技术领域technical field
本发明涉及电力系统基于戴维南等值的电压稳定在线分析技术领域，尤其涉及一种基于单一状态断面的广域戴维南等值参数在线计算方法。The invention relates to the technical field of on-line analysis of voltage stability based on Thevenin equivalents in electric power systems, in particular to an on-line calculation method for wide-area Thevenin equivalent parameters based on a single state section.
背景技术Background technique
随着电网互联规模的扩大、电力需求的快速增长，电力系统运行点越来越接近稳定极限。在线监视电网电压稳定的研究引起了国内外学者广泛关注与重视。基于戴维南等值的电压稳定在线分析，因其方法概念清晰、原理简单等优点使之成为电压稳定领域一个重要的研究方向。With the expansion of grid interconnection scale and the rapid growth of power demand, the operating point of power system is getting closer and closer to the stability limit. The research on online monitoring of power grid voltage stability has aroused extensive attention and attention from scholars at home and abroad. The on-line analysis of voltage stability based on Thevenin equivalent has become an important research direction in the field of voltage stability because of its clear concept and simple principle.
快速准确评估关键负荷节点的戴维南等值参数直接决定了该方法应用在在线电压稳定监视与控制中的可行性和有效性。国内外学者就基于局部量测提高戴维南等值参数计算精度实现电压稳定分析提出了多种方法，如Z-V空间供应侧特性曲线法、扩展PV曲线跟踪估计戴维南等值参数的方法等，但算法的基础都是假设量测数据窗内戴维南等值参数不变。这一前提条件与系统运行的实际情况并不吻合，经过分析参数漂移与时变问题，发现利用最小二乘拟合在电网发生较大扰动情况下会出现数值不稳定的情况。The rapid and accurate evaluation of Thevenin equivalent parameters of key load nodes directly determines the feasibility and effectiveness of this method in online voltage stability monitoring and control. Scholars at home and abroad have proposed a variety of methods based on local measurement to improve the calculation accuracy of Thevenin equivalent parameters to achieve voltage stability analysis, such as the Z-V space supply-side characteristic curve method, the method of extending PV curve tracking to estimate Thevenin equivalent parameters, etc., but the algorithm is limited The basis is to assume that the Thevenin equivalent parameters in the measurement data window remain unchanged. This precondition is not consistent with the actual situation of the system operation. After analyzing the parameter drift and time-varying problems, it is found that the least squares fitting will cause numerical instability in the case of large disturbances in the power grid.
基于局域量测的戴维南等值参数辨识方法取得了长足的进步，但参数时变与漂移问题当电网非线性增强或者两个邻域数据变化很接近时，仍然会影响基于连续系统状态断面局域量测数据的戴维南等值参数辨识精度。随着风电光伏等可再生能源大规模接入给系统运行带来较大随机性和波动性，这一问题将更为突出。随着PMU的推广，广域测量系统日趋成熟，基于全局量测的单一系统状态断面数据求解负荷节点的戴维南等值参数成为新的研究思路，常见的方法有：The Thevenin equivalent parameter identification method based on local measurement has made great progress, but the parameter time-varying and drifting problems will still affect the cross-sectional situation based on the continuous system state when the nonlinearity of the power grid is enhanced or the data changes of two neighborhoods are very close. Identification accuracy of Thevenin equivalent parameters for domain measurement data. This problem will become more prominent as the large-scale integration of renewable energy such as wind power and photovoltaics brings greater randomness and volatility to system operation. With the promotion of PMU, the wide-area measurement system is becoming more and more mature. It has become a new research idea to solve the Thevenin equivalent parameters of load nodes based on the single system state section data of global measurement. The common methods are:
(1)将全网的节点分为电源、联络和负荷节点三类，根据联络节点注入电流为零的特征，将全网的节点电压方程变换为多节点多支路的戴维南等值形式，再对变换后的阻抗阵对角化，实现节点间的解耦变换，获得负荷节点的单电源单支路戴维南等值参数。(1) The nodes of the whole network are divided into three types: power supply, contact and load nodes. According to the characteristic that the injection current of the contact nodes is zero, the node voltage equation of the whole network is transformed into the Thevenin equivalent form of multi-node and multi-branch, and then The transformed impedance array is diagonalized to realize the decoupling transformation between nodes, and the Thevenin equivalent parameters of single power supply and single branch of the load node are obtained.
(2)提出耦合单端口网络概念，实现了基于单一状态断面下的戴维南等值计算，但在负荷增长方式非线性情况下，该方法计算结果对负荷裕度估计偏低，计算准确性上有待提高。(2) The concept of coupled single-port network is proposed, and the Thevenin equivalent calculation based on a single state section is realized. However, in the case of nonlinear load growth mode, the calculation result of this method has a low estimation of the load margin, and the calculation accuracy needs to be improved. improve.
