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  重庆大学学报  2017, Vol. 40 Issue (2): 70-79  DOI: 10.11835/j.issn.1000-582X.2017.02.010 RIS(文献管理工具)
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谢维兵, 刘敏, 周晓霞, 敬勇, 叶玲, 王强钢, 周念成. 含电压逆变型分布式电源配电网的短路电流计算[J]. 重庆大学学报, 2017, 40(2): 70-79. DOI: 10.11835/j.issn.1000-582X.2017.02.010.
XIE Weibing, LIU Min, ZHOU Xiaoxia, JING Yong, YE Ling, WANG Qianggang, ZHOU Niancheng. Short-circuit current calculation of inverter interfaced distributed generator based on voltage control in distribution network[J]. Journal of Chongqing University, 2017, 40(2): 70-79. DOI: 10.11835/j.issn.1000-582X.2017.02.010. .

作者简介

谢维兵(1970-), 男, 副教授, 主要从事电力系统的研究工作。

文章历史

收稿日期: 2016-09-01
含电压逆变型分布式电源配电网的短路电流计算
谢维兵1, 刘敏1, 周晓霞1, 敬勇1, 叶玲2, 王强钢2, 周念成2     
1. 国网重庆市电力公司技能培训中心, 重庆 400044;
2. 重庆大学 输配电装备及系统安全与 新技术国家重点实验室, 重庆 400044
摘要: 分布式发电接入改变了配电网潮流和短路电流分布,其提供的短路电流将对电网保护和重合闸动作产生影响。文中通过研究电压控制逆变型分布式电源(ⅡDG)的故障响应特性,分析配电网不对称故障时ⅡDG三相平均功率与正负序网功率关系,建立计及电压型ⅡDG对称控制特征的短路计算序分量模型。根据ⅡDG与配电网正负序网络的交互作用,推导电压型ⅡDG的故障电流变化规律,提出计算含电压型ⅡDG配电网短路电流的对称分量迭代算法。在PSCAD/EMTDC仿真软件中建立电压型ⅡDG的电磁暂态模型,仿真验证了该方法的正确性。
关键词: 逆变型分布式电源    电压控制    故障分析    对称分量    配电网    
Short-circuit current calculation of inverter interfaced distributed generator based on voltage control in distribution network
XIE Weibing1 , LIU Min1 , ZHOU Xiaoxia1 , JING Yong1 , YE Ling2 , WANG Qianggang2 , ZHOU Niancheng2     
1. Power Supply Bureau Skills Training Center of Chongqing, Chongqing 400044, P. R. China;
2. State Key Laboratory of Power Transmission Equipment & System Security and New Technology, Chongqing 400044, P. R. China
Abstract: The distribution of power flow and short-circuit current is changed by the distributed generation embedded in distribution network, and its short-circuit current affects the operation of protection and reclosing devices. The fault response characteristics of voltage controlled inverter interfaced distributed generator (ⅡDG) were studied, and the relationship between ⅡDG three-phase power and power components in the positive and negative sequence networks under asymmetrical fault condition were also analyzed. Then a sequence component model of voltage controlled ⅡDG for short-circuit current calculation was established. The fault current change law and recursion formula were gained according to the interaction between the ⅡDG and the sequence networks, and consequently the iterative algorithm of symmetrical components for short-circuit current calculation of distribution network with voltage controlled ⅡDG was proposed. The correctness of the proposed method was verified by the electromagnetic transient model of voltage controlled ⅡDG in PSCAD/EMTDC simulation software.
Key Words: inverter interfaced distributed generator    voltage control    fault analysis    symmetrical component    distribution network    

分布式发电接入改变了配电网潮流和短路电流分布[1-2],其与电网保护重合闸存在不匹配问题[3]。逆变型分布式电源(inverter interfaced distributed generator,IIDG)以快速灵活的控制性能,在配电网分布式发电中应用广泛。并网运行IIDG通常采用恒功率控制,按内环跟踪电量的不同,可将IIDG控制器分成电压控制型和电流控制型[4](简称电压型或电流型)。与同步发电机相比,IIDG具有不同的故障特征[2],对于电压型IIDG其在配电网短路后将出现典型的次暂态和暂态过程[5]。IIDG接入配电网的故障分析是电网保护整定和稳定运行的基础,但采用IEC60909等标准的等值电压源法进行计算存在较大的误差[6],因此,需要研究含电压型IIDG配电网故障电流的解析计算方法。

