Impact of control algorithm solutions on Modular Multilevel Converters electrical waveforms and losses F. Gruson1, J. Freytes2, S. Samimi2, P. Delarue3, X. Guillaud2, F. Colas1, M.M. Belhaouane2 1
L2EP, ARTS ET MÉTIERS PARISTECH 8Bd Louis XIV 59046 Lille, France +33 (0)3 20 62 29 49.
[email protected]
2
L2EP, ECOLE CENTRALE DE LILLE Cité Scientifique 59655 Villeneuve d'Ascq
France +33 (0)3-20-33-54-24
[email protected]
3
L2EP, LILLE UNIVERSITY Cité Scientifique 59655 Villeneuve d'Ascq
France +33 (0)3-20-43-42-53
[email protected]
Keywords «Modular Multilevel Converter», «MMC», «Converter control», «Converter Losses», », « Highvoltage direct-current (HVDC) transmission »,
Abstract Modular Multilevel Converters (MMC) are becoming increasingly popular with the development of HVDC connection and, in the future, Multi Terminal DC grid. A lot of publications have been published about this topology these last years since it was first proposed. Many of them deal with converter control methods, other address the method of estimating losses. Usually, the proposed losses estimation techniques are associated to simple control methods For VSC (Voltage Sources Converters) topology, the losses minimization is based on the limitation of the RMS currents values. This hypothesis is usually extended to the control of MMC, by limiting the differential currents to their DC component, without really being checked. This paper investigates the impact of two control algorithms variants on electrical quantities (currents, capacitor voltages ripple, losses). From the published results, it is shown that in some cases the usual choice is not the best one.
Introduction The great advances in power electronics and its control allowed considering the high voltage DC transmission systems (HVDC) as a feasible solution. The modular multilevel converter (MMC) is a reliable solution to connect HVDC grids to the HVAC (High Voltage AC). This converter is a three phase VSC that was first introduced in [1] and started to be one of the most promising converters for HVDC systems. Fig. 1 recalls the topology of the converter. The six arms of this three-phase converter are composed of elementary modules (named Sub Modules). Each module is a simple switching cell with a capacitor. Depending on the state of the cell, the capacitor voltage is introduced or not in series with the main electrical circuit. Due to this, the voltage between the ‘+’ pole (or ‘-‘pole) and one phase (a, b, c) may be modulated with an almost sinusoidal shape [2]. The discretization of the sinus depends on the number of modules. The MMC presents lots of advantages: transformer less, modularity, high voltage quality, no high voltage DC bus, but also some drawbacks: difficulty to control due principally to high number of control variables [4] and high capacitors voltages ripples due to currents flowing in them. The study of the MMC can be simplified by decoupling the problem of balancing the capacitor voltage within each arm and the global control (currents and output power control). This decoupling has been used in this paper. Assuming that the capacitor voltages of each Sub modules are well balanced.
idc
iub
iua SM1ua
SM1ub
SM 2ub
vmub
#
#
SM1uc
Arm
SM 2ua
vmua
Skiu
iuc SM 2uc
vmuc
#
SM nua
SM nub
SM nuc
Rarm Larm
Rarm Larm
Rarm Larm
vdc Rarm Larm
vmla
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ila
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SM1la
SM1lb
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SM 2lb
SM 2lc
vmlb
#
#
SM nla
ilb
vmlc
SM nlb
vci
C
vki Skil
iga
vga
R, L
igb
R, L
igc
R, L
vgb vgc
# ilc
SM nlc
Leg
Fig. 1: MMC Topology Each MMC arm (Fig. 1) could be aggregated in the equivalent structure. The Fig. 2 presents the equivalent circuit configuration of the MMC. This equivalent circuit is usually used to design the global control of the MMC as addressed in [5] and [6].