(3)利用PMU实时量测数据通过本地节点无功响应因子对系统无功响应因子的匹配来处理节点间耦合，以提高负荷裕度计算精度。但难以量化不同节点间的耦合关联，无法对发电机无功越限情况进行有效的量化计算。(3) Use the PMU real-time measurement data to process the inter-node coupling through the matching of the local node reactive power response factor to the system reactive power response factor, so as to improve the calculation accuracy of the load margin. However, it is difficult to quantify the coupling relationship between different nodes, and it is impossible to perform effective quantitative calculations on the situation of generator reactive power exceeding the limit.
以上方法求解过程中均需要对导纳阵求逆，加上后续相对复杂的矩阵和耦合处理，对于大系统的在线计算而言算量仍然较大。工程实际应用中更希望在单一状态断面下快速准确计算等值参数基础上，能根据负荷预测，量化各节点负荷变化以及各调控措施对未来状态下戴维南等值参数的影响，以便提前获得安全信息，为实现预防控制的优化创造条件。In the process of solving the above methods, the inversion of the admittance matrix is required, and the subsequent relatively complex matrix and coupling processing are still relatively large for the online calculation of large systems. In practical engineering applications, it is hoped that on the basis of fast and accurate calculation of equivalent parameters in a single state section, the load change of each node and the impact of each control measure on the Thevenin equivalent parameters in the future state can be quantified according to load forecasting, so as to obtain safety information in advance , to create conditions for the optimization of prevention and control.
发明内容Contents of the invention
本发明的目的就是为了解决上述问题，提出了基于单一状态断面的广域戴维南等值参数在线计算方法，该方法计算量小，稳定可靠，可在线完成关注节点等值参数的快速计算。The object of the present invention is to solve the above problems, and proposes an online calculation method of the wide-area Thevenin equivalent parameters based on a single state section.
为了实现上述目的，本发明采用如下技术方案：In order to achieve the above object, the present invention adopts the following technical solutions:
基于单一状态断面的广域戴维南等值参数在线计算方法，包括以下步骤：The online calculation method of wide-area Thevenin equivalent parameters based on a single state section includes the following steps:
(1)对当前状态负荷节点的负荷做等效阻抗处理；(1) Perform equivalent impedance processing on the load of the load node in the current state;
(2)对原系统节点导纳矩阵做修正处理，得到等效阻抗处理后的系统导纳矩阵；(2) Modify the original system node admittance matrix to obtain the system admittance matrix after equivalent impedance processing;
(3)断开当前状态负荷节点处的负荷阻抗，根据修正以后的导纳矩阵计算开路电压用的节点导纳矩阵；(3) Disconnect the load impedance at the load node in the current state, and calculate the node admittance matrix for the open circuit voltage according to the corrected admittance matrix;
(4)计算等效阻抗处理后当前状态负荷节点的节点电压方程；(4) Calculate the node voltage equation of the current state load node after the equivalent impedance processing;
(5)根据修正后的导纳矩阵和节点电压方程，计算负荷节点的开路电压，并将所述开路电压作为戴维南等值电势，进而获得所研究负荷节点的戴维南等值全部参数,得到电压稳定的判据。(5) According to the modified admittance matrix and node voltage equation, calculate the open circuit voltage of the load node, and use the open circuit voltage as the Thevenin equivalent potential, and then obtain all the Thevenin equivalent parameters of the load node under study, and obtain the voltage stability criterion.
所述步骤(1)的具体方法为：The concrete method of described step (1) is:
设系统PV与平衡节点个数之和为m，PQ节点数为r，总节点数为n；在广域量测条件下，系统的各节点电压幅值、相位和有功无功功率均为已知，计算时刻系统状态断面下，所有的PV节点和平衡节点均视为理想电压源，对于带负荷的PQ节点，其负荷均可以由该节点的功率和电压，计算得到一个等效负荷阻抗。Suppose the sum of PV and balance nodes in the system is m, the number of PQ nodes is r, and the total number of nodes is n; under wide-area measurement conditions, the voltage amplitude, phase and active and reactive power of each node in the system are It is known that under the system state section at the calculation time, all PV nodes and balance nodes are regarded as ideal voltage sources, and for the PQ node with load, its load can be calculated from the power and voltage of the node to obtain an equivalent load impedance.