时域仿真是研究IIDG故障特性的常用方法[7],但时域仿真耗时且难以得到解析解。文献[8]研究IIDG对配电网三相短路的故障电流稳态响应;文献[9]提出含DG配电网故障计算的叠加法,但没有考虑IIDG控制的动态过程。文献[10-11]认为电流型IIDG短路电流呈指数规律变化,仅根据配电网故障前后IIDG稳态电流计算其动态响应,无法确定故障电流越限时刻并且误差较大。电流型IIDG故障后的暂态冲击电流小,对配电网短路水平影响有限,文献[5]针对电压型IIDG的控制传递函数和故障中输出功率的变化,建立了IIDG短路计算的相分量模型。由于采用序分量法进行短路计算能够有效减小相分量法的复杂性和求解规模,而现有的IIDG控制策略中多采用对称控制[5, 12],因此,建立IIDG短路计算的序分量解析模型,更有利于IIDG控制方式与配电网故障分析方法的结合。

笔者研究了配电网故障时电压型IIDG的动态特性及其与正负序网络的交互作用关系,分析电压型IIDG的短路电流变化规律,建立了计及控制特性的电压型IIDG短路计算序分量模型,提出了含电压型IIDG配电网短路计算的对称分量迭代算法。在PSCAD/EMTDC中利用电压型IIDG电磁暂态模型进行动态仿真,验证了本文提出方法的正确性。

1 电压型IIDG序分量模型及故障分析 1.1 电压型IIDG短路计算序分量模型

配电网不同位置接入多台电压型IIDG,如图 1(a)所示为仅在节点i接入电压型IIDG,节点1为配电网与主网的连接点,EsZs分别为主网电源电压和短路阻抗。由图 1电压型IIDG控制结构可知,测量元件采集电压、电流信号计算IIDG输出功率测量值PgQg,分别与功率设定值比较经PI调节得到IIDG内电势的相角δ和幅值Em,再由锁相环和电压控制内环调节IIDG内电势[4]。对于电压型IIDG可将其等效成电压源接入配电网,从而可得图 2所示的含电压型IIDG配电网等值电路。

图 1 电压型IIDG控制模型 Figure 1 Control model of voltage controlled IIDG
图 2 含电压型IIDG配电网等值电路 Figure 2 Equivalent circuit of distribution network with a voltage controlled IIDG

含电压型IIDG配电网由IIDG物理电路、IIDG控制系统和网络方程3部分构成闭环系统,图 2ZtZfCf分别为升压变压器短路阻抗、IIDG滤波阻抗和滤波电容,Egugig分别为IIDG等值内电势、机端电压和电流,短路电流计算时忽略滤波电容。配电网中一般采用中性点不接地或经消弧线圈接地,研究中无需计及零序电压分量[13],研究中将IIDG物理电路分解成与正负序网络对应的正负序分量模型。

电压型IIDG控制电路如图 1(a)所示,其采用功率外环电压内环的控制策略,配电网故障时先由IIDG端电压和电流的正负序分量ug1ug1ig1ig2得到三相功率,再经PI传递函数生成IIDG内电势设定值,根据电压对称控制可得序网中IIDG正序内电势幅值和相位(负序内电势为0),代入正负序网即可计算IIDG短路电流序分量。逆变器的电压跟踪内环及闭锁控制框图如图 1(b),利用电压反馈比例调节外环使逆变器网侧电压跟踪参考值,再与电容电流测量值比较构成电容电流内环,经电流内环比例环节ki后生成三相调制信号mabc

此外,当IIDG故障电流中任一相电流超过热极限电流(一般为额定电流的1.5~2倍)时,根据图 1(b)的闭锁控制,IIDG保护动作发出闭锁信号使变流器快速闭锁[14],切除后无故障电流注入配电网[5]。笔者提出的IIDG故障电流对称分量法针对IIDG故障电流未超出电流限值的情况,故障过程中其电压内环仍可实现内电势的跟踪控制。

1.2 配电网不对称故障时IIDG三相功率

IIDG三相瞬时功率由其端电压矢量ug=(uga,ugb,ugc)和电流矢量ig=(iga,igb,igc)决定[13],即三相有功功率pg=ug·ig和无功功率qg=|ug×ig|。当配电网不对称故障时有ug=ug1+ug2ig=ig1+ig2,且设ug1=Ug1eu1ejωt、ig1=Ig1ei1ejωt、ug2=Ug2ejθ2uejωt、ig2=Ig2ei2ejωt则瞬时有功功率为

