CN102622475B

CN102622475B - Secondary programming model-based peak clipping and valley filling day-ahead optimization method for battery energy storage system

Info

Publication number: CN102622475B
Application number: CN201210050601.4A
Authority: CN
Inventors: 黄晓东; 余建国; 饶宏; 李永兴; 李勇琦; 钟朝现; 陆志刚; 王科; 陈柔伊; 董旭柱; 段卫国; 袁志昌; 陆超; 鲍冠南
Original assignee: China South Power Grid International Co ltd; China Southern Power Grid Tiaofeng Frequency Modulation Power Generation Co; Tsinghua University
Current assignee: China South Power Grid International Co ltd; Tsinghua University; Peak and Frequency Regulation Power Generation Co of China Southern Power Grid Co Ltd
Priority date: 2012-02-29
Filing date: 2012-02-29
Publication date: 2014-04-16
Anticipated expiration: 2032-02-29
Also published as: CN102622475A

Abstract

The invention relates to a peak clipping and valley filling day-ahead optimization method of a battery energy storage system based on a quadratic programming model. The target function in the model is a convex function, the quadratic programming to be solved is convex quadratic programming, theoretically, the global optimal solution can be found only by solving the KKT point, the calculation method is mature, and the initial feasible solution is convenient and easy to obtain. The method does not need to discretize the residual electric quantity of the battery in the solving process. The peak clipping and valley filling day-ahead optimization method of the battery energy storage system based on the quadratic programming model is ingenious in design, excellent in performance, convenient and practical.

Description

A day-ahead optimization method for peak-shaving and valley-filling of battery energy storage systems based on quadratic programming model

技术领域 technical field

本发明是一种基于二次规划模型的电池储能系统削峰填谷日前优化方法，属于基于二次规划模型的电池储能系统削峰填谷日前优化方法的改造技术。The invention is a prior-day optimization method for peak-shaving and valley-filling of a battery energy storage system based on a quadratic programming model, and belongs to the modification technology of the prior-day optimization method for peak-shaving and valley-filling of a battery energy storage system based on a quadratic programming model.

背景技术 Background technique

大规模电池储能系统(Battery Energy Storage System，BESS)通过在负荷高峰时放电，在负荷低谷时充电，可以实现对负荷的削峰填谷功能。对电网来说，削峰填谷能够推迟设备容量升级，提高设备利用率，节省设备更新的费用；对用户来说，可以利用峰谷电价差获得经济效益。在国外已有许多大规模BESS在运行；在国内，南方电网开展了MW级电池储能系统示范项目。The large-scale battery energy storage system (Battery Energy Storage System, BESS) can realize the peak-shaving and valley-filling function of the load by discharging at the peak load and charging at the low load. For the power grid, peak shaving and valley filling can delay equipment capacity upgrades, improve equipment utilization, and save equipment update costs; for users, they can use the difference in peak and valley electricity prices to obtain economic benefits. Many large-scale BESSs are already in operation abroad; in China, China Southern Power Grid has launched a MW-level battery energy storage system demonstration project.

削峰填谷日前优化是在新的一天开始前，根据预测出的日负荷曲线，优化出24小时的BESS最优充放电策略，即每个时刻电池是否充放电，充放电的功率大小为多少。在实时控制时，根据日前优化给出的充放电策略，以及当前时刻的负荷值、电池状态等数据，计算出充放电功率指令并下发给每组电力电子变流器。The optimization before the peak shaving and valley filling is to optimize the 24-hour BESS optimal charge and discharge strategy according to the predicted daily load curve before the start of a new day, that is, whether the battery is charged and discharged at each moment, and the power of the charge and discharge is how much . In real-time control, according to the charging and discharging strategy given by the previous optimization, as well as the current load value, battery status and other data, the charging and discharging power command is calculated and sent to each group of power electronic converters.