所述步骤(2)的具体方法为：The concrete method of described step (2) is:
设系统原来导纳矩阵为Y0，Y0中元素如下：Let the original admittance matrix of the system be Y0 , and the elements in Y0 are as follows:
矩阵中的元素Yij代表节点i和节点j之间的互导纳，Yii代表节点i的自导纳；将负荷阻抗归并到系统导纳矩阵Y0，只需修改与负荷节点相对应的导纳阵Y0的对角元素，其余元素不变；The element Yij in the matrix represents the mutual admittance between node i and node j, and Yii represents the self-admittance of node i; to merge the load impedance into the system admittance matrix Y0 , only need to modify The diagonal elements of the admittance matrix Y0 , the other elements remain unchanged;
则修正后的导纳矩阵为：Then the corrected admittance matrix is:
其中，r为PQ节点数，ZLi为第i个PQ节点的等效阻抗，表示负荷阻抗的导纳值。Among them, r is the number of PQ nodes, ZLi is the equivalent impedance of the i-th PQ node, Indicates the admittance value of the load impedance.
所述步骤(3)的具体方法为：The concrete method of described step (3) is:
将修正以后的导纳矩阵中当前状态负荷节点自导纳aii减去负荷阻抗，即形成计算开路电压用的节点导纳矩阵Y。Subtract the load impedance from the admittance aii of the current state load node in the corrected admittance matrix to form the node admittance matrix Y for calculating the open circuit voltage.
开路电压用的节点导纳矩阵Y具体为：The node admittance matrix Y for the open circuit voltage is specifically:
其中，对于待求开路电压的节点i，其对应自导纳应为表示负荷阻抗的导纳值，aii表示修正以后的导纳矩阵中前r个对角线元素。Among them, for the node i whose open circuit voltage is to be obtained, its corresponding self-admittance should be Represents the admittance value of the load impedance, and aii represents the first r diagonal elements in the corrected admittance matrix.
所述步骤(4)的具体方法为：The concrete method of described step (4) is:
在求解i节点开路电压时，节点电压向量中，PQ节点电压相量为待求量，PV节点和平衡节点电压相量为已知量；采用节点负荷阻抗等效后，节点注入电流向量中均为0，根据节点电压方程得出When solving the i-node open circuit voltage, the node voltage vector Among them, the PQ node voltage phasor is the quantity to be sought, and the PV node and balance node voltage phasors are known quantities; after adopting the node load impedance equivalent, the node injects the current vector middle are all 0, according to the node voltage equation
式中：节点导纳矩阵和电压向量中元素均为已知量；表示PQ节点1到r的电压，表示第i个PQ节点的开路电压，为待求量，表示PV和平衡节点的注入电流。Where: node admittance matrix and voltage vector middle element are known quantities; Indicates the voltage at PQ node 1 to r, Indicates the open circuit voltage of the i-th PQ node, which is the quantity to be sought, Indicates the injected current of PV and balance node.
所述节点电压方程中，The node voltage equation,
令make
则节点电压方程可写成如下的矩阵形式：Then the node voltage equation can be written in the following matrix form:
AU＝-BAU=-B
利用高斯消元法求解上述方程，求解出i节点处开路电压即为戴维南等值电势Use the Gaussian elimination method to solve the above equation, and solve the open circuit voltage at the i node Thevenin equipotential
由于导纳阵的稀疏性质，在利用高斯消去求解过程中，将系数矩阵A化简为上三角阵，并且由于只需要计算节点i的开路电压，因此回代过程中算到即可，无需把全部未知量都解出；如需要求解其他节点的等值参数，只需重新修正导纳阵Y1，形成新的节点电压方程，再次利用高斯消去求解。Due to the sparse nature of the admittance matrix, the coefficient matrix A is simplified into an upper triangular matrix in the process of solving by Gaussian elimination, and since only the open-circuit voltage of node i needs to be calculated, the calculation of That is, there is no need to solve all the unknowns; if you need to solve the equivalent parameters of other nodes, you only need to re-correct the admittance matrix Y1 to form a new node voltage equation, and use Gaussian elimination to solve it again.
所述步骤(5)的具体方法为：The concrete method of described step (5) is:
利用高斯消元法求解节点电压方程，即可求解出i节点处开路电压Using the Gaussian elimination method to solve the node voltage equation, the open circuit voltage at the i node can be solved
根据负荷预测所得各节点的负荷波动，计及各种调控措施量化计算出未来状态断面信息，即可快速计算各节点等值参数的变化，实现对未来状态下的等值参数的准确预估。According to the load fluctuation of each node obtained from the load forecast, and taking into account various control measures to quantitatively calculate the future state section information, the change of the equivalent parameter of each node can be quickly calculated, and the accurate prediction of the equivalent parameter in the future state can be realized.
本发明的有益效果是：The beneficial effects of the present invention are:
通过仿真算例分析验证了该方法的正确性和有效性。该方法不需要选择初值和假设条件，解决了现有基于局域量测算法系统内部发生扰动时戴维南等值参数计算偏差较大的问题，相比基于广域量测的耦合单端口方法计算得到的戴维南参数更为准确，且计算量小，鲁棒性好，能够适应电网不同运行工况方式。The correctness and effectiveness of the method are verified by simulation examples. This method does not need to select initial values and assumptions, and solves the problem of large deviations in the calculation of Thevenin equivalent parameters when the existing system based on local measurement algorithms is disturbed. The obtained Thevenin parameters are more accurate, and the calculation amount is small, the robustness is good, and it can adapt to different operating conditions of the power grid.
