Active power distribution network active and reactive power collaborative optimization scheduling method considering low-carbon demand response

Abstract

The invention discloses an active power distribution network active and reactive collaborative optimization scheduling method considering low-carbon demand response. The method comprises the following steps: establishing a stepped carbon transaction quantitative model; considering low-carbon demand response, and establishing a power distribution network low-carbon collaborative optimization model; a pelican optimization algorithm is improved, including adopting Bernoulli chaotic mapping to initialize a population so as to improve the distribution of an initial solution, introducing a weight factor omega to balance and improve the exploration and development ability of the algorithm and accelerate the convergence speed, and searching for a potential high-quality solution in combination with the alerter mechanism of a sparrow algorithm. Increasing Cauchy disturbance to enable the algorithm to jump out of local optimum; and solving the constructed low-carbon collaborative optimization model of the power distribution network by using an improved pelican optimization algorithm to obtain a model optimization scheduling scheme. According to the method, starting from a load side, the enthusiasm of a user to participate in demand response is stimulated by using carbon transaction, so that low-carbon demand response is realized; and system compensation equipment is combined to cooperatively optimize the power quality of the distribution network and reduce the carbon emission of the system, so that the environmental benefits are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of optimal dispatching of distribution networks, and particularly relates to an active distribution network active and reactive power collaborative optimal dispatching method considering low-carbon demand response. Background Technique

[0002] The large-scale access of a high proportion of new energy to the distribution network causes problems such as voltage over-limit, voltage fluctuation, and increased network loss in the distribution network due to the randomness and volatility of wind and light output. As an important means to optimize power quality, reactive power optimization has been widely studied by scholars. Reference [1] established a reactive power optimization model integrating an attention mechanism, which improved the prediction accuracy of wind and light output and the accuracy of feasible solutions, but the ability to respond to scenario changes was insufficient. References [2]-[5] proposed a reactive power optimization model considering the uncertainty of wind and light output, which improved the system's ability to cope with fluctuations on the source side, but it was difficult to fully absorb new energy in the network. Demand Response (DR) can improve the asset utilization rate and operation efficiency of the system by motivating users to change their consumption patterns, thereby ensuring the power supply reliability of the power grid. See Reference [6]. Reference [7] constructed a distribution network optimization model considering the participation degree of demand response, which reduced the operation cost of the system, but the optimization effect on power quality was relatively limited. References [8]-

[10] established a distribution network dispatching model for multi-side joint optimization of the source-network-load-storage, enhancing the flexibility and reliability of system dispatching. The above studies adopted different strategies to improve the safety and economy of system operation, but none of them fully explored the carbon emission reduction potential of the system.

[0003] Due to the large number of structural variables and non - linear constraints in the distribution network, the optimization problem of the distribution network belongs to a typical non - linear mixed - integer programming problem. Currently, the main methods to solve this problem are numerical optimization algorithms and intelligent algorithms. The numerical optimization algorithms will significantly increase the solving difficulty of the model and have a high sensitivity to the initial value as the dimension of the decision variables increases, and they rely strongly on characteristics such as the convexity and differentiability of the objective function, such as the non - linear programming in reference

[11] , the linear programming in reference

[12] , the interior - point method in reference

[13] , etc. The intelligent algorithms have good robustness and functionality when dealing with complex non - linear optimization problems, but the conventional intelligent algorithms are difficult to balance the optimization accuracy and speed during the optimization process. Reference

[14] proposed a Harris hawk algorithm improved based on adaptive grid, which improved the convergence performance of the algorithm, but its anti - interference ability is poor. Reference

[15] proposed a multi - strategy improved grey wolf algorithm, which well balances the global search ability and local exploration ability of the algorithm, but its solving efficiency is low. Reference

[16] incorporated the eddy current effect into the whale optimization algorithm, setting the algorithm to jump out of the local optimum for 20% of the time, and the exploration of the solution space is not comprehensive. The above studies have all made certain improvements to avoid falling into the local optimum, but there are still certain challenges in balancing the optimization accuracy and stability while ensuring the solving efficiency.

[0004] References:

[0005] Reference [1]: Xu Tao, Li Hugang, Yang Longyu, et al. Reactive power optimization of distribution network driven by the hybrid of attention mechanism and multi - objective particle swarm [J]. Power System and Clean Energy, 2024, 40(07): 146 - 154.

[0006] Reference [2]: Zhang Jingzhong, Meng Fei, Sun Yang, et al. Reactive power optimization control of new energy in distribution network considering active power uncertainty [J]. Electric Power, 2024, 57(03): 51 - 59.

[0007] Reference [3]: Wu Yingshuang, Feng Xiangyong, Wang Yin, et al. A sampling - based robust reactive power optimization method considering the output uncertainty of new energy power stations [J]. Journal of Electric Power Science and Technology, 2023, 38(02): 84 - 95.

[0008] Reference [4]: Yang Shunji, Li Qingsheng, Ming Zhiyong, et al. Multi - objective probabilistic reactive power optimization of distribution network considering source - load randomness [J]. Southern Power System Technology, 2023, 17(01): 125 - 135.

[0009] Reference [5]: Lu Jinling, Zhao Zenghui, Hu Xinghua, et al. Two - layer active and reactive power coordinated optimization of active distribution network considering PV volatility [J]. Proceedings of the CSU - EPSA, 2024, 36(05): 19 - 26.

[0010] Reference [6]: Wu Di, Wang Yunchu, Yu Chunlei, et al. Evaluation method for demand response potential of industrial users based on Gaussian process regression [J]. Electric Power Automation Equipment, 2022, 42(07): 94-101.

[0011] Reference [7]: Zhu Chaoting, Yang Lingjun, Cui Yibo, et al. Optimal dispatching of active distribution network considering user participation degree of demand response [J]. Electrical Measurement & Instrumentation, 2023, 60(04): 99-105+154.

[0012] Reference [8]: Yuan Guili, Ding Ning, Yang Biao, et al. Day-ahead dispatching of active distribution network with coordinated optimization of power source, grid, load and energy storage [J]. Science Technology and Engineering, 2024, 24(24): 10337-10347.

[0013] Reference [9]: Que Lingyan, Jiang Zhengwei, Yang Liqiang, et al. Coordinated control method of power source, grid, load and energy storage based on improved genetic algorithm [J]. Journal of Shenyang University of Technology, 2023, 45(06): 612-618.

[0014] Reference

[10] : Wang Yong, Liu Mengchen, Wang Hui, et al. Planning and dispatching of energy storage system on the distribution network side of cities considering coordinated operation of power source, grid, load and energy storage [J]. Advanced Technology of Electrical Engineering and Energy, 2024, 43(03): 73-82.

[0015] Reference

[11] : Zhang Jie, Zheng Yunyao, Liu Shengchun, et al. Dynamic reactive power optimization algorithm for regional power grid based on decoupled interior point method and mixed integer programming method [J]. Electric Power, 2023, 56(01): 112-118.

[0016] Reference

[12] : MAHZOUNI-SANI M, HAMIDI A, NAZARPOUR D, et al. Multi-objective linearised optimal reactive power dispatch of wind-integrated transmission networks [J]. IET Generation, Transmission & Distribution, 2019, 13(13): 2686-2696.

