0138] The combined heat and power unit operation constraint is:

[0139]

[0140]

[0141]

[0142]

[0143] In the formula, is the natural gas power consumed by the combined heat and power unit of community i at t, and are the power generation and heat generation of the combined heat and power unit of community i at t, is the power generation of the combined heat and power unit of community i at t+1, and are the power generation and heat generation efficiency of the combined heat and power unit of community i, ΔP i CHPis the upper limit of the hourly ramp rate of the community i cogeneration unit, and P i CHP are the upper and lower limits of the electromechanical power output of the cogeneration unit in community i, respectively;

[0144] The operating constraints of the electric boiler are:

[0145]

[0146]

[0147]

[0148] Where, is the electric power consumed by the electric boiler in community i at time t, is the electric power consumed by the electric boiler in community i at time t+1, ΔP i EB The upper limit of the hourly ramp rate of the community electric boiler is and P i EB are the upper and lower limits of the electric power output of the electric boiler in community i, is the heating power of the electric boiler in community i at time t, The heat production efficiency of the community electric boiler;

[0149] The gas boiler operation constraints are:

[0150]

[0151]

[0152] Where, is the natural gas power consumed by the gas boiler in community i at time t, is the heating power of the gas boiler in community i at time t, The heat production efficiency of the community gas boiler is and are the upper and lower limits of the thermal power output of the gas boiler in community i;

[0153] The electric energy storage operation constraints are:

[0154]

[0155]

[0156]

[0157]

[0158]

[0159] Where, and are the minimum and maximum permissible capacities of community i electric energy storage, t c The energy of the community i-electric energy storage, is the self-discharge rate of community i energy storage, is the energy change of community i’s electric energy storage within period τ, and are the charging and discharging power of the energy storage in community i at time t, and are the charging and discharging efficiencies of the community i energy storage, ΔT is the control period, and are the initial capacity and target capacity of community i electric energy storage, is the Boolean variable corresponding to the electric energy storage of community i at time t, and are the upper limits of charging and discharging power of community i energy storage respectively;

[0160] The thermal energy storage operation constraints are:

[0161]

[0162]

[0163]

[0164]

[0165]

[0166] Where, and are the minimum and maximum permissible capacities of thermal energy storage in community i, t c The energy of the community i-thermal storage at all times, is the self-heating rate of community i thermal energy storage, is the energy change of the thermal energy storage in community i within the period τ, and are the charging and discharging powers of the thermal energy storage of community i at time t, and are the charging and discharging efficiencies of the thermal energy storage in community i, ΔT is the control period, and are the initial capacity and target capacity of the thermal energy storage of community i, is the Boolean variable corresponding to the thermal energy storage of community i at time t, and are the upper limits of the community i's shiftable thermal energy charging and discharging power, respectively;

[0167] The shiftable load constraints are:

[0168]

[0169]

[0170]

[0171]

[0172] where, and are the community i's shiftable electrical and thermal loads at time t, respectively, and are the total shiftable electrical and thermal load demands of the community i in the optimization time horizon, respectively, and are the upper limits of the community i's shiftable electrical and thermal loads, Ω e,i and Ω h,i are the community i's shiftable electrical and thermal load dispatchable time sets;

[0173] The energy sharing constraints are:

[0174]

[0175]

[0176] where, is the community i's electrical power shared to other communities at time t, represents the community i's purchased power from other communities, represents the community i's sold power to other communities, and P i share are the upper and lower limits of the community i's shiftable electrical power, respectively;

[0177] The power transformer operation constraints are:

[0178]

[0179]

[0180]

[0181] where, P t Tr is the power transformer's transmission power at time t, P t RESis the shared wind power or photovoltaic power at time t, and P t Tr are the upper and lower limits of the power transformer transmission power, respectively, is the upper limit of the electrical power that community i can purchase;

[0182] The energy balance constraint is:

[0183]

[0184]

[0185]

[0186] wherein, is the electrical power generated by renewable energy sources in community i at time t, L e,i,t and L h,i,t are the fixed electrical and thermal loads of community i at time t.

