CN112018760A - 一种基于非同步数据的谐波状态估计方法 - Google Patents

一种基于非同步数据的谐波状态估计方法 Download PDF

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CN112018760A
CN112018760A CN202010880963.0A CN202010880963A CN112018760A CN 112018760 A CN112018760 A CN 112018760A CN 202010880963 A CN202010880963 A CN 202010880963A CN 112018760 A CN112018760 A CN 112018760A
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王杨
胡誉蓉
徐群伟
吴俊�
黄弘扬
楼柏良
吕文韬
马智泉
李培
陈锋
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Sichuan University
Electric Power Research Institute of State Grid Zhejiang Electric Power Co Ltd
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Abstract

本发明公开了一种基于非同步数据的谐波状态估计方法，包括以下步骤：S1、获取电能质量监测系统中主变压器被监测节点的电能质量监测记录数据；S2、根据电能质量监测记录数据和电力系统节点功率方程，构建基于非同步数据的谐波状态估计模型；S3、判断谐波状态估计模型可观矩阵是否满秩，若是，则电力系统网络可观，并进入步骤S4，若否，则电力系统网络不可观，根据注入等效推论增加布点，直到电力系统网络可观，并进入步骤S4；S4、建立解谐波状态目标函数，采用非线性优化算法求解谐波状态估计模型，得到电力系统网络的谐波状态估计值；本发明解决了如何利用我国现有电能质量在线监测系统进行谐波状态估计的问题。

Description

一种基于非同步数据的谐波状态估计方法
技术领域
本发明涉及电力系统领域，具体涉及一种基于非同步数据的谐波状态估计方法。
背景技术
随着分布式能源并网与电力电子设备的普遍使用，电力系统的谐波污染日益严重。谐波监测是治理谐波的前提，但考虑到测量装置的价格，监测所有节点、支路的谐波状态是不现实的，因此根据有限测量数据估算整个系统的谐波状况，对电力系统谐波治理具有重要意义。
已有的谐波状态估计模型大多基于理想化同步谐波数据建立，未考虑非实时、非同步等现实困难，致使其准确性在应用中难以得到保证。2012年以来，国家电网公司全面开展电能质量在线监测系统建设与实施，该系统已全面实现对110kV及以上电压等级主网回路、设备和电网电压考核点的运行数据自动采集。相比于理想化的谐波测量系统，电能质量在线监测系统的建设更加广泛，谐波数据测量更为全面。然而，考虑到数据通信、存储难度，该平台记录的谐波数据为3分钟统计值，其数据实时性、时间同步性均弱于理想化的谐波量测系统，故如何利用我国现有电能质量在线监测系统进行谐波状态估计是一件具有挑战与实际价值的工作。
同时现有方法均无法较好地应用于本发明问题中，其主要原因包括：1)现有电能质量监测系统仅提供节点注入功率，不包含支路潮流、节点向量与支路向量等，因此同步相量测量(Phasor Measurement Unit，PMU)相关的可观性分析法不适用；2)传统状态估计变量与本文状态估计变量不同，系统拓扑可观性分析的适用性不足。
发明内容
针对现有技术中的上述不足，本发明提供的一种基于非同步数据的谐波状态估计方法解决了如何利用我国现有电能质量在线监测系统进行谐波状态估计的问题。
