CN110943458A - 一种电力系统鲁棒解列方法 - Google Patents
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- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
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Abstract
本发明涉及一种电力系统鲁棒解列方法,其包括步骤:确定解列的目标函数和基本约束条件;构建解列的无功调整约束;构建解列的连通性约束;基于上述步骤构建考虑可再生能源不确定性的可调鲁棒解列模型,获取解列方案。其可以为电力系统运行人员进行主动解列控制提供相应支持。
Description
技术领域
本发明涉及电力系统领域,特别是涉及一种电力系统鲁棒解列方法。
背景技术
主动解列是电力系统稳定运行的最后一道防线,因此系统研究控制孤岛策略,预防停电和连锁故障事件的发生具有重要的理论和现实意义。可控孤岛的本质可以抽象为寻找一组受到各种安全约束的最优孤岛输电断面(即割集),从而将大规模电力系统分解为多个子电力系统,最小化电力中断和不平衡。
发明内容
基于此,本发明提出一种电力系统鲁棒解列方法。
一种电力系统鲁棒解列方法,包括如下步骤:
1)确定解列的目标函数和基本约束条件;
2)构建解列的无功调整约束;
3)构建解列的连通性约束;
4)基于步骤1)、2)、3)构建考虑可再生能源不确定性的可调鲁棒解列模型,获取解列方案。
上述技术方案中,步骤1)中确定解列的目标函数和基本约束条件,具体如下:
切负荷量是评价电力系统功率不平衡程度的一个重要指标,若考虑可再生能源的不确定性,则其不平衡程度会增加。因此,可调鲁棒解列是为了在可再生能源输入最极端的情况下极小化切负荷量
式中:x=[Pup,i,Pdown,i,Qup,i,Qdown,i,PLS,i,QLS,i,QSVC,i,QCB,i]是控制向量,ξ=[Pwind,i, Psolar,i,Qwind,i,Qsolar,i]是不确定参数向量;Ψ是不确定集。Pup,i,Pdown,i,Qup,i,Qdown,i分别是发电机i的上调、下调的有功和无功输出功率。PLS,i和QLS,i分别是节点i 的有功和无功切负荷量,QSVC,i和QCB,i分别是SVC和并联电容器在节点i的总无功补偿。Pwind,i,Qwind,i,Psolar,i,Qsolar,i分别是风电和光伏的有功、无功输出功率。Nbus是节点的数量。
节点注入功率与节点输出功率应当是相等的,因此功率平衡方程可以表示为:
式中:Pi和Qi是节点i的有功和无功注入功率,PL,i和QL,i分别是节点i出的有功和无功负荷,Pij和Qij分别是节点i到节点j的线路Li-j上流过的有功和无功潮流, Pgen,i和Qgen,i分别是发电机在节点i的有功和无功注入功率。Vi,θi,Vj,θj分别是节点i和j的电压幅值和相角;Gij和Bij分别是Li-j的电导和电纳,yij是01变量。
发电机的输出应在其最大和最小输出范围内;此外,发电机在短时间内的上、下功率输出也受到限制。因此,发电机输出约束可以表示为
由于热稳定性、电压稳定性和经济性的考虑,输电线路的潮流、母线电压和线路开关数受到限制。因此,这些物理极限约束可以分别表示为
Vi min≤Vi≤Vi max
显然,所要切除的有功和无功负荷不能超过原负荷,此约束可以表示为:
0≤PLS,i≤PL,i
0≤QLS,i≤QL,i
步骤2)中构建解列的无功调整约束,方法为:
在输电系统中,无功补偿广泛采用SVC和并联电容器技术。SVC可以连续输出或吸收无功功率,而并联器只能离散输出无功功率。因此,无功功率调节约束可以表示为
QCB,i=NCB,iQCB_each
步骤3)中构建解列的连通性约束,方法为:
一般地,每个孤岛都应该是一个连通图。因此采用如下约束
步骤4)中计算构建考虑可再生能源不确定性的可调鲁棒解列模型,进行假设检验,方法为:
为了考虑随机变量的不确定性,采用不确定性集描述变量的不确定性的鲁棒优化方法。第i个可再生能源的有功功率输出的相对不确定性可以定义为
式中:PRES,i=(Pwind,i,Psolar,i)和ΔPRES,i=(ΔPwind,i,ΔPsolar,i)分别是有功出力的实际值、预测值和实际值与预测值的范围之差,其中下标“wind”对应风电,“solar”对应光伏。建立不确定集Ψ为
式中:NRES是可再生能源的个数,ΓRES∈[0,NRES]是含可再生能源电力系统的总不确定性,可根据需求设定。可调参数ΠRES=ΓRES/NRES。因此,考虑可再生能源不确定性后的线路潮流有功约束可修正为:
式中:ΩRES是可再生能源的集合。用对偶范数理论形成鲁棒对等模型将上式转化为
相应地,线路潮流无功约束可以被转化为
最后,采用线性表示和大M方法将所有非线性约束线性化为线性约束即可得到鲁棒解列模型为
s.t.