idc
iub
iua
vmua
C N
vcua _ tot vmub
mua
Cdc
iuc C N
vcub _ tot vmuc
mub
C N muc
vcuc _ tot vga
iga
vgb
igb
vdc
igc ilb
ilb C N
vmla mla
vgc
ilc
vcla _ tot vmlb
C N
vclb _ tot vmlc
mlb
C N
vclc _ tot
mlc
Fig. 2: Equivalent circuit configuration of the MMC There are several proposed control techniques of MMC converters.. A large majority tackles the global control and a few deals with capacitor voltage balancing and ripple. Other papers address the capacity ripple voltages issue [7]. Recently, the studies of MMC silicon losses are also discussed. In addition, in [3] and [5], a global control (for the currents and the stored energy) with a rigorous methodology based on the inversion of the converter model is presented. This methodology highlights the important couplings which exist between the different parts of the system and also variants for the global control (control the stored energy with the DC power or the AC power for example). A common habit suggests that it is necessary to limit the RMS currents into converters (as presented in [8]) to limit the MMC losses. This paper proposes to evaluate the impact of two different global control algorithms both in terms of the electrical characteristics (constraints on currents, waves of equivalent capacitor voltages but also losses and performance of the converter). A tool to evaluate and discriminate the origins of losses precisely according to the choice of control is used. Results show that in some cases the usual choice is not the best one.
Modeling of the MMC converter Each of the six equivalent arm converters can be modeled by these equations:
⎧ v m l i = m l i v cl i _ tot ⎪ ⎨ C dv cl i _ tot ⎪ m l i il i = N dt ⎩
v m u i = m l i v clui _ tot m u i iu i =
with i ∈ ( a , b, c )
C d v clui _ tot N dt
(1)
Using the Kirchhoff laws leads to 11 independent differential equations. The system is then characterized by 11 independent state variables: the six voltages across the 6 equivalent capacitors and 5 currents (for example three arm currents and two phase currents, the other currents are linear dependent of the 5 chosen currents). In this purpose, the modeling is oriented by performing the change of variables: vmu i + vml i vml i − vmu i i + ili (2) i diff i = ui v diff i = vv i = with i ∈ ( a , b, c ) 2 2 2 The differential currents ( idiff a , idiff b , idiff c ) are composed by a DC component ( idiff i _ DC ) and harmonic components ( idiff i _ AC ). The sum of the DC component is the DC current ( idc ) delivered to the DC bus. The harmonic components represent the circulating currents within the different legs. Using the Kirchhoff laws for the DC side and according the new variables given by (2), we obtain: didiff i v dc (3) − v diff i = Larm + Rarm idiff i with i ∈ ( a , b, c ) 2 dt The AC currents are not independent since iga+igb+igc=0. The application of Park transformation gives the equations (4) and (5). vvd − v gd = ( L +
Larm di gd Rarm Larm ) + (R + )igd + ( L + ) ω i gq 2 2 2 dt
(4)
vvq − v gq = ( L +
Larm digq Rarm Larm ) + (R + ) iv − q − ( L + ) ω igd 2 2 2 dt
(5)
This converter has 11 independent state variables which requires 11 control loops to achieve the global control of the MMC converter. The block diagram of the MMC Model expressed by the previous equations is shown in Fig. 3.
mui
×
vmui
vvi +
1 2
-
cellule
1 n°3 Rarm ⎛ L ⎞ R+ + ⎜ L + arm ⎟ s 2 2 ⎠ ⎝
+ -
igi
1 2
iui
+
×
+
1
vcui _ tot
Ctot s
vgi mli
×
vmli
+
1 2
vdiff i
+
vdc 2 Fig. 3: Block diagram of the MMC model
1 Rarm + Larm s
-
idiff i +
ili
×
1 Ctot s
vcli _ tot
Control of the MMC Converter Current Control The currents control scheme is deduced from the inversion of the model [5] giving by the previous equations. Fig 4 presents the block diagram of the grid and differential currents control. The grid current control is a classical dq control method (igd and igq) where θs is the AC grid angle. The differential current controller regulates the DC component of this differential current but it can also cancel the circulating current [9,10]. These controllers allow controlling just five variables among the full state vector.
