CN114400712A - A Microgrid Swarm Optimization Scheduling Method Based on Improved Second-Order Particle Swarm Optimization - Google Patents

Abstract

A micro-grid group optimal scheduling method based on an improved second-order particle swarm algorithm is characterized by firstly respectively building mathematical models of various devices in a micro-grid group, building a micro-grid group optimal scheduling model with the aims of minimum comprehensive operation cost, maximum wind-light absorption rate and minimum power fluctuation of a connecting line of the micro-grid group as targets, then taking the output of wind power, photoelectricity, energy storage and a diesel engine set as the positions of particle swarms and a fitness function as a target function, and solving the optimal scheduling model by adopting the improved second-order particle swarm algorithm to obtain an optimal scheduling scheme of the micro-grid group. The method not only minimizes the overall operation cost of the micro-grid group, but also reduces the impact of the micro-grid connection on the power distribution network, and improves the accuracy and the calculation speed of the algorithm.

Description

A Microgrid Swarm Optimization Scheduling Method Based on Improved Second-Order Particle Swarm Optimization

technical field

The invention belongs to the field of power grid optimization and scheduling, in particular to a micro-grid group optimization scheduling method based on an improved second-order particle swarm algorithm.

Background technique

In recent years, with the large-scale use of fossil energy, the carbon dioxide content in the atmosphere has continued to rise, and environmental protection issues have become increasingly prominent. It has become a future trend to vigorously develop clean energy, especially wind power (Wind Turbine, WT) and photovoltaic (Photovoltaic, PV), but how to effectively absorb the intermittent and volatile scenery has become an urgent problem to be solved. Microgrid (MG) is a small power generation and distribution system that connects wind and solar loads nearby. By configuring a certain capacity of energy storage system (ESS) and diesel units, it can effectively promote the connection of a large number of wind and solar power. For consumption, how to properly manage the optimal scheduling between microgrids and between microgrids and distribution networks has become a hot research topic.

The interactive optimization scheduling model of microgrid group mainly involves optimization models and optimization algorithms. The optimization model mainly includes optimization objectives and constraints. The constraints are usually the operating constraints and power quality index constraints set within the microgrid. The optimization objectives usually include the cost of microgrid operation, tie line power fluctuations, power quality indicators and environmental protection, etc. . The optimization algorithms are mainly heuristic algorithms, such as genetic algorithm, ant colony algorithm and particle swarm algorithm, etc. The main focus is on the convergence, computing time and global optimization ability of the optimization algorithm, and how to use the high-performance optimization algorithm for microgrid The group optimization scheduling model becomes a key issue.

Particle swarm optimization is derived from a complex adaptive system and is a model for simulating the behavior of birds. After randomly obtaining an initial solution, it searches for the optimal value through iteration. Each particle has its own fitness function value, position coordinates, velocity size and direction, and searches in the feasible domain space according to the position of the global optimal particle and its own historical optimal position. However, the traditional particle swarm optimization algorithm has the shortcomings of insufficient optimization ability and convergence ability, and it needs to be improved so that it can be better used to solve the interactive optimal scheduling model of microgrid swarms.

SUMMARY OF THE INVENTION

The purpose of the present invention is to overcome the above problems existing in the prior art, and to provide a microgrid group optimization scheduling method based on an improved second-order particle swarm algorithm.

For achieving the above purpose, the present invention provides the following technical solutions:

A microgrid swarm optimization scheduling method based on an improved second-order particle swarm optimization algorithm, which sequentially includes the following steps:

Step A, respectively constructing mathematical models of various types of equipment inside the microgrid group, wherein the various types of equipment include wind turbines, photovoltaic generators, loads, energy storage equipment, and diesel generators;

Step B, establishing a microgrid group optimization scheduling model aiming at the minimum comprehensive operation cost of the microgrid group, the maximum wind and solar absorption rate, and the minimum power fluctuation of the tie line;

Step C. Taking the output of wind power, photovoltaic, energy storage, and diesel units as the position of the particle swarm, and the fitness function as the objective function, the improved second-order particle swarm algorithm is used to solve the above-mentioned optimal scheduling model, and the optimal scheduling scheme of the microgrid swarm is obtained.

Described step C comprises the following steps in turn:

Step C1, obtaining various equipment parameters and wind, light, and load operation data in the microgrid group, and initializing the basic parameters of the improved second-order particle swarm algorithm;

Step C2, use the chaotic map to generate the chaotic sequence, select the Logistic map model to generate the initial population, and denormalize the variables to the search space to obtain the initial position of the particle, set the number of iterations k=1, and each particle corresponds to each optimization scheduling plan;

Step C3, calculate the fitness value of each particle, and update the historical optimal value of each particle and the historical optimal value of the population;

Step C4, calculate the current inertia coefficient, learning factor and oscillation factor according to the number of iterations and the fitness value, and update the speed and position of the particle, and at the same time perform over-limit processing on the speed and position of the particle;

Step C5: Calculate the distance between any particle and the current optimal particle. If the calculated distance is smaller than the reference value, the optimal particle remains unchanged, so that other particles perform chaotic motion, and chaotic search is performed within a given number of steps. Replace original particles with new particles obtained from chaos search;

Step C6, judge whether to converge, if it converges, exit the iterative process, decode the particles, and obtain the optimal scheduling scheme of the microgrid group; if not, set k=k+1 and return to step C2 for the next iteration.