目前广泛采用的电池储能系统削峰填谷日前优化模型中，基于分时电价理论，以获得最大的经济效益为目标，一个小时对应一个负荷点，一天一共24个点。这样的模型优化出的结果过于粗糙，电池充放电起止时刻不精确，无法平抑分钟级时间尺度上的负荷功率波动。另外，电池的非线性物理约束使得优化模型难以求解。In the currently widely used optimization model of battery energy storage system for peak shaving and valley filling, based on the theory of time-of-use electricity price, with the goal of obtaining the greatest economic benefits, one hour corresponds to one load point, and there are 24 points in total in one day. The optimization results of such a model are too rough, and the start and end times of battery charging and discharging are not accurate, and it is impossible to stabilize the load power fluctuations on the minute-level time scale. In addition, the nonlinear physical constraints of the battery make the optimization model difficult to solve.

目前求解电池储能系统削峰填谷日前优化模型的方法主要是智能算法和动态规划算法。智能算法包括遗传算法、粒子群算法、模拟退火算法等。在智能算法中，选取合适的参数非常困难且智能算法无法保证每次都能求得全局最优解。动态规划算法中电池剩余电量被离散化，电池的出力只能在一系列离散值中选取。At present, the methods for solving the optimization model of the battery energy storage system before peak-shaving and valley-filling are mainly intelligent algorithms and dynamic programming algorithms. Intelligent algorithms include genetic algorithm, particle swarm algorithm, simulated annealing algorithm, etc. In the intelligent algorithm, it is very difficult to select the appropriate parameters, and the intelligent algorithm cannot guarantee that the global optimal solution can be obtained every time. In the dynamic programming algorithm, the remaining power of the battery is discretized, and the output of the battery can only be selected from a series of discrete values.

发明内容 Contents of the invention

本发明的目的在于考虑上述问题而提供一种能求出电池储能系统在一天中的最优充放电策略，以使得负荷曲线变得最为平坦的基于二次规划模型的电池储能系统削峰填谷日前优化方法。本发明不仅节省空间、成本低、使用安全、操作方便，使用寿命长。The purpose of the present invention is to consider the above problems and provide an optimal charging and discharging strategy for the battery energy storage system in a day, so that the load curve becomes the flattest peak shaving of the battery energy storage system based on the quadratic programming model Day-ahead optimization method for valley filling. The invention not only saves space, has low cost, is safe to use, is convenient to operate, and has long service life.

本发明的技术方案是：本发明的基于二次规划模型的电池储能系统削峰填谷日前优化方法，包括有以下步骤：The technical solution of the present invention is: the optimization method of the battery energy storage system based on the quadratic programming model according to the present invention, including the following steps:

1)系统初始化：1) System initialization:

输入参数及预测负荷文件，参数包括：一天中负荷数据点的个数N；相邻负荷数据的时间间隔Δt；电池组总容量S；电池剩余电量的上限S_high和下限S_low；电池剩余电量的初值S_initial和终值S_final；最大充放电功率限制值P_max；预测负荷文件中包括N个预测负荷数据，分别为D(i)，i＝1，2，…，N；Input parameters and forecast load files, parameters include: the number N of load data points in a day; the time interval Δt of adjacent load data; the total capacity of the battery pack S; the upper limit S _high and lower limit S _low of the remaining battery power; the remaining battery power The initial value S _initial and the final value S _final ; the maximum charge and discharge power limit value P _max ; the predicted load file includes N predicted load data, which are D(i), i=1, 2, ..., N;

2)建立电池储能系统日前优化模型：2) Establish a day-ahead optimization model of the battery energy storage system:

选取N个时刻BESS输出功率b(i)，i＝1，2，…，N作为控制变量，电池充电为正，放电为负。选取N个时刻电池的剩余电量s(i)，i＝0，1，2，…，N作为状态变量。将负荷方差选取为目标函数：Select BESS output power b(i) at N times, i=1, 2, ..., N as the control variable, the battery charge is positive, and the discharge is negative. Select the remaining power s(i) of the battery at N times, i=0, 1, 2, . . . , N as the state variable. The load variance is chosen as the objective function:

