含风电-光伏-光热电站电力系统N-k安全优化调度模型

目录

[1 主要内容](#1 主要内容)

[2 部分程序](#2 部分程序)

[3 部分结果](#3 部分结果)

[4 下载链接](#4 下载链接)

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1 主要内容

该程序参考《光热电站促进风电消纳的电力系统优化调度》光热电站模型，主要做的是考虑N-k安全约束的含义风电-光伏-光热电站的电力系统优化调度模型，从而体现光热电站在调度灵活性以及经济性方面的优势。同时代码还考虑了光热电站对风光消纳的作用，对比了含义光热电站和不含光热电站下的弃风弃光问题，同时还对比了考虑N-k约束下的调度策略区别。以14节点和118节点算例为例，对模型进行了系统性的测试，复现效果良好，是学习N-k约束以及光热电站调度的必备程序！程序采用matlab+cplex（mosek/gurobi）进行求解，可以选择已经安装的求解器进行求解。

• 程序算例

程序对于118节点系统采用了四个算例进行对比，14节点系统有3种算例对比，并增加了弃风量的对比程序。

• 程序模型

• 程序亮点

1. 采用光热电站模型，也是最近研究比较热的一个方向。
2. 采用转移分布因子矩阵处理潮流问题，这也是很多文献中都采用的方法。

2 部分程序

clc; clear; close all; % 关闭所有已打开的绘图窗口
%% 参数设定
NT = 24; % 时间范围
CoeffReseve_load = 0.03; 
CoeffReserve_VRE = 0.05; 
yita_TES = 0.98;  
yita_PB = 0.415;  
% 文章里Table 2的数据
Capacity_TES_CSP = 0; 
initial_TES_t0 = 0.5;  
initial_TES_t1 = 0.78;
TES_initial = 0.5;         
beta_Load = 3*10e3;  
    mpc = case14_1; % 载入数据 matpower 数据格式
%% 有功负荷 24h所有节点总的
%    mpc.load = [
%        2842.42  3020.2  3296.96  3444.44  3607.07  3891.91  4070.7  4295.95  4476.76  4661.61  4859.59  5077.77  ...
%        4717.17  4519.19  4301.01  3995.95  3703.03  3806.06  4037.37  4063.63  3721.21  3245.45  3097.97  2827.27
%    ]/6.3; 
​
   mpc.load = [
       683.42  792.2  896.96  1044.44  1087.07  1121.91  1200.7  1235.95  1326.76  1461.61  1489.59  1577.77  ...
       1417.17  1219.19  1101.01  1075.95  903.03  1186.06  1237.37  1463.63  1221.21  1005.45  827.97  807.27
    ]/2; 
​
​
    mpc.P_RE = [0.00   0.00   0.00   0.00   0.00   0.00   15.76   43.17   82.35   109.44   122.55   146.10   ...% PV
                126.66   86.05   60.05   52.82   25.78   4.28   0.00   0.00   0.00   0.00   0.00   0.00  
                100.26   133.95   147.28   134.11   170.52   159.44   138.55   72.83   58.83   73.37   79.90   80.54 ...  % Wind
                91.96   101.68   121.49   122.93   133.11   162.44   130.95   133.25   151.26   139.33   120.60   90.33
                ]*1; % 可再生能源 24小时数据（实际发电量）
%% 电网相关名称
    baseMVA = mpc.baseMVA;
    bus = mpc.bus;
    gen = mpc.gen;
    branch = mpc.branch;