In step C4, the inertia coefficient, learning factor, oscillation factor, speed and position are calculated and updated by the following formula:

λ ₁ <λ ₂ -1,λ ₃ <λ ₄ -1,0<λ ₂ <1,0<λ ₄ <1 k≥k _max /2

分别为第i个粒子在第k次迭代时的惯性系数、速度和位置，ω_min、ω_max分别为惯性系数的最小、最大值，f()为适应度函数，

为第k次迭代时种群的平均适应度值，p_g、p_i分别为粒子群、第i个粒子的历史最优位置，

分别为第k次迭代时的学习因子c₁、c₂，r₁、r₂为[0,1]内均匀分布的随机数，c_1b、c_1e、c_2b、c_2e分别为c₁、c₂迭代最开始的值和结束的值，λ₁、λ₃分别为当前迭代过程中第i个粒子最优和全局最优位置的振荡因子，λ₂、λ₄分别为上一次的迭代过程中第i个粒子最优和全局最优位置的振荡因子，d₁、d₂为c₁的控制因子，d₃、d₄为c₂的控制因子，k_max为最大迭代次数。In the above formula,

are the inertia coefficient, velocity and position of the ith particle at the k-th iteration, respectively, ω _min and ω _max are the minimum and maximum values of the inertia coefficient, respectively, f() is the fitness function,

is the average fitness value of the population at the k-th iteration, p _g and p _i are the historical optimal positions of the particle swarm and the i-th particle, respectively,

are the learning factors c ₁ , c ₂ in the k-th iteration, respectively, r ₁ , r ₂ are random numbers uniformly distributed in [0,1], c _1b , c _1e , c _2b , and c _2e are c ₁ , c 1e , c 2b , and c 2e respectively c ₂ The initial value and the end value of the iteration, λ ₁ , λ ₃ are the oscillation factors of the i-th particle optimal and global optimal position in the current iteration process, respectively, λ ₂ , λ ₄ are the last iteration process, respectively Oscillation factor of the optimal and global optimal position of the i-th particle, d ₁ and d ₂ are the control factors of c ₁ , d ₃ and d ₄ are the control factors of c ₂ , and km _max is the maximum number of iterations.

In step C2, the logistic mapping model is:

为混沌变量在第k次迭代时的d维分量。In the above formula,

is the d-dimensional component of the chaotic variable at the k-th iteration.

In step C5, the distance between the arbitrary particle and the current optimal particle is calculated according to the following formula:

为第k次迭代时第i个粒子与当前最佳粒子之间的距离，

为第i个粒子在第k次迭代过程中的d维分量，p_gd为当前最佳粒子的d维分量，n为粒子的维数，即优化变量的个数。In the above formula,

is the distance between the i-th particle and the current best particle at the k-th iteration,

is the d-dimensional component of the i-th particle in the k-th iteration process, p _gd is the d-dimensional component of the current optimal particle, and n is the dimension of the particle, that is, the number of optimization variables.

In step B, the objective function f of the microgrid group optimization scheduling model is:

minf=ω ₁ f ₁ +ω ₂ f ₂ +ω ₃ f ₃

分别为第t个时刻微电网群向配电网的购电功率和售电功率，且

c_fuel,i、c_M,i、c_E,i分别为柴油机组等效的单位燃料费用、维护费用和环境成本费用，

分别为柴油机组和储能设备的出力，c_DS,i、c_d,i分别为储能设备的维护费用和折旧费用，Δt为单个时段的时长，a_i、b_i、c_i分别为柴油机组费用函数的二次项、一次项和常数项系数，

分别为第i个微电网第t个时刻风电、光伏削减后的有功出力，

分别为第i个微电网第t个时刻风电、光伏的最大有功出力，P_t ^Line为第t个时刻微电网群与配电网交互的功率，

为微电网群与配电网交互的功率的平均值。In the above formula, f ₁ , f ₂ , and f ₃ are the comprehensive operation cost, wind-solar consumption rate, and tie line power fluctuation of the microgrid group, respectively, and ω ₁ , ω ₂ , and ω ₃ are the comprehensive operation cost, wind-solar consumption rate, respectively. , the weight of the power fluctuation of the tie line, N _MG and T are the number of microgrids and the number of calculation periods, respectively, c _t,buy , c _t,sell are the unit price and unit price of electricity,

are the purchasing power and selling power of the microgrid group to the distribution network at the t-th time, respectively, and

c _fuel,i , c _M,i , c _E,i are the equivalent unit fuel cost, maintenance cost and environmental cost of diesel unit respectively,

are the output of diesel units and energy storage equipment, respectively, c _DS,i , cd _,i are the maintenance cost and depreciation cost of energy storage equipment, respectively, Δt is the duration of a single period, a _i , _{bi , c i are} the diesel engine respectively the quadratic, linear, and constant coefficients of the group cost function,

are the active power output of the i-th microgrid at the t-th moment after the reduction of wind power and photovoltaic power, respectively,

are the maximum active power output of wind power and photovoltaics of the i-th microgrid at the t-th time, respectively, P _t ^Line is the interaction power between the micro-grid group and the distribution network at the t-th time,

is the average value of the power that the microgrid group interacts with the distribution network.

