energies Article Co-Design Optimization of Direct Drive PMSGs for Offshore Wind Turbines Based on Wind Speed Profile Linh Dang, Serigne Ousmane Samb, Ryad Sadou and Nicolas Bernard * IREENA, Nantes University, CRTT 37 Bd de l’Université, 44600 Saint-Nazaire, France; [email protected] (L.D.); [email protected] (S.O.S.); [email protected] (R.S.) * Correspondence: [email protected] Abstract: This paper presents a new method to optimize, from a working cycle defined by torque and speed profiles, both the design and the control strategy of permanent magnet synchronous generators (PMSGs). The case of a 10 MW direct-drive permanent magnet generator for an Offshore wind turbine was chosen to illustrate this method, which is based on the d–q axis equivalent circuit model. It allows to optimize, with a reduced computation time, the design, considering either a flux weakening control strategy (FW) or a maximum torque per Ampere control (MTPA) strategy, while respecting all the constraints—particularly the thermal constraint, which is characterized by a transient regime. The considered objective is to minimize the mass and the average electric losses over all working points. Thermal and magnetic analytical models are validated by a 2D finite element analysis (FEA). Keywords: PMSG; co-design optimization; flux weakening control; MTPA control; wind speed profile; offshore wind energy Citation: Dang, L.; Ousmane Samb, S.; Sadou, R.; Bernard, N. Co-Design Optimization of Direct Drive PMSGs for Offshore Wind Turbines Based on 1. Introduction Wind Speed Profile. Energies 2021, 14, Offshore wind generation has taken an increasingly important place in the European 4486. https://doi.org/10.3390/ wind power development, in recent years. It presents high availability, stable wind speed en14154486 and less environmental constraints. In order to reduce the costs, increasing the turbine power is a strong trend. However, it leads to increase in active and structural masses, Academic Editor: Davide Astolfi which are limited by technology, transport and installation. Therefore, maximizing the power density is a crucial criterion in the design process. Received: 18 June 2021 In that case, variable-speed wind turbines with pitch control are used to optimize the Accepted: 21 July 2021 Published: 24 July 2021 turbine output power [1,2]. Generally, the working cycle is not taken into account in the design process. In most cases, the generator is only designed for the rated power [3–6]. Publisher’s Note: MDPI stays neutral Such a method can lead to oversize the generator, particularly when it works in a variable with regard to jurisdictional claims in thermal regime. On the other hand, the maximization of the energy efficiency, that can be published maps and institutional affil- achieved by a flux weakening mode, for example [7], implies that all working points have iations. to be taken into account [8]. One of the most important issues in a design process which considers several thou- sands of working points is that, in addition to optimizing the geometric parameters, it must also optimize the time-dependent control parameters id(t) and iq(t) while respecting all the constraints in each point, leading to a huge computation time. To overcome this Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. problem, the solutions currently proposed in the electrical engineering literature limit the This article is an open access article optimization problem to the most representative working points [9–11], which makes the distributed under the terms and result approximate, because the control strategy, as well as the thermal transient, is not conditions of the Creative Commons managed. Attribution (CC BY) license (https:// The aim of this paper is to present an optimal design methodology to solve this creativecommons.org/licenses/by/ problem. The proposed method allows to optimize simultaneously the geometry as well as 4.0/). the control parameters (id(t) and iq(t)) of each working point for the following two cases: Energies 2021, 14, 4486. https://doi.org/10.3390/en14154486 https://www.mdpi.com/journal/energies Energies 2021, 14, x FOR PEER REVIEW 2 of 17 Energies 2021, 14, 4486 The aim of this paper is to present an optimal design methodology to solve this prob-2 of 17 lem. The proposed method allows to optimize simultaneously the geometry as well as the control parameters (푑(푡) and 푞(푡)) of each working point for the following two cases: a maximum torque per Ampere (MTPA) control with 푑(푡) = 0 and a flux weakening (FW) a maximum torque per Ampere (MTPA) control with i (t) = 0 and a flux weakening (FW) control with (푡) = (푡) ≠ 0. The case of a 푞 −phasesd 10 MW direct-drive surface control with 푑i (t) =푑i 표푝푡 (t) 6= 0. The case of a q—phases 10 MW direct-drive surface mounted PMSGd was chosend opt to illustrate our study, with an offshore wind speed profile mounted PMSG was chosen to illustrate our study, with an offshore wind speed profile