$\eqalign{ & {p_g} = {\mathit{\boldsymbol{u}}_g}\mathit{\boldsymbol{\cdot}}{\mathit{\boldsymbol{i}}_g} = {U_g}^1{I_g}^1cos({\theta _u}^1{\theta _i}^1) + {U_g}^2{I_g}^2cos({\theta _u}^2{\theta _i}^2) + \cr & {U_g}^1{I_g}^2(2\omega t + {\theta _u}^1{\theta _i}^2) + \cr & {U_g}^2{I_g}^1cos(2\omega t + {\theta _u}^2{\theta _i}^1) = {P_g}^1 + {P_g}^2 + {p_{2\omega }}^{12} + {p_{2\omega }}^{21} \cr} $ (1)

式中:Pg1和Pg2为瞬时有功直流分量;p2ω12和p2ω21为有功倍频分量,有功倍频分量在半周波的整数倍时间内的均值为0。三相功率为瞬时有功的半周平均值为 Pg=Ug1Ig1cos(θu1θi1)+Ug2Ig2cos(θu2θi2)=Pg1+Pg2

${P_g} = {U_g}^1{I_g}^1cos({\theta _u}^1 - {\theta _i}^1) + {U_g}^2{I_g}^2cos({\theta _u}^2{\theta _i}^2) = {P_g}^1 + {P_g}^2$ (2)

由于序电压电流矢量外积ug1×ig1和ug2×ig2反向,可得三相无功功率平均值为

$\eqalign{ & {Q_g} = {u_g}^1 \times {i_g}^1 + {u_g}^2 \times {i_g}^2 = {u_g}^1 \times {i_g}^1{u_g}^2 \times {i_g}^2 = \cr & {U_g}^1{I_g}^1sin({\theta _u}^1{\theta ^1}_i){U_g}^2{I_g}^2sin({\theta _u}^2{\theta _i}^2) = {Q_g}^1{Q_g}^2 \cr} $ (3)
1.3 电压型IIDG稳态运行点及短路计算原理

假设图 2中配电网含n个节点,并有m台电压型IIDG接入配电网。取节点1为主网等值电源点,节点2至(m+1)为电压型IIDG接入节点。对于第i台电压型IIDG,节点i的戴维南等效电路如图 3所示,其中等值电势为节点i的开路电压${\dot U}$ioc,等值内阻抗即为节点i的自阻抗Zii,节点i开路电压[15]

图 3m台电压型IIDG配电网的节点i戴维南等值电路 Figure 3 Thevenin equivalent circuit of node i in distribution network with m sets of voltage controlled IIDG
${{\dot U}_{ioc}} = \mathop \sum \limits_{j = 1,j \ne i}^{m + 1} {Z_{ij}}{{\dot I}_j} = {Z_{i1}}{{\dot I}_{s1}} + \mathop \sum \limits_{j = 2,j \ne i}^{m + 1} {Z_{ij}}{{\dot I}_{gj}},{\rm{ }}i = 2, \ldots ,m + 1$ (4)

式中${\dot I}$s1=${\dot E}$s/Zs和${\dot I}$gj分别为电源点的诺顿等值电流和第j台IIDG注入电流。正常运行时并网IIDG采用恒功率控制,根据图 3等值电路、式(4)和Pgi+jQgi=${\dot U}$gi${\dot I}$gi*即可计算含m台IIDG配电网的稳态运行点。

以IEEE-34节点配电网接入3台电压型IIDG为例,配电馈线末端三相故障时各台IIDG端电压如图 4(a)所示,可见IIDG端电压跌落过程中未出现明显暂态电压分量,由于PQ控制的响应时间快于网络的固有衰减时间常数[16],因此,暂态分量不明显,故障后IIDG等效电路的开路电压阶跃变化至故障稳态值。

图 4(b)给出了电压型IIDG对配电网三相短路的动态响应,短路后IIDG端电压跌落,其输出电流Ig出现峰值,之后逐渐衰减变化至稳态故障电流。电压型IIDG内电势由控制器和配电网共同决定(图 1),为实现IIDG控制与网络方程的解耦计算,设Δt时间间隔(取Δt=0.01 s计算电流有效值)内电势保持不变,即IIDG内电势随时间近似为阶跃变化规律。