The constraints of the objective function include:

Load Balance Constraints:

为第i个微电网第t个时刻的负荷大小，

为第i个微电网第t个时刻与配电网交互的功率；In the above formula,

is the load size of the i-th microgrid at the t-th time,

is the power of the i-th microgrid interacting with the distribution network at the t-th time;

Landscape output constraints:

Tie line power capacity constraints:

为第i个微电网的交互功率上限，

为总交互功率的上限值；In the above formula,

is the upper limit of the interactive power of the i-th microgrid,

is the upper limit of the total interactive power;

ESS operating constraints:

分别为第i个储能设备第t个时刻的放、充电功率，

分别为第i个储能设备的放、充电功率上限值，E_t,i、E_i,max分别为第i个储能设备第t个时刻储存的能量和储存容量额定值，SOC_t,i为第i个储能设备第t个时刻的荷电量，SOC_i,min、SOC_i,max分别为第i个储能设备充放电过程中荷电量的下限值和上限值，η_d、η_c分别为储能设备的放、充电效率；In the above formula,

are the discharge and charging power of the i-th energy storage device at the t-th time, respectively,

are the upper limit values of the discharge and charging power of the i-th energy storage device, E _t,i and E _i,max are the energy and storage capacity ratings of the i-th energy storage device at the t-th time, respectively, SOC _{t, i} is the charge amount of the i-th energy storage device at the t-th time, SOC _i,min and SOC _i,max are the lower and upper limit values of the charge amount during the charging and discharging process of the i-th energy storage device, respectively, η _d , η _c are the discharge and charging efficiencies of the energy storage device, respectively;

Diesel unit output constraints:

分别为柴油机组出力的下限值和上限值，

分别为第i个柴油机组的最大向下爬坡速率和最大向上爬坡速率。In the above formula,

are the lower limit and upper limit of the output of the diesel unit, respectively,

are the maximum downhill ramp rate and the maximum uphill ramp rate of the i-th diesel unit, respectively.

Compared with the prior art, the beneficial effects of the present invention are:

1. A microgrid group optimization scheduling method based on the improved second-order particle swarm algorithm of the present invention firstly constructs the mathematical models of various types of equipment inside the microgrid group, and establishes a microgrid group with the smallest comprehensive operating cost and the largest wind and solar energy consumption rate. , The optimal scheduling model of the microgrid group with the goal of minimizing the power fluctuation of the tie line, and then taking the output of wind power, photovoltaic, energy storage, and diesel units as the position of the particle swarm, and the fitness function as the objective function, the improved second-order particle swarm algorithm is used to solve the above By optimizing the dispatching model, the optimal dispatching scheme of the microgrid group is obtained. This method can minimize the overall operating cost of the microgrid group by dispatching the dispatchable resources within the microgrid group, and at the same time reduce the impact of the microgrid grid connection on the distribution network. Therefore, the method of the present invention reduces the impact of the grid connection of the microgrid on the distribution network while minimizing the overall operating cost of the microgrid group.

2. The improved second-order particle swarm algorithm used in the microgrid swarm optimization scheduling method based on the improved second-order particle swarm algorithm of the present invention first uses the chaotic map to generate the chaotic sequence, selects the Logistic map model to generate the initial population, and reverses the variables Normalize to the search space, get the initial position of the particle, and calculate the distance between any particle and the current best particle after calculating the updated inertia coefficient, learning factor, oscillation factor, particle velocity and position, if the calculated distance is less than The reference value, the optimal particle remains unchanged, so that other particles perform chaotic motion, perform chaotic search within a given number of steps, and replace the original particle with the new particle obtained from the chaotic search. On the one hand, this process will make the initial value of the population The distribution is more uniform and the searchable space is increased. On the other hand, calculating the distance between any particle and the current best particle, and performing chaotic search when the distance is too small can ensure a certain variability, so that the algorithm can jump out to a certain extent. Local optimization increases the global optimization ability. Therefore, the improved second-order particle swarm algorithm of the present invention not only makes the initial value distribution of the population more uniform, but also can increase the global optimization ability.

3. The second-order particle swarm algorithm used in the microgrid swarm optimization scheduling method based on the improved second-order particle swarm algorithm of the present invention improves the inertia coefficient, learning factor and speed update formula. The calculation of the inertia coefficient and learning factor is given by The conventional linear decrement becomes nonlinear decrement, which can increase the search ability in the early stage and enhance the convergence ability in the later stage, thereby improving the accuracy and calculation speed of the algorithm. Therefore, the improved second-order particle swarm algorithm of the present invention improves the accuracy and calculation speed of the algorithm.

Description of drawings

FIG. 1 is a flow chart of the improved second-order particle swarm algorithm in the present invention.

FIG. 2 is a structural diagram of a microgrid group in Embodiment 1. FIG.

FIG. 3 is a diagram of the internal structure of the microgrid in Embodiment 1. FIG.

Detailed ways

The present invention will be further described below with reference to the specific drawings and embodiments.

