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
[email protected] Abstract — Modular Multi-level Converters (MMC) have emerged as the preferred technology for High Voltage DC transmission installations. The inclusion of these converters, characterized by complex control schemes, in large AC grids may cause AC/DC 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 (2-level), to use such models when studying AC/DC 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 HVDC 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/EMTDC. A close match between the original system and the benchmark confirms the validity of the MMC RDM proposed. Index Terms—HVDC, MMC, reduced dynamic model, DIgSILENT PowerFactory, PSCAD/EMTDC, 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 (HVDC) 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) [2]. 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 DC 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]. DIgSILENT 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, HVDC 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 HVDC projects based on modular multilevel VSCs, this constraint leads to complications and restrictions in the analysis of such systems. Although the realization of 2-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/DC 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/EMTDC. The comparison and benchmark between the two systems is carried out in Section IV through time-domain simulations in normal and abnormal conditions.
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.
AC voltage sources. Since the software does not recognize any grid which does not contain active elements, the DC side must be represented using controlled DC voltage instead of DC current sources. Unlike Matlab Simulink, PowerFactory does not allow to link together at the same bus bar AC and DC components; therefore an artificial connection is emulated via the control system. TABLE I
Parameter Prated VDC VAC Frequency Phase Inductor Arm Inductor
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 DC 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 (Pac = Pdc + Ploss) is applied on the current sources on the DC side [3]. Vj,up DC SIDE Iloss
AC SIDE
Idc
I’dc Ce Vj,low
MMC RDM PROPERTIES Value 800 MW ±320 kV 320 kV 50 Hz 40.7 mH 163 mH
B. Control System The traditional control strategy for detailed MMC models [11], [12], 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 DC controller.
Figure 1: Traditional MMC RDM topology [3].
Vup
DC SIDE
Larm,up
VAC
Lphase
Vsig j,low
Larm,low
Xsource
VDC
VsigDC
Iac j,ref
Pow MGMT
err j,up Imeas UP
Iac j,up
Imeas LOW
Iac j,low
Current Controller
Ej,up Ej,low
Parm j,up
Vmeas UP
Vac j,up
Vmeas LOW
Vac j,low
DC Meas
Power Parm j,low Calc
Energy Calc Ej
err j,low
Vsig j,up
Vsig j,low
Vbal,j Vert Balance
Horiz & Average Balance
ENERGY BALANCING
DC Signal Generator
Vdc Idc
CURRENT CONTROL
Vmeas Grid
Line DC,low
Vlow CONVERTER
Figure 2: 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
DC CONTROL Vset
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 (2). The real, imaginary and zero sequences are referred as ir, ii, i0; iα, iβ, i𝛾 are intermediate variables to calculate the phase currents ia, ib, ic. The rating of the measurement device is indicated by irated, whereas inom is the current nominal value. An equivalent formulation is valid for the voltage. 𝑖𝛼 (𝑡) 𝑖𝑟 [𝑖𝛽 (𝑡) ] = [ 𝑖𝑖 ] ∗ (𝑖𝑛𝑜𝑚⁄𝑖𝑟𝑎𝑡𝑒𝑑 ) 𝑖0 𝑖𝛾 (𝑡)
(1)
Vup
Signal Generator
Figure 3: Scheme of MMC RDM control system.
Line DC,up
AC SIDE
phi
Idc_avg
Vsig j,up
PLL
MEASUREMENTS
Hbal,j
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 DC side contains two DC voltage sources, one is controlled via the inner control algorithms, and the other just sustains the Vdc in a stand-alone configuration. AC transformers are not included at this stage. Figure 2 shows the topology of a standalone MMC RDM, and Table I lists its properties.
Vgrid,j
II.
VDC
Vlow
1 0 1 𝑖𝛼 (𝑡) 𝑖𝑎 (𝑡) 1 √3 − 1 [𝑖𝛽 (𝑡)] [𝑖𝑏 (𝑡)] = 2 2 1 √3 𝑖 (𝑡) 𝑖𝑐 (𝑡) [− 2 − 2 1] 𝛾
A. PowerFactory (2)
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 DC 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 (Ej,up and Ej,low), as calculated in (3) and (4). The physical AC current and voltage are indicated as iac j and uac j, iac and uac are the quantities measured on the DC side. The signs are defined according to the convention used. E𝑗,𝑢𝑝 = ∫ (−𝑖𝑎𝑐 𝑗,𝑢𝑝 (𝑡) + E𝑗,𝑙𝑜𝑤 = ∫ (𝑖𝑎𝑐 𝑗,𝑙𝑜𝑤 (𝑡) +
𝑖𝑑𝑐 (𝑡) 3 𝑖𝑑𝑐 (𝑡) 3
) ∗ (−𝑢𝑎𝑐 𝑗,𝑢𝑝 (𝑡) + ) ∗ (𝑢𝑎𝑐 𝑗,𝑙𝑜𝑤 (𝑡) +
𝑢𝑑𝑐 (𝑡)
2 𝑢𝑑𝑐 (𝑡) 2
) 𝑑𝑡
) 𝑑𝑡
(3)
+ 𝐻𝑏𝑎𝑙,𝑗 + 𝑉𝑏𝑎𝑙,𝑗
2 𝐼𝑎𝑐 𝑗,𝑟𝑒𝑓
𝐼𝑗,𝑙𝑜𝑤 = −
2
+ 𝐻𝑏𝑎𝑙,𝑗 + 𝑉𝑏𝑎𝑙,𝑗
MMC1
400 MW
MMC2
P,Q
400 MW
VDC-Q
T1
320 kV
VAC 2 T2
320 kV
Figure 4: HVDC point to point link. TABLE II
CONVERTERS PROPERTIES
MMC1 320 kV ± 320 kV 800 MW 0 MVAr
VAC VDC Set-point
TABLE III
The current controller elaborates the control voltage signals to send to the arms. In the power management block, the AC current references (Iac 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 (Vbal,j) and horizontal (Hbal,j) balancing currents gives a reference current set (Ij,up, Ij,low). This will then be compared to the measured upper and lower AC arm currents (ia, ib, ic). The resulting error signals (errj,up, errj,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, Vsig j,up and Vsig j,low [14], [15], [17]. 𝐼𝑎𝑐 𝑗,𝑟𝑒𝑓
VAC 1
MMC2 320 kV ± 320 kV ± 320 kV 0 MVAr
(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 DC 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].