[0017] Reference

[13] : Zhang Jie, Wang Hengfeng, Liu Shengchun, et al. Dynamic reactive power optimization method for regional power grid based on interior point method and neighbourhood search decoupled dynamic programming method [J]. Electric Power, 2023, 56(02): 59-67.

[0018] Literature

[14] : Cong Fanping, Zhou Jianping. Multi-objective Reactive Power Optimization of Distribution Network with Multiple Energy Routers Based on Improved Harris Hawk Optimization Algorithm [J]. Smart Power, 2023, 51(09): 66-73.

[0019] Literature

[15] : Xia Zhenglong, Lu Liangshuai, Wu Qifan, et al. Application of Improved Grey Wolf Algorithm in Reactive Power Optimization of Distribution Network with Wind Power [J]. Smart Power, 2023, 51(06): 63-70.

[0020] Literature

[16] : Xia Zhenglong, Chen Yu, Lu Liangshuai, et al. Research on Dynamic Reactive Power Optimization of Distribution Network Based on Multi-objective Whale Algorithm [J / OL]. Journal of Henan Normal University (Natural Science Edition), 2025, (01): 116-126 [2024-11-27]. Summary of the Invention

[0021] Aiming at the problems of voltage over-limit and unfulfilled emission reduction potential caused by high proportion of photovoltaic access to the distribution network, the present invention introduces a carbon trading mechanism into the traditional reactive power optimization method, and proposes an active distribution network active and reactive power coordinated optimization scheduling method considering low-carbon demand response. This method starts from the load side, uses carbon trading to stimulate the enthusiasm of users to participate in demand response, and then realizes low-carbon demand response; and combines system compensation equipment to coordinately optimize the power quality of the distribution network and reduce system carbon emissions, improving its environmental benefits.

[0022] The technical solution adopted by the present invention is as follows:

[0023] An active distribution network active and reactive power coordinated optimization scheduling method considering low-carbon demand response, comprising the following steps:

[0024] Step 1: Establish a stepped carbon trading quantification model;

[0025] Step 2: Considering low-carbon demand response, establish a low-carbon coordinated optimization model for the distribution network;

[0026] Step 3: Improve the pelican optimization algorithm, including initializing the population using Bernoulli chaotic mapping to improve the distribution of the initial solution, introducing a weight factor ω to balance and enhance the exploration and exploitation capabilities of the algorithm while accelerating the convergence speed, combining the warning mechanism of the sparrow algorithm to search for potential high-quality solutions, and adding Cauchy perturbation to make the algorithm jump out of the local optimum;

[0027] Step 4: Use the improved pelican optimization algorithm in Step 3 to solve the low-carbon coordinated optimization model of the distribution network constructed in Step 2, and obtain the optimized scheduling scheme of the model.

[0028] In the above Step 1, the establishment of the stepped carbon trading quantification model includes:

[0029] Obtain carbon emission allowances in a distributive manner. The formula for the initial carbon emission allowances is as follows:

[0030]

[0031] In formula (1): D is the carbon emission quota; γ co2 is the unit carbon emission quota of the unit; P e,t is the electricity purchase volume from the superior power grid at time t; Δt is the time interval; T is the dispatching period.

[0032] Define that the actual carbon emission intensity of the user is proportional to the actual output of the generating units in the superior power grid:

[0033]

[0034] In formula (2): E is the actual carbon emission; η сο2 is the carbon emission when the unit generates one unit of electricity; P t is the electricity generation of the unit. Select a stepped carbon price for trading, that is, under the benchmark of the carbon emission allowance, the price of carbon trading changes with the actual carbon emission. The more the actual carbon emission exceeds the carbon emission allowance, the higher the price. Conversely, the higher the income that can be obtained; the price of carbon trading is as follows:

[0035]

[0036] In formula (3): is the carbon trading price; E c is the quota surplus; τ is the basic price of market carbon trading; l is the length of the divided carbon trading price interval; υ is the trading price growth rate.

[0037] In step 2, the low-carbon collaborative optimization model of the distribution network specifically includes:

[0038] Taking the minimum of active power loss, voltage deviation, and system comprehensive operation cost as the optimization goal. At the same time, to encourage users' low-carbon behaviors, a carbon trading mechanism is incorporated into the optimization model to guide power users to adjust their consumption patterns;

[0039] The objective function is as follows:

[0040] 1) Minimum active power loss:

[0041]

[0042] In formula (4): f1 is the active power loss; l ij,t is the square of the current between nodes i and j; B is the branch set; r ij is the resistance between branches i and j.

[0043] 2) Minimum voltage deviation:

[0044]

[0045] In Equation (5): f2 is the voltage deviation; N b is the number of network nodes; v j is the square of the voltage magnitude at node j; v j,N is the square of the rated voltage at node j.

[0046] 3) Minimize the comprehensive operation cost of the system:

[0047]

[0048] In Equation (6): f3 is the comprehensive operation cost of the system; T is the time period; N is the number; is the power purchase cost; is the power purchase quantity from the superior power grid; c loss is the network loss cost; r ij is the resistance between nodes i and j; I ij,t is the square of the branch current between nodes i and j at time t; c PV is the curtailment cost of light; c cut is the interrupted load cost; c TL is the transferred load cost; c WT is the curtailment cost of wind; N branch is the set of branches; N PV is the set of nodes with PV access; N cut is the set of interrupted loads; N IL is the set of transferred loads; N WT is the set of nodes with WT access; N ESS is the set of nodes with ESS access; are the curtailment of light and wind of PV and wind turbines at time t, respectively; are the interrupted load quantity and transferred load quantity at time t, respectively; are the charge and discharge powers of the energy storage system ESS at time t, respectively.

[0049] Normalize the objective function, and the formula is as follows

[0050]

[0051] In Equation (7): x′ is the value after normalization; x is the value before normalization; x max and x min are the maximum and minimum values of the data before normalization, respectively.

[0052] Then the normalized objective function is:

[0053] f = w1f1 + w2f2 + w3f3 (8);

[0054] In Equation (8): f is the normalized objective function value; w1, w2, and w3 represent the weight coefficients.

[0055] The constraint conditions of the objective function include:

[0056] 1) Power flow constraint:

[0057]

[0058] In Equation (9): P i , Q i are the active and reactive powers injected into node i, respectively; G ij , B ij and δ ij are the branch conductance, susceptance, and phase angle difference between nodes i and j, respectively; U i is the voltage of node i; U j is the voltage of node j; N l is the number of branches connected to node i.

[0059] 2) Safe operation constraint:

[0060]

[0061] In Equation (10): v i,min , v i,max are the squared lower and upper limits of the voltage magnitude of node i, respectively; l ij,max is the squared upper limit of the branch current magnitude between nodes i and j; v i,t is the squared voltage value at node i at time t; l ij,t is the squared branch current between nodes i and j at time t.

[0062] 3) Operating constraint of the on-load tap changer (OLTC) of the voltage regulator:

[0063]

[0064] In Equation (11): is the actual tap position of the OLTC between nodes i and j at time t; and are the lower and upper limits of the tap positions of the OLTC, respectively; T ij,t is the tap position of the OLTC at time t; is the adjustment step of the OLTC.

