Optimal Control Design for Modular Multilevel Converters Operating on Multi-Terminal DC Grid Mohamed Moez Belhaouane∗ , Julian Freytes∗ , Mohamed Ayari† , Frderic Colas‡ , Franois Gruson‡ , Naceur Benhadj Braiek† , and Xavier Guillaud∗ ∗ L2EP, Ecole Centrale de Lille, 59650, Villeneuve dAscq, France. {mohamed-moez.belhaouane, xavier.guillaud}@ec-lille.fr † LSA, Ecole Polytechnique de Tunisie, BP. 743, La Marsa, Tunisie. {mohamed.ayari, naceur.benhadj}@ept.rnu.tn ‡ L2EP, Arts et Mtiers ParisTech, 8 Bv Louis XIV, 59046 Lille, France. {frederic.colas}@lille.ensam.fr, {françois.gruson}@ensam.eu Abstract—This paper proposes an advanced control strategy for Modular Multilevel Converters (MMC) integrated in Multiterminal DC grid. In this present work, a three terminal MMC-MTDC system connecting onshore AC systems with an offshore wind farm is setup. Firstly, the voltage droop control associated to the conventional cascaded controllers for MMC stations is studied, the dynamic behavior of the DC voltage is analyzed and some drawbacks are outlined. In order to improve the dynamic behavior of the controlled DC bus voltage and the stability of MTDC system, an optimal multivariable control strategy of each MMC converter is proposed and integrated in a voltage droop controller strategy. The designed advanced controller allows to improve the overall DC grid stability and to reach the droop values designed on static considerations with acceptable dynamic behavior. By means of numerical simulations in EMTP-RV software, it is shown that the proposed control strategy performs well the stability of MTDC grid with 400level model for MMC compared with the classic existing control methods. Index Terms—Modular Multilevel Converters (MMCs), MultiTerminal DC grids (MTDC), Droop voltage controller, Multivariable state space controller, linear optimal quadratic controller. I. I NTRODUCTION Currently, the need to transmit high amounts of electrical energy to different places, located at a great distances and the ability to connect more than two HVDC station by a DC grid, make the emergence of MTDC systems suitable for the integration of large scale renewable energy sources. Hence, the development of multiterminal DC grids (MTDC) to exploit and connect remotely located offshore wind energy resources to onshore AC systems is an important step towards the integration of renewable energy in the grid [1] thanks to the improvement of reliability, the decrease of conversion losses and the minimization of environmental and energetic cost [2]. Before, the converter substations of HVDC systems were equipped with classical Voltage Source Converters (VSCs) such as for Cross Sound Project [3]. However, according to a typical three level converters, it is difficult to reach the desired DC bus voltage levels, e.g. 640 KV, due to the large voltage stress on each switch. For this reason, MMC converters have gained popularity and are currently an appropriated solution since a higher number of voltage levels help to decrease the AC harmonic content, avoid the need of passive filters and decrease switching losses [4], [5]. Then, MMC has prodigious potential mainly in transmission applications, such as wind farm connection, point to point HVDC links, multiterminal operation and passive network power supply. Furthermore, some research concerning the modeling and control of multiterminal DC systems on VSCs converters have been proposed in literature [6]. Many studies have been carried out on the control design of MTDC systems using the Voltage Droop Control strategy [7]. The main idea of the droop control method, when more than one converter are controlling the DC voltage at the same time, is inspired from the primary frequency control [8].The implementation of power voltage droop suspends the requirement to have a master converter in the MTDC network and ensure the correct power sharing in case of a power variation or, worse, a converter tripping. So, different droop controller techniques have been investigated [2], regarding the control of MTDC grids. In [9], an analytical expression for estimating the distribution of balancing power which accounts for dc line voltage drops is derived. In [10], a scheme for adapting the droop coefficients to share the burden according to the available headroom of each converter station is proposed. However, in most of the suggested approaches, the droop is set to a value close to 5%, i.e., typical value for frequency droop controllers. Nevertheless the design of droop parameters is based on steady states criterions [11]. The dynamic behaviors have not been accorded a considerable attention in these previous studies for the sizing of the droop value. The use of a low droop constant value may