Appilied energy论文复现：计及光伏电站快速无功响应特性的分布式电源优化配置方法程序代码！

本程序参考Applied energy论文《Optimal siting and sizing of distributed generation in distribution systems with PV solar farm utilized as STATCOM (PV-STATCOM)》，文中主要对光伏电站、微燃机等分布式电源进行优化配置，程序较为简单和基础，具有较强的可扩展性和适用性，注释清晰，干货满满，下面对文章和程序作简要介绍。

创新点：

1. 在分布式电源的优化配置问题中计及了光伏电站的快速无功响应特性，以体现PV-STATCOM这一新技术对分布式电源配置方案的影响，进而有效响应了近年来因产业升级而日渐增加的敏感负荷的用电需求。

2. 选取了光伏电站、微型燃气轮机两种典型的分布式电源进行优化配置问题的研究，通过构建加权电压支撑能力指标以表征配电系统中光伏电站对敏感负荷节点的电压支撑能力，并将其嵌入到分布式电源优化配置模型中以求解最优的分布式电源安装位置和安装容量，以及对应的电压暂降过程仿真，充分证明了本研究的价值和意义。

文中结果：

程序结果：

部分程序：

%计算电压支撑能力指标
% Program for Newton-Raphson Load Flow Analysis..
nbus = 33;                  
mpc=IEEE33BW;
T=24;
nb=33;
nl=32;
N=5;%光伏断面数量
Wref=0;%电力支撑指标下限
pref=0;%光伏渗透率约束下限
rmt=0.0001;%微燃机出力下限
dw_pv=[1 3 8 5 2];%每个光伏区间单位光伏有功出力
Y =[8.60890545517020 - 4.38848759645336i,-8.60890545517020 + 4.38848759645336i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 00.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,-0.675684973458593 + 0.889394050182110i,1.61983928437771 - 1.72970736243838i,-0.944154310919121 + 0.840313312256273i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i;0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.638181753905898i,1.15270060498254 - 1.01042169531650i,-0.278801443624791 + 0.372239941410601i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i;0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i;0.00000000000000 + 0.00000000000000i,-3.19139102810467 + 3.04544326767306i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i;0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.000.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000.00000000000000i,0.00000000000000 + 0.00000000000000i;0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,-0.685901016646612 + 0.541617384080303i,1.37813650857855 - 1.08327620483196i,-0.692235491931937 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,-0.692235491931937 + 0.541658820751653i,0.692235491931937 - 0.541658820751653i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i;0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,-3.91132581228411 + 1.99227137433585i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,-2.79428122129950 + 1.42270405602406i,3.32556722153864 - 1.89112873819902i,-0.531286000239134 + 0.468424682174957i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.0007 + 0.615869856836191i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i;0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.0000.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000.513100757068179i,1.88471913450910 - 2.10469649825879i,-1.36554428748186 + 1.59159574119061i,0.00000000000000 + 0.00000000000000i;0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,0.00000000000000 + 0.00000000000000i,-0.858092532269815 + 1.33419548565823i,0.858092532269815 - 1.33419548565823i];          % Calling ybusppg.m to get Y-Bus Matrix..
busd =[1,1,1,0,0,0,0,0,0,0;
    2,3,1,0,0,0,0.100000000000000,0.0600000000000000,0,0;
    3,3,1,0,0,0,0.0900000000000000,0.0400000000000000,0,0;
    4,3,1,0,0,0,0.120000000000000,0.0800000000000000,0,0;
    5,3,1,0,0,0,0.0600000000000000,0.0300000000000000,0,0;
    6,3,1,0,0,0,0.0600000000000000,0.0200000000000000,0,0;
    7,3,1,0,0,0,0.200000000000000,0.100000000000000,0,0;
    8,3,1,0,0,0,0.200000000000000,0.100000000000000,0,0;
    9,3,1,0,0,0,0.0600000000000000,0.0200000000000000,0,0;
    10,3,1,0,0,0,0.0600000000000000,0.0200000000000000,0,0;
    11,3,1,0,0,0,0.0450000000000000,0.0300000000000000,0,0;
    12,3,1,0,0,0,0.0600000000000000,0.0350000000000000,0,0;
    13,3,1,0,0,0,0.0600000000000000,0.0350000000000000,0,0;
    14,3,1,0,0,0,0.120000000000000,0.0800000000000000,0,0;
    15,3,1,0,0,0,0.0600000000000000,0.0100000000000000,0,0;
    16,3,1,0,0,0,0.0600000000000000,0.0200000000000000,0,0;
    17,3,1,0,0,0,0.0600000000000000,0.0200000000000000,0,0;
    18,3,1,0,0,0,0.0900000000000000,0.0400000000000000,0,0;
    19,3,1,0,0,0,0.0900000000000000,0.0400000000000000,0,0;
    20,3,1,0,0,0,0.0900000000000000,0.0400000000000000,0,0;
    21,3,1,0,0,0,0.0900000000000000,0.0400000000000000,0,0;
    22,3,1,0,0,0,0.0900000000000000,0.0400000000000000,0,0;
    23,3,1,0,0,0,0.0900000000000000,0.0500000000000000,0,0;
    24,3,1,0,0,0,0.420000000000000,0.200000000000000,0,0;
    25,3,1,0,0,0,0.420000000000000,0.200000000000000,0,0;
    26,3,1,0,0,0,0.0600000000000000,0.0250000000000000,0,0;
    27,3,1,0,0,0,0.0600000000000000,0.0250000000000000,0,0;
    28,3,1,0,0,0,0.0600000000000000,0.0200000000000000,0,0;
    29,3,1,0,0,0,0.120000000000000,0.0700000000000000,0,0;
    30,3,1,0,0,0,0.200000000000000,0.600000000000000,0,0;
    31,3,1,0,0,0,0.150000000000000,0.0700000000000000,0,0;
    32,3,1,0,0,0,0.210000000000000,0.100000000000000,0,0;
    33,3,1,0,0,0,0.0600000000000000,0.0400000000000000,0,0];      % Calling busdatas..
BMva = 100;                 % Base MVA..
bus = busd(:,1);            % Bus Number..
type = busd(:,2);           % Type of Bus 1-Slack, 2-PV, 3-PQ..
V = busd(:,3);              % Specified Voltage..
del = busd(:,4);            % Voltage Angle..
    Pg = busd(:,5)/BMva;        % PGi..
    Qg = busd(:,6)/BMva;        % QGi..
    Pl = busd(:,7)/BMva;        % PLi..
    Ql = busd(:,8)/BMva;        % QLi..
    Qmin = busd(:,9)/BMva;      % Minimum Reactive Power Limit..
    Qmax = busd(:,10)/BMva;     % Maximum Reactive Power Limit..
P = Pg - Pl;                % Pi = PGi - PLi..
Q = Qg - Ql;                % Qi = QGi - QLi..
Psp = P;                    % P Specified..
Qsp = Q;                    % Q Specified..
G = real(Y);                % Conductance matrix..
B = imag(Y);                % Susceptance matrix..