Referring to Figure 1, a microgrid swarm optimization scheduling method based on the improved second-order particle swarm algorithm includes the following steps in sequence:

Step A, respectively constructing mathematical models of various types of equipment in the microgrid group, wherein the various types of equipment include wind turbines, photovoltaic generators, loads, energy storage equipment, and diesel generators;

Step B, establishing a microgrid group optimization scheduling model aiming at the minimum comprehensive operation cost of the microgrid group, the maximum wind and solar absorption rate, and the minimum power fluctuation of the tie line;

Step C. Taking the output of wind power, photovoltaic, energy storage, and diesel units as the position of the particle swarm, and the fitness function as the objective function, the improved second-order particle swarm algorithm is used to solve the above-mentioned optimal scheduling model, and the optimal scheduling scheme of the microgrid swarm is obtained.

Described step C comprises the following steps in turn:

Step C1, obtaining various equipment parameters and wind, light, and load operation data in the microgrid group, and initializing the basic parameters of the improved second-order particle swarm algorithm;

Step C2, use the chaotic map to generate the chaotic sequence, select the Logistic map model to generate the initial population, and de-normalize the variables to the search space to obtain the initial position of the particle, set the number of iterations k=1, and each particle corresponds to each optimization scheduling plan;

Step C3, calculate the fitness value of each particle, and update the historical optimal value of each particle and the historical optimal value of the population;

Step C4, calculate the current inertia coefficient, learning factor and oscillation factor according to the number of iterations and the fitness value, and update the speed and position of the particle, and at the same time perform over-limit processing on the speed and position of the particle;

Step C5: Calculate the distance between any particle and the current optimal particle. If the calculated distance is less than the reference value, the optimal particle remains unchanged, so that other particles perform chaotic motion, and chaotic search is performed within a given number of steps. Replace original particles with new particles obtained from chaos search;

Step C6, judge whether to converge, if it converges, exit the iterative process, decode the particles, and obtain the optimal scheduling scheme of the microgrid group; if not, set k=k+1 and return to step C2 for the next iteration.

In step C4, the inertia coefficient, learning factor, oscillation factor, speed and position are calculated and updated by the following formula:

λ ₁ <λ ₂ -1,λ ₃ <λ ₄ -1,0<λ ₂ <1,0<λ ₄ <1 k≥k _max /2

分别为第i个粒子在第k次迭代时的惯性系数、速度和位置，ω_min、ω_max分别为惯性系数的最小、最大值，f()为适应度函数，

为第k次迭代时种群的平均适应度值，p_g、p_i分别为粒子群、第i个粒子的历史最优位置，

分别为第k次迭代时的学习因子c₁、c₂，r₁、r₂为[0,1]内均匀分布的随机数，c_1b、c_1e、c_2b、c_2e分别为c₁、c₂迭代最开始的值和结束的值，λ₁、λ₃分别为当前迭代过程中第i个粒子最优和全局最优位置的振荡因子，λ₂、λ₄分别为上一次的迭代过程中第i个粒子最优和全局最优位置的振荡因子，d₁、d₂为c₁的控制因子，d₃、d₄为c₂的控制因子，k_max为最大迭代次数。In the above formula,

are the inertia coefficient, velocity and position of the ith particle at the k-th iteration, respectively, ω _min and ω _max are the minimum and maximum values of the inertia coefficient, respectively, f() is the fitness function,

is the average fitness value of the population at the k-th iteration, p _g and p _i are the historical optimal positions of the particle swarm and the i-th particle, respectively,

are the learning factors c ₁ , c ₂ in the k-th iteration, respectively, r ₁ , r ₂ are random numbers uniformly distributed in [0,1], c _1b , c _1e , c _2b , and c _2e are c ₁ , c 1e , c 2b , and c 2e respectively c ₂ The initial value and the end value of the iteration, λ ₁ , λ ₃ are the oscillation factors of the i-th particle optimal and global optimal position in the current iteration process, respectively, λ ₂ , λ ₄ are the last iteration process, respectively Oscillation factor of the optimal and global optimal position of the i-th particle, d ₁ and d ₂ are the control factors of c ₁ , d ₃ and d ₄ are the control factors of c ₂ , and km _max is the maximum number of iterations.

In step C2, the logistic mapping model is:

为混沌变量在第k次迭代时的d维分量。In the above formula,

is the d-dimensional component of the chaotic variable at the k-th iteration.

In step C5, the distance between the arbitrary particle and the current optimal particle is calculated according to the following formula:

为第k次迭代时第i个粒子与当前最佳粒子之间的距离，

为第i个粒子在第k次迭代过程中的d维分量，p_gd为当前最佳粒子的d维分量，n为粒子的维数，即优化变量的个数。In the above formula,

is the distance between the i-th particle and the current best particle at the k-th iteration,

is the d-dimensional component of the i-th particle in the k-th iteration process, p _gd is the d-dimensional component of the current optimal particle, and n is the dimension of the particle, that is, the number of optimization variables.