give high dynamics for the DC bus voltage inducing important oscillations which can deteriorate the stability of the MTDC system. It is important to remark that for the results mentioned above, the control methodologies of MTDC-based converters are subjected to conventional controllers such as PI/PID controllers. Thus, in order to overcome these problems, the proposed idea in this paper consists to associate a classical droop control with advanced controllers for each MMC converter which constitutes the DC grid. This allows improving the overall DC grid stability and reaching the droop values designed on static considerations with acceptable dynamic behavior. The proposed multivariable optimal control method for MMC converters allows transferring the desired power, minimizing the circulating currents and controlling the stored energy of the MMC converter. The optimal control technique provides a uniform control law for all states variables to overcome the known drawbacks of conventional cascaded control structure based on PI/PID controllers, like stability problem which can be caused by the effects of interaction between the inner and outer loops. The paper is organized as follows: Section II presents the studied three terminal MMC-HVDC systems. In section III, the description and modeling of the used MMC converter in MTDC system are presented. Based on this, Section IV mainly focuses on the conventional controllers and the proposed control strategy of MMC converter integrated in MTDC transmission system. In section V, performance of the proposed control strategy based on optimal control method associated to the droop technique, is evaluated for a multi-terminal DC system Finally, Section VI concludes this paper. II. T HE S TUDIED THREE TERMINAL MMC-HVDC S YSTEM The proposed MMC-MTDC test system used to assess control performance of the DC grid is presented in Fig. 1. This studied system is composed of three converter stations, two stations are onshore and one is offshore. The two onshore stations are directly linked by a 75 km long DC cable. An offshore wind farm is connected to the two onshore stations through DC cables with different lengths (see Fig. 1). In order to deliver the wind power to the DC grid, only grid side converters are equipped with voltage droop controllers, offshore station is controlling its power flow to supply the wind power into DC grid. Thus, the control system must perform the transfer of the wind farm power to the onshore grid and also a power transfer between the two onshore injection points. As already said above, the voltage droop controller is inspired by the primary frequency control [8]. The frequency counterpart in the DC system is the DC voltage level. Hence, according to the same principle, the power flow can be controlled by a power-voltage droop. However, the voltage droop controller is designed by a simple proportional controller depicted in Fig. 2. Furthermore, different droop techniques within MTDC grids such as dead band droop method or piecewise droop method are proposed in literature [7]. In this study, the classical droop technique is adopted which has some advantages and gives interesting results by increasing the reliability and reducing the stress on the DC grid. From the voltage droop controller presented by Fig. 2, it yields 1 ∆vdc , where ∆pg (in W the following relation ∆pg = − Kdroop or pu) is the deviation power injected into the AC grid, ∆p∗g0 is the power set point, ∆vdc (in V or pu) is the deviation of DC voltage and Kdroop (in V /W or pu/pu) is the droop value. Figure 1. MMC converter based 3-terminal MTDC system Figure 2. DC voltage Droop Controller III. MTDC BASED C ONVETER : MMC CONVERTER A. Description and Topology of MMC Converter Figure 3. MMC topology The MMC topology is recalled in Fig. 3. Each phaseleg consists of two arms, i.e., an upper arm (represented by subscript ”u”) and a lower arm (represented by subscript ”l”). Each arm is comprised of N series- connected, nominally identical, half-bridge SMs, one inductor, and one resistor. Each SM can provide two voltage levels at its terminals, i.e., zero or vcmi, j ,m=u,l; j=a,b,c. , depending on the state of its complementary switches S1 and S2 [12]. The index ” j = a, b, c” are designated, throughout the present paper, as the three-phase variables and asterix symbol for the reference signal. Each arm includes also an arm inductance Larm and arm resistance Rarm . In the AC-side, the filter is modeled by the inductance L f and the resistance L f . So, regarding the published works, different models can be used according to the type of study and required accuracy. Since the detailed IGBT-based model is nonlinear and quite complex to be used in control task, a simplified