vcui _ tot
mui mli
÷
÷
+
+
+
+
+
− +
Ci pu ( s )
+ +
Ci pu ( s )
P −1 (θs )
+
vcli _ tot
θs
+ +
G vdc / 2
igq
L'pu ω pu
vgi
Ci diff ( s )
L'pu ω pu -+
G idiff i
+ − + −
igd
idiff i _ref
PR (θ s )
igd ref igq ref θs
igi
Fig. 4: Grid and differential currents control block diagram
Since the currents igd, igq and the three differential currents (idiff) are controlled, the power exchanged between the AC and the DC grid source is also controlled. A power unbalance between AC and DC induces a variation of the stored energy into the equivalent capacitor of each arm; so varying the vcui_tot and vcli_tot voltages since there are the last 6 uncontrolled state variables.
Stored Energy Control As presented in [5], the stored energy into each equivalent arm capacitor can be defined by the total stored energy in each leg (Wcli + Wcui) and the differential stored energy in each leg (Wcli - Wcui) by the following equations where Wcli is the stored energy into the lower side equivalent arm capacitor of the phase i and Wcui for the upper side: ⎧⎛ d (Wcl i + Wcui ) ⎞ ⎪⎜ ⎟ = Vdc .idiff i− DC − pAC _ i dt ⎠T ⎪⎝ with i ∈ ( a, b, c ) (6) ⎨ d W − W ( ) ⎛ ⎞ cl i cui ⎪ ˆ ⎟ = vˆvi idiff i − AC ⎪⎜ dt ⎠T ⎩⎝ Where pAC_i is the active power of the phase i in the AC grid. The last equation (6) show that, for each arm, the idiffi-DC controls the total stored energy and therefore the capacitor voltage sum (vcui_tot + vcli_tot) and the idiff-AC controls the differential stored energy and therefore the capacitor voltage difference (vcui_tot - vcli_tot). The stored energy control scheme is deduced from the inversion of equation (6). The Fig 5 presents the block diagram of the general stored energy control.
idiff i − DC ref
pdiff i − DC ref
÷
+
vdc idiff i − AC ref
CvDC ( s )
+
-
+
+
pACi
÷
pdiff i − AC ref
+
CvAC ( s )
-
+
+
+
vdc
+
2 vcui _ tot _ref
-
2 vcli _ tot _ref
+
-
Filter
2 vcui _ tot
Filter
2 vcli _ tot
Fig. 5: Stored energy control block diagram
In the total stored energy control (upper part of Fig. 5), a compensation term appears which is the injected in or consumed in each arms by the AC phases (pAC_i). If we want to be rigorous in the energetic model inversion presented equation 5, the total stored energy control must compensate the pAC i instantaneous value. This AC grid power is composed of a DC term equal to the global AC power divide by 3 and an AC term representing the AC grid fluctuating power as shown in (7) P p AC i = AC + Vgi I gi cos(2ω t + ϕ ) with i ∈ ( a, b, c ) (7) 3 Where ω is the AC grid pulsation and φ is the phase shift between the AC current and AC voltage. Considering the power balancing where the AC power is equal to the DC power, the current idiffi-DC can be written as: V I cos(ϕ ) Vg I g + idiff i − DC = g g cos(2ω t + ϕ ) with i ∈ ( a, b, c ) (8) VDC VDC In order to limit the losses due to this control and therefore by idiffi-DC, we usually limit the differential current RMS value. The usual energy control only considers the average power of the AC grid (Pac) and not the instantaneous power of each phase. Considering this hypothesis, (7) could be modified as shown in (9) and consequently its control is shown in Fig 6. This choice implies that the fluctuating power injected in or consumed by each arm by the AC phases is not taken into account and therefore the idiffDC linked to this fluctuating power is neglected too (second part of (8)). This choice involves in additional ripples in the voltages of the equivalents capacitors since the balance of the instantaneous AC and DC power is not respected but respects the balancing in average value. ⎧⎪⎛ d (Wcl i + Wcu i ) ⎞ (9) ⎨⎜ ⎟ ≈ Vdc .idiff i − DC − PAC / 3 with i ∈ ( a, b, c ) dt ⎠T ⎩⎪⎝
idiff i − DC ref
Pdiff i − DC ref
÷
+
vdc idiff i − AC ref
÷
CvDC ( s )
+
-
CvAC ( s )
+ +
Pac / 3 pdiff i − AC ref
+
-
+
+ +
vdc
+
2 vcui _ tot _ref
-
2 vcli _ tot _ref
+
-
Filter
2 vcui _ tot
Filter
2 vcli _ tot
Fig. 6: Stored energy control block diagram
The choice of neglecting or not the fluctuating part of the AC power modifies the control. This modification generates a different quantity of activated sub-modules and therefore the current passes
through a different number of IGBT and diodes. The conduction losses are assumed to be mainly in the MMC. Indeed the large number of components in series and an IGBT generates more than a diode conduction losses, it may have sense to use a control inducing a slightly larger current if this current passes through more diodes since diode produce lower conduction losses than an IGBT for the same current. So the hypothesis of limiting the RMS current can be questionable in this case. It is possible to compensate either the average value of pAC i or its instantaneous value.
