Modular Multilevel Converter with Full-Bridge Submodules and Improved Low-Frequency Ripple Suppression for Medium-Voltage Drives Liqun He, Kai Zhang, Jian Xiong, Shengfang Fan
Yaosuo Xue
State Key Laboratory of Advanced Electromagnetic Engineering and Technology (AEET) Huazhong University of Science and Technology Wuhan 430074, China
[email protected]
Corporate Technology Siemens Corporation Princeton, NJ 08540, USA
[email protected]
Abstract—Due to the low-frequency voltage fluctuation problem, application of modular multilevel converters (MMC) in wide-speed-range medium-voltage (MV) drives is still difficult. This paper proposes a new approach to this problem. Firstly, full-bridge submodules (FB-SM) are used in place of the traditional half-bridge submodules (HB-SM). The former can significantly reduce the low-frequency pulsating power in the SM capacitors. Secondly, an improved “square wave plus third-order harmonic injection” with quasi-resonant (QR) control scheme is proposed to transfer the low-frequency ripple power into highfrequency ones. Simulation and experimental results prove the validity of proposed method. A comparison between the FB-SM based and HB-SM based MMCs showed good potential of the former in MV drive applications. Keywords—modular multilevel submodule; medium-voltage drives
I.
converter;
full-bridge
INTRODUCTION
As the most promising multilevel converter topology, the modular multilevel converter (MMC) has found popular applications in constant-voltage constant-frequency (CVCF) scenarios, such as high voltage direct current (HVDC) transmission systems. Since it gets rid of the cumbersome multi-winding transformers, the MMC should also have the potential to replace the cascaded H-bridge (CHB) multilevel converters in medium-voltage (MV) drives. However, up to the present MMCs are still only fit for MV drives with limited speed-adjusting ranges, such as fan/blower applications. The obstacle to wide-speed-range applications of MMCs is the low frequency voltage fluctuation problem. There is an inherent, fundamental component in the pulsating power of the MMC’s submodule (SM) capacitors (which is proportional to the output/stator current and dc supply voltage). When the speed of the ac machine drops, this power component tends to bring larger voltage fluctuation of the SM capacitor, since a capacitor exhibits higher impedances at lower frequencies. When the speed approaches zero, the amplitude of the lowfrequency voltage fluctuation will approach infinity [1].
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An effective way to suppress the low-frequency voltage fluctuation is injecting common-mode voltages and circulating currents. In [2]-[6], high-frequency sinusoidal common-mode voltages and circulating currents with the same frequency are injected to each phase. By doing this, low-frequency pulsating powers in the SM capacitors are transformed into highfrequency ones, resulting in much smaller voltage fluctuations. Though it can reduce the magnitude of capacitor voltages ripples, this method increases arm current and power loss. To address this, voltage and current with square-waves or sinusoidal-harmonic waves are injected instead of sinusoidal ones in [7]-[9]. Compared with [2]-[6], this method can reduce arm current by 40%. However, in experiments starting torque is restricted to 40% rated value, which means overcurrent will occur if the machine is started with full load torque. Moreover, in high power MV drives switching frequency is usually limited (sometimes only a few hundred hertz). Square-wave current reference can be fairly difficult for the control system to track. This paper proposes a new approach to the low frequency operation problem. First of all, half-bridge (HB) submodules are replaced by full-bridge (FB) submodules. Although FB-SM based MMC uses twice more power devices, it is found to be able to significantly reduce the fundamental frequency pulsating power, which is the reason behind the low frequency voltage fluctuation. “Square wave plus third-order harmonic injection” method with quasi-resonant controllers is proposed to improve the low frequency ripple suppression. Simulation and experiments proved the validity of the proposed method. A comparison between FB-SM based MMC and HB-SM based MMC is also given. II.
