Reduced Dynamic Model of a Modular Multilevel Converter in PowerFactory

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1 Reduced Dynamic Model of a Modular Multilevel Converter in PowerFactory C.E. Spallarossa, M.M.C. Merlin, Y.Pipelzadeh, T.C. Green Control and Power Research Group Imperial College London, London, UK claudia.spallarossa10@imperial.ac.uk Abstract Modular Multi-level Converters (MMC) have emerged as the preferred technology for High Voltage transmission installations. The inclusion of these converters, characterized by complex control schemes, in large AC grids may cause AC/ interactions that need to be fully investigated. The evaluation to what extent the slower portion of the MMC dynamics interact with the dynamics of a transmission network is of primary importance. It becomes critical for the grid operators, which usually rely on more traditional VSC topologies (-level), to use such models when studying AC/ interactions. This paper presents the development of a MMC reduced dynamic model (RDM) in PowerFactory that will facilitate the analysis of large AC systems incorporating MMC based VSC HV links. The MMC control scheme is designed following an alternative strategy which considers the energy balancing and the storage capability of the converter. The system is arranged as a point to point link, its operations are validated against a detailed equivalent circuit (DEC) based model in PSCAD/EMT. A close match between the original system and the benchmark confirms the validity of the MMC RDM proposed. Index Terms HV, MMC, reduced dynamic model, PowerFactory, PSCAD/EMT, EMT-programs. I. INTRODUCTION Over the last few decades Voltage Source Converters (VSCs) have become the most adopted conversion technology for High Voltage Direct Current (HV) installations [1]. The conventional types of VSCs (two-level and three-level) are being replaced by a better performing and innovative topology known as the Modular Multilevel Converter (MMC) []. The MMC consists of three phase units, which are composed by an upper and a lower arm. A variable number of cells, according to the converter voltage rating required, are connected in series to form each arm. Every cell comprises two pair of switching components (IGBT and diode), and a capacitor [3]. The MMC voltage output is a staircase AC voltage signal obtained combining the voltage output of every cell. The low harmonic content of the MMC voltage output allows the elimination of AC filters. Other advantageous features are the reduction of power losses due to lower switching frequency, easy scalability to higher voltages and increased reliability thanks to adding redundant cells [4]. Reduced dynamic models (RDMs) of power electronics systems are often used to represent static switching converters for system level studies. Since the application of complex and accurate switching models entails a long computing time for electro-magnetic transient type (EMT) simulations, the RDMs are becoming a significant alternative for large-signal timedomain transient studies. A RDM approximates the initial system by averaging the effect of fast switching within a prototypical switching interval [5]. An exhaustive overview of the averaging techniques for power electronics converters is proposed by [3], and more accurate procedures are further discussed in [4], [6], [7]. PowerFactory is a well-known power system analysis software used by a large number of transmission system operators. This tool deals with the planning, operation and expansion of power networks; it caters for all standard power system analysis requirements, comprising the handling of large transmission networks, HV technology and renewable energy source installations such as wind power [8]. The capability of PowerFactory to deal with system-level studies is recognized world-wide, however the software was not conceived to support detailed power electronics design. Due to the increasing number of HV projects based on modular multilevel VSCs, this constraint leads to complications and restrictions in the analysis of such systems. Although the realization of -level VSC is still possible, the development of a MMC model is not trivial because of the difficulty of dealing with the cells switching components and the high frequency converter dynamics. The development of a MMC RDM in PowerFactory is therefore motivated by the urgency of having a MMC block available for transient stability studies of AC/ systems, along with the complexity of realizing a full detailed converter model. The focus of this paper is the description of the MMC RDM developed in PowerFactory. In order to validate the operations of such system, arranged as point to point link, an equivalent scheme is modeled in PSCAD/EMT. The comparison and benchmark between the two systems is carried out in Section IV through time-domain simulations in normal and abnormal conditions.