图 4 配电网三相故障时IIDG电压和电流 Figure 4 Voltage and current of IIDG when three-phase short-circuit occurs at distribution grid

由于电压型IIDG控制器的电流内环调节速率快于功率外环,使得图 4中内电势在第1个Δt内与故障前基本一致。对于第i台电压型IIDG,设故障后开路电压由${\dot U}$ioc变化至${\dot U}$iocs,且各步长的IIDG内电势为${\dot E}$gi(0),${\dot E}$gi(1),…,${\dot E}$gi(k),…。含电压型IIDG配电网短路计算时,先由${\dot E}$gi(1)=${\dot E}$gi(0)计算第1个Δt内IIDG的故障峰值电流。在第2个Δt后IIDG的内电势依次发生阶跃变化,根据图 3可计算第k个Δt内电压型IIDG故障输出电流的稳态正弦分量为

${{\dot I}_{gi\left( k \right)s}} = {{{{\dot E}_{gi(k)}} - {{\dot U}_{iocs}}} \over {{Z_{ii}} + {Z_{gi}}}} = {{{{\dot E}_{gi(k)}} - {{\dot U}_{iocs}}} \over {{Z_{ii}} + {Z_{gi}}}} = {I_{gi\left( k \right)s}}{e^{{\theta _{is}}}}$ (5)

若上式中稳态电流瞬时值满足余弦特性,当t=0时配电网发生故障,则第k个Δt内IIDG的故障电流响应为

${i_{gi(k)}}\left( t \right) = ({I_{gi(k1)}}{\rm{cos}}{\theta _i}{I_{gi\left( k \right)s}}{\rm{cos}}{\theta _{is}}){e^{t/{\tau _{gi}}}} + {I_{gi\left( k \right)s}}{\rm{cos}}(\omega t + {\theta _{is}})$ (6)

其中τgi为第i台IIDG衰减时间常数,由网络参数可计算得到;θiθis分别为IIDG故障电流瞬时和稳态值的相角,由式(6)可得第k个Δt内IIDG故障电流的有效值为

${I_{gi(k)}}\left( t \right) = \sqrt {{{[({I_{gi(k1)}}{\rm{cos}}{\theta _i}{I_{gi\left( k \right)s}}{\rm{cos}}{\theta _{is}}){e^{t/{\tau _{gi}}}}]}^2} + {{({I_{gi\left( k \right)s}})}^2}} $ (7)
图 5 电压型IIDG故障电流变化规律 Figure 5 Fault current of voltage controlled IIDG

当Δt较小时Ig(k)(t)≈(Igi(k-1)cos θi-Igi(k)scos θis)e-t/τgi+ Igi(k)s,对于第i台电压型IIDG,其故障电流在每个Δt内均近似按时间常数τgi呈指数衰减变化,其在各Δt内IIDG的输出有功和无功功率亦近似呈现指数规律变化。

式(7)中取tt时可得第k个Δt末端的IIDG故障电流Igi(k)t),如图 5所示,将其作为第k+1个步长的起始电流。再利用IIDG的控制策略更新其内电势,结合网络方程计算第k+1个步长的稳态电流Igi(k+1)s。据此利用IIDG故障电流在Δt内指数衰减规律,即可计算下一时刻的IIDG故障电流。

2 含电压型IIDG配网短路计算对称分量法 2.1 IIDG故障电流初始值计算

利用1.3节方法和配电网原节点阻抗矩阵计算正常运行时各IIDG端电压${\dot U}$gi(0)和电流${\dot I}$gi(0),再由${\dot E}$gi(0)=${\dot U}$gi(0)+Zgi${\dot I}$gi(0)可得电压型IIDG故障前的内电势。配电网短路后,在原节点阻抗矩阵中追加IIDG正负序阻抗,形成新的n×n阶正负节点阻抗矩阵Z1Z2,可得配电网正常运行时各节点电压为

${{\dot U}_{(0)}} = {Z^1}{{\dot I}_{(0)}} = {Z^1}{\left[ {{{\dot I}_{s1}},{{\dot I}_{2(0)}}, \ldots ,{{\dot I}_{m + 1(0)}},0, \ldots ,0} \right]^T}$ (8)