[0065] 4) Operating constraint of the energy storage device:

[0066]

[0067] In Equation (12): are the lower and upper limits of the charging power of the energy storage device at node j, respectively; are the lower and upper limits of the discharging power of the energy storage device at node j, respectively; A char is the charging decision variable; A disc is the discharging decision variable; E j,t is the energy stored in the energy storage device at time t; are the charging and discharging efficiencies of the energy storage device, respectively; are the upper and lower limits of the energy storage capacity, respectively; is the charging power of the energy storage device at node j at time t; is the discharging power of the energy storage device at node j at time t; E j,t-1 is the capacity of the energy storage device at node j at time t-1; Δt is the time interval.

[0068] 5) Static Var Compensator (SVC) operation constraints:

[0069]

[0070] In equation (13): are the upper and lower limits of the reactive power output of the SVC, respectively; is the reactive power output of the SVC at node j at time t.

[0071] 6) Distributed power generation output constraints:

[0072]

[0073] In equation (14): is the distributed power generation output; are the upper and lower limits of the distributed power generation output, respectively.

[0074] 7) Low-carbon demand response constraints:

[0075]

[0076] In equation (15): are the upper and lower limits of the load curtailment at time t, respectively; is the load curtailment at time t is the lower limit of the power removed at time t; is the power removed at time t; is the upper limit of the power removed at time t; is the lower limit of the power imported at time t; is the power imported at time t; is the upper limit of the power imported at time t; T is the time period; t is the time.

[0077] In step 3, the hunting process of the Pelican Optimization Algorithm includes two stages: surrounding the prey and flying over the water surface:

[0078] 1) Population initialization: Suppose there are S pelicans in m - dimensional space. The position of the p - th pelican in the m - dimensional space is X = [X1, X2,..., X S , then the formulas for the population and objective - function matrix of p pelicans in the m - dimensional space are as follows:

[0079]

[0080] In formula (16),

[0081]

[0082] In formula (17), F is the fitness function; F1 is the fitness value of the 1 - st pelican; F2 is the fitness value of the 2 - nd pelican; F S The fitness value of the S - th pelican; F(X1) is the fitness value of the 1 - st pelican; F(X2) is the fitness value of the 2 - nd pelican; F(X p ) is the fitness value of the p - th pelican; F(X S ) The fitness value of the S - th pelican; S is the number of pelicans.

[0083] The Pelican Optimization Algorithm (POA) is initialized randomly, and the formula is as follows:

[0084] x p,d = l d + rand·(u d - l d )(18);

[0085] In formula (18): x p,d is the position of the pelican individual p after initialization in the d - th dimension; rand is a random number within [0, 1]; u d , l d are the upper and lower limits of the boundaries in the d - th dimension respectively.

[0086] 2) The first stage: Approaching the prey

[0087] In this stage, the pelican gradually approaches the prey based on the randomly generated prey position.

[0088]

[0089] In formula (19): is the position of the pelican individual p after update in the exploration stage in the d - th dimension; I is a random integer of 1 or 2; p p is the position of the prey in the p - th dimension; are the positions of the pelican individual p after update in the first stage respectively; is the fitness value of the pelican individual p after update in the first stage; X pis the position vector of pelican individual p; F p is the fitness value of pelican individual p before update; F l is the fitness value of the prey.

[0090] 3) The second stage: flight on the water surface

[0091] After the pelican reaches the water surface, it spreads its wings to collect prey and put it into the gular pouch. This strategy can capture more prey and improve the exploration ability of the algorithm;

[0092]

[0093] In formula (20): is the position of pelican individual p in the d-th dimension after the second stage update; R is a random integer of 1 or 2; T0 is the maximum number of iterations; t0 is the current number of iterations.

[0094] In step 3,

[0095] (1). Bernoulli chaos mapping to initialize the population strategy:

[0096] The initialization and Bernoulli chaos mapping formula are as follows:

[0097]

[0098] In formula (21): x p is the position of the p-th pelican individual; z p is the state variable; μ is a constant; u and l are the upper and lower limits of the position respectively; z p+1 is the value of the state variable after iteration.

[0099] (2). Introduce a non-linear inertia weight:

[0100] Introduce a non-linear inertia weight ω to balance the exploration and exploitation capabilities of the algorithm. The calculation method is as follows:

[0101]

[0102] In formula (22): ω is the inertia weight; e is the exponential function.

[0103] In the early stage of algorithm iteration, the value of the inertia weight ω is small and the growth rate is slow, which is conducive to the algorithm to search in a larger optimization range and improve the global exploration ability of the algorithm. In the later stage of algorithm iteration, the value of the inertia weight ω gradually becomes larger and the growth rate accelerates, making the optimization individuals more dependent on the current optimal solution.

[0104] (3). Sparrow alert mechanism:

[0105] When a pelican individual senses that the surrounding environment is too stable or dangerous, the individual takes action to flee the current area and search for potential safe areas. By learning from potential excellent individuals, the individual's position is optimized, and the global convergence ability of the algorithm is improved;

[0106]

[0107] In Equation (23): is the updated position of pelican individual p in the d-th dimension; x p,d,t is the position of pelican individual p before update in the d-th dimension; x' p,d,t are the current best and worst positions of the individual respectively; β is a random number following a normal distribution, used to control the step size; K is a random number in the interval [-1, 1]; ε is a very small positive number to prevent the denominator from being zero; f p 、f g and f w are the current fitness value, the global best and the worst fitness values respectively; f p >f g indicates that the sentinel is in a poor position or has detected a potential danger and needs to flee from this position; f p ≤f g indicates that the sentinel is in a better position.

[0108] (4). Cauchy perturbation strategy:

[0109] Introduce the pelican algorithm POA into the Cauchy mutation strategy. When the individuals are in an aggregated state, use the Cauchy operator to generate a larger mutation step size to help the algorithm jump out of the local optimum;

[0110]

[0111] In Equation (24): is the updated value of the i-th individual in the j-th dimension; x * i,j,t is the current individual's best position;;

[0112] cauchy(0, 1) is the Cauchy operator.

[0113] In step 4, the low-carbon collaborative optimization model of the distribution network is solved, including the following steps:

[0114] step1: Obtain the source-load and power purchase data before optimization,

[0115] step2: Input algorithm-related parameters such as the number of iterations, population size, dimension, etc.;

[0116] step3: Define the objective function of the optimization model as the fitness function of the algorithm, and set relevant decision variables in the algorithm

[0117] Step 4: Input the distribution network structure data and the data obtained in step 1 into the algorithm

[0118] Step 5: Use the algorithm to iteratively solve and obtain the scheduling strategy.

[0119] The present invention provides an active distribution network active and reactive coordinated optimization dispatching method considering low-carbon demand response, and the technical effects are as follows:

[0120] 1) The present invention uses the carbon trading mechanism to deeply explore the carbon emission reduction potential on the load side, and combines other control resources to coordinate and optimize system operation. After the strategy optimization of the present invention, the network loss is reduced by 26.5%, the voltage deviation is only 0.035pu, and the system carbon emissions are reduced by 25.5%, which can effectively improve the environmental benefits of the system while meeting the safety and economic benefits requirements of the distribution network.