pv = find(type == 2 | type == 1);   % PV Buses..
pq = find(type == 3);               % PQ Buses..
npv = length(pv);                   % No. of PV buses..
npq = length(pq);                   % No. of PQ buses..

Tol = 1;  
Iter = 1;
while (Tol > 1e-5)  % Iteration starting..
    
    P = zeros(nbus,1);
    Q = zeros(nbus,1);
    % Calculate P and Q
    for i = 1:nbus
        for k = 1:nbus
            P(i) = P(i) + V(i)* V(k)*(G(i,k)*cos(del(i)-del(k)) + B(i,k)*sin(del(i)-del(k)));
            Q(i) = Q(i) + V(i)* V(k)*(G(i,k)*sin(del(i)-del(k)) - B(i,k)*cos(del(i)-del(k)));
        end
    end

    % Checking Q-limit violations..
    if Iter <= 7 && Iter > 2    % Only checked up to 7th iterations..
        for n = 2:nbus
            if type(n) == 2
                QG = Q(n)+Ql(n);
                if QG < Qmin(n)
                    V(n) = V(n) + 0.01;
                elseif QG > Qmax(n)
                    V(n) = V(n) - 0.01;
                end
            end
         end
    end
    
    % Calculate change from specified value
    dPa = Psp-P;
    dQa = Qsp-Q;
    k = 1;
    dQ = zeros(npq,1);
    for i = 1:nbus
        if type(i) == 3
            dQ(k,1) = dQa(i);
            k = k+1;
        end
    end
    dP = dPa(2:nbus);
    M = [dP; dQ];       % Mismatch Vector
    
    % Jacobian
    % J1 - Derivative of Real Power Injections with Angles..
    J1 = zeros(nbus-1,nbus-1);
    for i = 1:(nbus-1)
        m = i+1;
        for k = 1:(nbus-1)
            n = k+1;
            if n == m
                for n = 1:nbus
                    J1(i,k) = J1(i,k) + V(m)* V(n)*(-G(m,n)*sin(del(m)-del(n)) + B(m,n)*cos(del(m)-del(n)));
                end
                J1(i,k) = J1(i,k) - V(m)^2*B(m,m);
            else
                J1(i,k) = V(m)* V(n)*(G(m,n)*sin(del(m)-del(n)) - B(m,n)*cos(del(m)-del(n)));
            end
        end
    end
    
    % J2 - Derivative of Real Power Injections with V..
    J2 = zeros(nbus-1,npq);
    for i = 1:(nbus-1)
        m = i+1;
        for k = 1:npq
            n = pq(k);
            if n == m
                for n = 1:nbus
                    J2(i,k) = J2(i,k) + V(n)*(G(m,n)*cos(del(m)-del(n)) + B(m,n)*sin(del(m)-del(n)));
                end
                J2(i,k) = J2(i,k) + V(m)*G(m,m);
            else
                J2(i,k) = V(m)*(G(m,n)*cos(del(m)-del(n)) + B(m,n)*sin(del(m)-del(n)));
            end
        end
    end
    
    % J3 - Derivative of Reactive Power Injections with Angles..
    J3 = zeros(npq,nbus-1);
    for i = 1:npq
        m = pq(i);
        for k = 1:(nbus-1)
            n = k+1;
            if n == m
                for n = 1:nbus
                    J3(i,k) = J3(i,k) + V(m)* V(n)*(G(m,n)*cos(del(m)-del(n)) + B(m,n)*sin(del(m)-del(n)));
                end
                J3(i,k) = J3(i,k) - V(m)^2*G(m,m);
            else
                J3(i,k) = V(m)* V(n)*(-G(m,n)*cos(del(m)-del(n)) - B(m,n)*sin(del(m)-del(n)));
            end
        end
    end

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