PROBLEM DESCRIPTION
A. MMC Based Ac Drives A three-phase MMC inverter driving an ac motor is shown in Fig.1. Each phase contains an upper and a lower arm. Each arm consists of N SMs. Topology of the SMs can be a half bridge (in Fig.1(b)) or a full bridge (in Fig.1(c)). Detailed
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comparison of HB-SM and FB-SM based MMC is given in Section V-C. B. Capacitor Voltage Ripple and Conventional Suppression Methods According to operating principle of the MMC, the power of each arm (total power of the SMs within each arm) of the MMC contains ac components. Specifically, if the circulating current is controlled in such a way as to provide all the secondorder ripple power needed by the load motor, then powers of the upper- and lower arms of each phase can be expressed as: v dc I x 2 2 p px = v px i px = 4 sin (ω1t + θ x − ϕ ) (1 − M sin (ω1t + θ x ) ) (1) p = v i = − vdc I x sin (ω t + θ − ϕ ) (1 − M 2 sin 2 (ω t + θ ) ) 1 1 nx nx x x nx 4
where x = u~w, Ix is the amplitude of stator current, ω1 is the stator frequency, θx is the phase angle of stator voltage, φ is the power factor angle of the ac machine, and M is the modulation index corresponding to the stator voltage. At low speeds, M is small and the dominant components of the arm powers are the fundamental ones. Since the frequency is low, these fundamental frequency ripple powers give rise to significant voltage fluctuations, which can be approximately expressed in (2). Eq. (2) clearly shows that the voltage ripples are proportional to stator current and inversely proportional to stator frequency, which greatly limits MMC’s application in MV drives. As the state-of-the-art solution, low-frequency terms in (1) can be compensated by injecting high-frequency common-
mode voltage vcm and circulating currents icmx into output voltage vx and circulating current izx respectively. Then arm voltages and arm currents can be expressed as: v px = vdc / 2 − v x − vcm vnx = vdc / 2 + v x + vcm
(3)
i px = izx + ix / 2 + icmx (4) inx = izx − ix / 2 + icmx Then (1) becomes: pxp = ( vdc / 2 − v x − vcm )(izx + ix / 2 + icmx ) = p x _ cm + px _ dm (5) pxn = ( vdc / 2 + v x + vcm )(izx − ix / 2 + icmx ) = p x _ cm − px _ dm Where: 1 1 p x _ cm = vdc icmx − vcmix (6) 2 2 v i v p x _ dm = dc x (1 − ( x ) 2 ) − vcm icmx − v x icmx − vcm izx (7) 4 vdc / 2 Low-frequency ripple powers come from the first term in (7), which can be compensated by the second term vcmicm.
A basic choice of vcm and icmx is [3] (also called “sinusoidal wave method”): (1 − M )vdc sin(ωcm t ) vcm = 2 (8) i = ix 1 − ( M sin(ω t + θ ) )2 sin(ω t ) x cm 1 cmx 1 − M
(
)
The frequency of vcm and icmx is fcm (angular frequency ωcm).
M 2 I x cos ϕ Ix M 2 I x cos ϕ M2 Δ ≈ + − − + − − cos ω θ (1 ) cos ω θ ϕ cos ( 3ω1t + 3θ x − ϕ ) v t t ( ) ( ) x x 1 1 cpx 8ω1C 4ω1C 4 48ω1C 2 2 2 Δv ≈ − M I x cos ϕ cos (ω t + θ ) + I x (1 − M ) cos (ω t + θ − ϕ ) + M I x cos ϕ cos ( 3ω t + 3θ − ϕ ) cnx x x x 1 1 1 8ω1C 4ω1C 4 48ω1C u-phase
v-phase
SM1
SM1
w-phase S1 SM1 Arm
SMN vdc +
-
x L
-
SMN x = u, v, w
ipx
L
dc side
SMN
+ vj
C
+ -
S2
vc
(b)
M
ix inx SM1
SM1
SM1
S1
S3
vj+ SMN
SMN
SMN
(a)
S2
+ C - vc
S4 (c)
Fig. 1. (a) Main circuit of MMC for ac drives. (b) Topology of HB-SM. (c) Topology of FB-SM.