[0187] In this embodiment, based on the above objective function and the operating constraints, a rolling optimization scheduling model of the multi-community integrated energy system is constructed, and an improved adaptive ADMM algorithm is used to perform distributed iterative optimization on the rolling optimization scheduling model, specifically including:

[0188] 1) The energy sharing and power transformer operation coupling constraints are decoupled by introducing auxiliary variables, and are expressed as:

[0189]

[0190]

[0191] wherein, and are the upper and lower limits of the power transformer transmission power, respectively, and are the corresponding auxiliary variables;

[0192] 2) The rolling optimization scheduling model is converted into a compact form, and is expressed as:

[0193] min F(P) + D(W)

[0194] s.t. AP = W

[0195] wherein, D is an auxiliary function, D(W) = 0, P is a set of decision variables, wherein the decision variables include W is a set of auxiliary variables, wherein the auxiliary variables include A is a relationship matrix of the decision variables and the auxiliary variables;

[0196] 3) The compact form of the above rolling optimization scheduling model is established, and its augmented Lagrange equation is:

[0197]

[0198] In the formula, L ρ (P, W, λ) is the augmented Lagrange equation, λ is the Lagrange multiplier, and ρ is the penalty factor.

[0199] The improved adaptive ADMM algorithm is used for distributed iterative optimization of the rolling optimization scheduling model, including the following steps:

[0200] 1) Each community's energy management system independently and in parallel solves its own autonomous optimization sub-problem, which is expressed as:

[0201]

[0202] In the formula, k represents the current iteration number, P i,k+1 is the set of decision variables of community i in the k+1th iteration, P i is the set of decision variables of community i, ρ k is the penalty factor in the kth iteration, W i,k is the set of auxiliary variables corresponding to community i in the kth iteration, λ k is the Lagrange multiplier in the kth iteration;

[0203] 2) According to the optimization results of each community, the power transformer updates the auxiliary variables, which is expressed as:

[0204]

[0205] In the formula, P k+1 is the set of decision variables of all communities in the k+1th iteration, W k+1 is the set of auxiliary variables of all communities in the k+1th iteration;

[0206] 3) The coordinator coordinates the operation of the community and the power transformer based on the update information of the two, and iteratively solves the Lagrange multiplier, which is expressed as:

[0207] λ k+1 = λ k + ρ k (AP k+1 -W k+1 )

[0208] In the formula, λ k+1 is the Lagrange multiplier in the k+1th iteration;

[0209] 4) The adaptive spectral penalty factor value ρ k+1 of the next iteration is calculated.

[0210] 5) judging whether the optimization result meets the condition, if the primal residual and the dual residual of the optimization result are less than the set threshold value respectively, it is judged that the optimal scheduling strategy is reached at this time, and the optimization result is output; if the optimization result does not meet the condition, the iteration number is increased by one, and steps 1)-4) are repeated until the condition is met.

[0211] wherein the adaptive spectral penalty factor calculation process is:

[0212]

[0213]

[0214]

[0215]

[0216]

[0217]

[0218] Δλ k =λ k -λ k0

[0219]

[0220]

[0221]

[0222]

[0223]

[0224]

[0225]

[0226] In the formula, is the auxiliary Lagrange multiplier of the k+1th iteration, k0 represents the iteration number before k, is the difference value of the auxiliary Lagrange multiplier at the k0th iteration and the kth iteration, is the dual function of F, is the approximate linear value of the differential of the function at the kth iteration, and are the functions of the kth iteration based on the steepest gradient and the minimum gradient respectively the local curvature estimate of the function k is the function derived from the kth iteration of the synthesis of the steepest gradient and the minimum gradient-based the local curvature estimate of the function k is the difference between the Lagrange multiplier at the k0th iteration and the kth iteration, is the dual function of D, is the approximation linear value of the differential of the function at the kth iteration, and are the functions derived from the kth iteration of the steepest gradient and the minimum gradient-based the local curvature estimate of the function k is the function derived from the kth iteration of the synthesis of the steepest gradient and the minimum gradient-based the local curvature estimate of the function and are the criteria for measuring the reliability of the kth iteration of the functions k and k , lim is the step threshold value.

