Distributed continuation power flow method for integrated transmission and active distribution network

J. Mod. Power Syst. Clean Energy (2015) 3(4):573–582 DOI 10.1007/s40565-015-0167-2 Distributed continuation power flow method for integrated transmission and active distribution network Jinquan ZHAO1, Xiaolong FAN1, Changnian LIN2, Wenhui WEI2 Abstract As the integration of distributed generations (DGs) transforms the traditional distribution network into the active distribution network, voltage stability assessments (VSA) of transmission grid and distribution grid are not suitable to be studied separately. This paper presents a distributed continuation power flow method for VSA of global transmission and distribution grid. Two different parameterization schemes are adopted to guarantee the coherence of load growth in transmission and distribution grids. In the correction step, the boundary bus voltage, load parameter and equivalent power are communicated between the transmission and distribution control centers to realize the distributed computation of load margin. The optimal multiplier technique is used to improve the convergence of the proposed method. The three-phase unbalanced characteristic of distribution networks and the reactive capability limits of DGs are considered. CrossCheck date: 11 October 2015 Received: 5 June 2015 / Accepted: 13 October 2015 / Published online: 25 November 2015  The Author(s) 2015. This article is published with open access at Springerlink.com & Jinquan ZHAO Xiaolong FAN Changnian LIN Wenhui WEI 1 Research Center for Renewable Energy Generation Engineering (Hohai University), Ministry of Education, Nanjing 210098, China 2 Beijing Kedong Electrical Control System Cooperation Limited, Beijing 110179, China Simulation results on two integrated transmission and distribution test systems show that the proposed method is effective. Keywords Integrated transmission and distribution grid, Distributed computation, Voltage stability, Continuation power flow, Three-phase distribution network, Distribution generation 1 Introduction The voltage collapse is one of the most serious risks for modern power systems [1]. Compare with other kinds of stability problems, the long term voltage stability problems can be simulated and approximated by using the static model and methods. In traditional voltage stability assessments (VSA), the transmission power systems (TPSs) and the distribution networks (DNs) are studied separately, which may result in inaccurate assessment results. With high penetration of distributed generations (DGs) and electric vehicles into the distribution grid, the power flows and voltage-reactive power characteristics of the distribution girds have been changed significantly [2]. As a consequence, the DNs have become increasingly active and they are not suitable to be treated as the equivalent loads in power flow analysis of TPSs [3, 4]. Thus, voltage stability problems for TPSs and DNs are not suitable to be solved separately and it is necessary to study the VSA methods for global power grid. There are several technological challenges in solving the global power flow problem. Firstly, the transmission and distribution grids are operated and managed by different control centers in existing dispatch and control system of power grid. The models of TPSs and DNs are maintained separately and transferring models is against privacy 123 574 protection rules, so it is hard to directly solve a whole power flow model in the field. Secondly, the transmission and distribution grids are different in voltage level, topology structure and impedance parameters, which would lead to numerical difficulties. Thirdly, the size of the integrated power system is considerably large. In addition, the threephase unbalanced characteristic of the distribution grids is prominent while the transmission grids are balanced. A ‘‘master-slave-splitting’’ (MSS) based method was proposed in [5, 6]. By decomposing the global power flow into a single transmission power flow master sub-problem and multiple distribution power flow sub-problems, this method addresses the above challenges effectively. The continuation power flow (CPF) is an important tool for assessing power system voltage stability [7–9]. The CPF method has been validated to be a good method to compute the load margins of both TPSs and DNs and it could consider the inequality constraints which describe the nonlinear characteristics of electrical components [10– 17]. In [18] a distributed CPF method was presented to compute the available transfer capability (ATC) of interconnected power grid which is composed of many transmission sub-grids. Based on a reduced network equivalent model, a distributed CPF method for VSA of a transmission sub-grid within the large interconnected power grid was proposed in [19]. However, both of them cannot be directly used to solve the integrated transmission and distribution grid. In [20], an expanded CPF based on masterslave distributed method was presented to compute the total transfer capability of integrated power system. Unfortunately, because the same parameterization technique is used in CPF computation of both transmission and distribution grids in this CPF method, the uniformity of load increases of TPS and DNs and accuracy of voltage stability critical point are difficult to be guaranteed. This paper presents a distributed continuation power flow (DCPF) method for integrated transmission and distribution grid. The transmission CPF/PF and distribution PF/CPFs are run iteratively and only the load parameter, the powers and voltage phasors of the boundary buses are communicated between the control centers. The different parameterization schemes are used to realize the uniform load increase of TPS and DNs. The parameterization switching logic and the optimal multiplier Newton power flow technique are adopted to improve the convergence. The reactive capability limits of DGs in unbalanced threephase distribution networks are also considered by using the bus type double switching logics. At last, some numerical examples are given to show the effectiveness of our method. 123 Jinquan ZHAO et al. 2 Global VSA problem formulation Figure 1 shows the global power grid which consisting of one transmission grid and n distribution grids. In Fig. 1, the transmission and distribution grids are denoted by T and D and they are connected at the point of common couple (PCC) buses. The global VSA problem can be formulated as follows. max k ð1Þ s:t: f T;p ðxpcc ; xT Þ þ kDPT;g ¼ 0 ð2Þ f T;q ðxpcc ; xT Þ ¼ 0 ð3Þ fDi ;pcc;p ðxT ; xDi ;pcc ; xDi Þ ¼ 0 i ¼ 1; 2;    ; n ð4Þ fDi ;pcc;q ðxT ; xDi ;pcc ; xDi Þ ¼ 0 i ¼ 1; 2;    ; n ð5Þ f Di ;p ðxDi ;pcc ; xDi Þ  kDPDi ¼ 0 i ¼ 1; 2;    ; n ð6Þ f Di ;q ðxDi ;pcc ; xDi Þ  kDQDi ¼ 0 i ¼ 1; 2;    ; n ð7Þ  T;g QT;g  QT;g ðxT ; xpcc Þ  Q ð8Þ QDi ;DG ðxDi Þ\0 ð9Þ nT;g X k¼1 DPT;g;k ¼ i ¼ 1; 2;    ; n nDi ;L n X X ð10Þ DPDi ;j i¼1 j¼1 where k is the load parameter; n is the number of distri (...truncated)