为了达到上述发明目的，本发明采用的技术方案为：一种基于非同步数据的谐波状态估计方法，包括以下步骤：
S1、获取电能质量监测系统中主变压器被监测节点的电能质量监测记录数据；
S2、根据电能质量监测记录数据和电力系统节点功率方程，构建基于非同步数据的谐波状态估计模型；
S3、判断谐波状态估计模型可观矩阵是否满秩，若是，则电力系统网络可观，并进入步骤S4，若否，则电力系统网络不可观，根据注入等效推论增加布点，直到电力系统网络可观，并进入步骤S4；
S4、建立解谐波状态目标函数，采用非线性优化算法求解谐波状态估计模型，得到电力系统网络的谐波状态估计值。
进一步地，步骤S1中电能质量监测记录数据包括：谐波电压幅值、谐波电压非同步相角、谐波有功功率和谐波无功功率。
进一步地，步骤S2中电力系统节点功率方程为：
Figure BDA0002654102110000021
Figure BDA0002654102110000022
其中，i,j为电力系统网络中任意两个节点，θij为第i个节点电压相位与第j个节点电压相位的差值，Pi为第i个节点的谐波有功平均值，Vi为第i个节点的电压幅值均值，Vj为第j个节点的电压幅值均值，n为电力系统网络中所有节点数量，Gij为第i个节点到第j个节点的导纳实部，Bij为第i个节点到第j个节点的导纳虚部，Qi为第i个节点的谐波无功均值。
进一步地，步骤S2中谐波状态估计模型为：
Figure BDA0002654102110000031
其中，r为按照节点编号从小到大顺序排列的已测节点序列，m为电力系统网络中所有已测节点数量，a,b为已测节点序列r中任意两个已测节点，ra为已测节点序列r中第a个已测节点的编号，rb为已测节点序列r中第b个已测节点的编号，t为按照节点编号从小到大顺序排列的未测节点序列，未测节点序列t中有n-m个未测节点，n为电力系统网络中所有节点数量，c为未测节点序列t中第c个未测节点，tc为未测节点序列t中第c个未测节点编号；θra为已测节点ra的电压相位，θrb为已测节点rb的电压相位，θtc为未测节点tc的电压相位，δra为已测节点ra的相位误差，δrb为已测节点rb的相位误差，δtc为未测节点tc的相位误差，αra-rb为已测节点ra,rb之间的电压相位差，αra-tc为已测节点ra与未测节点tc之间的电压相位差，DPra为已测节点ra的谐波有功平衡，DQra为已测节点ra的谐波无功平衡，Pra为已测节点ra的谐波有功平均值，Qra为已测节点ra的谐波无功均值，Vra为已测节点ra的电压幅值平均值，Vrb为已测节点rb的电压幅值平均值，Vtc为未测节点tc的电压幅值，Gra-rb为已测节点ra到rb导纳实部，Bra-rb为已测节点ra到rb导纳虚部，Gra-tc为已测节点ra到未测节点rc导纳实部，Bra-tc为已测节点ra到未测节点rc导纳虚部。
上述进一步方案的有益效果为：通过谐波状态估计模型，充分利用了电能质量在线监测系统记录的非实时非同步数据，实现了非同步测量数据的同步谐波状态估计。
进一步地，步骤S3中谐波状态估计模型可观矩阵H为：
Figure BDA0002654102110000041
Figure BDA0002654102110000042
或
Figure BDA0002654102110000043
Figure BDA0002654102110000044
Figure BDA0002654102110000045
或
Figure BDA0002654102110000046
Figure BDA0002654102110000047
当ra≠rb时：
Figure BDA0002654102110000048
当ra＝rb时：
Figure BDA0002654102110000049