[0227] wherein the optimization result is judged whether to meet the condition, wherein the condition is:

[0228] ||r k ||2=||AP k -W k ||2≤∈ tol

[0229] ||d k ||2=||ρ k A T (W k -W k-1 )||2≤∈ tol

[0230] In the formula, r k and d k are the original residual and the dual residual of the kth iteration, A T is the transpose of the matrix A, W k-1 is the set of auxiliary variables corresponding to all communities of the k-1th iteration, ∈ tol is the convergence criterion.

[0231] The embodiment takes the multi-community integrated energy system shown in Figure 2 as an example, uses the modeling tool Yalmip based on MATLAB and calls the CPLEX solver to solve the model. In specific implementation, the convergence criterion ∈ tol , the step threshold value ∈ lim and the maximum iteration number are respectively set to 10-3 , 0.25 and 5000. The optimization results are shown in Table 1, Figures 5-7 In display.

[0232] Table 1 Optimization results

[0233] Optimization mode Total cost / 10 3 Yen Renewable energy consumption rate / % Autonomous optimization 91.556 53.74 Coordinated optimization considering energy sharing 84.645 72.32

[0234] Table 1 shows the optimization results under both autonomous and collaborative optimization modes. As shown in Table 1, the total operating cost in the collaborative mode is 7.55% lower than in the autonomous mode, demonstrating that the collaborative optimization model proposed in this paper can improve social economic benefits while taking into account energy sharing. Furthermore, the renewable energy capacity ratio in the collaborative optimization model with energy sharing is 34.9% higher than in the autonomous mode. This demonstrates that energy sharing can improve the utilization rate of renewable energy within the system, reduce the amount of energy purchased from the grid, and thus reduce the system's operating costs.

[0235] Figure 5 The power curves of the power transformer under autonomous optimization and collaborative optimization considering energy sharing are shown. The area between the upper and lower dashed lines represents the feasible area of ​​the power transformer, and the shaded area approximately represents the overload degree of the power transformer. Figure 5 As shown in the figure, under autonomous optimization mode, the power transformer is severely overloaded between 3:00 and 5:00 and 16:00. However, the load line under the collaborative optimization mode with energy sharing is lower than the load line under autonomous optimization, and the power transformer continues to operate within the feasible area during the scheduling cycle. This shows that the overload problem of the power transformer can be successfully avoided through system energy sharing and collaborative optimization.

[0236] In order to analyze the effectiveness of the proposed adaptive ADMM, the model is solved using ADMM, RBADMM and adaptive ADMM algorithms respectively, where RBADMM is the residual balanced ADMM. The characteristics of each method are shown below.

[0237] 1) ADMM: penalty factor ρ k It remains unchanged and is consistent with the initial value ρ0 in all iterations.

[0238] 2) RBADMM: Penalty factor ρ k The update is performed based on the principle of balancing the original residual and the dual residual.

[0239] 3) Adaptive ADMM: Penalty factor ρ k Updates are performed using a spectral penalty factor.

[0240] like Figure 6As shown, the convergence performance of RBADMM is not stable. While RBADMM converges faster in certain time periods, such as 4:00-6:00, 8:00-9:00, and 12:00-1:00, it fails to converge within 5,000 iterations in other time periods, such as 1:00-3:00, 7:00, 10:00-11:00, and 14:00-17:00. In contrast, the adaptive ADMM algorithm requires the fewest iterations of the three methods, demonstrating a clear advantage in convergence speed. Furthermore, as the hourly schedule is completed, the rolling horizon moves forward, and the size of the optimization problem gradually decreases. During the period 20:00-24:00, the optimization horizon shortens from 4 hours to only 1 hour. The convergence speeds of the three methods are fast and very similar, demonstrating that the adaptive ADMM maintains a stable convergence speed when solving problems of different sizes.