    gencost = mpc.gencost;
    RE = mpc.RE;
    CSP = mpc.CSP;
    P_RE = mpc.P_RE;
​
N = length(bus(:,1));      % 网络中所有节点数
N_Br = length(branch(:,1));% 线路数
N_Gen = length(gen(:,1));  % 火电发电机组数
N_RE = length(RE(:,1));    % 可再生能源节点机组数
N_CSP = length(CSP(:,1));  % CSP发电站数
​
% 常规机组相关数据提取, 取数据矩阵中的列向量 和功率有功的项，均需标幺值化，以便运算和求解
P_Gen_max = gen(:,9)/baseMVA; 
P_Gen_min = gen(:,10)/baseMVA; 
type_Gen = gen(:,22); 
P_Gen_up = gen(:,23) /baseMVA;  
P_Gen_down = gen(:,24) /baseMVA;
T_Gen_min_on = gen(:,25); 
T_Gen_min_off = gen(:,26); 
c_ST_g = gen(:,28);
c_G_g = gen(:,30); 
​
% CSP机组相关数据提取
P_CSP_max = CSP(:,9)/baseMVA; 
P_CSP_min = CSP(:,10)/baseMVA; 
P_CSP_up = CSP(:,23)/baseMVA;   
P_CSP_down = CSP(:,24)/baseMVA; 
T_CSP_min_on = CSP(:,25); 
T_CSP_min_off = CSP(:,26);
c_CSP_g = CSP(:,30);       
​
PtCSP_fore = [ % 可用的太阳能热功率向量 
    0.00   0.00   0.00   0.00   0.00   0.00   190.57   390.57   790.57 990.57   1390.57   1891.03 ...
    2111.64   2200.92   2202.36   2118.26   1895.37   1408.35   0.00   0.00   0.00   0.00   0.00   0.00 ]/20;
PtCSP_fore = PtCSP_fore/baseMVA; 
P_RE = P_RE/baseMVA; % 可再生能源PV WT机组出力
​
beta_Load = beta_Load*baseMVA^2; % $/MWh -> $/p.u.
​
M_bus_G = zeros(N,N_Gen); % 发电机机组-索引矩阵
for row = 1:N
    if abs(find(mpc.gen(:,1) == row)) > 0  % 发电机节点号 与 行号对应
        M_bus_G(row,find(mpc.gen(:,1) == row)) = 1; % M_bus_G相应处置1
    end
end
​
M_bus_RE = zeros(N,N_RE); % 可再生能源机组-索引矩阵
for row = 1:N
    if abs(find(mpc.RE(:,1) == row))>0
        M_bus_RE(row,find(mpc.RE(:,1) == row)) = 1;
    end
end
​
M_bus_CSP = zeros(N,N_CSP); % CSP机组-索引矩阵
for row = 1:N
    if abs(find(mpc.CSP(:,1) == row))>0
        M_bus_CSP(row,find(mpc.CSP(:,1) == row)) = 1;
    end
end
GSDF = makePTDF(mpc); % 发电转移分布因子矩阵，表征节点注入功率在全网络的分布
​
%% 负荷矩阵数据，按照 算例数据mpc.bus(:,3) 中各节点负荷的比例分配
    PD = bus(:,3)/baseMVA; 
    P_factor = PD/sum(PD);
    P_sum = mpc.load/baseMVA; 
    PD = P_factor*P_sum;      
​
%% 决策变量命名
    PG_G = sdpvar(N_Gen,NT,'full');  
    PG_RE = sdpvar(N_RE,NT,'full');   % （风光并网量）
    PG_CSP = sdpvar(N_CSP,NT,'full'); 
    PC_Load = sdpvar(N,NT,'full');   
    