其中，Ma-rb为矩阵Mm×n中第a行第rb列的元素，Ma-tc为矩阵Mm×n中第a行第tc列的元素，在矩阵Mm×n中，行数与电力系统网络的已测节点个数对应，列数与电力系统网络的总节点个数对应，Na-c为矩阵Nm×(n-m)中第a行第c列的元素，在矩阵Nm×(n-m)中，行数与电力系统网络的已测节点个数对应，列数与电力系统网络的未测节点个数对应，Ka-rb为矩阵Km×n中第a行第rb列的元素，Ka-tc为矩阵Km×n中第a行第tc列的元素，在矩阵Km×n中，行数与电力系统网络的已测节点个数对应，列数与电力系统网络的总节点个数对应，La-c为矩阵Lm×(n-m)中第a行第c列的元素，在矩阵Lm×(n-m)中，行数与电力系统网络的已测节点个数对应，列数与电力系统网络的未测节点个数对应，Ma-ra为矩阵Mm×n中对角线上第a行第ra列的元素，Bra-ra为已测节点ra的导纳虚部，Ka-ra为矩阵Km×n中对角线上第a行第ra列的元素。
进一步地，步骤S4中非线性优化算法为信赖域法。
进一步地，步骤S3中根据注入等效推论增加布点的方法为：
A1、根据已测量节点注入量测可等效成与该节点相连的某一支路潮流量测；
A2、根据支路潮流量测，将未测节点与已测量节点联系起来，用于增加电能质量监测系统的布点。
进一步地，步骤S4中解谐波状态目标函数f为：
Figure BDA0002654102110000051
综上，本发明的有益效果为：本发明基于电能质量监测记录数据非实时非同步的特点，在谐波状态估计模型中以相角误差补偿的方式将非同步问题同步化，计及电力系统网络正常程度波动对电能质量监测平台统计数据的影响，较准确估计电力系统网络谐波状态；计及电力系统网络异常程度波动对电能质量监测平台统计数据的影响，具有一定的抗差能力；谐波状态估计过程仅需节点谐波电压幅值平均值、相角平均值以及谐波有功无功平均值，数据可从安装在主变压器的电能质量监测装置得到，计算简便，具有工程实用性。
附图说明
图1为一种基于非同步数据的谐波状态估计方法的流程图；
图2为实施例1中5次谐波的谐波状态估计对比结果；
图3为实施例1中7次谐波的谐波状态估计对比结果；
图4为实施例1中11次谐波的谐波状态估计对比结果；
图5为实施例1中13次谐波的谐波状态估计对比结果；
图6为实施例1中已测量节点电压相角相对误差；
图7为实施例2中不同波动情况下5次谐波相对误差对比；
图8为实施例2中不同波动情况下7次谐波相对误差对比。
具体实施方式
下面对本发明的具体实施方式进行描述，以便于本技术领域的技术人员理解本发明，但应该清楚，本发明不限于具体实施方式的范围，对本技术领域的普通技术人员来讲，只要各种变化在所附的权利要求限定和确定的本发明的精神和范围内，这些变化是显而易见的，一切利用本发明构思的发明创造均在保护之列。
如图1所示，一种基于非同步数据的谐波状态估计方法，包括以下步骤：
S1、获取电能质量监测系统中主变压器被监测节点的电能质量监测记录数据；
步骤S1中电能质量监测记录数据包括：谐波电压幅值、谐波电压非同步相角、谐波有功功率和谐波无功功率。
电能质量监测系统当前主要安装在新能源、大型负荷等重要变电站的主变压器上，主要量测量为基波、谐波电压、电流、功率等电气数据。分布于电力系统网络的各个电能质量监测系统按照IEEE1159.3-2019电能质量数据交换格式PQDIF，通过以太网将数据上传至主站系统中的电能质量监管中心。数据具有如下特点：
非实时性：电能质量监测系统每10个周期进行一次谐波分析计算，每隔3分钟统计900个数据的平均值、最大值和最小值并记录于PQDIF文件中。
非同步性：考虑到傅里叶分析频率漂移带来的相角误差与谐波相角测量对时钟的高要求，当前监测数据均以本地A相电压相位为参考值，即系统没有全局平衡节点。
S2、根据电能质量监测记录数据和电力系统节点功率方程，构建基于非同步数据的谐波状态估计模型；
步骤S2中电力系统节点功率方程为：
Figure BDA0002654102110000071
Figure BDA0002654102110000072