$\begin{matrix} min min & f f ((b b)) = = \frac{11}{N N} {Σ Σ}_{i i = = 11}^{N N} {((((D D. ((i i)) + + b b ((i i)))) - - \frac{11}{N N} {Σ Σ}_{i i = = 11}^{N N} ((D D. ((i i)) + + b b ((i i))))))}^{22} \end{matrix}$

约束条件包括容量约束：Constraints include capacity constraints:

S_low≤s(i)≤S_high，i＝0，1，2，...，NS _low ≤ s(i) ≤ S _high , i=0, 1, 2, . . . , N

s(0)＝S_initial s(0)=S _initial

s(i)＝s(i-1)+b(i)×Δt，i＝1，2，...Ns(i)=s(i-1)+b(i)×Δt, i=1, 2,...N

s(N)＝S_final s(N)=S _final

和功率约束：and power constraints:

-P_max≤b(i)≤P_max，i＝1，2，...，N-P _max ≤ b(i) ≤ P _max , i=1, 2, . . . , N

忽略电池内部损耗，则上述模型为二次规划模型，可以采用有效集算法进行求解；Neglecting the internal loss of the battery, the above model is a quadratic programming model, which can be solved by the effective set algorithm;

3)采用有效集算法求解二次规划问题：3) Use the effective set algorithm to solve the quadratic programming problem:

由于目标函数是二次多项式，为了便于说明，将其转化为以下形式：Since the objective function is a quadratic polynomial, for the sake of illustration, it is transformed into the following form:

$\begin{matrix} min min & f f ((x x)) = = \frac{11}{22} {x x}^{T T} Hx Hx + + {c c}^{T T} x x \end{matrix}$

其中，H为N阶对称正定矩阵，x＝[b(1)，b(2)，...，b(N)]^T，c为N维列向量。有效集算法将既含有等式约束，又含有不等式约束的问题转化为只包含等式约束的问题来进行求解。在每次迭代中，有效集算法以已知的可行点x^k为起点，将在该点起作用的不等式约束作为等式约束，在该点不起作用的不等式约束暂且不管。则问题转化为如下形式：Wherein, H is an N-order symmetric positive definite matrix, x=[b(1), b(2), . . . , b(N)] ^T , and c is an N-dimensional column vector. The effective set algorithm transforms a problem containing both equality constraints and inequality constraints into a problem containing only equality constraints for solution. In each iteration, the effective set algorithm takes the known feasible point x ^k as the starting point, takes the inequality constraints that work at this point as equality constraints, and ignores the inequality constraints that do not work at this point. Then the problem is transformed into the following form:

min f(x)min f(x)

s.t.Ax＝bs.t.Ax=b

极小化目标函数f(x)，求得新的可行点后，再重复以上做法；Minimize the objective function f(x), obtain a new feasible point, and then repeat the above method;

4)将日前优化结果b(i)，i＝1，2，…，N输出给削峰填谷实时控制部分。4) Output the day-ahead optimization results b(i), i=1, 2, . . . , N to the real-time control part for peak shaving and valley filling.

上述极小化目标函数f(x)的具体步骤如下：The specific steps for minimizing the objective function f(x) above are as follows:

31)给定初始可行点31) Given an initial feasible point

b(i)的选择方法如下：进行除法运算The selection method of b(i) is as follows: perform division

$\frac{{S S}_{final final} - - {S S}_{initial initial}}{Δt Δt \times \times {P P}_{max max}}$

假设商为p，余数为q，则初始的电池出力为Assuming that the quotient is p and the remainder is q, the initial battery output is

$b b ((i i)) = = \{\begin{matrix} {P P}_{max max},, & i i \leq \leq p p \\ q q,, & i i = = p p + + 11 \\ 00,, & i i > > p p + + 11 \end{matrix}$

求出相应的起作用约束集，确定起作用约束矩阵A。置k＝1；Find the corresponding active constraint set and determine the active constraint matrix A. set k=1;