In step B, the objective function f of the microgrid group optimization scheduling model is:

minf=ω ₁ f ₁ +ω ₂ f ₂ +ω ₃ f ₃

分别为第t个时刻微电网群向配电网的购电功率和售电功率，且

c_fuel,i、c_M,i、c_E,i分别为柴油机组等效的单位燃料费用、维护费用和环境成本费用，

分别为柴油机组和储能设备的出力，c_DS,i、c_d,i分别为储能设备的维护费用和折旧费用，Δt为单个时段的时长，a_i、b_i、c_i分别为柴油机组费用函数的二次项、一次项和常数项系数，

分别为第i个微电网第t个时刻风电、光伏削减后的有功出力，

分别为第i个微电网第t个时刻风电、光伏的最大有功出力，P_t ^Line为第t个时刻微电网群与配电网交互的功率，

为微电网群与配电网交互的功率的平均值。In the above formula, f ₁ , f ₂ , and f ₃ are the comprehensive operation cost, wind-solar consumption rate, and tie line power fluctuation of the microgrid group, respectively, and ω ₁ , ω ₂ , and ω ₃ are the comprehensive operation cost, wind-solar consumption rate, respectively. , the weight of the power fluctuation of the tie line, N _MG and T are the number of microgrids and the number of calculation periods, respectively, c _t,buy , c _t,sell are the unit price and unit price of electricity,

are the purchasing power and selling power of the microgrid group to the distribution network at the t-th time, respectively, and

c _fuel,i , c _M,i , c _E,i are the equivalent unit fuel cost, maintenance cost and environmental cost of diesel unit respectively,

are the output of diesel units and energy storage equipment, respectively, c _DS,i , cd _,i are the maintenance cost and depreciation cost of energy storage equipment, respectively, Δt is the duration of a single period, a _i , _{bi , c i are} the diesel engine respectively the quadratic, linear, and constant coefficients of the group cost function,

are the active power output of the i-th microgrid at the t-th moment after the reduction of wind power and photovoltaic power, respectively,

are the maximum active power output of wind power and photovoltaics of the i-th microgrid at the t-th time, respectively, P _t ^Line is the interaction power between the micro-grid group and the distribution network at the t-th time,

is the average value of the power that the microgrid group interacts with the distribution network.

The constraints of the objective function include:

Load Balance Constraints:

为第i个微电网第t个时刻的负荷大小，

为第i个微电网第t个时刻与配电网交互的功率；In the above formula,

is the load size of the i-th microgrid at the t-th time,

is the power of the i-th microgrid interacting with the distribution network at the t-th time;

Landscape output constraints:

Tie line power capacity constraints:

为第i个微电网的交互功率上限，

为总交互功率的上限值；In the above formula,

is the upper limit of the interactive power of the i-th microgrid,

is the upper limit of the total interactive power;

ESS operating constraints:

分别为第i个储能设备第t个时刻的放、充电功率，

分别为第i个储能设备的放、充电功率上限值，E_t,i、E_i,max分别为第i个储能设备第t个时刻储存的能量和储存容量额定值，SOC_t,i为第i个储能设备第t个时刻的荷电量，SOC_i,min、SOC_i,max分别为第i个储能设备充放电过程中荷电量的下限值和上限值，η_d、η_c分别为储能设备的放、充电效率；In the above formula,

are the discharge and charging power of the i-th energy storage device at the t-th time, respectively,

are the upper limit values of the discharge and charging power of the i-th energy storage device, E _t,i and E _i,max are the energy and storage capacity ratings of the i-th energy storage device at the t-th time, respectively, SOC _{t, i} is the charge amount of the i-th energy storage device at the t-th time, SOC _i,min and SOC _i,max are the lower and upper limit values of the charge amount during the charging and discharging process of the i-th energy storage device, respectively, η _d , η _c are the discharge and charging efficiencies of the energy storage device, respectively;

Diesel unit output constraints:

分别为柴油机组出力的下限值和上限值，

分别为第i个柴油机组的最大向下爬坡速率和最大向上爬坡速率。In the above formula,

are the lower limit and upper limit of the output of the diesel unit, respectively,

are the maximum downhill ramp rate and the maximum uphill ramp rate of the i-th diesel unit, respectively.

The parameters adopted in the present invention are described as follows:

Control factor: the present invention adopts control factors d ₁ , d ₂ , d ₃ , and d ₄ to control the shape of the function curve of the learning factors c ₁ , c ₂ changing with the number of iterations.

Oscillation factor: in the present invention, the oscillation factors λ ₁ , λ ₂ , λ ₃ , λ ₄ represent the weight of the particle velocity update affected by the particle position, λ ₁ and λ ₃ are affected by the particle position at the current stage, and λ ₂ and λ ₄ are affected by the upper One-stage particle position influence.