    onoff_gen = binvar(N_Gen,NT,'full');
    onoff_CSP = binvar(N_CSP,NT,'full'); 
    
    Branch = sdpvar(N_Br,NT,'full');   
    Cost_StartUp  = sdpvar(N_Gen,NT-1,'full');
    
    Pt_TES_charge = sdpvar(N_CSP,NT,'full');  
    Pt_TES_discharge= sdpvar(N_CSP,NT,'full');
    Et_TES = sdpvar(N_CSP,NT,'full');         
    
%% 约束条件列写   
    Cons = [];
    for t = 1:NT
        if t >= 2 % type(1-水电, 2-火电机组)
            for i = 1:N_Gen % 火电机组-最小启/停时间约束 式(8-9)
                if (type_Gen(i,1)==2) || (type_Gen(i,1)==5) 
                    for tao = t + 1:min(t+T_Gen_min_on(i,1)-1,NT)   
                        Cons = [Cons, onoff_gen(i,t)-onoff_gen(i,t-1) <= onoff_gen(i,tao)];
                    end
                    for tao = t + 1:min(t+T_Gen_min_off(i,1)-1,NT) 
                        Cons = [Cons, onoff_gen(i,t-1)-onoff_gen(i,t) <= 1-onoff_gen(i,tao)];
                    end
                end
            end
            for i = 1:N_CSP  
                for tao = t+1:min(t+T_CSP_min_on(i,1)-1,NT)
                    Cons = [Cons, onoff_CSP(i,t)-onoff_CSP(i,t-1) <= onoff_CSP(i,tao)]; % CSP机组最小启/停时间约束
                end
                for tao = t+1:min(t+T_CSP_min_off(i,1)-1,NT)
                    Cons = [Cons, onoff_CSP(i,t-1)-onoff_CSP(i,t) <= 1-onoff_CSP(i,tao)];
                end
            end
        end 
        if t >= 2 % 火电机组 爬坡约束 式(6-7)
            Cons = [Cons,  PG_G(:,t) - PG_G(:,t-1) <= ...
                     onoff_gen(:,t-1).* P_Gen_up*60 + ... 
                    (onoff_gen(:,t)-onoff_gen(:,t-1)) .* P_Gen_min + ... 
                    (1-onoff_gen(:,t)) .* P_Gen_max];  
            Cons = [Cons, -PG_G(:,t) + PG_G(:,t-1) <= ...
                    onoff_gen(:,t) .* P_Gen_down*60 + ...
                   (onoff_gen(:,t-1)-onoff_gen(:,t)) .* P_Gen_min + ...  
                   (1-onoff_gen(:,t-1)) .* P_Gen_max];
               
            % CSP 机组 爬坡约束 式(6-7)
            Cons = [Cons,  PG_CSP(:,t) - PG_CSP(:,t-1) <= ...
                     onoff_CSP(:,t-1).* P_CSP_up*60 + ... %  
                     (onoff_CSP(:,t)-onoff_CSP(:,t-1)) .* P_CSP_min + ...
                     (1-onoff_CSP(:,t)) .* P_CSP_max]; 
            Cons = [Cons, -PG_CSP(:,t) + PG_CSP(:,t-1) <= onoff_CSP(:,t) .* P_CSP_down*60 + ...  
                    (onoff_CSP(:,t-1)-onoff_CSP(:,t)) .* P_CSP_min + ...  
                    (1-onoff_CSP(:,t-1)) .* P_CSP_max];
        end
    end
    % 机组出力的上下边界约束-式(3) % t(1-水电,2-火电, 5-燃气发电机组 6-CSP)
  Ind_2_5 = union(find(type_Gen(:,1) == 2),find(type_Gen(:,1) == 5)); 
   Cons = [Cons, onoff_gen(Ind_2_5,:) .* (P_Gen_min(Ind_2_5,1) * ones(1,NT)) ...    
           <= PG_G(Ind_2_5,:) <= ...
          onoff_gen(Ind_2_5,:) .* (P_Gen_max(Ind_2_5,1) * ones(1,NT))];  
        
   
        
    Cons = [Cons, onoff_CSP.*(P_CSP_min*ones(1,NT)) <= PG_CSP <= onoff_CSP.*(P_CSP_max*ones(1,NT))]; % CSP机组出力-边界约束
%     Cons = [Cons, onoff_CSP == ones(1,24)]; % CSP机组 
  
    Cons = [Cons, sum(PG_G,1) + sum(PG_RE,1) + sum(PG_CSP,1) == sum(PD - PC_Load,1)]; % 式(2)
   
    Cons = [Cons, Branch == GSDF*(M_bus_G*PG_G + M_bus_RE*PG_RE + M_bus_CSP*PG_CSP - (PD-PC_Load))]; % 
%     Cons = [Cons, -branch(:,6)*ones(1,NT) <= GSDF*(M_bus_G*PG_G+M_bus_RE*PG_RE+M_bus_CSP*PG_CSP-(PD- PC_Load)) <= branch(:,6)*ones(1,NT)]; % 
    Cons = [Cons, -999*ones(N_Br,NT) <= GSDF*(M_bus_G*PG_G+M_bus_RE*PG_RE+M_bus_CSP*PG_CSP-(PD-PC_Load)) <= 999*ones(N_Br,NT)]; % 118系统有186条线路
   
    Cons = [Cons, 0 <= PG_RE <= P_RE]; % 可再生出力
 
    Cons = [Cons, [60;50;100;80;40]/baseMVA * ones(1,24) <= PG_G ];
  
    Cons = [Cons, 0 <= PC_Load <= PD]; % 式(22)    
  