其中${\dot I}$i(0)=${\dot E}$gi(0)/Zgi为第i台电压型IIDG正序诺顿电路的等值电流。当配电网节点f发生不对称故障时,以a相经阻抗zf短路接地为例,由于第1个迭代步长中${\dot E}$gi(1)=${\dot E}$gi(0),此时节点电压正常分量与故障前配电网节点电压相等${\dot U}$o(1)=${\dot U}$(0),则第1个步长的故障电流序分量为

${{\dot I}^1}_{f(1)} = {{\dot I}^2}_{f(1)} = {{{{\dot U}^1}_{f(0)} + {{\dot U}^2}_{f(0)}} \over {{Z^1}_{ff} + {Z^2}_{ff} + {z_f}}}$ (9)

根据故障分析叠加原理,计算正负序故障分量网络中各节点电压为

$\eqalign{ & \Delta {{\dot U}^1}_{(1)} = {Z^1}_{1f}, \ldots ,{Z^1}_{if} \ldots ,{Z^1}{_{nf}^T}\left( {{{\dot I}^1}_{f(1)}} \right), \cr & \Delta {{\dot U}^2}_{(1)} = {Z^2}_{1f}, \ldots ,{Z^2}_{if} \ldots ,{Z^2}{_{nf}^T}({{\dot I}^2}_{f(1)}) \cr} $ (10)

配电网正常运行时三相对称,第1个迭代步长中网络无负序电压正常分量,故障后各节点电压序分量为${\dot U}$(1)1=${\dot U}$o(1)+Δ${\dot U}$(1)1和${\dot U}$(1)2=Δ${\dot U}$(1)2,则配电网中第i台电压型IIDG故障峰值电流的正负序分量为

$\eqalign{ & {{\dot I}^2}_{gi(1)}{\rm{ = }}{{{{\dot E}^2}_{gi(1)} - {{\dot U}^2}_{i(1)}} \over {{Z^2}_{gi}}} = {{0 - {{\dot U}^2}_{i(1)}} \over {{Z^2}_{gi}}}, \cr & {{\dot I}^2}_{gi(1)} = {{{{\dot E}^2}_{gi(1)}{{\dot U}^2}_{i(1)}} \over {{Z_{gi}}^2}} = {{0 - {{\dot U}^2}_{i(1)}} \over {{Z_{gi}}^2}},i = 2, \ldots ,m + 1 \cr} $ (11)
2.2 电压型IIDG内电势序分量迭代计算

图 1功率外环PI传递函数为GPIP(s)=kpP+kiP/s和GPIQ(s)=kpQ+kiQ/s,且第k-1个步长内IIDG电势的相角和幅值为δ(k-1)和Em(k-1)。由于功率偏差dPg和dQg经PI调节后更新内电势相角和幅值,则第i台IIDG内电势的相角和幅值递推公式为

$\eqalign{ & {\delta _{i(k)}} = {\delta _{i(k - 1)}} + {k_p}^P(d{P_{gi(k)}} - d{P_{gi(k1)}}) + {{{k_i}^P\Delta t} \over 2}\cdot(d{P_{gi(k)}} + d{P_{gi(k - 1)}}), \cr & i = 2, \ldots ,m + 1, \cr & {E_{mi(k)}} = {E_{mi(k - 1)}} + {k_p}^Q(d{Q_{gi(k)}} - d{Q_{gi(k - 1)}}) + {{{k_i}^Q\Delta t} \over 2}\cdot(d{Q_{gi(k)}} + d{Q_{gi(k - 1)}}), \cr & i = 2, \ldots ,m + 1, \cr} $ (12)

三相电压经对称分解得到电压型IIDG在正负序网电势${\dot E}$gi(k)1=Emi(k)1ei1(k)和${\dot E}$gi(k)2=Emi(k)2ei2(k),研究中电压型IIDG采用对称控制[5, 12],其三相电压仅包含正序分量即${\dot E}$gi(k)1=Emi(k)ei(k)和${\dot E}$gi(k)2=0。

2.3 IIDG故障电流序分量迭代计算

为计算电压型IIDG的故障稳态电流,若配电网故障时IIDG的内电势恒为${\dot E}$gi(k)1,根据式(8)-(10)可得故障网络节点稳态电压的正常分量${\dot U}$o(k)s1和故障分量Δ${\dot U}$(k)s1、Δ${\dot U}$(k)s2。由叠加原理计算第k个步长的故障稳态电压${\dot U}$(k)s1=${\dot U}$o(k)s1+Δ${\dot U}$(k)s1和${\dot U}$(k)s2=Δ${\dot U}$(k)s2,从而得第k个步长中电压型IIDG的故障稳态电流和功率计算公式为