Simulation Results These two variants of the control strategy have been implemented in EMTPRV and Matlab-Simulink® software. The simulation results are given for an 1100MVA MMC converter. The system parameters are illustrated in Table I.
Table I: MMC parameters L = 50mH
Larm=50mH
C = 10mF
Vdc = 640kV
R = 50mΩ
Rarm=50mΩ
N = 400
Vg = 640kV
SN = 1100MVA
The settling times for control loops are given in Table II.
Table II: Control loops setting time responses Tr igdq=5ms
Tr idiffi=10ms
Tr ∑Vci_tot=100ms
Tr ΔVci_tot =100ms
Electrical Results Figs 7 and 8 shows the simulation results for a slope in the AC power references (Pac) at t=0.1s (the active power from 0 to 0.8 GW and the reactive one from 0 to 100MVAR). At 0.55s, the control switches from the average power compensation (Pac/3) to the instantaneous one for each phase (paci). 8
Active Power (W)
10
x 10
8 6
Pac Pdc Pref
4 2 0 0
0.1
0.2
0.3
0.4 0.5 time (s)
0.6
0.7
0.8
0.9
0.8
0.9
7
Réactive Power (VAR)
12
x 10
10 8 6
Qmes Qref
4 2 0 0
0.1
0.2
0.3
0.4 0.5 time (s)
0.6
0.7
Fig. 7: Active and reactive power simulation waveforms
Figure 7 shows the active and reactive power. Notice that a transient appears at t = 0.55s due to a sudden transition between the two variants of control. As it can be observed that that these powers stabilize again at the same value as then the first part.
Equivalent Capacitor Voltages (V) AC Grid Currents (A)
5
x 10 7
Δ = 100kV
Δ = 104kV
6.5 6 0
0.1
0.2
0.3
0.4 0.5 Time (s)
0.6
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0.4 0.5 Time (s)
0.6
0.7
0.8
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2000 0 -2000 0
differential Currents (A)
1000 500 0 -500 0
Fig. 8: Equivalent capacitor voltages, AC grid currents and differential currents
Fig 8 shows the internal electrical quantities of the MMC (equivalent capacitor voltages, AC grid currents and differential currents). It shows that the change of the control variant does not alter the AC grid currents (transiently and in steady state), thus generating no impact on the AC grid. In this same figure, the equivalent capacitor voltage changes slightly but the voltage ripple is an important parameter. The choice to compensate the average power implies that the fluctuating power injected in or consumed by each arm of the AC phases is neglected. This choice involves additional ripples in the voltages of the equivalent capacitors since the balance of the instantaneous AC and DC power is not respected. In this simulation, when the control compensates the instantaneous power, the equivalent capacitor voltage ripple is reduced by 4kV compared to the control with the average power compensation (100kV compare to 104kV) As shown in Figure 6, all of this permits to reduce the voltage ripple across the equivalent capacitors by 4% thus involving in lower solicitation and increase their life time. In Fig 8, it is possible to note that the differential currents are constant when the average power is compensated. When the control compensates the instantaneous power, these same currents keep the same DC component and an AC component appears at twice the frequency of the AC grid. The fluctuating power giving by the AC side introduces a current harmonic at twice the AC frequency into the circulating current (idiff i), if the control compensates the instantaneous active power of the each phase (pAC i). On one hand, this current harmonic reduces the differential stored energy part, on the other hand the idiff i RMS value increases by 11.5% (from 521A to 581A) and therefore as we could expect usually the losses would be greater.