其中，i,j为电力系统网络中任意两个节点，θij为第i个节点电压相位与第j个节点电压相位的差值，Pi为第i个节点的谐波有功平均值，Vi为第i个节点的电压幅值均值，Vj为第j个节点的电压幅值均值，n为电力系统网络中所有节点数量，Gij为第i个节点到第j个节点的导纳实部，Bij为第i个节点到第j个节点的导纳虚部，Qi为第i个节点的谐波无功均值。
步骤S2中谐波状态估计模型为：
Figure BDA0002654102110000081
其中，r为按照节点编号从小到大顺序排列的已测节点序列，m为电力系统网络中所有已测节点数量，a,b为已测节点序列r中任意两个已测节点，ra为已测节点序列r中第a个已测节点的编号，rb为已测节点序列r中第b个已测节点的编号，t为按照节点编号从小到大顺序排列的未测节点序列，未测节点序列t中有n-m个未测节点，n为电力系统网络中所有节点数量，c为未测节点序列t中第c个未测节点，tc为未测节点序列t中第c个未测节点编号；θra为已测节点ra的电压相位，θrb为已测节点rb的电压相位，θtc为未测节点tc的电压相位，δra为已测节点ra的相位误差，δrb为已测节点rb的相位误差，δtc为未测节点tc的相位误差，αra-rb为已测节点ra,rb之间的电压相位差，αra-tc为已测节点ra与未测节点tc之间的电压相位差，DPra为已测节点ra的谐波有功平衡，DQra为已测节点ra的谐波无功平衡，Pra为已测节点ra的谐波有功平均值，Qra为已测节点ra的谐波无功均值，Vra为已测节点ra的电压幅值平均值，Vrb为已测节点rb的电压幅值平均值，Vtc为未测节点tc的电压幅值，Gra-rb为已测节点ra到rb导纳实部，Bra-rb为已测节点ra到rb导纳虚部，Gra-tc为已测节点ra到未测节点rc导纳实部，Bra-tc为已测节点ra到未测节点rc导纳虚部。
S3、判断谐波状态估计模型可观矩阵是否满秩，若是，则电力系统网络可观，并进入步骤S4，若否，则电力系统网络不可观，根据注入等效推论增加布点，直到电力系统网络可观，并进入步骤S4；
步骤S3中谐波状态估计模型可观矩阵H为：
Figure BDA0002654102110000091
Figure BDA0002654102110000092
或
Figure BDA0002654102110000093
Figure BDA0002654102110000094
Figure BDA0002654102110000095
或
Figure BDA0002654102110000096
Figure BDA0002654102110000097
当ra≠rb时：
Figure BDA0002654102110000098
当ra＝rb时：
Figure BDA0002654102110000099
其中，Ma-rb为矩阵Mm×n中第a行第rb列的元素，Ma-tc为矩阵Mm×n中第a行第tc列的元素，在矩阵Mm×n中，行数与电力系统网络的已测节点个数对应，列数与电力系统网络的总节点个数对应，Na-c为矩阵Nm×(n-m)中第a行第c列的元素，在矩阵Nm×(n-m)中，行数与电力系统网络的已测节点个数对应，列数与电力系统网络的未测节点个数对应，Ka-rb为矩阵Km×n中第a行第rb列的元素，Ka-tc为矩阵Km×n中第a行第tc列的元素，在矩阵Km×n中，行数与电力系统网络的已测节点个数对应，列数与电力系统网络的总节点个数对应，La-c为矩阵Lm×(n-m)中第a行第c列的元素，在矩阵Lm×(n-m)中，行数与电力系统网络的已测节点个数对应，列数与电力系统网络的未测节点个数对应，Ma-ra为矩阵Mm×n中对角线上第a行第ra列的元素，Bra-ra为已测节点ra的导纳虚部，Ka-ra为矩阵Km×n中对角线上第a行第ra列的元素。
步骤S3中根据注入等效推论增加布点的方法为：
A1、根据已测量节点注入量测可等效成与该节点相连的某一支路潮流量测；
A2、根据支路潮流量测，将未测节点与已测量节点联系起来，用于增加电能质量监测系统的布点。
