Reliability evaluation of modular multilevel converter based on Markov model

J. Mod. Power Syst. Clean Energy https://doi.org/10.1007/s40565-019-0515-8 Reliability evaluation of modular multilevel converter based on Markov model Liang ZHANG1,2 , Dan ZHANG3, Ting HUA1, Jihong ZHU2, Gang CHEN4, Tongzhen WEI5, Ting YANG1 Abstract The modular multilevel converter (MMC) is now the most attractive topology for medium and high voltage power conversion applications with several advantages over the traditional voltage source converter (VSC). However, due to a large number of sub-modules (SMs) in the MMC, system reliability is a big challenge in its practical application, where each SM may be considered as a potential point of failure. In this paper, a reliability evaluation based on the Markov model is proposed for the MMC. The failure rates of the power electronic devices and SMs are firstly analyzed. Then, the Markov model and the state transition equation of the system are built in detail. A general reliability evaluation function is established, in which the mean time to failure and reliability evaluation of the MMC with redundant SMs are also discussed. Finally, a practical direct current (DC) distribution example for reliability evaluation is analyzed, and the results verify that CrossCheck date: 21 December 2018 the reliability evaluation based on the Markov model could provide a useful reference for project design. Keywords Modular multilevel converters, Reliability evaluation, Markov model 1 Introduction The offshore wind power has been widely developed in Europe, China, the United States and Australia [1]. Voltage source converter (VSC) based high voltage direct current (HVDC) transmission systems, including multi-terminal HVDC systems, are widely applied to transmit the power [2, 3], in which the modular multilevel converter (MMC) topology attracts the most attention of researchers [4]. The MMC topology is also used in DC distribution and power quality control, such as a unified power flow controller (UPFC) and static synchronous compensator (STATCOM) [5, 6]. Most research has focused on the operation and control Ting YANG Received: 23 December 2017 / Accepted: 24 December 2018 Ó The Author(s) 2019 & Liang ZHANG 1 School of Power Electric Engineering, Nanjing Institute of Technology, Nanjing 211167, China 2 State Key Laboratory of Intelligent Technology and Systems, Tsinghua University, Beijing 100084, China 3 School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China 4 State Grid Jiangsu Electric Power Company Xuzhou Power Supply Company, Xuzhou 221005, China 5 Institute of Electrical Engineering, Chinese Academy of Sciences, Beijing 100190, China Dan ZHANG Ting HUA Jihong ZHU Gang CHEN Tongzhen WEI 123 Liang ZHANG et al. strategy of MMCs [7–11], while their failure prediction has not received much discussion, although it is an important issue in power systems [12, 13]. Hence, there is a big motivation to find a solution for reliability evaluation and submodule (SM) redundancy configuration of the MMC. Some tentative work has been done in previous studies. For example, redundancy and reliability indexes of the MMC were defined in [14], but the general reliability function was not built. Also, using the k-out-of-n: G model and Gamma distribution, a reliability function of MMC was established [15], wherein the failure rates of SM components were based on the experience-hypothesis. Explicit models of components were not given. Some research has focused on the optimal number of SMs, without considering reliability evaluation [16, 17]. In this paper, the Markov model is proposed to analyze the failure rates of the MMC and its SMs, based on a graphical representation of system states. A general function for reliability evaluation of the MMC is given. The mean time to failure and reliability evaluation of the MMC with a redundant SM are both discussed. The paper is organized as follows. In Section 2, the basic operation principles of the MMC are presented. In Section 3, the cause and impact of SM failure are discussed. Reliability analysis of MMC is given in Section 4, and with a redundant SM in Sections 5. Finally, an example analysis is provided in Section 6. S1 P 3 Cause and impact of SM fault Each SM may be considered as a potential point of failure [19]. Hence, it is important to know the causes and impact of a SM fault. 123 + uc + SM S2 D2 iaP Udc /2 SM LS ujm L0 o Udc /2 c b a SM iaN SM N Fig. 1 Diagram of MMC Table 1 Working mode of SM State S1 S2 ON ON OFF uc OFF OFF ON 0 BLOCK OFF OFF 2 Basic operation principles of MMC A three-phase MMC is shown in Fig. 1, which consists of six arms, with n SMs in each arm [18]. L0 is the arm inductor; Udc is the DC bus voltage; ujm (j=a, b, c) is the output voltage of phase j and uc is the capacitor rated voltage. Each SM has three states, as shown in Table 1. State A is called ‘‘ON’’ state, where switch S1 is ON and switch S2 is OFF. The output voltage is uc . State B is called the ‘‘OFF’’ state, where switch S1 is OFF switch S2 is ON. The output voltage is 0 V. State C is called the ‘‘BLOCK’’ state, where switch S1 and switch S2 are OFF. In the ‘‘BLOCK’’ state, when the current is flowing into the SM, iSM is positive and the output voltage is uc . When the current is flowing out of SM,iSM is negative and the output voltage is 0 V. D1 iSM uSM Positive uc Negative 0 3.1 Causes of SM fault There are three main causes to trigger the failure of a SM. 1) Damage to a power electronic component 2) The overload capability of power electronic components, such as insulated gate bipolar transistors (IGBTs) and diodes, is limited, so overvoltage and overcurrent might break them. Therefore, the damage to a power electronic component is one of the most common reasons to cause the SM fault. Damage to a passive component The DC capacitor is a key passive component in a SM, and damage to it would also cause a SM fault. Fortunately, its failure rate is lower than that of power electronic devices. Reliability evaluation of modular multilevel converter based on Markov model 3) 0 A faulty trigger pulse If the trigger pulse signal experiences interference, it could not operate the SM correctly, and this might lead the SM to a fault in either short circuit or open circuit mode [20]. y P ðpt Þi si B B i¼1 þ pI kEOS kdiode ¼ BðpU k0 Þ @ son þ soff |fflfflffl{zfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflffl} kover kdie 4 Reliability analysis of MMC To evaluate the MMC’s reliability, an analysis of the reliability of semiconductor devices (IGBTs and diodes) and capacitors is first required for use in the Markov model. 4.1 Component failure rate Power electronic components play an important role in reliability of the whole system, so it is necessary to estimate their failure rates [21, 22]. An extensive database of various types of parts is provided in the RDF-2000 [23], which is widely accepted and frequently used to (...truncated)