Losses Results The losses estimation method has been iterated for different active and reactive power references in Matlab-Simulink® software. The losses estimation is computed with a full numerical approach which consists in the simulation of the entire MMC and its control system similar than [11] by storing into the workspace the capacitor voltages, the current in the inductors and the states of all switches. To have the most accurate results and thus overall view of the converter, the losses in the passive elements were taken into account since the choice of the control will cause a different RMS differential currents values and therefore different passive elements losses.
Conduction losses Fig. 9a shows the silicon components conduction losses which depend on the operating point and the control. Fig. 9b shows a top view of the Fig. 9a. In this Fig, a red color means that the control with the average power compensation produce more conduction losses.
(a) Fig. 9: Silicon components conduction losses
(b)
In the red area of the Fig 9b, differential currents pass through more diodes when they are higher than the average value and therefore les IGBTs. This Fig 9b Results show that, in this red area, the usual control is not the best one since the MMC converter using considerable number of semiconductor and the conduction losses are not only related to the RMS current value but also to the way of this current (diode or IGBT) and therefore to the control. Switching losses
Fig. 10 shows the Silicon components switching losses. Results show that in some operating point the control with the average power compensation produce more losses but sometimes it is not the case. The switching losses are difficult to extrapolate since it depends on the balancing control algorithm and especially the hysteresis band accepted between the instantaneous higher and the lower capacitor voltage in each arm.
Fig. 10: Silicon components switching losses
Passive elements losses
Fig. 11 shows the passive elements losses. We can deduce from this figure than the passive losses is always bigger for the control with the instantaneous power compensation since the differential current RMS value is always higher. This loss counteracts the gain obtained by the conduction losses. In this fact, it is necessary to take the passive elements losses into account in order to giving a global vision of the MMC losses.
Fig. 11: Passive elements losses
Total losses
Fig 12a shows the global MMC losses taking to account the conduction losses, the switching losses and the passives elements losses for the two variants of control. This figure highlights that the total loss with the control by compensating the average power (named Pavg) are not always less than the other (named Pinst). Fig 12b shows the difference between these two variants in percent’s. In the blue area, the control which compensates the average power is more efficient. In the red one, the control which compensates the instantaneous power is more efficient.
(b) (a) Fig. 12: Total Losses
As common, one suggests that it is necessary to limit the RMS currents into converters to limit their losses. Fig 12 Results show that in some cases the usual choice is not the best one since the MMC converter using considerable number of semiconductor and the global losses are not only related to the RMS current value but also to the way of this current (diode or IGBT) and therefore to the control.
Conclusion This paper presents the impact of two control variants: compensation of the average or the instantaneous power of the energy control loop in terms of the electrical characteristics (differential and AC grid currents, capacitor voltages ripple, losses). The control strategy and the simulation results are presented. The differential currents are constant when the average power is compensated. When the control compensates the instantaneous power, these same currents keep the same DC component added to an AC component appears at twice the frequency of the AC grid. Since the global energy stored into each arm is correctly controlled and fluctuating power of each arm introduces a current harmonic at twice the AC frequency into the circulating current (idiff i), if the control compensates the instantaneous active power of the each phase (pAC i). This current harmonic also reduces the differential stored energy part and therefore the ripple of the capacitor voltages. But the idiff i RMS value increases by 11.5% (from 521A to 581A) and therefore as we could expect usually the losses would be greater. As usual, one suggests that it is necessary to limit the RMS currents inside converters to limit their losses. From the simulations results, it can be concluded that that in some cases the usual choice is not the best one since the MMC converter using considerable number of semiconductor and the losses are not only related to the RMS current value but also to the way of this current (diode or IGBT) and therefore to the control.
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