S4、建立解谐波状态目标函数，采用非线性优化算法求解谐波状态估计模型，得到电力系统网络的谐波状态估计值。
步骤S4中非线性优化算法为信赖域法。
步骤S4中解谐波状态目标函数f为：
Figure BDA0002654102110000101
实施例1：
以IEEE30节点系统中负荷2、5、7、8、12、19、21、30为非线性负荷进行仿真验证，非线性负荷以电流源模型对其进行建模，谐波频谱如表1，根据步骤S3，节点3、5、9、16、19、23、27可为本算例中的未测量节点，节点1为全局平衡节点。
表1谐波负荷频谱表
Figure BDA0002654102110000102
Figure BDA0002654102110000111
第一步，在PSCAD搭建IEEE30节点系统，设γi为各节点基波电压相角值；
第二步，为模拟电网实际波动，假设PQ负荷在额定值±5％范围内随机波动；第三步，对900组(3分钟)数据分别进行基波潮流计算；
第四步，根据频谱表计算谐波源；
第五步，执行谐波潮流计算，得到各节点谐波数据。
第六步，以900组PQ负荷波动计算对应的谐波数据作为电能质量监测系统在三分钟内测到的谐波数据，电压幅值取计算均值，电压相角为均值减去(γi*h)，h为谐波次数，从而模拟PQDIF记录的谐波相角以本地基波相角为参考值的特点，将这些数据代入谐波状态估计模型进行计算。
以900组谐波潮流计算均值为真实值，正常波动情况下的谐波状态估计对比结果如图2～5、6所示，从各次谐波的未测量节点电压幅值、相角与已测量节点的相角相对误差中可以看出，该方法能较好地估计出谐波状态。
实施例2
增大波动范围x，分析负荷剧烈波动对模型计算结果的影响。数据准备流程仍以实施例1所述，各PQ负荷在额定值的±x％范围内随机波动，生成900组谐波测量数据。
以900组谐波潮流计算均值为真实值，5次、7次谐波未测量节点与已测量节点的电压幅值、相角相对误差对比情况分别如图4、5所示。
从图7、8的对比中可以看出，5次、7次谐波的估计误差随着负荷波动增大而增大，整体上结果在x＝30以下的估计结果准确性均较高，说明提出的谐波状态估计模型具有一定的抗差能力，但是整体的准确度随着网络波动程度变大而逐渐增大。

Claims (8)

1.一种基于非同步数据的谐波状态估计方法，其特征在于，包括以下步骤：
S1、获取电能质量监测系统中主变压器被监测节点的电能质量监测记录数据；
S2、根据电能质量监测记录数据和电力系统节点功率方程，构建基于非同步数据的谐波状态估计模型；
S3、判断谐波状态估计模型可观矩阵是否满秩，若是，则电力系统网络可观，并进入步骤S4，若否，则电力系统网络不可观，根据注入等效推论增加布点，直到电力系统网络可观，并进入步骤S4；
S4、建立解谐波状态目标函数，采用非线性优化算法求解谐波状态估计模型，得到电力系统网络的谐波状态估计值。
2.根据权利要求1所述的基于非同步数据的谐波状态估计方法，其特征在于，所述步骤S1中电能质量监测记录数据包括：谐波电压幅值、谐波电压非同步相角、谐波有功功率和谐波无功功率。
3.根据权利要求1所述的基于非同步数据的谐波状态估计方法，其特征在于，所述步骤S2中电力系统节点功率方程为：
Figure FDA0002654102100000011
Figure FDA0002654102100000012
其中，i,j为电力系统网络中任意两个节点，θij为第i个节点电压相位与第j个节点电压相位的差值，Pi为第i个节点的谐波有功平均值，Vi为第i个节点的电压幅值均值，Vj为第j个节点的电压幅值均值，n为电力系统网络中所有节点数量，Gij为第i个节点到第j个节点的导纳实部，Bij为第i个节点到第j个节点的导纳虚部，Qi为第i个节点的谐波无功均值。
4.根据权利要求1所述的基于非同步数据的谐波状态估计方法，其特征在于，所述步骤S2中谐波状态估计模型为：
Figure FDA0002654102100000021
