IEEE PEDS 2019, Toulouse, France 9-12 July 2019 Particle Swarm Optimization Tuning of MMCs in a Time-Invariant Framework Gilbert Bergna-Diaz * , Andrea Formentini ‡ , Pericle Zanchetta ‡ and Elisabetta Tedeschi * * Dept. of Electric Power Engineering ‡ Power Electronics, Machines and Control Group (PEMC) Norwegian University of Science and Technology (NTNU) The University of Nottingham - Nottingham Trondheim, Norway Nottingham, United Kingdom {gilbert.bergna, elisabetta.tedeschi}@ntnu.no {andrea.formentini, pericle.zanchetta}@nottingham.ac.uk 978-1-5386-6499-5/19/$31.00 ©2019 IEEE Abstract—This work investigates the Particle Swarm Optimiza- tion (PSO) algorithm as a tool to tune the control parameters of a Modular Multilevel Converter (MMC) in a single-terminal HVdc configuration. More precisely, due to its inherent capacity of handling system non-linearities, the PSO algorithm is used to tune a nonlinear control structure based on passivity arguments capable of ensuring global asymptotic stability of the converter. This nonlinear control strategy was successfully applied to the MMC in HVdc configuration in previous efforts, albeit with sub- optimal tuning, and therefore below par performance. Thus, this work aims to contribute to the state of the art by proving that system performance under the nonlinear control structure of interest can be further improved via PSO-tuning. Finally, to reduce the computational burden, we propose to apply the PSO algorithm directly to a recent state-space representation of an MMC with a constant equilibrium point. I. I NTRODUCTION Multi-Terminal (MT) High-Voltage Direct-Current (HVdc) transmission systems are arguably one of the major infrastruc- ture developments in this day and age, considered the preferred solution for integrating large volumes of renewable energy into the existing power grids, over very long distances [1]. Although two-level voltage source converters (2L-VSCs) have been traditionally used as the main component of MT-HVdc grids, attention has shifted to Modular Multilevel Converters (MMCs) [2], as the new preferred solution, mainly due to their reduced losses, modularity, scalability, low harmonic distortion and consequently reduced filtering requirements [3]. It is expected that the MMCs forming an MT-HVdc grid will need to guarantee a certain degree of interoperability between all the system components and associated controllers. In other words, stability and performance requirements of the overall interconnected system will need to be ensured. This becomes both, particularly important and challenging due to the expected multi-vendor nature of the system [4], as the local power converter controllers will usually be subjected to confidentiality agreements. A straightforward solution to overcome this problem is indeed relying on local controllers with plug and play features. A possible approach for a plug and play stability guaranteed control design with simple PI controllers for the MMC was implemented in [5], [6], based on the passivity theory [7]– [10], and therefore extending to the MMC case the works of [11], [12] originally applied to 2L-VSCs. Nonetheless, even if global asymptotic stability was guaranteed, the controller in [5], [6] had sub-optimal tuning, and therefore below par performance. Thus, we are interested here in improving the tuning and consequently the performance of the nonlinear control applied to the MMC in [5], [6]. Towards this end, in this paper we investigate the potential of applying the Particle Swarm Optimization (PSO) algorithm [13], originally proposed in [14], to tune the MMC control parameters of the nonlinear control structure presented in [5], [6]. The PSO algorithm has been chosen due to its capability of handling system nonlinearities, its simple implementation and relatively low computational cost, compared to other methods [15], as well as its success in the power system community [16]. However, its heuristic nature still makes it computationally intensive. Therefore, it will be of interest to use a model able to reduce as much as possible the computational cost of the algorithm. Thus, this work is based on the steady-state time-invariant (SSTI) representation of the MMC proposed in [17], [18] which stabilizes at a constant equilibrium point instead of an oscillatory orbit. Using this equivalent state-space representation will allow for: 1) The use of efficient variable-step solvers; i.e., once the constant equilibrium is approached, the solver can use larger steps, decreasing the computational burden. 2) Initializing the converter variable at a constant equilib- rium point, which in turns allow to apply the PSO tuning algorithm under an event of interest (e.g.: reference change) from the first iteration. 3) Simple inclusion of constant references in the objective function; as opposed to generating oscillatory references which are more computationally costly. It is therefore proposed here as a suitable MMC model for tuning the control parameters by means of the PSO method- ology. The rest of the paper is organized as follows. In section II, the MMC average modelling conventions, as well as the equivalent model with time-invariant solutions proposed in [17] are briefly recalled. Section III gives a brief summary