2 II. REDUCED DYNAMIC MODEL OF MMC IN POWERFACTORY This section describes the topology and the control system of the MMC RDM developed in PowerFactory. The RDM is the only viable approach considering the software limited abilities in the power electronics modeling field. Additionally the software is designed to work using real, imaginary and zero sequence, thus the translation to the time domain is required for realizing an accurate converter model. A. Structure Several reduced dynamic models for VSC MMC have already been proposed by [3], [4], [6], [7], [9], [10]. For this study, particular attention is devoted to the RDM based on switching functions where the switching components are not explicitly represented but modeled as controlled voltage and current sources [3], [9]. Figure 1 illustrates the AC and side representation for the MMC RDM. On the AC side, each arm is represented by an arm reactor and a controlled voltage source. To ensure the correct power transfer, the principle of power balance (P ac = P dc + P loss ) is applied on the current sources on the side [3]. AC SIDE Vj,up I dc Vj,low Iloss SIDE Figure 1: Traditional MMC RDM topology [3]. The design of a MMC RDM in PowerFactory presents several differences to the conventional representation. Unlike what is established in the literature [3], [4], [9], the proposed MMC RDM topology outlines only two controlled voltage sources, two arm inductors and a phase inductor. The three phases for the upper or the lower arms are compacted inside a single voltage source, but still controlled independently. The side contains two voltage sources, one is controlled via the inner control algorithms, and the other just sustains the V dc in a stand-alone configuration. AC transformers are not included at this stage. Figure shows the topology of a standalone MMC RDM, and Table I lists its properties. VAC AC SIDE Xsource Vsig j,up Lphase Vsig j,low Larm,up Larm,low Vup Vsig Vlow Line,up Line,low CONVERTER Ce SIDE V Figure : MMC RDM structure in PowerFactory. Despite the differences in the converter layout, the MMC RDM topology in PowerFactory is demonstrated to be equivalent to [3]. A significant simplification of the control architecture justifies the use of two instead of six controlled AC voltage sources. Since the software does not recognize any grid which does not contain active elements, the side must be represented using controlled voltage instead of current sources. Unlike Matlab Simulink, PowerFactory does not allow to link together at the same bus bar AC and components; therefore an artificial connection is emulated via the control system. TABLE I Parameter P rated V V AC B. Control System Frequency Phase Inductor Arm Inductor MMC RDM PROPERTIES Value 800 MW ± 50 Hz 40.7 mh 163 mh The traditional control strategy for detailed MMC models [11], [1], whose aim is the formulation of voltage reference signals for the switching cells, can be implemented on RDMs with some simplifications, such as the removal of the low level controller for the cell rotation algorithm. In this paper the control architecture is designed according to [13], [14]. It embraces an energy balancing control philosophy, which considers the amount of energy stored in each converter arm to originate the reference signals that keep the arms energy at nominal values and reduce to zero the energy exchange among the arms [14]. As Figure 3 shows, the scheme consists of several components: the measurement phase, the energy balancing blocks, the current controller and the controller. MEASUREMENTS Imeas UP Imeas LOW UP LOW Meas Iac j,up Iac j,low Vac j,up Vac j,low PLL phi Parm j,up Power Parm j,low Calc Pow MGMT Energy Calc Ej,up Ej,low Ej Iac j,ref ENERGY BALANCING Vert Vbal,j Balance Horiz & Average Balance Hbal,j _avg err j,up Current Controller err j,low Grid Signal Generator Figure 3: Scheme of MMC RDM control system. Vgrid,j Vset Signal Generator CONTROL The voltage and current measurement blocks evaluate the phase voltage and current in each arm. Since the measurement signals are expressed in positive, negative and zero sequence, Clarke transformation is applied to translate them into time domain according to (1) and (). The real, imaginary and zero sequences are referred as i r, i i, i 0 ; i α, i β, i γ are intermediate variables to calculate the phase currents i a, i b, i c. The rating of the measurement device is indicated by i rated, whereas i nom is the current nominal value. An equivalent formulation is valid for the voltage. i α (t) [ i β (t)] = [ i γ (t) i r ii ] (i nom i rated ) (1) i 0 Vsig j,up Vsig j,low CURRENT CONTROL V Vup Vlow