32)将坐标移至x^k，令32) Move the coordinates to x ^k , let

δ＝x-x^k δ=xx ^k

将问题转化为transform the problem into

$\begin{matrix} min min & \frac{11}{22} {δ δ}^{T T} Hδ Hδ + + &dtri; &dtri; f f {(({x x}^{k k}))}^{T T} δ δ \end{matrix}$

s.t.Aδ＝0s.t. Aδ = 0

设其最优解为δ^k，若δ^k＝0，则进行步骤35)；否则进行步骤33)；Let the optimal solution be δ ^k , if δ ^k =0, go to step 35); otherwise go to step 33);

33)假设有m^k个不起作用的不等式约束，为：33) Assume there are m ^k non-working inequality constraints, as:

a_ix≥b_i，i＝1，2，...，m^k a _i x ≥ bi , _i =1, 2, ..., m ^k

令make

${\overset{^^}{a a}}_{k k} = = min min {{\frac{{b b}_{i i} - - {a a}_{i i} x x}{{a a}_{i i} {δ δ}^{k k}} | | i i = = 1,2 1,2,, . . . . . .,, {m m}^{k k},, {a a}_{i i} {δ δ}^{k k} < < 00}}$

${α α}_{k k} = = min min {{11,, {\overset{^^}{α α}}_{k k}}}$

x^k+1＝x^k+α_kδ^k；x ^k+1 = x ^k +α _k δ ^k ;

34)若a_ix≥b_i，i＝1，2，...，m^k中有约束变为起作用约束，则更新起作用约束集，返回步骤32)；若a_ix≥b_i，i＝1，2，...，m^k中没有约束变为起作用约束，置k为k+1，进行步骤35)；34) If a _i x ≥ _bi , i=1, 2, ..., m ^k has constraints that become active constraints, then update the active constraint set and return to step 32); if a _i x ≥ b _i , i=1, 2, ..., there is no constraint in m ^k to become an effective constraint, put k as k+1, and proceed to step 35);

35)根据KKT条件计算起作用约束的拉格朗日乘子。若所有乘子均为非负数，则停止计算，得到最优解x^k；否则，从所有对应于不等式约束的、值为负数的拉格朗日乘子中取出值最小的，将其对应的不等式约束从起作用约束集中删除，返回步骤32)。35) Calculate the Lagrangian multipliers of the active constraints according to the KKT condition. If all the multipliers are non-negative numbers, stop the calculation and get the optimal solution x ^k ; otherwise, take the smallest value from all the negative Lagrange multipliers corresponding to the inequality constraints, and divide its corresponding Inequality constraints are removed from the set of active constraints, return to step 32).

本发明的优点在于，模型中的目标函数为凸函数，要求解的二次规划为凸二次规划，理论上只要求得KKT点就找到了全局最优解，计算方法成熟，初始可行解方便易得。本发明求解过程中不需要将电池的剩余电量离散化。本发明是一种设计巧妙，性能优良，方便实用的基于二次规划模型的电池储能系统削峰填谷日前优化方法。The advantage of the present invention is that the objective function in the model is a convex function, and the quadratic programming to be solved is a convex quadratic programming. Theoretically, only the KKT point is required to find the global optimal solution, the calculation method is mature, and the initial feasible solution is convenient. easy. In the solving process of the present invention, it is not necessary to discretize the remaining power of the battery. The present invention is a cleverly designed, excellent performance, convenient and practical optimization method for peak-shaving and valley-filling battery energy storage systems based on a quadratic programming model.

附图说明 Description of drawings

图1是削峰填谷日前优化部分和实时控制部分的关系图；Figure 1 is a diagram of the relationship between the optimization part and the real-time control part before peak shaving and valley filling;

图2是第一组预测负荷数据进行削峰填谷前后曲线图；Figure 2 is the first group of predicted load data curves before and after peak shaving and valley filling;

图3是对第一组预测负荷进行削峰填谷的电池出力曲线图；Fig. 3 is a graph of battery output for peak-shaving and valley-filling for the first group of predicted loads;

图4是第二组预测负荷数据进行削峰填谷前后曲线图；Fig. 4 is the curve diagram before and after the second group of predicted load data is shifted and filled;

图5是对第二组预测负荷进行削峰填谷的电池出力曲线图。Fig. 5 is a graph of battery output for peak-shaving and valley-filling for the second group of predicted loads.