Example 1:

A microgrid group optimization scheduling method based on improved second-order particle swarm algorithm, the method takes a microgrid group as the research object (see Figure 2 for its structure), and performs the following steps in sequence:

1. Construct the mathematical models of various devices in the microgrid group respectively. The internal structure of the microgrid is shown in Figure 3, where the devices include wind turbines, photovoltaic generators, loads, energy storage equipment and diesel generators;

2. Based on the above-mentioned various types of equipment, establish an optimal scheduling model for the micro-grid group with the goal of minimizing the comprehensive operation cost of the micro-grid group, maximizing the wind-solar consumption rate, and minimizing the power fluctuation of the tie line:

minf=ω ₁ f ₁ +ω ₂ f ₂ +ω ₃ f ₃

分别为第t个时刻微电网群向配电网的购电功率和售电功率，且

c_fuel,i、c_M,i、c_E,i分别为柴油机组等效的单位燃料费用、维护费用和环境成本费用，

分别为柴油机组和储能设备的出力，c_DS,i、c_d,i分别为储能设备的维护费用和折旧费用，Δt为单个时段的时长，a_i、b_i、c_i分别为柴油机组费用函数的二次项、一次项和常数项系数，

分别为第i个微电网第t个时刻风电、光伏削减后的有功出力，

分别为第i个微电网第t个时刻风电、光伏的最大有功出力，P_t ^Line为第t个时刻微电网群与配电网交互的功率，

为微电网群与配电网交互的功率的平均值；In the above formula, f is the objective function of the model, f ₁ , f ₂ , and f ₃ are the comprehensive operating cost, wind-solar absorption rate, and tie line power fluctuation of the microgrid group, respectively, ω ₁ , ω ₂ , and ω ₃ are respectively The weight of comprehensive operating cost, wind and solar absorption rate, and power fluctuation of tie line, N _MG and T are the number of microgrids and the number of calculation periods, respectively, ct _,buy , _ct,sell are the direction of the microgrid group at the t-th time, respectively. The unit price of electricity purchased and sold of the distribution network,

are the purchasing power and selling power of the microgrid group to the distribution network at the t-th time, respectively, and

c _fuel,i , c _M,i , c _E,i are the equivalent unit fuel cost, maintenance cost and environmental cost of diesel unit respectively,

are the output of diesel units and energy storage equipment, respectively, c _DS,i , cd _,i are the maintenance cost and depreciation cost of energy storage equipment, respectively, Δt is the duration of a single period, a _i , _{bi , c i are} the diesel engine respectively the quadratic, linear, and constant coefficients of the group cost function,

are the active power output of the i-th microgrid at the t-th moment after the reduction of wind power and photovoltaic power, respectively,

are the maximum active power output of wind power and photovoltaics of the i-th microgrid at the t-th time, respectively, P _t ^Line is the interaction power between the micro-grid group and the distribution network at the t-th time,

is the average value of the power that the microgrid group interacts with the distribution network;

The constraints of the objective function include:

Load Balance Constraints:

为第i个微电网第t个时刻的负荷大小，

为第i个微电网第t个时刻与配电网交互的功率；In the above formula,

is the load size of the i-th microgrid at the t-th time,

is the power of the i-th microgrid interacting with the distribution network at the t-th time;

Landscape output constraints:

Tie line power capacity constraints:

为第i个微电网的交互功率上限，

为总交互功率的上限值；In the above formula,

is the upper limit of the interactive power of the i-th microgrid,

is the upper limit of the total interactive power;

ESS operating constraints:

分别为第i个储能设备第t个时刻的放、充电功率，

分别为第i个储能设备的放、充电功率上限值，E_t,i、E_i,max分别为第i个储能设备第t个时刻储存的能量和储存容量额定值，SOC_t,i为第i个储能设备第t个时刻的荷电量，SOC_i,min、SOC_i,max分别为第i个储能设备充放电过程中荷电量的下限值和上限值，η_d、η_c分别为储能设备的放、充电效率；In the above formula,

are the discharge and charging power of the i-th energy storage device at the t-th time, respectively,

are the upper limit values of the discharge and charging power of the i-th energy storage device, E _t,i and E _i,max are the energy and storage capacity ratings of the i-th energy storage device at the t-th time, respectively, SOC _{t, i} is the charge amount of the i-th energy storage device at the t-th time, SOC _i,min and SOC _i,max are the lower and upper limit values of the charge amount during the charging and discharging process of the i-th energy storage device, respectively, η _d , η _c are the discharge and charging efficiencies of the energy storage device, respectively;

Diesel unit output constraints:

分别为柴油机组出力的下限值和上限值，

分别为第i个柴油机组的最大向下爬坡速率和最大向上爬坡速率；In the above formula,

are the lower limit and upper limit of the output of the diesel unit, respectively,

are the maximum downhill ramp rate and the maximum uphill ramp rate of the i-th diesel unit, respectively;

3. Obtain the installed capacity of wind turbines and photovoltaic generators in different microgrids, and obtain the operating data of wind and solar loads, boundary parameters of equipment, etc., and initialize and improve the basic parameters of the second-order particle swarm algorithm;

4. Take the output of wind power, photovoltaic, energy storage, and diesel units as the position of the particle swarm, use the chaotic map to generate the chaotic sequence, select the Logistic mapping model to generate the initial population, and de-normalize the variables to the search space to obtain the initial position of the particle , let the number of iterations k=1, each particle corresponds to each optimization scheduling scheme, wherein, the logistic mapping model is:

为混沌变量在第k次迭代时的d维分量；In the above formula,

is the d-dimensional component of the chaotic variable at the k-th iteration;

5. Calculate the fitness value of each particle, and update the historical optimal value of each particle and the historical optimal value of the population;

6. Calculate the current inertia coefficient, learning factor and oscillation factor according to the number of iterations and the fitness value, update the speed and position of the particle, and perform over-limit processing on the speed and position of the particle, wherein the inertia coefficient, learning factor , Oscillation Factor, Velocity and Position Updates are calculated by the following formulas:

λ ₁ <λ ₂ -1,λ ₃ <λ ₄ -1,0<λ ₂ <1,0<λ ₄ <1k≥k _max /2

分别为第i个粒子在第k次迭代时的惯性系数、速度和位置，ω_min、ω_max分别为惯性系数的最小、最大值，f()为适应度函数，

为第k次迭代时种群的平均适应度值，p_g、p_i分别为粒子群、第i个粒子的历史最优位置，

为第k次迭代时的学习因子，r₁、r₂为[0,1]内均匀分布的随机数，c_1b、c_1e、c_2b、c_2e分别为c₁、c₂迭代最开始的值和结束的值，λ₁、λ₃分别为当前迭代过程中第i个粒子最优和全局最优位置的振荡因子，λ₂、λ₄分别为上一次的迭代过程中第i个粒子最优和全局最优位置的振荡因子，d₁、d₂为c₁的控制因子，d₃、d₄为c₂的控制因子，k_max为最大迭代次数；In the above formula,

are the inertia coefficient, velocity and position of the ith particle at the k-th iteration, respectively, ω _min and ω _max are the minimum and maximum values of the inertia coefficient, respectively, f() is the fitness function,

is the average fitness value of the population at the k-th iteration, p _g and p _i are the historical optimal positions of the particle swarm and the i-th particle, respectively,

is the learning factor at the k-th iteration, r ₁ and r ₂ are random numbers uniformly distributed in [0,1], c _1b , c _1e , c _2b , and c _2e are the first iterations of c ₁ and c ₂ , respectively. value and end value, λ ₁ and λ ₃ are the oscillation factors of the optimal and global optimal positions of the ith particle in the current iteration process, respectively, λ ₂ and λ ₄ are the most optimal position of the ith particle in the previous iteration process, respectively. Oscillation factors of the optimal and global optimal positions, d ₁ and d ₂ are the control factors of c ₁ , d ₃ and d ₄ are the control factors of c ₂ , and km _max is the maximum number of iterations;

7. Calculate the distance between any particle and the current optimal particle according to the following formula. If the calculated distance is less than the reference value, the optimal particle will remain unchanged, so that other particles will perform chaotic motion and chaotic within a given number of steps. Search, replacing the original particles with new particles from the chaos search:

为第k次迭代时第i个粒子与当前最佳粒子之间的距离，

为第i个粒子在第k次迭代过程中的d维分量，p_gd为当前最佳粒子的d维分量，n为粒子的维数，即优化变量的个数；In the above formula,

is the distance between the i-th particle and the current best particle at the k-th iteration,

is the d-dimensional component of the i-th particle in the k-th iteration process, p _gd is the d-dimensional component of the current optimal particle, and n is the dimension of the particle, that is, the number of optimization variables;

8. Determine whether it converges. If it converges, exit the iterative process, decode the particles, and obtain the optimal scheduling scheme of the microgrid group; if it does not converge, set k=k+1 and return to step 4 for the next iteration.

Claims (7)

1. a microgrid group optimization scheduling method based on improved second-order particle swarm algorithm, is characterized in that: The optimal scheduling method sequentially includes the following steps: Step A, respectively constructing mathematical models of various types of equipment in the microgrid group, wherein the various types of equipment include wind turbines, photovoltaic generators, loads, energy storage equipment, and diesel generators; Step B, establishing a microgrid group optimization scheduling model aiming at the minimum comprehensive operation cost of the microgrid group, the maximum wind and solar absorption rate, and the minimum power fluctuation of the tie line; Step C. Taking the output of wind power, photovoltaic, energy storage, and diesel units as the position of the particle swarm, and the fitness function as the objective function, the improved second-order particle swarm algorithm is used to solve the above-mentioned optimal scheduling model, and the optimal scheduling scheme of the microgrid swarm is obtained. 2. a kind of microgrid group optimization scheduling method based on improved second-order particle swarm algorithm according to claim 1, is characterized in that: Described step C comprises the following steps in turn: Step C1, obtaining various equipment parameters and wind, light, and load operation data in the microgrid group, and initializing the basic parameters of the improved second-order particle swarm algorithm; Step C2, use the chaotic map to generate the chaotic sequence, select the Logistic map model to generate the initial population, and de-normalize the variables to the search space to obtain the initial position of the particle, set the number of iterations k=1, and each particle corresponds to each optimization scheduling plan; Step C3, calculate the fitness value of each particle, and update the historical optimal value of each particle and the historical optimal value of the population; Step C4, calculate the current inertia coefficient, learning factor and oscillation factor according to the number of iterations and the fitness value, and update the speed and position of the particle, and at the same time perform over-limit processing on the speed and position of the particle; Step C5: Calculate the distance between any particle and the current optimal particle. If the calculated distance is smaller than the reference value, the optimal particle remains unchanged, so that other particles perform chaotic motion, and chaotic search is performed within a given number of steps. Replace original particles with new particles obtained from chaos search; Step C6, judge whether to converge, if it converges, exit the iterative process, decode the particles, and obtain the optimal scheduling scheme of the microgrid group; if not, set k=k+1 and return to step C2 for the next iteration. 3. a kind of microgrid group optimization scheduling method based on improved second-order particle swarm algorithm according to claim 2, is characterized in that: In step C4, the inertia coefficient, learning factor, oscillation factor, speed and position are calculated and updated by the following formula:

λ ₁ <λ ₂ -1,λ ₃ <λ ₄ -1,0<λ ₂ <1,0<λ ₄ <1 k≥k _max /2 In the above formula,

are the inertia coefficient, velocity and position of the ith particle at the k-th iteration, respectively, ω _min and ω _max are the minimum and maximum values of the inertia coefficient, respectively, f() is the fitness function,

is the average fitness value of the population at the k-th iteration, p _g and p _i are the historical optimal positions of the particle swarm and the i-th particle, respectively,

is the learning factor c ₁ at the kth iteration,

is the learning factor c ₂ in the k-th iteration, r ₁ and r ₂ are random numbers uniformly distributed in [0,1], c _1b , c _1e , c _2b , and c _2e are c ₁ , c ₂ iteration maximum The starting value and the ending value, λ ₁ and λ ₃ are the oscillation factors of the i-th particle optimal and global optimal position in the current iteration process, respectively, λ ₂ , λ ₄ are the i-th particle in the previous iteration process, respectively. Oscillation factors for the optimal and global optimal positions of particles, d ₁ and d ₂ are the control factors of c ₁ , d ₃ and d ₄ are the control factors of c ₂ , and km _max is the maximum number of iterations. 4. a kind of microgrid group optimization scheduling method based on improved second-order particle swarm algorithm according to claim 2, is characterized in that: In step C2, the logistic mapping model is:

In the above formula,

is the d-dimensional component of the chaotic variable at the k-th iteration. 5. a kind of microgrid group optimization scheduling method based on improved second-order particle swarm algorithm according to claim 2, is characterized in that: In step C5, the distance between the arbitrary particle and the current optimal particle is calculated according to the following formula:

In the above formula,

is the distance between the i-th particle and the current best particle at the k-th iteration,

is the d-dimensional component of the i-th particle in the k-th iteration process, p _gd is the d-dimensional component of the current optimal particle, and n is the dimension of the particle, that is, the number of optimization variables. 6. a kind of microgrid group optimization scheduling method based on improved second-order particle swarm algorithm according to claim 1 and 2, is characterized in that: In step B, the objective function f of the microgrid group optimization scheduling model is: minf=ω ₁ f ₁ +ω ₂ f ₂ +ω ₃ f ₃

In the above formula, f ₁ , f ₂ , and f ₃ are the comprehensive operation cost, wind-solar consumption rate, and tie line power fluctuation of the microgrid group, respectively, and ω ₁ , ω ₂ , and ω ₃ are the comprehensive operation cost, wind-solar consumption rate, respectively. , the weight of the power fluctuation of the tie line, N _MG and T are the number of microgrids and the number of calculation periods, respectively, c _t,buy , c _t,sell are the unit price and unit price of electricity,

are the purchasing power and selling power of the microgrid group to the distribution network at the t-th time, respectively, and

c _fuel,i , c _M,i , c _E,i are the equivalent unit fuel cost, maintenance cost and environmental cost of diesel unit respectively,

are the output of diesel units and energy storage equipment, respectively, c _DS,i , cd _,i are the maintenance cost and depreciation cost of energy storage equipment, respectively, Δt is the duration of a single period, a _i , _{bi , c i are} the diesel engine respectively the quadratic, linear, and constant coefficients of the group cost function,

are the active power output of the i-th microgrid at the t-th moment after the reduction of wind power and photovoltaic power, respectively,

are the maximum active power output of wind power and photovoltaics of the i-th microgrid at the t-th time, respectively, P _t ^Line is the interaction power between the micro-grid group and the distribution network at the t-th time,

is the average value of the power that the microgrid group interacts with the distribution network. 7. A kind of microgrid group optimization scheduling method based on improved second-order particle swarm algorithm according to claim 1 and 2, is characterized in that: The constraints of the objective function include: Load Balance Constraints:

In the above formula,

is the load size of the i-th microgrid at the t-th time,

is the power of the i-th microgrid interacting with the distribution network at the t-th time; Landscape output constraints:

Tie line power capacity constraints:

In the above formula,

is the upper limit of the interactive power of the i-th microgrid,

is the upper limit of the total interactive power; ESS operating constraints:

In the above formula,

are the discharge and charging power of the i-th energy storage device at the t-th time, respectively,

are the upper limit values of the discharge and charging power of the i-th energy storage device, E _t,i and E _i,max are the energy and storage capacity ratings stored by the i-th energy storage device at the t-th time, respectively, SOC _{t, i} is the charge amount of the i-th energy storage device at the t-th time, SOC _i,min and SOC _i,max are the lower and upper limit values of the charge amount during the charging and discharging process of the i-th energy storage device, respectively, η _d , η _c are the discharge and charging efficiencies of the energy storage device, respectively; Diesel unit output constraints:

In the above formula,

are the lower limit and upper limit of the output of the diesel unit, respectively,

are the maximum downhill rate and the maximum uphill rate of the i-th diesel unit, respectively.

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