measured in the North Sea and the two following objective functions: mass minimization measured in the North Sea and the two following objective functions: mass minimization and energy loss minimization. and energy loss minimization. The paper is organized as follows. In Section 2, the principle of the design methodol- The paper is organized as follows. In Section2, the principle of the design methodol- ogy is presented and, in Section 3, the sizing model and the constraints used are given. In ogy is presented and, in Section3, the sizing model and the constraints used are given. In Section 4, the results are presented and discussed. Finally, the selected optimal machine Section4, the results are presented and discussed. Finally, the selected optimal machine is isvalidated validated by by the the use use of of a a magnetic magnetic and and thermal thermal 2D 2D finite finite element element analysis analysis (FEA). (FEA). AtAt last, last, let let u uss note thatthat aa first first presentation presentation of of the the methodology methodology was was partially partially presented pre- sentedat the at International the International Conference Conference on Electrical on Electrical Machines Machines ICEM ICEM 2020 2020 [12 ],[12] where, where only only the theFW FW control control was was considered. considered. The The articlearticle proposesproposes a more complete complete version version,, where where the the twotwo controls controls (FW (FW and and MTP MTPA)A) are arestudied studied and andcompared. compared. The mecha The mechanicalnical constraints constraints con- sideredconsidered are also are more also more realistic. realistic. 2.2. Optimal Optimal Design Design Methodology Methodology TheThe presented presented methodology methodology is is based based on on the the d d–q–q axis axis equivalent equivalent circuit circuit model model taking taking ironiron losses losses into into account account via via the the iron iron loss loss resistance resistance ℛR휇m(푡()t) (see(see Figure Figure 1)[) [1313,,1414]].. (a) (b) FigureFigure 1. 1. (a()a d)- d-axisaxis equivalent equivalent circuit circuit;; (b ()b q)- q-axisaxis equivalent equivalent circuit circuit.. TheThe optimization optimization parameters parameters can can be be categorized categorized into into three three groups groups as as follows follows:: • • TheThe time time-dependent-dependent control control variables variables are the d–qd–q axis currentscurrents ioq표푞(t()푡)and andiod (표푑t)(.푡 In). ourIn ourmethod, method, they they will will be be analytically analytically expressed expressed for for the the two two control control strategies strategies considered. consid- • eredThe. rotor variable Bf m, the magnitude of the air-gap flux density created by the ( ) • Themagnets rotor variable represented 퐵푓푚 in, the the magnitude circuit via the of the electromotive air-gap flux force densitye0 t created. It will by be optimizedthe mag- analytically to minimize the energy losses for the considered working cycle. Note that nets represented in the circuit via the electromotive force 푒0(푡). It will be optimized analyticallythe magnets to are minimize sized (shape the energy and remanence) losses for afterwards,the considered from workingBf m opt. cycle. Note • thatThe the stator magnets geometry are sized variables (shape are andR remanence), rs, rw, wmag afterwards,, ns, tLR pfromand 퐵q푓푚(see 표푝푡. Figure 2), which are in the expressions of coefficient kf, armature reactance (X(t)) and resistance Energies 2021, 14, x FOR PEER REVIEW• The stator geometry variables are 푅, 푟푠, 푟푤, 푤푚푔, 푛푠, 휏퐿푅 푝 and 푞 (see Figure3 of2) 17, (R , R (t)) (see Figure1). These parameters will be optimized by the use of a genetic whichc arem in the expressions of coefficient 푘휙 , armature reactance (푋(푡)) and re- algorithm to minimize both the mass and the energy losses. sistance (ℛ푐, ℛ휇(푡)) (see Figure 1). These parameters will be optimized by the use of a genetic algorithm to minimize both the mass and the energy losses. Figure 2. Design and geometric parameters of the PMSG. Figure 2. Design and geometric parameters of the PMSG. The proposed optimization method is performed in three steps. The proposed optimization method is performed in three steps. In step 1, for the FW control, the optimal current 표푑 표푝푡(푡) that minimizes the total electric losses 푃푡표푡 for each working point is expressed analytically. For the MTPA con- trol, this current is zero. For both of these controls, the 푞-axis current is directly imposed by the torque. The analytical expressions of the currents allow to express 푃푡표푡 as a function 표 of the other optimization parameters, so that 푃푡표푡 = 푓 (푅, 푟푠, 푟푤, 푤푚푔, 휏퐿푅, 푛푠, 푝, 푞, 퐵푓푚). In step 2, from the previous expression of 푃푡표푡, the optimal flux density 퐵푓푚 표푝푡 that minimizes the energy losses 푊푡표푡 is analytically expressed, allowing to express 푊푡표푡 as a function of the remaining optimization parameters as 푊푡표푡 = 표 푓 (푅, 푟푠, 푟푤, 푤푚푔, 휏퐿푅, 푛푠, 푝, 푞).