model is proposed in order to simplify the study. In this model, each MMC arm is averaged using the switching function concept of a half-bridge converter. IV. C ONTROL T ECHNIQUES OF MMC C ONVERTER A. Classical control strategy of MMC converter [4] In this study, an energy based control is considered. This supposes to control the AC and DC power independently. On the AC side, the grid currents are regulated using a classical (d − q) frame control to decouple active and reactive powers, and ensure the stability of grid currents. B. Modeling of MMC Converter Based on the average model widely presented in [13] and applying the Kirchhoff theorem, the mathematical equations that govern the dynamic behavior of MMC converter in phase j are given as follows: diu j dig j vdc − vmu j − Rarm iu j − Larm = vg j + Rig j + L 2 dt dt (1) dil j dig j vdc − vml j − Rarm il j − Larm = vg j + Rig j + L 2 dt dt (2) By adding and subtracting the equations (1) and (2), the dynamics of the main currents of MMC converter ig j and idi f f j are obtained as dig j R0 1 1 = − 0 ig j + 0 vv j − 0 vg j dt L L L didi f f j Rarm 1 =− idi f f j + vdi f f j dt Larm Larm (3) (4) dc where i +i uj l j Larm 0 R0 = R + Rarm 2 ; L = L + 2 ; ig j = iu j − il j ; idi f f j = 2 ; vml j +vmu j vml j −vmu j vdc ; v = ; v − v = vv j = di f f j di f f j dc di f f j 2 2 2 Applying the Park transformation on the differential equation given by (3), we get: digd R0 1 = − 0 igd + 0 vd dt L L digq R0 1 = − 0 igq + 0 vq dt L L (5) with vd = L0 ωigq + vvd − vgd ; vq = −L0 ωigd + vvq − vgq . As discussed previously in [13], the total energy per phase Wtot j stored in an arm is depending on the instantaneous AC power pac j and the power exchanged with the DC bus pdc j which depends on the DC component of the differential currents. Then the dynamics of total stored energy per phase is expressed by 2 dvctot dWtot j j = Ctot = pdc j − pac j dt dt (6) where pac j = 31 vgd igd and pdc j = vdc idi f f j . The total capacitor per arm is defined by Ctot = C N, with C and N are respectively the capacitor and the number of submodules (SM) per arm. Figure 4. AC power, Sum Energy and DC bus voltage control via conventional controllers. On the DC side, the differential currents controllers allow regulating the DC components of idi f f j and can eliminate the circulating current [20]. When the MMC converter is integrated in MTDC system illustrated by Fig. 1, two control modes are identified. In the power control mode concerning the offshore station, the DC bus voltage is imposed (selector in position 1, see Fig. 4). The regulation of the stored energy inside MMC converters is settled via the differential currents references given in (abc) frame. Three independent energy control loops have to be implemented to define the three independent references for each differential current loop. The power flowing through the converter is controlled by the reference on the direct component of grid current [4]. As shown in Fig. 4, the structure of the control strategy is deduced by the model inversion method. However, in the DC voltage control mode concerning the onshore stations (selector in position 2, see as well Fig. 4), the DC voltage is variable and consequently a voltage droop control presented above is required in order to regulate the DC bus voltage to its operating point. Note that all the control loops of the global control scheme given by Fig. 4 are based on PI- controllers (Proportional-Integral) with poles placement control design technique. It is important to underline that in this study, the references of the stored energy are considered as constants. In addition, the transfer functions Cv (s) in the Laplace domain, of the designed ∗PI-controllers in ”abc” frame, are expressed ∆p by Cv (s) = 2 ∗di f f2 = k pv (1 + k1I ). (vctot −vctot ) v B. The proposed advanced control strategy This section, based on the developed state equations, presents a state space controller design to control the MMC dynamics. 1) Linear state space deviation model: According to equations (4), (5) and (6) a linear state space model of MMC converter can be written according to the T following state vector x ∈ ℜ8 = igd igq idi f f j v2ctot j and input vector T 5 u ∈ ℜ = vd vq vdi f f jdc : ẋ = Ax + Bu (7) where the parameters matrix A and the input matrix B, are of appropriate dimensions and depend on MMC system parameters, illustrated in Table I. In the equilibrium point Xe , the system (7) can be expressed as follows: Ẋe = AXe + BUe i∗gd = = R0 i v∗q where Xe = v∗d Ps vgd i∗gq = R0 igq (8) v2∗ ctot j T = Rarm i∗di f f j T i∗di f f j = v∗di f f jdc Ps 3vdc and Ue = . gd Around the equilibrium point Pe = Xe Ue , the relations (7) and (8) lead to the following linear small signal model: ∆ẋ(8×1) = A(8×8) ∆x(8×1) + B(8×5) ∆u(5×1) (9) where ∆x = x − Xe and ∆u = u −Ue . The output vector are defined as: y ∈ ℜ5 = igd igq v2ctot j T (10) The small-signal of (10) can be written as: ∆y = C.