在准确的超短期负荷预测，计及各种调控措施可快速预估未来系统的状态，在预估系统状态断面信息基础上按本发明所提方法可对戴维南等值参数变化轨迹给出较为准确的在线预估，为预防性控制措施的优化奠定理论基础和时间裕量。同时所提方法也适用于分析电力系统中长期过程中的戴维南等值参数的变化问题，为调控中心利用戴维南等值模型分析在线电压稳定性提供了有益的参考，有较好的在线应用前景。In accurate ultra-short-term load forecasting, taking into account various control measures, the state of the future system can be quickly estimated. On the basis of estimating the state section information of the system, the method proposed in the present invention can give a relatively accurate change track of Thevenin equivalent parameters. The online estimation of the system lays a theoretical foundation and time margin for the optimization of preventive control measures. At the same time, the proposed method is also suitable for analyzing the change of Thevenin equivalent parameters in the medium and long-term process of the power system, which provides a useful reference for the control center to use the Thevenin equivalent model to analyze the online voltage stability, and has a good online application prospect.
附图说明Description of drawings
图1(a)为等值前的电力系统示意图；Figure 1(a) is a schematic diagram of the power system before equivalence;
图1(b)为等值后的电力系统示意图；Figure 1(b) is a schematic diagram of the equivalent power system;
图2为负荷等效为阻抗后的系统示意图；Figure 2 is a schematic diagram of the system after the load is equivalent to impedance;
图3为节点i的开路电压系统示意图Figure 3 is a schematic diagram of the open circuit voltage system of node i
图4为本发明实施例IEEE3机9节点系统结构图；Fig. 4 is the IEEE3 machine 9 node system structural diagram of the embodiment of the present invention;
图5为本发明实施例电压幅值偏差对比；Fig. 5 is the comparison of the voltage amplitude deviation of the embodiment of the present invention;
图6为本发明实施例New England 10机39节点系统结构图；Fig. 6 is a system structure diagram of New England 10 machines and 39 nodes according to the embodiment of the present invention;
图7为本发明实施例节点29电压幅值对比。FIG. 7 is a comparison of voltage amplitudes at node 29 according to an embodiment of the present invention.
具体实施方式：detailed description:
下面结合附图与实施例对本发明做进一步说明：Below in conjunction with accompanying drawing and embodiment the present invention will be further described:
一、基于单一状态断面的广域戴维南等值的基本思想1. Basic idea of wide-area Thevenin equivalent based on single state section
戴维南等值是以某一节点为对象，以该节点对地端口向系统侧观测的等值网络。如图1(a)所示的电力系统(以负荷1为例)，在任一时间断面，任何复杂的电力系统均可以看作是对任一节点的等值电势Eth经过一等值阻抗Zth向该节点供电的等值网络，如图1(b)所示，负荷1对应节点。The Thevenin equivalent is an equivalent network that takes a certain node as the object and observes from the port of the node to the system side. The power system shown in Figure 1(a) (taking load 1 as an example), at any time section, any complex power system can be regarded as the equivalent potential Eth of any node passing through an equivalent impedance Zth is the equivalent network that supplies power to this node, as shown in Figure 1(b), load 1 corresponds to the node.
设系统PV与平衡节点个数之和为m，PQ节点数为r，总节点数为n。在广域量测条件下，系统的各节点电压幅值、相位和有功无功功率均为已知，计算时刻系统状态断面下，所有的PV节点和平衡节点均视为理想电压源，对于带负荷的PQ节点，其负荷均可以由该节点的功率和电压，计算得到一个等效负荷阻抗，即对于负荷节点i，其等效阻抗为：Let the sum of the system PV and the number of balance nodes be m, the number of PQ nodes be r, and the total number of nodes be n. Under wide-area measurement conditions, the voltage amplitude, phase and active and reactive power of each node of the system are known, and all PV nodes and balance nodes are regarded as ideal voltage sources under the system state section at the calculation time. For the PQ node of the load, the load can be calculated from the power and voltage of the node to obtain an equivalent load impedance, that is, for the load node i, the equivalent impedance is:
式中Pi和Qi分别为节点i的电压、电流相量和有功、无功功率。In the formula Pi and Qi are voltage, current phasor and active and reactive power of node i respectively.