[0121] 2) The optimization strategy proposed in the present invention can respond to the operation requirements of different stages in real time by coordinating the compensation resources within the network, thereby improving the operation safety and economy of the system.

[0122] 3) This invention improves the standard POA algorithm with multiple strategies, effectively solving the problem of slow convergence speed and easy falling into local optimum of POA. Compared with GJO algorithm and NGO algorithm, IPOA algorithm shows better optimization performance, and the safety and economic benefits of the optimized system are better.

[0123] 4) In view of the problems of slow convergence and easy falling into local optimum of the standard POA algorithm, the present invention adopts Bernoulli chaotic mapping to initialize the population to improve the distribution of initial solutions; introduces the weight factor ω to accelerate the convergence speed while balancing and improving the exploration and development capabilities of the algorithm; combines the sentinel mechanism of the sparrow algorithm to search for potential high-quality solutions; adds Cauchy perturbation to help the algorithm jump out of the local optimum, and improves the standard POA algorithm through multi-strategy fusion. BRIEF DESCRIPTION OF THE DRAWINGS

[0124] The present invention will be further described below in conjunction with the accompanying drawings and embodiments:

[0125] Figure 1(a) shows the particle distribution generated by Tent’s chaotic mapping;

[0126] Figure 1(b) shows the particle distribution generated by Bernoulli chaotic mapping.

[0127] Figure 2 Flowchart for the improved Pelican optimization algorithm.

[0128] Figure 3 It is an improved IEEE33 node power distribution system.

[0129] Figure 4 Wind power output prediction data obtained for typical wind and light scenarios.

[0130] Figure 5 System carbon emissions under 4 scenarios;

[0131] Figure 6 Load curves under 4 scenarios;

[0132] Figure 7 System network loss conditions under four scenarios;

[0133] Figure 8 Voltage comparison diagram of node 18 under different scenarios.

[0134] Figure 9 Operating condition diagram of OLTC.

[0135] Figure 10(a) is the operating condition diagram of ESS1.

[0136] Figure 10(b) is the operating condition diagram of ESS1.

[0137] Figure 11 Operating condition diagram of SVC.

[0138] Figure 12 Iteration curves of different algorithms. Detailed implementation manners

[0139] An active distribution network active and reactive power collaborative optimization scheduling method considering low-carbon demand response. First, the present invention starts from flexible loads, fully exploits the carbon reduction potential on the load side by using the stepped carbon trading mechanism, and combines the regulation characteristics of on-load tap changer (OLTC), static var compensator (SVC), and energy storage system (ESS) to establish a low-carbon collaborative optimization model for the distribution network, improving the power quality and low-carbon environmental protection of the system. Then, the following improvements are made to the standard pelican optimization algorithm:

[0140] 1) Use Bernoulli chaotic mapping to initialize the population to improve the distribution of the initial solution;

[0141] 2) Introduce a weight factor ω to balance and enhance the exploration and exploitation capabilities of the algorithm while accelerating the convergence speed;

[0142] 3) Combine the scout mechanism of the sparrow algorithm to search for potential high-quality solutions;

[0143] 4) Add Cauchy perturbation to help the algorithm jump out of local optima.

[0144] Finally, the improved pelican optimization algorithm is used to solve the model, and the optimized scheduling scheme of the model is obtained.

[0145] (1). Step carbon trading quantification model:

[0146] Carbon trading is a mechanism that incorporates the emission rights of carbon dioxide into the market for trading to control carbon emissions. First, individuals obtain carbon emission quotas through allocation or auction, and then users participate in trading based on their actual carbon emissions. If the actual carbon emission intensity is greater than the quota, they need to purchase the excess part, otherwise they can sell the surplus quota.

[0147] In the present invention, carbon emission allowances are obtained through allocation, and the formula for the initial carbon emission allowance is as follows:

[0148]

[0149] In formula (1): D is the carbon emission quota; γ co2 is the unit carbon emission quota of the unit; P e,t is the power purchase amount from the superior power grid at time t; Δt is the time interval; T is the scheduling period.

[0150] The present invention defines that the actual carbon emission intensity of the user is proportional to the actual output of the generating units in the superior power grid.

[0151]

[0152] In formula (2): E is the actual carbon emission; η сο2 is the carbon emission when the unit generates one unit of electricity; P t is the power generation of the unit.

[0153] To better reflect the market supply and demand relationship, a stepped carbon price is selected for trading, that is, based on the benchmark of the carbon emission quota, the trading price changes with the actual carbon emissions. The more the actual carbon emissions exceed the quota, the higher the price, and vice versa, the higher the profit that can be obtained. The carbon trading price is as follows:

[0154]

[0155] In formula (3): C co2 is the carbon trading price; E c is the quota surplus; τ is the market carbon trading base price; l is the length of the carbon trading price interval divided; υ is the trading price growth rate.

[0156] (2). Distribution network collaborative optimization model considering low-carbon demand response:

[0157] By establishing the objective function and related constraints, the corresponding compensation resource scheduling scheme is obtained.

[0158] 2.1. Objective function:

[0159] Taking into account the operation economy and power supply reliability of the distribution network, with the minimum of network loss, voltage deviation and system comprehensive operation cost as the optimization objectives, and at the same time to encourage users' low-carbon behavior, the carbon trading mechanism is incorporated into the optimization strategy to guide power users to adjust their consumption patterns.

[0160] (1) Minimum active power loss:

[0161]

[0162] In formula (4): f1 is the active power loss; l ij,t is the square of the current between nodes i and j; B is the set of branches; r ij is the resistance between branches i and j.

[0163] (2) Minimum voltage deviation:

[0164]

[0165] In formula (5): f2 is the voltage deviation; N b is the number of network nodes; v j is the square of the voltage amplitude at node j; v j,N is the square of the rated voltage at node j;

[0166] (3) Minimum comprehensive operation cost:

[0167]

[0168] In formula (6): f3 is the system comprehensive operation cost; T is the time period; N is the number; is the power purchase cost; is the power purchase quantity from the superior power grid; c loss is the network loss cost; r ij is the resistance between nodes i and j; I ij,t is the square of the branch current between nodes i and j at time t; c PV is the curtailment cost of light; c cut is the interruption load cost; c TL is the transfer load cost; c WT is the curtailment cost of wind; N branch is the set of branches; N PV is the set of nodes with PV access; N cut is the set of interrupted loads; N IL is the set of transferred loads; N WT is the set of nodes with WT access; N ESS is the set of nodes with ESS access; are the curtailment of light and wind of PV and wind turbines at time t, respectively; are the interrupted load and transferred load at time t, respectively; are the charging and discharging powers of the energy storage system ESS at time t, respectively; are the curtailment of photovoltaic power and wind power curtailment of wind turbines at time t, respectively; are the interrupted load and transferred load at time t, respectively; are the charging and discharging powers of the energy storage system ESS at time t, respectively.