具体实施方式 Detailed ways

本发明方法提出建立削峰填谷日前优化的二次规划模型，以最小化负荷方差作为目标函数，采用有效集算法进行求解。The method of the invention proposes to establish a quadratic programming model optimized before peak shaving and valley filling, takes the minimum load variance as the objective function, and uses an effective set algorithm to solve the problem.

研究发现，忽略电池的内部损耗后，当采用最小化负荷方差作为目标函数时，可以将削峰填谷日前优化模型写成凸二次规划的形式。凸二次规划具有良好的性质，在理论上，只要求出KKT解即可找到全局最优解。The study found that after ignoring the internal loss of the battery, when the minimum load variance is used as the objective function, the peak-shaving and valley-filling optimization model can be written in the form of a convex quadratic programming. Convex quadratic programming has good properties. In theory, only the KKT solution is required to find the global optimal solution.

削峰填谷日前优化模块从削峰填谷实时控制部分获得数据，并将优化出的电池充放电策略输出到实时控制模块作为控制的依据(图1)。The optimization module before peak shaving and valley filling obtains data from the real-time control part of peak shaving and valley filling, and outputs the optimized battery charging and discharging strategy to the real-time control module as the basis for control (Figure 1).

本发明方法各环节的具体设计步骤如下：The concrete design steps of each link of the inventive method are as follows:

步骤1：根据输入的参数，求解初始可行解b(i)，i＝1，2，…，N，确定初始可行解的方法如下：进行除法运算Step 1: According to the input parameters, solve the initial feasible solution b(i), i=1, 2, ..., N, the method of determining the initial feasible solution is as follows: Carry out the division operation

求出相应的起作用约束集，确定出起作用约束矩阵A。Find the corresponding active constraint set and determine the active constraint matrix A.

步骤2：进行迭代过程，求出最优控制策略Step 2: Perform an iterative process to find the optimal control strategy

若优化模型中没有不等式约束，则可以直接采用拉格朗日方法求出KKT点。因为不等式约束的存在，在可行点处选择起作用约束组成等式约束，不起作用约束暂且不管。将坐标移至x^k，令If there is no inequality constraint in the optimization model, the KKT point can be obtained directly by using the Lagrangian method. Because of the existence of inequality constraints, the effective constraints are selected to form equality constraints at the feasible point, and the ineffective constraints are ignored for the time being. Move the coordinates to x ^k , let

δ＝x-x^k δ=xx ^k

将问题转化为求解以下的优化模型Transform the problem into solving the following optimization model

s.t.Aδ＝0s.t. Aδ=0

此模型只包含等式约束，可采用拉格朗日方法进行求解。求出的解可能不满足某些不起作用的不等式约束。每次选取一个越界最大的不等式约束加入到起作用集当中，重新求解上述模型，直至求出的最优解满足全部的不等式约束。This model contains only equality constraints and can be solved using Lagrangian methods. The solution found may not satisfy some inequalities constraints that do not work. Each time, a inequality constraint with the largest out-of-bounds is selected and added to the active set, and the above model is re-solved until the optimal solution obtained satisfies all the inequality constraints.

求解起作用集中的等式、不等式对应的拉格朗日乘子，若乘子均为非负数，说明找到了KKT点，对应的可行解为全局最优解；若存在某些拉格朗日乘子为负数，说明有些不等式不应该放入起作用集当中。每次将最小的负的乘子所对应的不等式从起作用集中去除，重新进行迭代，直至最终找到KKT点。Solve the Lagrangian multipliers corresponding to the equations and inequalities in the active set. If the multipliers are all non-negative numbers, it means that the KKT point has been found, and the corresponding feasible solution is the global optimal solution; if there are some Lagrangian The multiplier is negative, indicating that some inequalities should not be put into the active set. Each time the inequality corresponding to the smallest negative multiplier is removed from the active set, and iterated again until the KKT point is finally found.