其中，r为按照节点编号从小到大顺序排列的已测节点序列，m为电力系统网络中所有已测节点数量，a,b为已测节点序列r中任意两个已测节点，ra为已测节点序列r中第a个已测节点的编号，rb为已测节点序列r中第b个已测节点的编号，t为按照节点编号从小到大顺序排列的未测节点序列，未测节点序列t中有n-m个未测节点，n为电力系统网络中所有节点数量，c为未测节点序列t中第c个未测节点，tc为未测节点序列t中第c个未测节点编号；θra为已测节点ra的电压相位，θrb为已测节点rb的电压相位，θtc为未测节点tc的电压相位，δra为已测节点ra的相位误差，δrb为已测节点rb的相位误差，δtc为未测节点tc的相位误差，αra-rb为已测节点ra,rb之间的电压相位差，αra-tc为已测节点ra与未测节点tc之间的电压相位差，DPra为已测节点ra的谐波有功平衡，DQra为已测节点ra的谐波无功平衡，Pra为已测节点ra的谐波有功平均值，Qra为已测节点ra的谐波无功均值，Vra为已测节点ra的电压幅值平均值，Vrb为已测节点rb的电压幅值平均值，Vtc为未测节点tc的电压幅值，Gra-rb为已测节点ra到rb导纳实部，Bra-rb为已测节点ra到rb导纳虚部，Gra-tc为已测节点ra到未测节点rc导纳实部，Bra-tc为已测节点ra到未测节点rc导纳虚部。
5.根据权利要求4所述的基于非同步数据的谐波状态估计方法，其特征在于，所述步骤S3中谐波状态估计模型可观矩阵H为：
Figure FDA0002654102100000031
Figure FDA0002654102100000032
或
Figure FDA0002654102100000033
Figure FDA0002654102100000034
Figure FDA0002654102100000035
或
Figure FDA0002654102100000036
Figure FDA0002654102100000037
当ra≠rb时：
Figure FDA0002654102100000038
当ra＝rb时：
Figure FDA0002654102100000039
其中，Ma-rb为矩阵Mm×n中第a行第rb列的元素，Ma-tc为矩阵Mm×n中第a行第tc列的元素，在矩阵Mm×n中，行数与电力系统网络的已测节点个数对应，列数与电力系统网络的总节点个数对应，Na-c为矩阵Nm×(n-m)中第a行第c列的元素，在矩阵Nm×(n-m)中，行数与电力系统网络的已测节点个数对应，列数与电力系统网络的未测节点个数对应，Ka-rb为矩阵Km×n中第a行第rb列的元素，Ka-tc为矩阵Km×n中第a行第tc列的元素，在矩阵Km×n中，行数与电力系统网络的已测节点个数对应，列数与电力系统网络的总节点个数对应，La-c为矩阵Lm×(n-m)中第a行第c列的元素，在矩阵Lm×(n-m)中，行数与电力系统网络的已测节点个数对应，列数与电力系统网络的未测节点个数对应，Ma-ra为矩阵Mm×n中对角线上第a行第ra列的元素，Bra-ra为已测节点ra的导纳虚部，Ka-ra为矩阵Km×n中对角线上第a行第ra列的元素。
6.根据权利要求1所述的基于非同步数据的谐波状态估计方法，其特征在于，所述步骤S4中非线性优化算法为信赖域法。
7.根据权利要求1所述的基于非同步数据的谐波状态估计方法，其特征在于，所述步骤S3中根据注入等效推论增加布点的方法为：
A1、根据已测量节点注入量测可等效成与该节点相连的某一支路潮流量测；
A2、根据支路潮流量测，将未测节点与已测量节点联系起来，用于增加电能质量监测系统的布点。
8.根据权利要求4所述的基于非同步数据的谐波状态估计方法，其特征在于，所述步骤S4中解谐波状态目标函数f为：
Figure FDA0002654102100000041
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