[0241] Figure 7 It reflects the number of iterations of distributed optimization based on ADMM, RBADMM and adaptive ADMM with different initial penalty parameter values ​​in the collaborative optimization mode considering energy sharing. Figure 7 As shown in Figure 2, in almost all cases, the number of iterations of the adaptive ADMM is less than that of the ADMM and RBADMM. The curve of the ADMM varies greatly, indicating that the convergence speed of the ADMM is very sensitive to the choice of the initial penalty factor. In addition, Figure 5 It can be seen that the optimal penalty factor for this example is between 10 -4 and 10 -3 Compared with ADMM, the number of iterations of adaptive ADMM is much less than ADMM when the initial value of penalty factor is small or large. -2 When ρ0=10, ADMM and RBADMM require 35599 and 58505 iterations respectively. However, adaptive ADMM only requires 7154 iterations, which is 79.9% and 87.8% less than ADMM and RBADMM respectively. -5 When , the number of iterations of adaptive ADMM is 55.6% less than that of ADMM. Both RBADMM and AADMM can maintain a stable number of iterations under a wide range of penalty factors ρ0. However, RBADMM has the most iterations among the three methods because it sometimes cannot converge the residual value to 10 within the maximum number of iterations. -3 level.

[0242] The above embodiments are the preferred embodiments of the present application, but the embodiments of the present application are not limited to the above embodiments, and any changes, modifications, substitutions, combinations, simplifications, etc. made without departing from the spirit and principles of the present application should be equivalent replacement manners and should be included in the protection scope of the present application.

Claims

1. An adaptive optimization method for the coordinated operation of multi-community integrated energy systems, characterized in that: The following steps are involved: 1) Establishing a feasible domain for safe operation of a power transformer to evaluate its load capacity; the feasible domain of the power transformer refers to all possible load ranges that meet all current and temperature constraints, i.e., C&T constraints, within which the power transformer can operate safely; 2) Establishing a rolling optimization scheduling model for a multi-community integrated energy system, with minimizing the total operating cost of the multi-community integrated energy system as the objective function, and imposing community operating constraints, including cogeneration unit operating constraints, electric boiler operating constraints, gas boiler operating constraints, electric energy storage operating constraints, thermal energy storage operating constraints, shiftable load constraints, energy sharing constraints, power transformer operating constraints, and energy balance constraints; wherein the power transformer operating constraints are set based on the feasible region of the power transformer determined in step 1) to ensure the safe operation of the power transformer; The objective function is to minimize the total operating cost of the multi-community integrated energy system, that is, to minimize the sum of the operating costs of each community, including the purchase cost of electricity and natural gas. The objective function expression is as follows: Where F is the total operating cost of the system, i is the community number, t is the scheduling time, represents the set of all community integrated energy systems, represents the scheduling time set, v e,t 、v g,t are the electricity purchase price and gas purchase price at time t, G i,t are the electricity and gas purchase power of community i at time t, respectively. Taking into account the volatility of renewable energy output and the uncertainty of load, a rolling horizon optimization method is adopted. That is, at time t, optimization is performed based on the actual data at the current time t and the forecast values ​​of renewable energy output and load demand for the remaining time periods. Only the decision at the current time t is executed. At the next time t+1, the scheduling time range is moved forward by one hour, and the optimal solution for the next time period is determined based on the new forecast data. 3) Using an improved adaptive ADMM algorithm, the rolling optimization scheduling model is subjected to distributed iterative optimization to obtain the optimal scheduling strategy; wherein ADMM is the alternating direction multiplier method, and the specific improvements in the improved adaptive ADMM algorithm are: proposing an adaptive spectral penalty factor, that is, a penalty factor update method that automatically selects an appropriate value based on the current state, so as to effectively reduce the impact of the penalty factor selection and its initial value on the algorithm, thereby accelerating the ADMM optimization process.

2. The adaptive optimization method for collaborative operation of multi-community integrated energy systems according to claim 1, characterized in that: The construction process of the feasible region is as follows: 1) Convert the C&T limit to an equivalent maximum steady-state load and establish the relationship between the maximum steady-state load and the ambient temperature as follows: Given an initial value of the ambient temperature and a steady-state load, calculate the hotspot temperature (HST) and top oil temperature (TOT) under that steady-state load according to the IEC60076 standard, and gradually increase the load until the HST and TOT reach the C&T limit; 2) Based on the relationship between the maximum steady-state load and the ambient temperature established above, the HST and TOT temperature limit values ​​are converted into the corresponding maximum load values ​​at each ambient temperature. The minimum value among the maximum load values ​​corresponding to the current, HST, and TOT limit values ​​is taken as the maximum load for safe operation of the power transformer at that ambient temperature; 3) Based on the predicted temperature curve within the dispatching period, the C&T limit value of the power transformer is selected to obtain the maximum load for safe operation corresponding to the temperature at each moment. The area below the maximum load is the feasible region for safe operation of the power transformer.