$\eqalign{ & {{\dot I}^1}_{gi\left( k \right)s} = {{{{\dot E}^1}_{gi(k)}{{\dot U}^1}_{i\left( k \right)s}} \over {{Z_{gi}}^1}},{\rm{ }}{{\dot I}^2}_{gi\left( k \right)s} = {{0 - {{\dot U}^2}_{i\left( k \right)s}} \over {{Z_{gi}}^2}}, \cr & \left[ \matrix{ {P^1}_{gi(k)s} \hfill \cr {P^2}_{gi(k)s} \hfill \cr} \right] + {\rm{j}}\left[ \matrix{ {Q^1}_{gi(k)s} \hfill \cr {Q^2}_{gi(k)s} \hfill \cr} \right] = \left[ \matrix{ {{\dot U}^1}_{i\left( k \right)s}{\left( {{{\dot I}^1}_{gi\left( k \right)s}} \right)^*} \hfill \cr {{\dot U}^2}_{i\left( k \right)s}{\left( {{{\dot I}^2}_{gi\left( k \right)s}} \right)^*} \hfill \cr} \right],i = 2, \cdots m + 1 \cr} $ (13)

由于第k-1次迭代过程的IIDG故障电流有效值Igi(k-1),即为第k次迭代的故障电流起始值,则第k个步长IIDG的故障电流序分量有效值为

$\eqalign{ & {I^1}_{gi(k)} = {I^1}_{gi\left( k \right)s} + \left( {{I^1}_{gi(k1)} - {I^1}_{gi\left( k \right)s}} \right){e^{\Delta t/{\tau ^1}_{gi}}} \cr & {I^2}_{gi(k)} = {I^2}_{gi\left( k \right)s} + ({I^2}_{gi(k1)}{I^2}_{gi\left( k \right)s}){e^{\Delta t/{\tau ^2}_{gi}}},i = 2, \ldots ,m + 1 \cr} $ (14)

式中:τgi1和τgi2分别为第i台IIDG的正序和负序电流衰减时间常数,第k个步长IIDG在正负序网的输出功率为

$\left[ \matrix{ {P^1}_{gi(k)} \hfill \cr {Q^1}_{gi(k)} \hfill \cr} \right] = \left[ \matrix{ {P^1}_{gi\left( k \right)s} \hfill \cr {Q^1}_{gi\left( k \right)s} \hfill \cr} \right] + \left[ \matrix{ {P^1}_{gi(k1)} - {P^1}_{gi\left( k \right)s} \hfill \cr {Q^1}_{gi(k1)} - {Q^1}_{gi\left( k \right)s} \hfill \cr} \right]{e^{\Delta t/{\tau ^1}_{gi}}}$ (15a)
$\left[ \matrix{ {P^2}_{gi(k)} \hfill \cr {Q^2}_{gi(k)} \hfill \cr} \right] = \left[ \matrix{ {P^2}_{gi\left( k \right)s} \hfill \cr {Q^2}_{gi\left( k \right)s} \hfill \cr} \right] + \left[ \matrix{ {P^2}_{gi(k1)} - {P^2}_{gi\left( k \right)s} \hfill \cr {Q^2}_{gi(k1)} - {Q^2}_{gi\left( k \right)s} \hfill \cr} \right]{e^{\Delta t/{\tau ^2}_{gi}}},i = 2, \ldots ,m + 1$ (15b)
2.4 含电压型IIDG配电网故障电流的计算步骤

利用电压型IIDG序分量模型与正负序网络的交互关系,可计算配电网发生不同类型故障时IIDG的故障电流响应。设配电网f节点发生短路故障,则电压型IIDG故障电流的计算步骤如下:

1) 形成原始配网正序和负序网络的n(n阶节点阻抗矩阵Z01和Z02,其中节点编号:节点1为主网电源点,节点2至m+1为电压型IIDG接入节点。

2) 设m台电压型IIDG功率设定值为Pgi+jQ*gi=${\dot U}$gi(0)${\dot I}$*gi(0),联立${\dot U}$gi(0)=${\dot U}$ioc+Zii${\dot I}$gi(0)和式(4),解方程得到m台电压型IIDG在输出功率为设定值时的故障前机端电压${\dot U}$gi(0)和电流${\dot I}$gi(0),计算m台电压型IIDG的故障前内电势${\dot E}$gi(0)