此处的等效阻抗并非把PQ节点的负荷按恒阻抗模型来处理，仅用于当前状态的负荷等效计算，当系统运行状态发生变化时，该等效阻抗是变化的。等效后系统如图2所示。The equivalent impedance here does not treat the load of the PQ node as a constant impedance model, but is only used for the equivalent calculation of the load in the current state. When the operating state of the system changes, the equivalent impedance changes. The equivalent system is shown in Figure 2.
等效处理后的系统求取某负荷节点戴维南等值参数时，可根据戴维南等值电势的定义即该节点的开路电压来计算Ethi，然后根据式(2)求取其等值阻抗Zthi。When calculating the Thevenin equivalent parameters of a load node after equivalent processing, Ethi can be calculated according to the definition of Thevenin equivalent potential, that is, the open circuit voltage of the node, and then its equivalent impedance Zthi can be calculated according to formula (2) .
二、广域戴维南等值电势计算方法2. Calculation method of wide-area Thevenin equivalent potential
图2系统的节点导纳矩阵可以通过对原节点导纳矩阵进行修正得到。设系统原来导纳矩阵为Y0，Y0中元素如下The node admittance matrix of the system in Fig. 2 can be obtained by modifying the original node admittance matrix. Let the original admittance matrix of the system be Y0 , and the elements in Y0 are as follows
矩阵中的元素Yij代表节点i和节点j之间的互导纳，Yii代表节点i的自导纳；下面矩阵中的元素含义与此相同；The element Yij in the matrix represents the mutual admittance between node i and node j, and Yii represents the self-admittance of node i; the meaning of the elements in the matrix below is the same;
将负荷阻抗归并到系统导纳矩阵只需修改与负荷节点相对应的导纳阵的对角元素。Incorporating load impedances into the system admittance matrix requires only modification of the diagonal elements of the admittance matrix corresponding to the load nodes.
则修正后的导纳矩阵为Then the corrected admittance matrix is
求解负荷节点i处的戴维南等值参数时，只需断开节点i处的负荷阻抗，求解其开路电压即为戴维南等值电势。When solving the Thevenin equivalent parameter at the load node i, it is only necessary to disconnect the load impedance at the node i, and the open circuit voltage is obtained as the Thevenin equivalent potential.
节点i负荷的等效阻抗断开后，系统结构如图3所示。After the equivalent impedance of node i load is disconnected, the system structure is shown in Figure 3.
只要将Y1中i节点自导纳aii减去负荷阻抗如式(5)所示，即可形成计算开路电压用的节点导纳矩阵如式(6)所示的导纳矩阵Y。As long as the self-admittance aii of node i in Y1 is subtracted from the load impedance as shown in formula (5), the admittance matrix Y of the node admittance matrix for calculating the open circuit voltage can be formed as shown in formula (6).
除bii外，Y与Y1的元素都相同。Except for bii , Y has the same elements as Y1 .
在求解i节点开路电压时，节点电压向量中，PQ节点电压相量为待求量，PV节点和平衡节点电压相量为已知量。采用节点负荷阻抗等效后，节点注入电流向量中均为0，根据节点电压方程可以得出When solving the i-node open circuit voltage, the node voltage vector Among them, the PQ node voltage phasor is the quantity to be sought, and the PV node and balance node voltage phasors are known quantities. After using the node load impedance equivalent, the node injection current vector middle are all 0, according to the node voltage equation, it can be obtained that
式中：节点导纳矩阵和电压向量中元素均为已知量。Where: node admittance matrix and voltage vector middle element are known quantities.
根据以上节点电压方程，可以得到r个方程组成的方程组如式(8)所示：According to the above node voltage equations, the equation group consisting of r equations can be obtained as shown in formula (8):
令make
则式(8)可以写成如下的矩阵形式Equation (8) can be written in the following matrix form
AU＝-B (9)AU=-B (9)
利用高斯消元法求解方程(9)，即可求解出i节点处开路电压即为戴维南等值电势由于导纳阵的稀疏性质，在利用高斯消去求解过程中，将系数矩阵A化简为上三角阵的计算量较小，而且由于只需要计算节点i的开路电压，因此回代过程中算到即可，也无需把全部未知量都解出，进一步加快了求解速度。如需要求解其他节点的等值参数，只需重新修正导纳阵Y1，形成式(9)所示的方程，再次利用高斯消去求解即可。Using the Gaussian elimination method to solve equation (9), the open circuit voltage at node i can be solved Thevenin equipotential Due to the sparse nature of the admittance matrix, in the process of using Gaussian elimination to solve the problem, the calculation amount of simplifying the coefficient matrix A to the upper triangular matrix is relatively small, and since only the open circuit voltage of node i needs to be calculated, the calculation of That is enough, and it is not necessary to solve all the unknowns, which further speeds up the solution speed. If you need to solve the equivalent parameters of other nodes, you only need to re-correct the admittance matrix Y1 to form the equation shown in formula (9), and use Gaussian elimination again to solve it.