3. The adaptive optimization method for collaborative operation of multi-community integrated energy systems according to claim 2, characterized in that: Establish a rolling optimization dispatch model for multi-community integrated energy systems, including: Imposing community operation constraints, including cogeneration unit operation constraints, electric boiler operation constraints, gas boiler operation constraints, electric energy storage operation constraints, thermal energy storage operation constraints, shiftable load constraints, energy sharing constraints, power transformer operation constraints, and energy balance constraints; The operating constraints of the cogeneration unit are: Where, is the natural gas power consumed by the cogeneration unit in community i at time t, and are the electricity generation power and heat generation power of the cogeneration unit in community i at time t, is the power generation power of the cogeneration unit in community i at time t+1, and are the electricity and heat production efficiencies of the cogeneration unit in community i, ΔP i CHP is the upper limit of the hourly ramp rate of the community i cogeneration unit, and P i CHP are the upper and lower limits of the electromechanical power output of the cogeneration unit in community i, respectively; The operating constraints of the electric boiler are: Where, is the electric power consumed by the electric boiler in community i at time t, is the electric power consumed by the electric boiler in community i at time t+1, ΔP i EB The upper limit of the hourly ramp rate of the community electric boiler is and P i EB are the upper and lower limits of the electric power output of the electric boiler in community i, is the heating power of the electric boiler in community i at time t, The heat production efficiency of the community electric boiler; The gas boiler operation constraints are: Where, is the natural gas power consumed by the gas boiler in community i at time t, is the heating power of the gas boiler in community i at time t, The heat production efficiency of the community gas boiler is and are the upper and lower limits of the thermal power output of the gas boiler in community i; The electric energy storage operation constraints are: Where, and are the minimum and maximum permissible capacities of community i electric energy storage, t c The energy of the community i-electric energy storage, is the self-discharge rate of community i energy storage, is the energy change of community i’s electric energy storage within period τ, and are the charging and discharging power of the energy storage in community i at time t, and are the charging and discharging efficiencies of the community i energy storage, ΔT is the control period, and are the initial capacity and target capacity of community i electric energy storage, is the Boolean variable corresponding to the electric energy storage of community i at time t, and are the upper limits of charging and discharging power of community i energy storage respectively; The thermal energy storage operation constraints are: Where, and are the minimum and maximum permissible capacities of thermal energy storage in community i, t c The energy of the community i-thermal storage at all times, is the self-heating rate of community i thermal energy storage, is the energy change of the thermal energy storage in community i within the period τ, and are the charging and discharging powers of the thermal energy storage of community i at time t, and are the charging and discharging efficiencies of the thermal energy storage in community i, ΔT is the control period, and are the initial capacity and target capacity of the thermal energy storage of community i, is the Boolean variable corresponding to the thermal energy storage of community i at time t, and are the upper limits of charging and discharging power of community i thermal energy storage, respectively; The translational load constraint is: Where, and are the transferable electricity and heat loads of community i at time t, and Optimize the total shiftable electricity and heat load demand in the time domain for community i, and are the upper limits of the power of the portable electric and thermal loads of community i, Ω e,i and Ω h,i are the dispatchable time sets of the shiftable electricity and heat loads of community i respectively; The energy sharing constraint is: Where, is the electric power shared by community i to other communities at time t, represents the power purchased by community i from other communities, represents the power sold by community i to other communities, and P i share are the upper and lower limits of the electric power that community i can share; The power transformer operation constraints are: Where, P t Tr is the transmission power of the power transformer at time t, P t RES is the shared wind or photovoltaic power generation power at time t, and P t Tr are the upper and lower limits of the power transmission power of the power transformer, is the upper limit of the electric power that community i can purchase; The energy balance constraint is: Where, is the electric power generated by renewable energy in community i at time t, L e,i,t and L h,i,t are the fixed electricity and heat loads of community i at time t, respectively.