[0169] To enhance the stability and solution efficiency of the algorithm in dealing with complex optimization problems and to achieve an effective trade-off between different objectives, the present invention normalizes the objective function, and the formula is as follows:

[0170]

[0171] In formula (7): x′ is the value after normalization; x is the value before normalization; x max and x min are the maximum and minimum values of the data before normalization, respectively.

[0172] The objective function after normalization is:

[0173] f = w1f1 + w2f2 + w3f3 (8);

[0174] In formula (8): f is the value of the normalized objective function; w1, w2, and w3 represent the weight coefficients.

[0175] 2.2. Constraint conditions:

[0176] (1) Power flow constraint:

[0177]

[0178] In formula (9): P i and Q i are the active and reactive powers injected into node i, respectively; G ij and B ij and δ ij are the branch conductance, susceptance, and phase angle difference between nodes i and j, respectively; U i is the voltage of node i; U j is the voltage of node j; N l is the number of branches connected to node i.

[0179] (2) Safe operation constraint:

[0180]

[0181] In formula (10): v i,min and v i,maxThey are the square values of the lower and upper limits of the voltage magnitude of node i; l ij,max is the square of the upper limit of the branch current magnitude between node i and node j; v i,t is the square of the voltage at node i at time t; l ij,t is the square of the branch current between node i and node j at time t.

[0182] (3) Operating constraints of the OLTC:

[0183]

[0184] In Equation (11): is the actual tap position of the OLTC between node i and j at time t; and are the upper and lower limits of the tap positions of the OLTC respectively; T ij,t is the tap position of the OLTC at time t; is the regulation step size of the OLTC.

[0185] (4) Operating constraints of the energy storage device:

[0186]

[0187] In Equation (12): are the lower and upper limits of the charging power of the energy storage device at node j respectively; are the lower and upper limits of the discharging power of the energy storage device at node j respectively; A char is the charging decision variable; A disc is the discharging decision variable; E j,t is the energy stored in the energy storage device at time t; are the charging and discharging efficiencies of the energy storage device respectively; are the upper and lower limits of the energy storage capacity respectively; is the charging power of the energy storage device at node j at time t; is the discharging power of the energy storage device at node j at time t; E j,t-1 is the energy storage device capacity at node j at time t - 1; Δt is the time interval.

[0188] (5) Operating constraints of the SVC:

[0189]

[0190] In Equation (13): are the upper and lower limits of the reactive power output of the SVC respectively; is the reactive power output of the SVC at node j at time t.

[0191] (6) Output constraints of distributed power sources:

[0192]

[0193] In formula (14): is the output of the distributed power source; are the upper and lower limits of the output of the distributed power source respectively.

[0194] (7) Low-carbon demand response constraint

[0195]

[0196] In formula (15): are the upper and lower limits of the load curtailment at time t respectively; is the lower limit of the power removed at time t; is the power removed at time t; is the upper limit of the power removed at time t; is the lower limit of the power imported at time t; is the power imported at time t; is the upper limit of the power imported at time t; T is the time period; t is the time.

[0197] (III) Model solving algorithm:

[0198] The Pelican Optimization Algorithm (POA) is a meta-heuristic optimization algorithm that simulates the hunting behavior of pelicans. The hunting process mainly includes two stages: surrounding the prey and flying over the water surface.

[0199] 3.1 Standard pelican optimization algorithm:

[0200] (1) 1) Population initialization: Suppose there are S pelicans in an m-dimensional space. The position of the p-th pelican in the m-dimensional space is X = [X1, X2,..., X S , then the formulas for the population and the objective function matrix of the p-th pelican in the m-dimensional space are as follows:

[0201]

[0202] In formula (16),

[0203]

[0204] In formula (17), F is the fitness function; F1 is the fitness value of the first pelican; F2 is the fitness value of the second pelican; F S is the fitness value of the S-th pelican; F(X1) is the fitness value of the first pelican; F(X2) is the fitness value of the second pelican; F(X p ) is the fitness value of the p-th pelican; F(X S ) is the fitness value of the S-th pelican; S is the number of pelicans.

[0205] The POA optimization algorithm is initialized randomly, and the formula is as follows:

[0206] x p,d = l d + rand·(u d - l d )(18);

[0207] In formula (18): x i,d is the position of the pelican individual p after initialization in the d-th dimension; rand is a random number within [0, 1]; u d , l d are the upper and lower limits of the boundaries in the d-th dimension respectively.

[0208] (2) Approaching the prey (the first stage)

[0209] In this stage, the pelican gradually approaches the prey based on the randomly generated prey position.

[0210]

[0211] In formula (19): is the position of the pelican individual p after update in the d-th dimension in the exploration stage; I is a random integer of 1 or 2; p p is the position of the prey in the p-th dimension; are the positions of the pelican individual p after update in the first stage respectively; is the fitness value of the pelican individual p after update in the first stage; X p is the position vector of the pelican individual p; F p is the fitness value of the pelican individual p before update; F l is the fitness value of the prey.

[0212] (3) Flying on the water surface (the second stage)

[0213] After the pelican reaches the water surface, it spreads its wings to collect prey and put it into the throat pouch. This strategy can capture more prey and improve the exploitation ability of the algorithm.

[0214]

[0215] In formula (20): is the position of the pelican individual p in the d-th dimension after update in the second stage; R is a random integer of 1 or 2; T0 is the maximum number of iterations; t0 is the current number of iterations.

[0216] 3.2. Improved whale optimization algorithm:

[0217] Aiming at the problems existing in the standard POA algorithm, the present invention uses the Bernoulli chaotic map to initialize the population to improve the distribution of the initial solution; introduces a weight factor ω to balance and enhance the exploration and exploitation capabilities of the algorithm while accelerating the convergence speed; combines the scout mechanism of the sparrow algorithm to search for potential high-quality solutions; and adds Cauchy perturbation to help the algorithm jump out of local optima. In summary, the present invention proposes an improved pelican optimization algorithm (Improve Pelican Optimization Algorithm, IPOA).

[0218] (1) Bernoulli chaotic map-based population initialization strategy:

[0219] The distribution of the initial solution largely affects the search efficiency and optimization accuracy of the algorithm. The standard POA algorithm uses random numbers to initialize the population, resulting in poor uniformity of the distribution of the initial solution. The present invention uses the Bernoulli chaotic map to initialize the population, which is superior to the commonly used Tent chaotic map in terms of value uniformity and stability. The initialization and the Bernoulli chaotic map formula are as follows:

[0220]

[0221] In Equation (21): x p is the position of the p-th pelican individual; z p is the state variable; μ is a constant; u and l are the upper and lower limits of the position respectively; z p+1 is the value of the state variable after iteration.

[0222] Set the population size to 1000 and the dimension to 1. The distributions of particles initialized by the Tent chaotic map and the Bernoulli chaotic map are shown in Figures 1(a) and 1(b). It can be seen from Figures 1(a) and 1(b) that compared with the initialization by the Tent chaotic map, the distribution of particles generated by the strategy of the present invention is more uniform and the population diversity is higher.

[0223] (2) Improvement of the convergence factor: introducing a non-linear inertia weight;

[0224] To improve the optimization speed and accuracy of the algorithm, the present invention introduces a non-linear inertia weight ω in the search stage to balance the exploration and exploitation capabilities of the algorithm. The calculation method is as follows.