戴维南等值参数包括等值电势和等值阻抗。获得全部参数的目的是可以适用于不同的电压稳定判据。基于戴维南等值的电压稳定判据包括基于电压和阻抗比较两种类型，如果仅求得戴维南等值电势仅适用于电压判据，因此还需求取阻抗参数。获得等值电势后，求取等值阻抗的方法是大家都知道的。Thevenin equivalent parameters include equivalent potential and equivalent impedance. The purpose of obtaining all parameters is to be applicable to different voltage stability criteria. The voltage stability criterion based on the Thevenin equivalent includes two types based on voltage and impedance comparison. If only the Thevenin equivalent potential is obtained, it is only applicable to the voltage criterion, so the impedance parameter also needs to be obtained. After obtaining the equivalent potential, the method of obtaining the equivalent impedance is known to everyone.
三、仿真算例分析3. Simulation example analysis
以IEEE-9节点和New England 10机39节点系统为例进行仿真计算，分析验证本方明所提方法的正确性和有效性。对于戴维南等值参数计算准确性验证，算例中以潮流计算结果作为系统运行状态断面数据，通过对比节点负荷波动后实际潮流计算所得电压与应用该节点戴维南等值后的两节点系统计算负荷波动后的电压之间误差的大小来衡量参数辨识结果的优劣。等值参数计算越准确，负荷波动后实际潮流所得该节点电压幅值与戴维南等值的两节点系统计算所得电压幅值之间的偏差就越小。Taking the IEEE-9 node and the New England 10-machine 39-node system as examples, the simulation calculation is carried out to analyze and verify the correctness and effectiveness of the method proposed by Fang Ming. For the verification of the calculation accuracy of Thevenin equivalent parameters, in the calculation example, the calculation results of the power flow are used as the cross-section data of the system operation status, and the voltage calculated by the actual power flow after the node load fluctuation is compared with the calculated load fluctuation of the two-node system after applying the Thevenin equivalent value of the node The size of the error between the final voltages is used to measure the quality of the parameter identification results. The more accurate the calculation of the equivalent parameters is, the smaller the deviation between the voltage amplitude of the node obtained from the actual power flow after the load fluctuation and the voltage amplitude calculated by the Thevenin equivalent two-node system will be.
改进的基于全微分的戴维南等值参数跟踪算法是目前基于局域量测的最新方法，对于等值过程中系统内部变化有较好的适应性，因此选用该方法以及传统的最小二乘法在IEEE3机9节点系统上与本发明所提方法进行对比；并以New England 10机39节点系统为例与基于单一系统状态断面数据将负荷节点等值为耦合单端口网络方法进行对比。结果表明，本发明所提方法不论是在计算准确性还是在计算量上均优于以往方法。The improved Thevenin equivalent parameter tracking algorithm based on full differential is the latest method based on local measurement at present, and it has better adaptability to the internal changes of the system in the equivalent process. Therefore, this method and the traditional least square method are selected in IEEE3 A comparison is made with the method proposed in the present invention on a 9-node system with 10 machines; and a comparison is made with the method of coupling the load node equivalents to a single-port network based on the state section data of a single system using the New England 10-machine 39-node system as an example. The results show that the method proposed by the present invention is superior to the previous methods in terms of calculation accuracy and calculation amount.
3.1IEEE-9节点仿真系统算例3.1 IEEE-9 node simulation system example
IEEE3机9节点系统结构如图4所示。假设已知t1和t5时刻系统潮流断面数据，且相邻两时刻潮流断面间各PQ节点负荷均有较大范围以内的随机波动，PV节点的有功出力随负荷波动等比例变化。根据改进的基于全微分的戴维南等值参数跟踪算法，先计算戴维南等值初值，再代入改进的计算方程求得PQ节点的戴维南等值参数。以节点6为例，根据最小二乘法原理，应用t1和t5时刻节点6的电压相量和有功、无功功率，可计算出t5时刻的戴维南等值参数Eth61，Zth61。根据本发明所提方法，可直接利用t5时刻的潮流断面数据计算节点6的戴维南等值参数Eth63，Zth63。IEEE3 machine 9-node system structure is shown in Figure 4. Assuming that the power flow section data of the system at time t1 and t5 are known, and the load of each PQ node between two adjacent time flow sections has random fluctuations within a large range, the active output of PV nodes changes in proportion to the load fluctuation. According to the improved Thevenin equivalent parameter tracking algorithm based on full differential, the initial value of Thevenin equivalent is calculated first, and then the Thevenin equivalent parameter of the PQ node is obtained by substituting the improved calculation equation. Taking node 6 as an example, according to the principle of least square method, the Thevenin equivalent parameters Eth61 and Zth61 at time t5 can be calculated by using the voltage phasor and active and reactive power of node 6 at time t1 and t5. According to the method proposed in the present invention, the Thevenin equivalent parameters Eth63 and Zth63 of node 6 can be calculated directly by using the tidal current section data at time t5.