3 1 0 1 i a (t) [ i b (t)] = 1 i 3 α (t) 1 [ i β (t)] () i c (t) [ 1 i ] γ (t) 1 3 The energy balancing strategy aims to regulate the energy content of both the whole converter and every arm. In the RDM the measurement of individual cell voltages is not available, thus the energy per arm is calculated as the integral of the power. The power calculation block considers the AC and components and estimates power in each arm. The energy calculation block performs a filtering stage (notch filter) and an integration stage in order to determine the energy content of the upper and lower arms for phase j=a, b, c (E j,up and E j,low ), as calculated in (3) and (4). The physical AC current and voltage are indicated as i ac j and u ac j, i ac and u ac are the quantities measured on the side. The signs are defined according to the convention used. E j,up = ( i ac j,up (t) + i dc (t) E j,low = (i ac j,low (t) + i dc(t) 3 3 ) ( u ac j,up (t) + u dc(t) ) dt (3) ) (u ac j,low (t) + u dc(t) ) dt (4) The complete energy management system is composed by average, horizontal and vertical balancing techniques [15]. These mechanisms generate additional currents to ensure: the energy balance between the AC and converter side (average), the storage of the same amount of energy in all the phases (horizontal), the balance between the upper and lower arms within each phase (vertical) [15], [16]. The current controller elaborates the control voltage signals to send to the arms. In the power management block, the AC current references (I ac j,ref ) are constructed using P and Q references and the AC grid phase angles measured with a Phase Lock Loop (PLL). As expressed in (5) and (6), the combination of these with the vertical (V bal,j ) and horizontal (H bal,j ) balancing currents gives a reference current set (I j,up, I j,low ). This will then be compared to the measured upper and lower AC arm currents (i a, i b, i c ). The resulting error signals (err j,up, err j,low ) are fed into the AC signal generator which applies a Linear Quadratic Regulator (LQR) control algorithm to elaborate the voltage commands for the controlled AC sources, V sig j,up and V sig j,low [14], [15], [17]. I j,up = I ac j,ref + H bal,j + V bal,j (5) I j,low = I ac j,ref + H bal,j + V bal,j (6) The controlled voltage source is managed through the signal generator. The actual current, the reference current and the current output of the average energy balancing are combined to produce the voltage command for the controlled voltage source. III. MODELLING OF MMC BASED VSC HV LINK A point to point link was modeled using the MMC RDM described in Section II. An equivalent scheme was modeled in PSCAD/EMT and used as a benchmark. A. PowerFactory The MMC-based link is laid out as a balanced monopole, like shown in Figure 4. The converters are rated at ±, 800 MW and described in Table II. The outer control strategy defines (rectifier) to work in P-Q control mode, whereas MMC (inverter) is set to operate in V-Q control mode. The AC grids are represented as equivalent voltage sources. The lines are modeled as underground cables and implemented using a lumped parameter model (Table III). VAC 1 T1 P,Q 400 MW 400 MW MMC V-Q Figure 4: HV point to point link. TABLE II T CONVERTERS PROPERTIES MMC V AC V ± ± Set-point 800 MW 0 MVAr ± 0 MVAr TABLE III CABLES PARAMETERS Parameter Value Parameter Value V rated Resistance 1 mω/km I rated 1 ka Capacitance 0.1 µf/km Length 100 km Inductance 0.36 mh/km B. PSCAD/EMT VAC A single-line diagram of the MMC station and its associated controls are shown in Figure 5. The PLL ensures that the d axis of a synchronously rotating reference frame d -q is locked with to ensure decoupled control of P and Q. The MMC stations considered here are represented as a detailed equivalent circuit (DEC) based model. The internal controls include the lower level controls (capacitor energy balancing, circulating current suppression) and upper level controls (power controllers, decoupled current control) [18]. The MMC settings match those provided in Table II. Each MMC station includes 401-levels per phase. The MMC- HV link includes two underground cables. The single-core cables are modeled using a frequency-dependent model [19]. I Y ac, d q P, Q PLL, I d q q V c, R c L c RLC filter d d q 401-level MMC station Lower level controls (capacitor balance, firing strategy, etc) d q Firing pulses v* v d'q' Upper level controls, decoupled current control cable V dc (Reference set-points) P*,*, Q*, Vac* Figure 5: Single line diagram of a MMC. R c and L c are the aggregated resistance and inductance of converter transformer and phase reactors. V