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(2)
The dominant fundamental-frequency (ω1) term in (1) will then be cancelled out by the same-frequency component of vcmicmx. Since injected circulating current icmx increases loss (in the inductors, power devices, etc.) and injected vcm may cause over-modulation, “third-order harmonic injection” method [7], “square wave injection” method [7], [8] as well as hybrid technique [9] are proposed. However, with these methods in experiments load torque is still limited to 40% rated value if overcurrent is to be avoided. Besides, the bandwidth of the current controller has to be high enough to track the square wave reference, which is often unrealistic in high-power applications. To address these problems, FB-SM based MMC is adopted in this paper, adopting “square wave plus third-order harmonic injection” method and quasi-resonant controllers. III.
FB-SM BASED MMC
A. Working Principle Regardless of SM configuration, the following equations always hold for MMC (neglecting voltage drop on buffer inductors): vdc = v xp + v xn (9) v x = ( v xn − v xp ) / 2 For HB-SM based MMC, arm voltages are unipolar, i.e.: v xp = vdc / 2 − v x ≥ 0 v xn = vdc / 2 + v x ≥ 0
(10)
0 ≤ v xp ≤ vdc , 0 ≤ v xn ≤ vdc vdc v ≤ v x ≤ dc − 2 2
(11)
based MMC in practical. For FB-SM based MMC, arm voltages can be bipolar, then (10) and (11) are rewritten as: v xp ≤ Nvc v xn ≤ Nvc
(12)
vdc (13) 2 By setting vc > vdc / N, ac output voltage of FB-SM based MMC could surpass that of HB-SM based MMC in case of the same dc-link voltage. For instance, setting vc = 1.5vdc / N for HB-SM based MMC, its output range extends to vx ≤ vdc, double of HB-SM based MMC. In another word, same phase output voltage can be achieved with half the original dc voltage (0.5vdc) and 25% lower SM capacitor voltage (0.75vdc/N). According to (1), halved dc link voltage means halved lowfrequency ripple power. The burden of the injection method is therefore greatly reduced, making it possible to start up the ac machine with nearly full load torque and without overcurrent. | v x | ≤ Nvc −
B. Modulation and Capacitor Voltage Balance
Therefore:
Consequently, if capacitor voltage of SM is set to vc ≥ vdc / N, HB-SM based MMC produce ac output voltage with amplitude 0.5vdc at most. vc = vdc / N is usually set for HB-SM
Fig. 3. Nominalized carrier waves, continuous as well as discretized reference signal of PDPWM for FB-SM based MMC (N = 2).
Fig. 2. Switching states distribution and capacitor voltage balancing method for FB-SM based MMC (N = 2).
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I zx∗ ∗ 1zx
i
v2∗ xcom
izx∗
I zx* 0
izx
∗ vxp
v2∗ x
Vdc / 2
∗ icmx
vx∗ ix vdc
∗ cm
v
vx∗ ∗ vcm
izx
v1x∗
∗ vxn
Fig. 4. Overall control structure with low-frequency ripple voltage suppression embedded.
Modulation methods for HB-SM based MMC can be directly applied to FB-SM based MMC, with slight modification. Phase-Disposition (PD) PWM method is adopted here. Taking N = 2 as instance, there are 2N + 1 levels in arm voltage, and 2N stacked carrier waves, as shown in Fig. 2. Compared with HB-SM based MMC with the same N, equivalent switching frequency is doubled. After generating discretized reference vpwm from above PWM method, switching states are distributed to SMs and achieving capacitor voltage balance at the same time. SM states are defined as Sj = 0, 1, 2 in accord with SM output voltage vj = -vc, 0, vc. Flowchart of distribution and balancing method is shown in Fig. 3. The algorithm in Fig. 3 is based on N = 2, and can be easily extended to FB-SM based MMC with more submodules. It is implemented in a field programmable gate array (FPGA), and vpwm(k) is sampled during each system clock cycle of FPGA. IV.
LOW-FREQUENCY OPERATION TECHNIQUE
A. Improved Injecting Method to Decrease Arm Current Pressure To ensure precision tracking control of injected current especially with low switching frequencies, a “square wave plus third-order harmonic injection” method is applied, in which vcm is of square wave, while icmx is a same-frequency sine wave with a third-order harmonic, as shown below:
vcm
icmx =
(1 − M )vdc 2K cm = (1 M )vdc − − 2 K cm
(
(0 < t ≤
1 ) 2 f cm
1 1 ( )