∆x (11) Finally, from (13) and (15), the augmented state space model is given as: ż = Āz + B̄u + ξ¯ (16) w = C̄z T T where z = ∆x v and w = y v B 012×1 A 08×5 ¯ ; B̄ = ;ξ = Ā = ; −C 05×5 05×5 ∆y∗ C 05×5 05×1 I5×5 05×1 C̄ = 05×8 0 1 01×5 0 2) Optimal Control Design: This section, based on LQR control method, provides the optimal control algorithm of the MMC converter. The considered continuous-time quadratic cost function is given as follows [15]: Z +∞ J= (w − w∗ )T Q̄ (w − w∗ ) + uT Ru u dt (17) 0 where Q̄ = diag Qy Qv with Qy ≥ 0; Ru > 0 are the weights matrices which specifies the desired performances. The minimization of the criterion (17) expresses adequately the desired performance of the designed control law providing the best compromise between the references tracking problem with good performances and the minimization of the control energy cost. The resolution of this multivariable optimal control problem leads to the following linear state-space feedback control law: ∆u = −Kz + Ny∗ ;K = KP KI (18) where KP and KI are respectively the proportional and integral gains matrices, and N is a compensator gain to be selected for reference tracking. Fig. 5, sum up the linear multivariable optimal controller proposed for both control modes. In the position 1, the ”AC power control mode”, which the AC power reference is constant. In position 2, the optimal control is combined with ”power-droop voltage control”. For more details about the development of augmented state space model and the linear optimal control design, the readers are encouraged to consult [26]. where ∆y ∈ ℜ5 = y −Ye = ∆igd ∆igq ∆v2ctot j T V. MMC INTEGRATION IN MTDC SYSTEMS (12) Then, taking the equations (9) and (11), yields to: ∆ẋ = A∆x + B∆u ∆y = C∆x (13) Considering now the intermediate variable denoted v which designs the integrators outputs where the dynamic equation is given by v̇ = y∗ − y (14) which can be expressed as: v̇ = ∆y∗ −C∆x (15) A. Description and simulation data In this section, a simulation study is proposed for the MMCMTDC test system given by Fig. 1, where the all stations are controlled with both classic and advanced MMC control strategies. Some basic specifications of the MMC converter and DC cable are provided respectively in TABLES I and II. Furthermore, all the MMC conversion stations are 1000 MVA with 400 submodules per arm and a DC-link voltage of 640 KV. The DC capacitors are sized in order to have an electrostatic constant 1 2 CarmVdc 2 , where the equivalent value, expressed by HC = Pbase Figure 5. Advanced control structure associated to the droop controller value is indicated in TABLE I. The MMC stations are connected by three ±320 KV pairs of DC cables where the DC cable capacitor of each MMC converter is equal to Cdc = 15µF. The DC cable is modeled using a wideband line model (reference model in EMTPRV software) which the required data will be summarized in TABLE II. For simulation, all model developments and simulation studies are performed using EMTP-RV [16]. For significance and credibility of simulation results, it is important to note that the control implementation and the simulation study are based on Detailed Equivalent Circuit-based Model (DECM) of MMC converter with 400 SM/arm [17]. TABLE I. PARAMETERS THE STUDIED POWER SYSTEM . Parameter Value Rated voltage, Vg Rated power, Sg b Rated angular frequency, ωb Filter inductance, L f Filter resistance, R f Arm inductance, Larm Arm resistance, Rarm Arm capacitance, Carm Arm capacitance, Cdc SM electrostatic constant, Hc DC electrostatic constant, HDC Filter gain, T f il 325 kV 1 GVA 2.π.50 Hz 0.18 pu 0.005 pu 0.15 pu 0.01 pu 32.5 µF 15 µF 40 ms 3.1 ms 0.01 s TABLE II. DC CABLE SPECIFICATION [19]. Parameter Value Cable length Outer radius of sheath Outer radius of insulation Resistivity of core Resistivity of sheath Insulator relative permittivity Insulator loss factor 70 km 5.82 cm 6.39 cm 1.72e-08 Ωm 2.83e-08 Ωmm 2.5 0.0004 In this model the SM power switches are replaced by ON/OFF resistors with a small value of RON (inmilliohms) and a large value of ROFF (inmegaohms). This approach allows performing an arm circuit reduction for eliminating internal electrical nodes and allowing the creation of a Norton equivalent for each MMC arm. Indeed, the algorithm considers each SM separately and maintains a record for individual voltages. This allows to implement the lower level control composed of Nearest Level Control (NLC) modulation and Capacitor Balancing Algorithm (CBA). For more details, the reader can refer to [18]. The PI controllers gains of the classic control approach are synthesized in order to ensure a settling time around 5 ms for both MMC converter currents. For the outer control loops concerning the active power and the total stored energy, settling time is equal to 50 ms. The initial state of each MMC stations are 0.5 pu (station #1), 0.5 pu (station #2) and -1 pu (station #3). The simulated scenario used to assess the control methods performances is a sudden 20% power decrease. This event may occur if a feeder breaker trips in the wind farm. B. Simulation results and discussion For the simulation study and analysis, two different droop values have been chosen, as Kdroop = 0.6pu/pu and 0.1pu/pu to adjust the power deviation portion which is following through a converter station. The same droop value is considered for the two MMC stations. • Case 1: Kdroop = 0.6pu/pu As depicted in Fig. 6, the loss of production is equally shared between the two onshore stations since they have the same droop value. From Fig. 7(a), the DC bus voltage starts decrease until it reaches 601.6 KV at about 0.53s. Fig. 7(b) shows the DC-side power of the MMC: the optimal controller reduces clearly the transient ripple and cutback the overshoot of the power and voltage on DC side. Using the optimal state feedback control law which all state variables contribute to reject the effect of the disturbance, the internal MMC variables are controlled with a fast dynamics and good performances which improve the MTDC system stability. In this way, it is clear from Fig. 7(c) that through advanced control strategy, the three-phase differential currents are regulated reducing the transient oscillations Fig. 7(d) reveals a correct energy dynamic behavior even in the transient. However, the advanced controller is able to converge the initial states of the MMC to their desired values in the steady state operating point. In Fig. 9, compared to the conventional PI controller, the multivariable optimal allows regulating the differential currents of MMC with less overshoot and ripples. From the comparative analysis, these results show that even with a low droop value , the optimal control approach is able to regulate the DC bus voltage with good performances and to improve MTDC system stability. In addition, since the obtained control gains are not high and the control structure is simple, the optimization control design algorithm of linear feedback controller is fast and its implementation is easy compared to other advanced control methods given in literature. Figure 6. AC power responses for 0.6 pu step change on wind farm station. • Case 2: Kdroop = 0.1pu/pu Figure 8. Dynamic response with 10% of droop: (a) dc bus voltage of station n◦ 1 and (b) dc-side power of station n◦ 1. Figure 7. Simulation results and comparative study with 60% of droop. In order to show the influence of the droop sizing on the DC voltage dynamics and illustrate the capability of the advanced controller to improve dynamics and MTDC grid stability even for low droop values, a second simulation test is proposed. Figs. 8(a) and (b) show respectively the wind power change in DC bus voltage and DC power of station n◦ 1 with a lower droop value. It is clear from Fig. 8(a), that with 10% of droop value, the conventional PI controllers based on cascaded structure allow to regulate the DC bus voltage but with poor dynamics given by a fast frequency oscillations through the DC voltage which results a negative consequences on the DC cable characteristics where resonance phenomena could be generated. The result of Fig. 8(a) shows that compared to the conventional method, the advanced control strategy associated to the droop voltage controller, provides a more satisfactory dynamic response in dc side which highly reduces oscillations. Figure 9. Dynamic response of phase-a differential current of station n1 with 10% of droop VI. C ONCLUSIONS In this study, an advanced control strategy of MMC converters integrated in MTDC system is proposed. The novelty of this approach consists in the combination between the optimal state space control design of MMC stations and voltage droop control technique. An optimization problem is formulated and solved for the design of a state feedback control law to enlarge the region of stability for the MTDC grid. The proposed control method allows to reduce the oscillations and improves the DC bus voltage dynamics even for a lower droop parameters designed on static considerations. All power and control model developments have been performed using EMTP-RV software. Simulation results are provided to confirm and validate the effectiveness and robustness of the proposed strategy. 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