[0225]

[0226] In Equation (22): ω is the inertia weight; e is the exponential function.

[0227] In the early stage of algorithm iteration, the value of the inertia weight ω is small and the growth rate is slow, which is conducive to the algorithm searching for the optimal solution in a larger search range and improving the global exploration ability of the algorithm. In the later stage of algorithm iteration, the value of the inertia weight ω gradually becomes larger and the growth rate accelerates, making the searching individuals more dependent on the current optimal solution. The algorithm will quickly converge to the vicinity of the optimal solution, refine the search for the optimal solution, and improve the local development ability and the later convergence speed of the algorithm.

[0228] (3) Pelican warning mechanism

[0229] The strategy of the POA algorithm relying on the leader to search for the optimal solution in the exploration stage leads to poor global search ability of the algorithm. Inspired by the warning mechanism in the Sparrow Search Algorithm (SSA), it is set that when the pelican individuals feel that the surrounding environment is too stable or dangerous, the individuals take actions to escape from the current area and search for potential safe areas. By learning from potential excellent individuals to optimize the individual positions, the global convergence ability of the algorithm is improved.

[0230]

[0231] In Equation (23): is the updated position of the pelican individual p in the d-th dimension; x p,d,t is the position of the pelican individual p before update in the d-th dimension; x' p,d,t are the current best and worst positions of the individual respectively; β is a random number obeying the normal distribution, used to control the step size; K is a random number in the interval [-1, 1]; ε is a very small positive number to prevent the denominator from being zero; f p 、f g and f w are the current fitness value, the global best and the worst fitness values respectively; f p >f g means that the warning individual is in a poor position or finds potential danger and needs to escape from this position; f p ≤f g means that the warning individual is in a better position.

[0232] (4) Cauchy perturbation strategy:

[0233] In the later stage of algorithm iteration, the pelican individuals will be quickly assimilated by the current optimal solution and gather near the optimal solution, resulting in the stagnation of the algorithm search and prone to the "premature" phenomenon. The present invention introduces the Cauchy mutation strategy into the POA algorithm. When the individuals are in an aggregated state, the Cauchy operator is used to generate a larger mutation step size to help the algorithm jump out of the local optimum.

[0234]

[0235] In Equation (24): is the updated value of the i-th individual in the j-th dimension; x * i,j,t is the current individual's optimal position;

[0236] cauchy(0, 1) is the Cauchy operator.

[0237] The improved algorithm flow is as Figure 2 shown below:

[0238] (IV) Example verification:

[0239] The present invention conducts simulations based on an improved IEEE 33-node system. The reference voltage U B = 12.66 kV; the reference capacity S B = 10 MVA; the transformer tap setting is 1.025 ± 5 × 2.5%; the allowable range of the node voltage is 0.95 - 1.05 pu; energy storage devices with a capacity of 1000 kW·h are installed at nodes 24 and 31; PVs with a capacity of 1.5 MW are connected to nodes 3 and 18; wind powers with a capacity of 1 MW are connected to nodes 6 and 33; static var compensators are installed at nodes 5, 25, and 21, and their regulation range is -0.1 - 0.8 MVar; shiftable loads are connected to nodes 8 and 17, and an interruptible load is connected to node 14; the improved IEEE 33-node distribution system is as Figure 3 shown below:

[0240] The time-of-use electricity price set by the present invention is as follows: peak period (7:00 - 9:00 and 17:00 - 23:00) is 0.66 yuan / kW·h; flat period (23:00 - 00:00 and 00:00 - 7:00) is 0.44 yuan / kW·h; valley period (9:00 - 17:00) is 0.22 yuan / kW·h. The carbon trading base price in the stepped carbon trading is 200 yuan / t, the price growth coefficient is 25%, and the interval length is 0.3 t. Other relevant cost coefficient parameters are shown in Table 1:

[0241] Table 1 Cost coefficients

[0242]

[0243] 4.1, Day-ahead voltage optimization control:

[0244] The predicted wind and PV power output data obtained from typical wind and PV scenarios are as Figure 4 shown below:

[0245] To verify the superiority of the proposed strategy of the present invention in reducing system carbon emissions, improving its operation efficiency and security, the present invention sets up 4 scenarios for comparative analysis. Scenario 1: Only distributed power sources are connected to the distribution network; Scenario 2: Considering the output of the collaborative compensation device and the output of DR, but not considering the carbon trading mechanism; Scenario 3: Introducing the traditional carbon trading mechanism on the basis of Scenario 2; Scenario 4: Introducing the stepped carbon trading mechanism on the basis of Scenario 2, that is, the strategy of the present invention. The optimization results of different scenarios are shown in Table 2.

[0246] Table 2 Optimization Results of Different Scenarios

[0247]

[0248]

[0249] As can be seen from Table 2, comparing Scenario 4 with Scenario 2, the total system operation cost of Scenario 4 increases by 2.71% compared with Scenario 2. This is because after the optimization strategy introduces the carbon trading mechanism, under the influence of the higher carbon trading price and DR compensation incentive, the costs of both increase significantly. Although the remaining costs (such as power purchase cost, network loss cost, etc.) decrease to a certain extent, they cannot completely offset the increase in carbon trading cost and demand response cost, resulting in a certain increase in the total cost. Although the strategy of the present invention is not as good as Scenario 2 in terms of economic benefits, it has a certain improvement in environmental benefits.

[0250] Compared with the traditional carbon trading that completely relies on market supply and demand relationship, the stepped carbon trading mechanism can not only buffer the fluctuation of market trading price to a certain extent, but also reduce the carbon emissions of thermal power units in the upper grid by guiding users to change their electricity consumption habits. Therefore, the carbon trading cost of Scenario 4 decreases by 54.5% compared with Scenario 3, and the power purchase cost decreases by 0.6%. Since the carbon trading mechanism adopted by the present invention needs to cooperate more with demand response, this also leads to the highest demand response cost of the strategy of the present invention compared with other strategies. However, it can further reduce the network loss cost and curtailment cost of wind and solar power by 9.97% and 5.7% respectively on the basis of Scenario 3, effectively improving the system security and the consumption capacity of new energy. To more intuitively reflect the advantage of the strategy of the present invention in reducing system carbon emissions, the present invention solves the system carbon emissions and load curves under different scenarios, as shown in Figure 5 and Figure 6 respectively.

[0251] From Figure 5 and Figure 6It can be seen that compared with Scenario 1, the system carbon emissions in several other scenarios are reduced by 12.2%, 14.9%, and 25.5% respectively, and the carbon reduction effect of the strategy of the present invention is the best. Among them, the emission reduction effect is more significant during the peak load period from 17:00 to 23:00. However, during the period from 13:00 to 15:00, after Scenario 2 introduces the stepped carbon trading mechanism, the valley filling ability of the system is enhanced, the system load factor increases, resulting in an increase in the system carbon emissions. Therefore, the carbon reduction effect of Scenario 4 is not as good as that of Scenario 2. However, compared with other scenarios, Scenario 4 can fully tap the potential of users to participate in demand response while ensuring the system security, and maximize the reduction of system carbon emissions. To verify the advantages of the strategy of the present invention in improving the system security, the present invention respectively compares the system network losses and the voltage distribution of 18 nodes under four scenarios as Figure 7 and Figure 8 shown.