3) 利用Z01和Z02中节点2至m+1的自阻抗和电压型IIDG序分量模型的正负序阻抗,计算m台IIDG的正负序电流衰减时间常数τgi1和τgi2

4) 追加m台IIDG正负序阻抗,形成n×n阶阻抗矩阵Z1和Z2,根据式(8)-(11)计算第1个步长IIDG故障峰值电流${\dot I}$gi(1)1和${\dot I}$gi(1)2,及其平均功率Pgi(1)和Qgi(1),令${\dot I}$gi(k-1)1=${\dot I}$gi(1)1,${\dot I}$gi(k-1)2=${\dot I}$gi(1)2,Pgi(k-1)=Pgi(1),Qgi(k-1)=Qgi(1),进入5)。

5)正常运行时m台电压型IIDG的PI环节初始功率偏差dPi(0)=0和dQi(0)=0,计算第k-1个步长IIDG功率偏差dPgi(k-1)和dQgi(k-1),由式(12)计算第k个步长IIDG电势相角δi(k)和幅值Emi(k),进而得到IIDG正负序网等值电势${\dot E}$gi(k)1和${\dot E}$gi(k)2

6) 将m台IIDG的${\dot E}$gi(k)1和${\dot E}$gi(k)2代入故障正负序网,由叠加原理得到IIDG的稳态故障电压${\dot U}$i(k)s1和${\dot U}$i(k)s2,利用式(13)计算IIDG故障稳态电流${\dot I}$gi(k)s1和${\dot I}$gi(k)s2,以及故障稳态功率Pgi(k)s1、Pgi(k)s2、Qgi(k)s1和Qgi(k)s2

7) 根据式(14)得到m台IIDG故障电流${\dot I}$gi(k)1和${\dot I}$gi(k)2,通过式(15)计算第k个步长IIDG的正负序网功率Pgi(k)1、Pgi(k)2、Qgi(k)1和Qgi(k)2,并由式(2)和式(3)合成IIDG三相平均功率Pgi(k)和Qgi(k)

8) 若迭代次数k≤N(计算IIDG故障后10个周波的电流响应N=20),则k=k+1后转到5);否则故障分析结束,输出m台IIDG故障电流有效值。

3 算例研究

采用提出的算法计算含单台IIDG配电网和2台IIDG的配电网算例发生对称和不对称类型故障时,电压型IIDG的故障电流和内电势响应,比较提出的含IIDG配电网短路计算对称分量算法与PSCAD/EMTDC软件中电压型IIDG电磁暂态模型的动态仿真结果。

3.1 算例1

图 6所示的含单台IIDG的辐射型配电网,图中1.5 MW电压型IIDG的额定电压为0.62 kV,经升压变压器接入10 kV配网的节点3。针对图 6单机配电馈线结构,分别研究节点8发生三相短路和两相短路的两种情况,并分析配电网不对称故障时电压型IIDG的故障电流序分量变化规律。其中,各IIDG参数如表 1所示,系统参数如表 2所示。

图 6 单台电压型IIDG接入配电网结构图 Figure 6 Single line diagram of distribution feeder integrating with a voltage controlled IIDG
表 1 IIDG参数 Table 1 IIDG parameters
表 2 系统参数 Table 2 System parameters

图 78分别为节点8三相短路时IIDG1故障电流和内电势,馈线末端故障后电压型IIDG内电势基本不变而端电压大幅跌落,使得IIDG1出现故障峰值电流。图 7中IIDG电流在第1个步长的衰减速度最快(称为次暂态故障电流),之后10个周波内的电流缓慢衰减至稳态值(称为暂态故障电流)。

图 7 节点8三相短路时IIDG1故障电流变化 Figure 7 Fault current of IIDG1 when three-phase short-circuit occurs at Bus 8
图 8 节点8三相短路时IIDG1内电势变化 Figure 8 Electric potential of IIDG1 when three-phase short-circuit occurs at Bus 8