实施例：深圳某主变电站预测负荷日前优化结果Example: A day-ahead optimization result of predicted load in a main substation in Shenzhen

采用深圳某主变电站两个预测负荷曲线作为输入数据，两个预测负荷曲线如图2和图4中虚线，用二次规划模型及有效集算法进行求解。Two forecasted load curves of a main substation in Shenzhen are used as input data. The two forecasted load curves are shown as dotted lines in Figure 2 and Figure 4, and are solved by quadratic programming model and effective set algorithm.

安装在变电站的储能系统容量为5MW·4h，充放电功率限制为5MW。假设初始容量和终值容量都为0。The capacity of the energy storage system installed in the substation is 5MW·4h, and the charging and discharging power is limited to 5MW. Assume that both the initial capacity and the final value capacity are 0.

步骤1：求解初始可行解b(i)，i＝1，2，…，N。Step 1: Find the initial feasible solution b(i), i=1, 2, ..., N.

取初始解为：Take the initial solution as:

b(i)＝0，i＝1，2，...，Nb(i)=0, i=1, 2, ..., N

优化出的电池充放电策略如图3和图5所示。经过削峰填谷后的负荷曲线如图2和图4中的实线所示。可见负荷曲线变的平坦。第一组负荷数据的方差由之前的51.9032变为了25.6906，第二组负荷数据的方差由之前的42.7595变为了19.1785。The optimized battery charging and discharging strategy is shown in Figure 3 and Figure 5. The load curve after peak shaving and valley filling is shown as the solid line in Figure 2 and Figure 4 . It can be seen that the load curve becomes flat. The variance of the first set of load data changed from 51.9032 to 25.6906, and the variance of the second set of load data changed from 42.7595 to 19.1785.

Claims

1. A method for prior optimization of battery energy storage system peak shaving and valley filling based on quadratic programming model, characterized in that it includes the following steps:

1) System initialization:

Input parameters and forecast load files, the parameters include: the number N of load data points in a day; the time interval of adjacent load data

;The total capacity of the battery pack S;The upper limit of the remaining battery capacity

Figure 2012100506014100001DEST_PATH_IMAGE005

Figure 2012100506014100001DEST_PATH_IMAGE007

and lower limit

;Initial value of remaining battery capacity

and future value

;Maximum charging and discharging power limit value

;The forecast load file includes N1 forecast load data, respectively D(i), i=1,2,...,N1;

2) Establish a day-ahead optimization model of the battery energy storage system:

Select BESS output power b(i), i=1,2,...,N2 at N2 moments as the control variable, the battery charge is positive, and discharge is negative, and the remaining power of the battery at N moments is selected s(i), i=0 ,1,2,…,N are used as state variables, and the load variance is selected as the objective function:

Constraints include capacity constraints:

and power constraints:

Neglecting the internal loss of the battery, the above model is a quadratic programming model, which can be solved by the effective set algorithm;

3) Use the effective set algorithm to solve the quadratic programming problem:

Since the objective function is a quadratic polynomial, for the sake of illustration, it is transformed into the following form:

Among them, H is N3 order symmetric positive definite matrix,

, c is an N4-dimensional column vector, and the effective set algorithm converts the problem containing both equality constraints and inequality constraints into a problem containing only equality constraints for solution. In each iteration, the effective set algorithm uses the known Feasible point x ^k is the starting point, and the inequality constraints that work at this point are regarded as equality constraints, and the inequality constraints that do not work at this point are ignored for the time being, then the problem is transformed into the following form:

Minimize the objective function f(x), obtain a new feasible point, and then repeat the above method;

4) Output the day-ahead optimization results b(i), i=1,2,...,N to the real-time control part for peak shaving and valley filling.