[0252] From Figure 7 and Figure 8 it can be seen that after introducing low-carbon demand response into the traditional collaborative optimization strategy, with a more explicit emission reduction incentive for users, the enthusiasm of users to participate in the optimal dispatching is significantly improved. Compared with Scenario 1, the system network losses in the other three scenarios are reduced by 11.7%, 18.4%, and 26.5% respectively, and the lowest voltages of the 18 nodes are 0.952 pu, 0.956 pu, and 0.964 pu respectively. The system security is the best in the case of Scenario 4, which fully verifies that the strategy of the present invention can further optimize the system power quality and reduce the network loss by fully stimulating the dispatching potential of the regulation resource on the load side.

[0253] The dispatching plan of the strategy of the present invention is as Figure 9 、Figure 10(a), Figure 10(b), Figure 11 shown

[0254] From Figure 10(a), Figure 10(b) and Figure 11 it can be seen that the ESS charges during the periods with relatively low electricity prices from 12:00 to 17:00 and from 2:00 to 6:00, and discharges during the peak load periods from 7:00 to 9:00 and from 18:00 to 21:00 to achieve the purpose of peak shaving and valley filling and reducing network losses. Since the ESS is mainly used for peak regulation and is difficult to meet the reactive power deficit of the system, the SVC emits reactive power to raise the voltage during the peak load period, and the SVC absorbs reactive power during the period when the wind and light output is large and the load demand is low. The SVC adjusts its own reactive power output by dynamically tracking the system state to reduce voltage over-limit and voltage fluctuation.

[0255] 4.2. Algorithm performance analysis:

[0256] To verify the solution feasibility and advantages of the algorithm of the present invention, the IPOA, NGO, and GJO algorithms are respectively used to solve the optimization model, and the fitness convergence curves and optimization results of different algorithms are asFigure 12 as shown in Table 3.

[0257] According to Figure 12 it can be seen that the NGO, GJO, and IPOA algorithms need to iterate 150 times, 125 times, and 22 times respectively to achieve convergence. The algorithm of the present invention can find a better quality solution with a faster convergence speed and has better optimization performance.

[0258] Table 3 Optimization Results of Different Algorithms

[0259]

[0260] As can be seen from Table 3, the solution accuracies of the three algorithms for network loss and voltage deviation are not much different, but the model cost solved by the IPOA algorithm is lower, the operation time is faster, and the compromise between multiple objectives is more effectively achieved, verifying the feasibility and superiority of the improved IPOA algorithm for solving the optimization model.

Claims

1. An active distribution network active and reactive power collaborative optimal scheduling method considering low-carbon demand response, characterized in that It includes the following steps: Step 1: Establish a stepped carbon trading quantification model; Step 2: Considering low-carbon demand response, establish a low-carbon collaborative optimization model for the distribution network; Step 3: Improve the pelican optimization algorithm, including using Bernoulli chaotic mapping to initialize the population to improve the distribution of the initial solution, introducing a weight factor ω to balance and enhance the exploration and exploitation capabilities of the algorithm while accelerating the convergence speed, combining the vigilant mechanism of the sparrow algorithm to search for potential high-quality solutions, and adding Cauchy perturbation to make the algorithm jump out of the local optimum; Step 4: Use the improved pelican optimization algorithm in Step 3 to solve the low-carbon collaborative optimization model of the distribution network constructed in Step 2 to obtain the optimized scheduling plan of the model.

2. The active and reactive power coordinated optimal scheduling method for an active distribution network considering low-carbon demand response according to claim 1, wherein: In the said Step 1, the establishment of the stepped carbon trading quantification model includes: Obtain the carbon emission allowance by allocation, and the formula for the initial carbon emission allowance is as follows: In formula (1): D is the carbon emission quota; γ co2 is the unit carbon emission quota of the unit; P e,t is the electricity purchase volume from the superior power grid at time t; Δt is the time interval; T is the dispatching period; Define that the actual carbon emission intensity of users is proportional to the actual output of the generating units in the superior power grid: In formula (2): E is the actual carbon emission; η сο2 is the carbon emission when the unit power is generated by the unit; P t is the power generation of the unit; The stepped carbon price is selected for trading, that is, under the benchmark of the carbon emission quota, the price of carbon trading changes with the change of the actual carbon emission. The more the actual carbon emission exceeds the carbon emission quota, the higher the price. On the contrary, the higher the income can be obtained. The price of carbon trading is shown as follows: In formula (3): is the carbon trading price; E c is the quota surplus; τ is the market carbon trading base price; l is the length of the divided carbon trading price interval; υ is the trading price growth rate.

3. The active and reactive power coordinated optimal scheduling method for an active distribution network considering low-carbon demand response according to claim 1, characterized in that: In the said Step 2, the low-carbon collaborative optimization model of the distribution network specifically includes: Taking the minimum of active power loss, voltage deviation and system comprehensive operation cost as the optimization goal. At the same time, to encourage users' low-carbon behaviors, a carbon trading mechanism is incorporated into the optimization model to guide power users to adjust their consumption patterns; The objective function is as follows: 1) Minimize the active power loss: In formula (4): f1 is the active power loss; l ij,t is the square of the current between nodes i and j; B is the set of branches; r ij is the resistance between branches i and j; 2) Minimize the voltage deviation: In Equation (5): f2 is the voltage deviation; N b is the number of network nodes; v j is the square of the voltage magnitude at node j; v j,N is the square of the rated voltage at node j; 3) Minimize the system comprehensive operation cost: In Equation (6): f3 is the comprehensive operating cost of the system; T is the time period; N is the number; is the electricity purchase cost; P t buy is the electricity purchase quantity from the superior power grid; c loss is the network loss cost; r ij is the resistance between nodes i and j; I ij,t is the square of the branch current between nodes i and j at time t; c PV is the curtailment cost of light; c cut is the interrupted load cost; c TL is the transferred load cost; c WT is the curtailment cost of wind; N branch is the set of branches; N PV is the set of nodes with PV access; N cut is the set of interrupted loads; N IL is the set of transferred loads; N WT is the set of nodes with WT access; N ESS is the set of nodes with ESS access; ΔP t PV 、ΔP t WT are respectively the curtailment of light and wind of PV and wind turbines at time t; P t cut 、P t TL are respectively the interrupted load quantity and the transferred load quantity at time t; P t char 、P t disc are respectively the charge and discharge powers of the energy storage system ESS at time t.

4. The active and reactive power coordinated optimal scheduling method for an active distribution network considering low-carbon demand response according to claim 3, characterized in that: Normalize the objective function, and the formula is as follows In Equation (7): x' is the value after normalization; x is the value before normalization; x max and x min are the maximum and minimum values of the data before normalization, respectively; Then the normalized objective function is: f = w1f1 + w2f2 + w3f3 (8); In formula (8): f is the value of the normalized objective function; w1, w2, and w3 represent weight coefficients.