0≤PLS,i≤PL,i,0≤QLS,i≤QL,i
式中:上标“a”代表线性化时产生的辅助变量。
本发明的方法可以有效实现电力系统的鲁棒解列,而且与现有方法相比,本发明方法所得到的解列方案会根据系统状态发生改变,且可使得切负荷量始终保持最小,本发明为电力系统运行人员进行主动解列控制提供相应支持。
附图说明
图1为一个实施例的一种电力系统鲁棒解列方法流程图。
具体实施方式
为了更好地理解本发明的目的、技术方案以及技术效果,以下结合附图对本发明进行进一步的讲解说明。
参考图1,图1所示为一个实施例的一种电力系统鲁棒解列方法,包括如下步骤:
S10,确定解列的目标函数和基本约束条件:
切负荷量是评价电力系统功率不平衡程度的一个重要指标,若考虑可再生能源的不确定性,则其不平衡程度会增加。因此,可调鲁棒解列是为了在可再生能源输入最极端的情况下极小化切负荷量
式中:x=[Pup,i,Pdown,i,Qup,i,Qdown,i,PLS,i,QLS,i,QSVC,i,QCB,i]是控制向量,ξ=[Pwind,i, Psolar,i,Qwind,i,Qsolar,i]是不确定参数向量;Ψ是不确定集。Pup,i,Pdown,i,Qup,i,Qdown,i分别是发电机i的上调、下调的有功和无功输出功率。PLS,i和QLS,i分别是节点i 的有功和无功切负荷量,QSVC,i和QCB,i分别是SVC和并联电容器在节点i的总无功补偿。Pwind,i,Qwind,i,Psolar,i,Qsolar,i分别是风电和光伏的有功、无功输出功率。Nbus是节点的数量。
节点注入功率与节点输出功率应当是相等的,因此功率平衡方程可以表示为:
式中:Pi和Qi是节点i的有功和无功注入功率,PL,i和QL,i分别是节点i出的有功和无功负荷,Pij和Qij分别是节点i到节点j的线路Li-j上流过的有功和无功潮流, Pgen,i和Qgen,i分别是发电机在节点i的有功和无功注入功率。Vi,θi,Vj,θj分别是节点i和j的电压幅值和相角;Gij和Bij分别是Li-j的电导和电纳,yij是01变量。
发电机的输出应在其最大和最小输出范围内;此外,发电机在短时间内的上、下功率输出也受到限制。因此,发电机输出约束可以表示为
由于热稳定性、电压稳定性和经济性的考虑,输电线路的潮流、母线电压和线路开关数受到限制。因此,这些物理极限约束可以分别表示为
Vi min≤Vi≤Vi max
显然,所要切除的有功和无功负荷不能超过原负荷,此约束可以表示为:
0≤PLS,i≤PL,i
0≤QLS,i≤QL,i
S20,构建解列的无功调整约束;在一个实施例中:
在输电系统中,无功补偿广泛采用SVC和并联电容器技术。SVC可以连续输出或吸收无功功率,而并联器只能离散输出无功功率。因此,无功功率调节约束可以表示为
QCB,i=NCB,iQCB_each
S30,构建解列的连通性约束;在一个实施例中:
一般地,每个孤岛都应该是一个连通图。因此采用如下约束
S40,基于S10、S20、S30构建考虑可再生能源不确定性的可调鲁棒解列模型,进行假设检验;在一个实施例中:
为了考虑随机变量的不确定性,采用不确定性集描述变量的不确定性的鲁棒优化方法。第i个可再生能源的有功功率输出的相对不确定性可以定义为
式中:PRES,i=(Pwind,i,Psolar,i)和ΔPRES,i=(ΔPwind,i,ΔPsolar,i)分别是有功出力的实际值、预测值和实际值与预测值的范围之差,其中下标“wind”对应风电,“solar”对应光伏。建立不确定集Ψ为
式中:NRES是可再生能源的个数,ΓRES∈[0,NRES]是含可再生能源电力系统的总不确定性,可根据需求设定。可调参数ΠRES=ΓRES/NRES。因此,考虑可再生能源不确定性后的线路潮流有功约束可修正为:
式中:ΩRES是可再生能源的集合。用对偶范数理论形成鲁棒对等模型将上式转化为
相应地,线路潮流无功约束可以被转化为
最后,采用线性表示和大M方法将所有非线性约束线性化为线性约束即可得到鲁棒解列模型为
s.t.