采用本文算法得到的IIDG1故障电流峰值A和故障电流稳态值B分别为1.72 pu和0.95 pu,动态仿真的结果为1.78pu和0.96pu,即本文提出的算法与图 7所示的仿真结果基本吻合。由图 7图 8还可知配电网对称故障时,提出的对称分量迭代算法与文献[5]相分量法的计算结果相同。

图 9是节点8发生bc两相短路时IIDG1的故障电流正负序分量,图中正序电流Ig1的暂态过程变化较快,故障发生5个周波后即衰减至稳态值。两相短路时IIDG1的负序和正序峰值电流不同,负序电流Ig2达到峰值后衰减至稳态值,其在每个步长内亦近似呈指数规律变化。利用本文的含电压型IIDG配网短路电流对称分量算法,可计算IIDG1的正序电流峰值A1和稳态值B1为0.88 pu和0.50 pu,其负序电流峰值A2和稳态值B2为0.75 pu和0.66 pu。

图 9 节点8两相短路时IIDG1故障序电流变化 Figure 9 Fault current sequence component of IIDG1 when two-phase short-circuit occurs at Bus 8

图 9可见,笔者提出的电压型IIDG短路电流对称分量法的计算结果仅负序峰值电流A2低于仿真结果0.06 pu,其余故障序电流特征值与动态仿真结果一致。图 10为两相短路时故障点的负序电流,由于故障过程中IIDG控制的动态调节,故障点负序电流在故障瞬间也出现峰值电流Af2为24.8 pu,但相对于IIDG故障电流,故障点峰值电流Af2和稳态电流Bf2相差较小。

图 10 节点8两相短路时故障点负序电流变化 Figure 10 Fault current negative sequence component of fault point when two-phase short-circuit occurs at Bus 8

对称分量和相分量算法计算IIDG1输出的b相故障电流和内电势如图 11图 12所示。两种方法的故障电流稳态值相同,对于故障峰值电流,采用对称分量方法的结果为1.51pu,更接近动态仿真结果(文献[5]算法电流峰值为1.46 pu,动态仿真电流峰值为1.61 pu)。由于文献[5]算法迭代中不能得到相电流的相位,无法计算不对称故障时的故障电流正负序分量,而本文提出的算法能够准确计算含电压型IIDG配电网的故障序电流以及各相故障电流。

图 11 节点8两相短路时IIDG1故障b相电流变化 Figure 11 b phase fault current of IIDG1 when two-phase short-circuit occurs at Bus 8
图 12 节点8两相短路时IIDG1内电势变化 Figure 12 Electric potential of IIDG1 when two-phase short-circuit occurs at Bus 8
3.2 算例2

算例2的配电网结构如图 13所示,在算例1的基础上增加一台电压型IIDG接入配电网的节点5(参数见表 1表 2)。当节点8发生bc两相短路时,图 14图 15分别为IIDG1和IIDG2的正负序故障电流响应,可见对于含多IIDGs配电网,本文算法能够准确计算电压型IIDG故障正负序电流。

图 13 两台电压型IIDGs接入配电网结构图 Figure 13 Single line diagram of distribution feeder integrating with two voltage controlled IIDGs
图 14 两机算例中两相短路时IIDG1故障序电流变化 Figure 14 Fault current sequence component of IIDG1 when two-phase short-circuit occurs in two IIDGs system
图 15 两机算例中两相短路时IIDG2故障序电流变化 Figure 15 Fault current sequence component of IIDG2 when two-phase short-circuit occurs in two IIDGs system

两机算例中馈线末端故障时,由于IIDG2位于IIDG1的下游,与故障点的电气距离更近,两相短路后其故障正负序电流大于IIDG1的故障电流。当故障点逐渐向馈线上游移动时,IIDG2的故障电流将首先出现越限,此时IIDG2自身保护动作,配电网中将仅有IIDG1向电网注入故障电流。

4 结 语

笔者研究了配电网不对称故障时电压型IIDG的短路计算序分量模型,分析含电压型IIDG配电网短路计算的原理,提出了计算电压型IIDG故障电流序分量的对称分量算法。通过2个测试算例,用PSCAD/EMTDC软件对算法进行验证,所提出方法能准确计算配电网发生不同类型故障时电压型IIDG的故障电流序分量和相分量,估计电压型IIDG故障正负序电流在暂态过程中的变化趋势。所提出的方法可以加入到传统配电网的短路电流计算中,同时也可计及IIDG的限流约束。

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