    Cons = [Cons, sum(onoff_gen .* (P_Gen_max*ones(1,NT)) - PG_G,1) + ...
            sum(onoff_CSP .* (P_CSP_max*ones(1,NT)) - PG_CSP,1) >= ...
            sum(CoeffReseve_load*PD,1) + sum(CoeffReserve_VRE*PG_RE,1) ];
   
    Cons = [Cons, Cost_StartUp >= (onoff_gen(:,2:NT) - onoff_gen(:,1:NT-1)) .* (c_ST_g*ones(1,NT-1))]; % 传统机组启动成本
    Cons = [Cons, Cost_StartUp >= 0];
    
%%%%%% CSP电站运转内部约束 %%%%%%
    E_TES_max = Capacity_TES_CSP * P_CSP_max; 
   
    Cons = [Cons, PG_CSP/yita_PB + Pt_TES_charge - Pt_TES_discharge <= PtCSP_fore]; % CSP输出电功率与TES充/放热功率,预测光热功率关系
  
    Cons = [Cons, Et_TES(:,2:NT) == Et_TES(:,1:NT-1) + Pt_TES_charge(:,1:NT-1)*yita_TES - Pt_TES_discharge(:,1:NT-1)/yita_TES];
  Cons = [Cons, Et_TES(:,1) == TES_initial * E_TES_max]; 
    Cons = [Cons, Et_TES(:,1) == Et_TES(:,NT)];          
   
    Cons = [Cons, 0 <= Pt_TES_charge    <= Capacity_TES_CSP*ones(N_CSP,NT)]; 
    Cons = [Cons, 0 <= Pt_TES_discharge <= Capacity_TES_CSP*ones(N_CSP,NT)];
  
    Cons = [Cons, 0 <= Et_TES <= E_TES_max * ones(1,NT)];
​
%% 目标函数 
    obj = sum(c_G_g'*PG_G) + sum(c_CSP_g'*PG_CSP) + sum(sum(Cost_StartUp) + beta_Load*sum(sum(PC_Load)) ); 
    % 机组的边际发电成本 + 启动成本 + 负荷削减成本
    
    % 运行调度 
    ops = sdpsettings('solver','cplex'); %  gurobi
    ans = optimize(Cons,obj,ops)
    
%% 求解成功后取值
  PG_G = value(PG_G)  ; 
    PG_RE = value(PG_RE) ;  
    PG_CSP = value(PG_CSP) ; 
    PC_Load = value(PC_Load) ;   
    onoff_gen = value(onoff_gen) ; 
    onoff_CSP = value(onoff_CSP) ; 
    Branch = value(Branch) ;   
    Cost_StartUp  = value(Cost_StartUp);
    obj = value(obj); % 总成本
    Pt_TES_charge = value(Pt_TES_charge);   
    Pt_TES_discharge = value(Pt_TES_discharge); 
    Et_TES = value(Et_TES);                 
    
disp(['IEEE14 不考虑N-k的和无CSP的经济调度情况,运行成本为 ', num2str(obj)])
%% 绘图 
% 已知的相关输入数据
    figure
    subplot(3,1,1)
    plot(PtCSP_fore * baseMVA,'m-o');
  title('CSP预测功率值')
  xlabel('时间(h)');
    ylabel('功率(MW)');
    
    subplot(3,1,2)
    plot(P_RE(1,:) * baseMVA,'m-o'); hold on
    plot(P_RE(2,:) * baseMVA,'b-s');
  title('可再生能源预测出力值')
  xlabel('时间(h)');
    ylabel('功率(MW)');
    legend('光伏','风电')
    
    subplot(3,1,3)
    plot(sum(PD) * baseMVA,'r-v');
  title('24h负荷值')
  xlabel('时间(h)');
    ylabel('功率(MW)');
    
    
​
    
%    subplot(2,1,2)
%  bar(baseMVA*PG_RE',0.75,'stack'); hold on; % 各PV、Wind机组出力
%    legend('PV','Wind')
%    title('电网中可再生能源机组出力')
%  xlabel('时间(h)');
%    ylabel('功率(MW)');
    
%    figure
%    surf(baseMVA*PC_Load);
%    title('负荷削减量')
%  xlabel('时间(h)');
%    ylabel('功率(MW)');
​
​

3 部分结果

4 下载链接