0≤PLS,i≤PL,i,0≤QLS,i≤QL,i
式中:上标“a”代表线性化时产生的辅助变量。
为了证明本发明的有效性,将本发明与目前已有文献中的有序决策二叉树(OBDD)模型以及线性规划(MILP)模型进行了对比。由表1可以看出:i) 当PRES=0时,采用OBDD和MILP模型时,有五条线路被分断,其中OBDD切负荷量是最大的(108.1MW),MILP模型切负荷量较少;应用本发明所提模型时,只有三条线被分断,且其切负荷量最小(0MW)。ii)当PRES从0增大到1时,OBDD 和MILP模型的解列方案是不变的,而本发明所提的解列方案会根据系统状态发生改变,同时切负荷量也一直是最小的。因此,本发明所提的电力系统鲁棒解列方法相比其它方法具有很大的优越性。
表1不同解列模型的对比
Claims (5)
1.一种电力系统鲁棒解列方法,其特征在于,包括如下步骤:
1)确定解列的目标函数和基本约束条件;
2)构建解列的无功调整约束;
3)构建解列的连通性约束;
4)基于步骤1)、2)、3)构建考虑可再生能源不确定性的可调鲁棒解列模型,获取解列方案。
2.根据权利要求1所述的电力系统鲁棒解列方法,其特征在于,确定解列的目标函数和基本约束条件,具体如下:
切负荷量是评价电力系统功率不平衡程度的一个重要指标,若考虑可再生能源的不确定性,则其不平衡程度会增加,因此,可调鲁棒解列是为了在可再生能源输入最极端的情况下极小化切负荷量,即目标函数为:
式中:x=[Pup,i,Pdown,i,Qup,i,Qdown,i,PLS,i,QLS,i,QSVC,i,QCB,i]是控制向量,ξ=[Pwind,i,Psolar,i,Qwind,i,Qsolar,i]是不确定参数向量;Ψ是不确定集;Pup,i,Pdown,i,Qup,i,Qdown,i分别是发电机i的上调、下调的有功和无功输出功率。PLS,i和QLS,i分别是节点i的有功和无功切负荷量,QSVC,i和QCB,i分别是SVC和并联电容器在节点i的总无功补偿。Pwind,i,Qwind,i,Psolar,i,Qsolar,i分别是风电和光伏的有功、无功输出功率,Nbus是节点的数量;
节点注入功率与节点输出功率应当是相等的,因此功率平衡方程表示为:
式中:Pi和Qi是节点i的有功和无功注入功率,PL,i和QL,i分别是节点i出的有功和无功负荷,Pij和Qij分别是节点i到节点j的线路Li-j上流过的有功和无功潮流,Pgen,i和Qgen,i分别是发电机在节点i的有功和无功注入功率,Vi,θi,Vj,θj分别是节点i和j的电压幅值和相角;Gij和Bij分别是Li-j的电导和电纳,yij是01变量;
发电机的输出应在其最大和最小输出范围内,此外,发电机在短时间内的上、下功率输出也受到限制,因此,发电机输出约束为
由于热稳定性、电压稳定性和经济性的考虑,输电线路的潮流、母线电压和线路开关数受到限制,因此,这些物理极限约束分别表示为
Vi min≤Vi≤Vi max
显然,所要切除的有功和无功负荷不能超过原负荷,此约束表示为:
0≤PLS,i≤PL,i
0≤QLS,i≤QL,i。
5.根据权利要求1所述的电力系统鲁棒解列方法,其特征在于,构建考虑可再生能源不确定性的可调鲁棒解列模型,具体如下:
为了考虑随机变量的不确定性,采用不确定性集描述变量的不确定性的鲁棒优化方法,第i个可再生能源的有功功率输出的相对不确定性可以定义为
式中:PRES,i=(Pwind,i,Psolar,i)和ΔPRES,i=(ΔPwind,i,ΔPsolar,i)分别是有功出力的实际值、预测值和实际值与预测值的范围之差,其中下标“wind”对应风电,“solar”对应光伏,建立不确定集Ψ为
式中:NRES是可再生能源的个数,ΓRES∈[0,NRES]是含可再生能源电力系统的总不确定性,可根据需求设定,可调参数ΠRES=ΓRES/NRES,因此,考虑可再生能源不确定性后的线路潮流有功约束可修正为:
式中:ΩRES是可再生能源的集合,用对偶范数理论形成鲁棒对等模型将上式转化为
相应地,线路潮流无功约束可以被转化为
最后,采用线性表示和大M方法将所有非线性约束线性化为线性约束即可得到鲁棒解列模型为
s.t.
0≤PLS,i≤PL,i,0≤QLS,i≤QL,i
式中:上标“a”代表线性化时产生的辅助变量。
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