4. The adaptive optimization method for coordinated operation of multi-community integrated energy systems according to claim 3, characterized in that: The improved adaptive ADMM algorithm is used to perform distributed iterative optimization on the rolling optimization scheduling model, specifically including: 1) By introducing auxiliary variables, the coupling constraints of energy sharing and power transformer operation are decoupled, which can be expressed as: Where, and They are and Corresponding auxiliary variables; 2) Convert the rolling optimization scheduling model into a compact form, expressed as: minF(P)+D(W) stAP=W Where D is the auxiliary function, D(W)=0, and P is the set of decision variables, where the decision variables include W is a set of auxiliary variables, where the auxiliary variables include A is the relationship matrix between decision variables and auxiliary variables; 3) The augmented Lagrangian equation for the compact form of the above rolling optimization scheduling model is established as: Where, L ρ (P, W, λ) is the augmented Lagrangian equation, λ is the Lagrangian multiplier, and ρ is the penalty factor.

5. The adaptive optimization method for coordinated operation of multi-community integrated energy systems according to claim 4, characterized in that: The improved adaptive ADMM algorithm is used to perform distributed iterative optimization on the rolling optimization scheduling model, including the following steps: 1) Each community’s energy management system solves its own autonomous optimization subproblem independently and in parallel, which can be expressed as: Where k represents the current number of iterations, P i,k+1 is the set of decision variables of community i in the k+1th iteration, P i is the set of decision variables of community i, ρ k is the penalty factor for the kth iteration, W i,k is the set of auxiliary variables corresponding to community i in the kth iteration, λ k is the Lagrange multiplier of the kth iteration; 2) According to the optimization results of each community, the power transformer updates the auxiliary variables, which are expressed as: Where, P k+1 is the set of decision variables of all communities in the k+1th iteration, W k+1 is the set of auxiliary variables of all communities in the k+1th iteration; 3) The coordinator coordinates the operation of the community and the power transformer based on the updated information of the community and the power transformer, and iteratively solves the Lagrange multiplier, which is expressed as: l k+1 =λ k +r k (AP k+1 -W k+1 ) Where λ k+1 is the Lagrange multiplier of the k+1th iteration; 4) Calculate the adaptive spectral penalty factor value ρ for the next iteration k+1 ; 5) Determine whether the optimization result meets the conditions. If the original residual and the dual residual of the optimization result are less than the set threshold, it is determined that the optimal scheduling strategy is achieved at this time and the optimization result is output; If the optimization result does not meet the conditions, the number of iterations is increased by one, and the above steps 1)-4) are repeated until the conditions are met.

6. The adaptive optimization method for coordinated operation of multi-community integrated energy systems according to claim 5, characterized in that: The adaptive spectrum penalty factor calculation process is: Dl k =λ k -l k0 Where, is the auxiliary Lagrange multiplier for the k+1th iteration, k0 represents the number of iterations before k, is the difference between the auxiliary Lagrange multiplier at the k0th iteration and the kth iteration, is the dual function of F, is the function at the kth iteration The approximate linear value of the differential, and The functions derived based on the fastest gradient and the minimum gradient at the kth iteration are respectively The local curvature estimate, α k The k-th iteration function obtained by combining the fastest gradient and the minimum gradient The local curvature estimate, Δλ k is the difference between the Lagrange multiplier at the k0th iteration and the kth iteration, is the dual function of D, is the function at the kth iteration The approximate linear value of the differential, and The functions derived based on the fastest gradient and the minimum gradient at the kth iteration are respectively The local curvature estimate, β k is the kth iteration function obtained by combining the fastest gradient and the minimum gradient The local curvature estimate of and They are used to measure the k-th iteration α k and β k The reliability standard, ∈ lim is the step threshold.

7. The adaptive optimization method for collaborative operation of multi-community integrated energy systems according to claim 6, characterized in that: Determine whether the optimization result meets the conditions, where the conditions are: ||r k ||2=||AP k -W k ||2≤∈ tol ||d k ||2=||ρ k A T (W k -W k-1 )||2≤∈ tol Where r k and d k are the original residual and dual residual of the kth iteration, A T is the transpose of matrix A, W k-1 is the set of auxiliary variables corresponding to all communities in the k-1th iteration, ∈ tol is the convergence criterion.

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