A novel modular multilevel converter modelling technique based on semi-analytical models for HVDC application

J. Electrical Systems 12-4 (2016): 649-659 Ahmed Zama1*, 1,2 Seddik Bacha , Abdelkrim Regular paper Benchaib 1, David Frey1,2 and A novel modular multilevel converter Sebastien Silvant1 modelling technique based on JES Journal of Electrical Systems semi-analytical models for HVDC application Thanks to scalability, performance and efficiency, the Modular Multilevel Converter (MMC), since its invention, becomes an attractive topology in industrial applications such as high voltage direct current (HVDC) transmission system. However, modelling challenges related to the high number of switching elements in the MMC are highlighted when such systems are integrated into large simulated networks for stability or protection algorithms testing. In this work, a novel dynamic models for MMC is proposed. The proposed models are intended to simplify modeling challenges related to the high number of switching elements in the MMC. The models can be easily used to simulate the converter for stability analysis or protection algorithms for HVDC grids. Keywords: HVDC transmission; modular multilevel converter (MMC); full order model, reduced order model. Article history: Received 20 April 2016, Accepted 11 August 2016 1. Introduction Renewable energy generation, in form of offshore windfarms, is rapidly growing. The power generated has to be transmitted in order to make a connection to an AC network. In [1, 2], it has been proved that the optimal solution for such energy transmission is the High Voltage Direct Current (HVDC) technology. With the development of voltage source converter (VSC), the concept of connecting several off-shore wind farms with several onshore AC grids based on VSCs has become conceivable and can provide more flexibility in integration of renewable energy [3,4]. Compared with classical two level Voltage Source Converters (VSC), HVDC systems based on Modular Multilevel Converter (MMC) offer significant advantages. Regarding these advantages, straightforward voltage balancing, possibility of imbalanced operation, harmonic reduction…, it has been proved [1] that all the future HVDC developments will be based on such devices. This topology, invented by [5], helps reducing converter losses by using low switching frequency. In addition, filter requirements are mitigated by using a significant number of submodules (SMs) per phase. However, the large number of SM in the MMC introduces modelling challenges. For instance, in the electromagnetic transient (EMT) simulation programs, the switching operation is modelled by admittance matrix; the dimension of this matrix is given by the converters state variables number. This matrix must be inverted at each switching operation. Therefore, regarding the high dimension of the system and without an appropriate model according to this type of study, it is practically impossible to simulate, with accuracy, HVDC systems containing MMC converters on EMT-type * Corresponding author: A. Zama, SuperGrid Institute SAS, 130 Leon Blum, BP 1321, 69611 Villeurbanne, France, E-mail: 1 SuperGrid Institute SAS, 130 Leon Blum, BP 1321, 69611 Villeurbanne, France. 2 Grenoble Alpes University - G2Elab, 38031 Grenoble, France. Copyright © JES 2016 on-line : journal/esrgroups.org/jes A. ZAMA et al: A novel modular multilevel converter modelling technique.... simulation programs [6, 7]. To solve this issue, different models have been developed for studying the normal operation of MMC: Detailed model, Equivalent model and Averaged model [8, 9]. Another challenge of MMC modelling is to model the blocking state of SMs which is required to develop a protection strategies for HVDC system. The mathematical formulation has been already demonstrated but the proposed solution consists in switching between two circuit models (controlled and blocked) by using a numerical solution to achieve this transition between circuits. This paper presents an innovative solution for full order MMC type models: Detailed, Equivalent and Averaged based on a semi-analytical model for MMC arm in order to have the both states in the same model and accelerates the simulation. This contribution is based on an idea given by [10] applied to the reduced order averaged model of the MMC which is improved in this paper. The outline of this article is as follows. In Section 2, the basic operating principles of MMC are presented. In Section 3, different MMC models are discussed. The SemiAnalytical model for reduced order model is introduced in Section 4. The proposed full order MMC models with associated semi-analytical equations are presented in Section 5. To compare between these MMC models, some simulations and results are proposed in Section 6. 2. MMC operation and principle The topology of a typical three-phase half bridge MMC is shown in Fig 1-(a), every leg of the converter has two arms; each one has N identical SMs connected in series. Each SM has two power switches (two IGBTs with anti-parallel diodes) and one capacitor C connected as shown in Fig 1-(b). The SM can provide two different voltage levels, when S1 is ON and S2 is OFF. The SM provides voltage Vc when the capacitor can be charged or discharged depending on the current direction. When S2 is ON and S1 is OFF, the capacitor is bypassed by S2 and the SM has zero output voltage. In the blocked state: S1 and S2 are off, the capacitor may charge through S1 and cannot discharge. SM SM SM SM SM SM SM SM SM SM SM SM SM SM SM SM SM SM SM SM SM SM SM SM Fig. 1. (a) Three-phase half bridge MMC topology, (b) Half bridge submodule 650 J. Electrical Systems 12-4 (2016): 649-659 (1) Unlike a classical VSC, the MMC has a reactor in each arm. The converter reactors have two functions: Limitation of arm-current harmonics and fault currents. The applied modulation process is arranged to ensure the condition (1) of operation and to produce the desired (N+1) different levels for AC output voltage) where and are respectively upper and lower inserted SMs numbers. 3. MMC modeling The main families of MMC models are represented by the full order detailed continuous model, the full order sampled model and the reduced order averaged one. For more details, all these models are well documented in [11]. 3.1 Type 1: Full Order Detailed Model. The knowledge based model is close to physical system, it is named usually as the detailed model or the topological one. The switches model is simplified to a resistance which has two values: ON-state (mΩ) and OFF-state (MΩ) (See Fig.2-Type1) [12]. For more accurate studies, for example study of current distributions and losses calculations, the switches models are completed by a nonlinear representation of IGBTs. For our considered purposes, stability analysis and protection algorithms, the model presented in Fig. 1 is regarded as our Benchmark Model. The main drawback of this model (circuit based) is the needed computation time. 3.2 Type 2: Full Order Equivalent Model. In order (...truncated)