4 [kv] kv (a) Vac (a) Vac [kv] MMC 310. (b) (b) MMC [ka] (c) (c) 00. [MW] -4 Pac -80. Area -50. Area Active Power Pdc (d) Figure 6: System dynamic response in PowerFactory. (a) AC side Voltage; (b) Voltage; (c) current; (d) Active power from the AC and side. (d) Area1 Active Power Area Pdc Pac Figure 7: System dynamic response in PSCAD/EMT. (a) AC side Voltage; (b) Voltage; (c) current; (d) Active power from the AC and side. IV. SIMULATIONS AND RESULTS This section presents a set of time domain simulations performed in PowerFactory and PSCAD/EMT aiming to validate the response of the point to point link equipped with the MMC RDM. In PowerFactory the simulations are run as Electro Magnetic Transients (EMT) with a time step of 100 μs, for PSCAD/EMT the time step is 50 μs. The dynamic performance of the system was analyzed in normal and abnormal conditions (three phase fault at side). A. Normal and Abnormal Operations in PowerFactory Initially the HV link was tested for normal conditions, which are visible in Figure 6 and 9 before the fault occurs. At the initialization, the converter is quite responsive and the steady state is reached promptly. The waveforms are of high quality, with no harmonic distortion on the AC side or ripple on the side. A solid three-phase symmetrical fault is applied at T1 on at 1 s and it is cleared at 1. s, as shown in Figure 6 (a). Figures 6 (b), (c) and (d) illustrate the dynamic response from the side in term of V dc, I dc and active power. During the fault the overlapping and change of direction of the direct currents is caused by the flows of the energy stored in the arms. Figure 6 (d) shows the active power from the AC (blue) and (green) side; P dc follows the trend of P ac, directly affected by the fault. The discrepancy between the two power curves, named Area1 and Area, represents the energy behavior of the arms: in Area1 the cells are depleted (P dc <P ac ), whilst in Area they are supporting energy to the converter. The total energy deviation is depicted in Figure 8 for (blue) and MMC (green). Unlike in MMC, the energy in arms is subject to fluctuations: it dips down to MJ during the fault meaning each arm is depleted by.57 MJ, it rises up and regains zero deviation after the fault is cleared. The energy flows inside the stacks define the storage capability of the converter and correlate the behavior of the AC and side [0]. Figure 9 (a) and (b) represents the phase voltages for the upper and lower arms. The expected offset [1] is not visible as it has not been included directly in the definition of the voltage commands for the controlled source, but it has been considered in the energy mechanism. The waveforms are of good quality, they collapse during the fault and recover to the nominal value as soon as it is cleared [MJ] Total Energy Deviation [s] Figure 8: Total energy deviation for and MMC Vac Upper Arm Inverter [kv] (a) [s] Vac Lower Arm [kv] (b) [s] Figure 9: phase voltages Vac Lower for the Arm upper (a) and lower (b) arms. [kv] 0. B. Comparison between PowerFactory and PSCAD/EMT MMC [s] The equivalent point to point HV link developed in (b) 0. PSCAD/EMT was used as a benchmark. The same fault [s] event, shown in Figure 7 (a), was applied at T1. The response of the system is illustrated in Figure 7 (b), (c), (d) and compared to Figure 6 (b), (c), (d). It can be observed that the quantities are closely matched; the general trends are very similar, despite some differences due to the way the fault transient is defined and the level of detail the converter is modeled. Unlike in PSCAD/EMT, where the fault transients are gradual, in PowerFactory the fault starts abruptly causing high spikes on each signal at its beginning and end

5 The direct voltage presents the same trend in both cases (Figure 6 (b) and Figure 7 (b)). However, its deviation is certainly smaller in PowerFactory: V dc at MMC (green) is kept constant by the outer loop control, whereas the voltage variation at (blue) is limited thanks to the robustness of the Signal Generator block in the control system. In the MMC DEC the voltage depletion in each stack after the fault is reflected on V dc. The direct currents (in Figure 6 (c) and Figure 7 (c)) display a close behavior. The active power curves nearly match (Figure 6 (d) and Figure 7 (d)), P dc follows P ac reference, the same discrepancy (Area1 and Area) is observed in both cases and it indicates the storage capability of the MMC. V. CONCLUSIONS The increasing number of MMC based VSC HV projects leads to the necessity of analyzing large AC networks which contains such installations. This motivates the need of developing a MMC model for transmission system oriented platforms, like PowerFactory. Due to the software limited ability in power electronics design, a viable approach was the converter reduced dynamic model. The MMC RDM developed in PowerFactory is presented in this paper. An alternative energy balancing philosophy is adopted for designing its control system. The performance of the system, arranged in a point to point link, is validated against an equivalent scheme in PSCAD/EMT for an AC fault scenario. A close match was observed between the original system and the benchmark. The availability of a MMC RDM block in PowerFactory is of crucial importance as it will enable a wide range of studies concerning AC large grids and VSC MMC technologies. ACKNOWLEDGMENT The authors gratefully acknowledge the financial support provided by the Top & Tail Transformation programme (ESPRC grant EP/I031707/1) for Ms Spallarossa, the UK Power Electronics Centre (ESPRC grant EP/K035096/1) for Dr Merlin and Hubnet (ESPRC grant EP/I013636/1) for Dr Pipelzadeh. REFERENCES [1] D. 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