为对比t5时刻两组等值参数的准确性，保持其他节点条件不变，节点6的负荷在t5时刻负荷的基础上加入一组30个±35％范围内的随机扰动。扰动后节点6的负荷为S6m＝P6m+jQ6m(m＝1,2，…，30)。将S6m代入t5时刻IEEE3机9节点系统进行潮流计算获得节点6的电压幅值作为标准值。再将S6m代入节点6经戴维南等值后的两节点系统中，对等值参数分别为Eth61、Zth61和Eth62、Zth62以及Eth63、Zth63的两节点系统进行潮流计算获得电压幅值，与标准值进行对比，结果如图5所示。In order to compare the accuracy of the two sets of equivalent parameters at time t5 and keep other node conditions unchanged, a group of 30 random disturbances within the range of ±35% are added to the load of node 6 on the basis of the load at time t5. The load on node 6 after the disturbance is S6m =P6m +jQ6m (m=1, 2, . . . , 30). Substitute S6m into the IEEE 3-machine 9-node system at time t5 for power flow calculation to obtain the voltage amplitude of node 6 as the standard value. Substituting S6m into the two-node system after the Thevenin equivalent at node 6, and performing power flow calculation on the two-node system whose equivalent parameters are Eth61 , Zth61 , Eth62 , Zth62 , and Eth63 , Zth63 to obtain the voltage The amplitude is compared with the standard value, and the result is shown in Figure 5.
图中，电压1为标准值，电压2为本发明所提方法戴维南参数下计算所得电压幅值，电压3为传统最小二乘法计算参数下的电压幅值，电压4为改进的基于全微分的戴维南等值参数跟踪算法所得参数下的电压幅值。图中可见，改进的基于全微分的戴维南等值参数跟踪算法相比传统的最小二乘法有了一定的改善，但本发明方法计算与实际潮流计算结果偏差更小，相对上述两种方法更为准确。为进一步说明等值效果的对比，计算了三种方法的平均误差和最大误差。本发明所提方法的平均误差为0.0741％，最大误差为0.1217％；最小二乘法的平均误差为0.8248％，最大误差为1.4323％；改进的基于全微分的戴维南等值参数跟踪算法的平均误差为0.5605％，最大误差为0.9799％。由此可见，本发明所提方法相对基于局域量测的方法具有更高的准确性。In the figure, voltage 1 is a standard value, voltage 2 is the voltage amplitude calculated under the Thevenin parameter of the method proposed by the present invention, voltage 3 is the voltage amplitude under the traditional least square method calculation parameters, and voltage 4 is an improved method based on full differential The voltage amplitude under the parameters obtained by the Thevenin equivalent parameter tracking algorithm. It can be seen from the figure that the improved Thevenin equivalent parameter tracking algorithm based on full differential has a certain improvement compared with the traditional least squares method, but the deviation between the calculation of the method of the present invention and the actual power flow calculation is smaller, and it is more accurate than the above two methods. precise. To further illustrate the comparison of equivalent effects, the average error and maximum error of the three methods are calculated. The average error of the method proposed by the present invention is 0.0741%, and the maximum error is 0.1217%; the average error of the least squares method is 0.8248%, and the maximum error is 1.4323%; the average error of the improved Thevenin equivalent parameter tracking algorithm based on full differential is 0.5605%, with a maximum error of 0.9799%. It can be seen that the method proposed in the present invention has higher accuracy than the method based on local measurement.