5. The active and reactive power coordinated optimal scheduling method for an active distribution network considering low-carbon demand response according to claim 4, characterized in that: The constraint conditions of the objective function include: 1) Power flow constraint: In Equation (9): P i and Q i are the active and reactive powers of the injection node i, respectively; G ij and B ij and δ ij are the branch conductance, susceptance, and phase angle difference between nodes i and j, respectively; U i is the voltage of node i; U j is the voltage of node j; N l is the number of branches connected to node i. 2) Safe operation constraint: In Equation (10): v i,min and v i,max are respectively the squared values of the lower and upper limits of the voltage magnitude at node i; l ij,max is the squared upper limit of the branch current magnitude between node i and node j; v i,t is the squared voltage value at node i at time t; l ij,t is the square of the branch current between node i and node j at time t. 3) Operating constraint of the on-load tap changer (OLTC) of the voltage regulator: In formula (11): is the actual gear position of the OLTC between nodes i and j at time t; and are the upper and lower limits of the gear position of the OLTC respectively; T ij,t is the gear position where the OLTC is located at time t; is the adjustment step of the OLTC; 4) Operating constraint of the energy storage device: In Equation (12): are respectively the lower and upper limits of the charging power of the energy storage device at node j; are respectively the lower and upper limits of the discharging power of the energy storage device at node j; A char is the charging decision variable; A disc is the discharging decision variable; E j,t is the energy stored in the energy storage device at time t; are respectively the charging and discharging efficiencies of the energy storage device; are respectively the upper and lower limits of the energy storage capacity; is the charging power of the energy storage device at node j at time t; is the discharging power of the energy storage device at node j at time t; E j,t-1 is the energy storage device capacity at node j at time t - 1; Δt is the time interval; 5) Operating constraint of the static var compensator (SVC): In formula (13): are the upper and lower limits of the reactive power output of the SVC, respectively; is the reactive power output of the SVC at node j at time t; 6) Output constraint of distributed power sources: In formula (14): is the output of the distributed power source; are the upper and lower limits of the output of the distributed power source, respectively; 7) Low-carbon demand response constraint: In formula (15): P t cut,max and P t cut,min are respectively the upper and lower limits of the load shedding amount at time t; P t IL is the load shedding amount P at time t t TLO,min is the lower limit of the power removed at time t; P t TLO is the power removed at time t; P t TLO,max is the upper limit of the power removed at time t; is the lower limit of the power imported at time t; P t TLI is the power imported at time t; P t TLI,max is the upper limit of the power imported at time t; T is the time period; t is the time.

6. The active and reactive power coordinated optimal scheduling method for an active distribution network considering low-carbon demand response according to claim 1, characterized in that: In the said Step 3, the hunting process of the pelican optimization algorithm includes two stages: surrounding the prey and flying on the water surface: 1) Population initialization: Assume there are S pelicans in an m-dimensional space. The position of the p-th pelican in the m-dimensional space is X = [X1, X2,..., X S , then the formulas for the population and objective function matrix of the p-th pelican in the m-dimensional space are as follows: In formula (16), In Equation (17), F is the fitness function; F1 is the fitness value of the first pelican; F2 is the fitness value of the second pelican; F S is the fitness value of the S-th pelican; F(X1) is the fitness value of the first pelican; F(X2) is the fitness value of the second pelican; F(X p ) is the fitness value of the p-th pelican; F(X S ) is the fitness value of the S-th pelican; S is the number of pelicans; The pelican algorithm POA is initialized randomly, and the formula is as follows: x p,d = l d + rand·(u d - l d )(18); In formula (18): x p,d is the position of pelican individual p after initialization in the d-th dimension; rand is a random number within [0, 1]; u d , l d are the upper and lower limits of the boundary in the d-th dimension respectively; 2) The first stage: Approaching the prey: In this stage, the pelican gradually approaches the prey based on the randomly generated prey position; In formula (19): is the position of pelican individual p after update in the d-th dimension at the exploration stage; I is a random integer of 1 or 2; p p is the position of the prey in the p-th dimension; are the positions of pelican individual p after update in the first stage respectively; is the fitness value of pelican individual p after update in the first stage; X p is the position vector of pelican individual p; F p is the fitness value of pelican individual p before update; F l is the fitness value of the prey; 3) The second stage: Flying on the water surface After the pelican reaches the water surface, it spreads its wings to collect the prey and put it into the throat pouch. This strategy can capture more prey and improve the exploitation ability of the algorithm; In formula (20): is the position of the pelican individual p in the d-th dimension after the second-stage update; R is a random integer of 1 or 2; T0 is the maximum number of iterations; t0 is the current number of iterations.

7. The active and reactive power collaborative optimal scheduling method for active distribution network considering low-carbon demand response according to claim 1, characterized in that: The said Step 3 includes: Bernoulli chaotic mapping initialization population strategy; The initialization and Bernoulli chaotic mapping formula are as follows: In formula (21): x p is the position of the p-th pelican individual; z p is the state variable; μ is a constant; u and l are the upper and lower limits of the position respectively; z p+1 is the value of the state variable after iteration.

8. The active and reactive power coordinated optimal scheduling method for an active distribution network considering low-carbon demand response according to claim 7, characterized in that: The said Step 3 also includes: introducing a non-linear inertia weight; Introduce a non-linear inertia weight ω to balance the exploration and exploitation capabilities of the algorithm, and the calculation method is as follows: In formula (22): ω is the inertia weight; e is the exponential function; In the early stage of algorithm iteration, the value of the inertia weight ω is small and the growth rate is slow, which is beneficial for the algorithm to search in a larger optimization range and improve the global exploration ability of the algorithm; while in the later stage of algorithm iteration, the value of the inertia weight ω gradually becomes larger and the growth rate accelerates, making the optimization individuals more dependent on the current optimal solution.

9. The active and reactive power coordinated optimal dispatch method for active distribution network considering low-carbon demand response according to claim 8, characterized in that: Step 3 also includes: sparrow vigilant mechanism; When it is set that a pelican individual feels that the surrounding environment is too stable or dangerous, the individual takes actions to flee the current area and search for potential safe areas; the individual position is optimized by learning from potential excellent individuals to improve the global convergence ability of the algorithm; In Equation (23): is the updated position of pelican individual p in the d-th dimension; x p,d,t is the position of pelican individual p in the d-th dimension before update; x' p,d,t are the current best and worst positions of the individual respectively; β is a random number obeying the normal distribution, used to control the step size; K is a random number in the interval [-1, 1]; ε is a very small positive number to prevent the denominator from being 0; f p 、f g and f w are the current fitness value, the global best and worst fitness values respectively; f p >f g indicates that the sentinel is in a worse position or has detected a potential danger and needs to flee from this position; f p ≤f g indicates that the sentinel is in a better position.

10. The active and reactive power coordinated optimal scheduling method for an active distribution network considering low-carbon demand response according to claim 9, characterized in that: In step 3, the pelican algorithm POA is introduced into the Cauchy mutation strategy. When the individuals are in an aggregated state, the Cauchy operator is used to generate a relatively large mutation step size to help the algorithm jump out of the local optimum; In formula (24): is the updated value of the i-th individual in the j-th dimension; x * i,j,t is the current individual's optimal position;; cauchy(0,1) is the Cauchy operator.

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