𝐼𝑗,𝑢𝑝 =
The MMC-based link is laid out as a balanced monopole, like shown in Figure 4. The converters are rated at ±320 kV, 800 MW and described in Table II. The outer control strategy defines MMC1 (rectifier) to work in P-Q control mode, whereas MMC2 (inverter) is set to operate in VDC-Q control mode. The AC grids are represented as equivalent voltage sources. The DC lines are modeled as underground cables and implemented using a lumped parameter model (Table III).
Parameter Vrated Irated Length
DC CABLES PARAMETERS
Value 320 kV 1 kA 100 km
Parameter Resistance Capacitance Inductance
Value 11.3 mΩ/km 0.212 µF/km 0.362 mH/km
B. PSCAD/EMTDC 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 Vac 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 MMCHVDC link includes two underground DC cables. The 320 kV single-core cables are modeled using a frequency-dependent model [19]. P, Q
(5)
Vac
(6)
I
Y
ac, abc
Lc
Rc
401-level MMC station
V
c, abc
DC cable
Vdc
The controlled DC voltage source is managed through the DC signal generator. The actual DC current, the reference DC current and the DC current output of the average energy balancing are combined to produce the DC voltage command for the controlled DC voltage source. III.
MODELLING OF MMC BASED VSC HVDC LINK
A point to point link was modeled using the MMC RDM described in Section II. An equivalent scheme was modeled in PSCAD/EMTDC and used as a benchmark.
V
q ac, abc
RLC filter
Firing pulses
d
Lower level controls (capacitor balance, firing strategy, etc)
d
Vac PLL
abc
d’q’
vabc *
q d’q’
V ac I d’q’
V
abc
vd 'q' Upper level controls, decoupled current control
(Reference set-points)
P* ,Vdc*, Q*, Vac*
Figure 5: Single line diagram of a MMC. Rc and Lc are the aggregated resistance and inductance of converter transformer and phase reactors.
(b)
(c)
200. -40.0 -280. -520. -760. -1000. 0.90
Vac 1.14
1.26
1.38
Vdc
[s]
1.50
(a)
MMC1
Vdc MMC1 MMC2
MMC2
1.02
2.00 1.20 0.40 -0.40 -1.20 -2.00 0.90
[MW]
(d)
1.02
330. 326. 322. 318. 314. 310. 0.90
[kV]
[kA]
Vac
1.14
1.26
1.38
[s]
1.50
(b)
Idc
Idc
1.02
1.14
Pac
1.26
1.38
[s]
1.50
(c)
Area2
Area1
Pdc Pac
Area2
Area1
Pdc
Active Power
Active Power (d)
1.02
1.14
1.26
1.38
[s]
1.50
Figure 6: System dynamic response in PowerFactory. (a) AC side Voltage; (b) DC Voltage; (c) DC current; (d) Active power from the AC and DC side.
IV.
Figure 7: System dynamic response in PSCAD/EMTDC. (a) AC side Voltage; (b) DC Voltage; (c) DC current; (d) Active power from the AC and DC side.
SIMULATIONS AND RESULTS
This section presents a set of time domain simulations performed in PowerFactory and PSCAD/EMTDC 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/EMTDC the time step is 50 μs. The dynamic performance of the system was analyzed in normal and abnormal conditions (three phase fault at MMC1 side).
Figure 9 (a) and (b) represents the phase voltages for the upper and lower arms. The expected DC offset [12] 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. 19.5
Total Energy Deviation
11.7
A. Normal and Abnormal Operations in PowerFactory Initially the HVDC 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 DC side. A solid three-phase symmetrical fault is applied at T1 on MMC1 at 1 s and it is cleared at 1.2 s, as shown in Figure 6 (a). Figures 6 (b), (c) and (d) illustrate the dynamic response from the DC side in term of Vdc, Idc 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 DC (green) side; Pdc follows the trend of Pac, directly affected by the fault. The discrepancy between the two power curves, named Area1 and Area2, represents the energy behavior of the arms: in Area1 the cells are depleted (Pdc