3.2New England10机39节点仿真系统算例3.2 Calculation example of New England 10-machine 39-node simulation system
New England10机39节点系统结构如图6所示。为比较本发明所提方法与基于单一系统状态断面数据将负荷节点等值为耦合单端口网络方法的效果，在New England 10机39节点系统上进行仿真分析。对比方法与4.1中思路类似。首先基于一个潮流断面数据按本发明方法和基于单一系统状态断面数据将负荷节点等值为耦合单端口网络方法分别计算负荷节点i的戴维南等值参数Ethi1、Zthi1与Ethi2、Zthi2。然后保持其他节点条件不变，节点i的负荷在原有负荷的基础上加入一组共20个±35％范围内的随机扰动。扰动后节点i的负荷为Sim＝Pim+jQim(m＝1,2，…，20)。将Sim作为New England 10机39节点系统的i节点负荷进行潮流计算获得节点i的电压幅值作为标准值。再将Sim分别作为节点i经戴维南等值后的两节点系统的负荷，对等值参数分别为Ethi1、Zthi1和Ethi2、Zthi2的两节点系统进行潮流计算获得电压幅值，求得与标准值的相对误差百分比，节点29的对比结果如图7所示。The structure of the New England 10-machine 39-node system is shown in Figure 6. In order to compare the effect of the method proposed by the present invention and the method of coupling the load node equivalent value to a single-port network based on a single system state section data, a simulation analysis is carried out on a New England 10-machine 39-node system. The comparison method is similar to that in 4.1. Firstly, the Thevenin equivalent parameters Ethi1 , Zthi1 and Ethi2 , Zthi2 of the load node i are respectively calculated based on the method of the present invention based on the data of a power flow section and the equivalent value of the load node based on the single system state section data to couple the single-port network method. Then keep the conditions of other nodes unchanged, and add a group of 20 random disturbances in the range of ±35% to the load of node i on the basis of the original load. The load of node i after the disturbance is Sim =Pim +jQim (m=1, 2, . . . , 20). UsingSim as the i-node load of the New England 10-machine 39-node system, the power flow calculation is carried out to obtain the voltage amplitude of node i as the standard value. Then Sim is taken as the load of the two-node system after the Thevenin equivalent of node i respectively, and the voltage amplitude is obtained by performing power flow calculation on the two-node system whose equivalent parameters are Ethi1 , Zthi1 and Ethi2 , Zthi2 respectively, and find The relative error percentage with the standard value is obtained, and the comparison result of node 29 is shown in Figure 7.
图中电压幅值1为标准值，电压幅值2为采用本发明方法戴维南等值参数计算所得负荷节点电压幅值，电压幅值3为采用基于单一系统状态断面数据将负荷节点等值为耦合单端口网络方法所得戴维南等值参数的两节点潮流计算负荷节点电压幅值。由图中曲线所示，在负荷随机变化过程中，本发明方法计算的等值参数准确性高于基于单一系统状态断面数据将负荷节点等值为耦合单端口网络方法。Among the figure, the voltage amplitude 1 is a standard value, the voltage amplitude 2 is the load node voltage amplitude calculated by using the Thevenin equivalent parameters of the method of the present invention, and the voltage amplitude 3 is the coupling of the load node equivalent value based on the single system state section data. Two-node power flow calculation of Thevenin equivalent parameters obtained by the one-port network method load node voltage amplitude. As shown by the curve in the figure, in the process of random load variation, the accuracy of equivalent parameters calculated by the method of the present invention is higher than that of the method of coupling single-port network equivalents of load nodes based on single system state section data.
最后对每个负荷不为零的节点都按照上述思路进行对比，在各个节点上本发明所提方法的参数计算精度均高于基于单一系统状态断面数据将负荷节点等值为耦合单端口网络方法。Finally, each node whose load is not zero is compared according to the above ideas. The calculation accuracy of the parameters of the method proposed by the present invention is higher than that of the single-system state section data based on the load node equivalent value of the coupled single-port network method on each node. .
从计算量的比较上，如果单独计算某一节点的戴维南等值参数，本发明方法所需的计算时间比基于单一系统状态断面数据将负荷节点等值为耦合单端口网络方法小一个数量级，如果需要计算全部负荷节点的等值参数，则两者计算时间相当，其具体时间与系统的规模和负荷节点数目密切相关。就本仿真算例，计算平台为HP Z600工作站，CPU为双四核Xeon E5504，主频2G，内存4G，软件平台为MatLab，潮流工具为开源软件PSAT。计算全部负荷非零节点的戴维南等值参数时间均为5到6毫秒，完全满足在线实时应用的需要。From the comparison of the amount of calculation, if the Thevenin equivalent parameter of a certain node is calculated separately, the calculation time required by the method of the present invention is an order of magnitude smaller than the method of coupling the single-port network with the equivalent value of the load node based on the single system state section data, if If the equivalent parameters of all load nodes need to be calculated, the calculation time of the two is equivalent, and the specific time is closely related to the scale of the system and the number of load nodes. For this simulation example, the computing platform is HP Z600 workstation, the CPU is dual quad-core Xeon E5504, the main frequency is 2G, the memory is 4G, the software platform is MatLab, and the trend tool is open source software PSAT. The time to calculate the Thevenin equivalent parameters of all nodes with non-zero loads is 5 to 6 milliseconds, which fully meets the needs of online real-time applications.
上述虽然结合附图对本发明的具体实施方式进行了描述，但并非对本发明保护范围的限制，所属领域技术人员应该明白，在本发明的技术方案的基础上，本领域技术人员不需要付出创造性劳动即可做出的各种修改或变形仍在本发明的保护范围以内。Although the specific implementation of the present invention has been described above in conjunction with the accompanying drawings, it does not limit the protection scope of the present invention. Those skilled in the art should understand that on the basis of the technical solution of the present invention, those skilled in the art do not need to pay creative work Various modifications or variations that can be made are still within the protection scope of the present invention.
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