Average Modeling and Control of Module Multilevel Converter

Journal of International Council on Electrical Engineering Vol. 4, No. 2, pp.151~156, 2014 http://dx.doi.org/10.5370/JICEE.2014.4.2.151

Average Modeling and Control of Module Multilevel Converter GuoJu Zhang†, Yao Chen*, Lisa Qi**, Rongrong Yu* and Jiuping Pan** Abstract – Modular Multilevel Converter (MMC) has presents great potential in high power quality, low operation loss, scalability and high reliability, which make MMC a good choice for DC transmission, MV drive and other HV or MV applications. This paper describes the average modeling and control of MMC. Firstly, the operation principles of MMC are analyzed，based on which the average MMC model is deduced. Secondly, the control methods for DC voltage control, circulating current suppression, and capacitor voltage balancing, etc are developed. Finally, the effectiveness of the proposed average model is verified by comparing the simulation results of an MVDC distribution system using detailed MMC models. The correctness of the designed control methods also demonstrated through simulation. It is also proven to be feasible of using MMC in MVDC applications. Keywords: Module Multilevel Converter (MMC), Average model, MVDC system, Simulation analysis

thus have great engineering application value. This paper describes the average modeling of MMC and control method thereof. In section 2, the operation principles of MMC are analyzed and the average model is deduced. In section 3, the control method including outer loop and inner loop control is developed. In section 4, an MVDC distribution system model is setup with both detailed and average MMC models. The effectiveness of the proposed average model and the control are demonstrated by simulation results.

1. Introduction MMC is first proposed by R.Marquardt in 2002[1], compared with other high-voltage high-power converter topology such as direct series/parallel connection, or multilevel technology, MMC presents great potential in high power quality, low operation loss, high scalability and reliability. These advantages make MMC a good choice for DC transmission, MV drive and other HV or MV applications [2-5]. The current research on MMC focuses on working principles, control strategies, modulation strategies and parameters design, for example direct module method and nearest level modulation[8-9], capacitors voltages balancing scheme[10-11], circulating current control [12-13], etc. However, few papers discuss the average modeling of MMC. Paper [14] proposes a time-domain analytical model which combines switching function and instantaneous power to give the analytical equations for voltage and current of each arm and each sub module. But such time-domain analytical model and other detailed MMC simulation models featured in accurate dynamics have high requirement on both hardware and software simulation platforms, and so that still not satisfactory to support efficient simulation studies. Average modeling of MMC aims to realize fast, stable, and reliable MMC simulation with proper accuracy. It can reduce the computation load of simulation platforms, and

2. Operation principles The circuit topology of MMC is shown in Fig. 1, con-sidering the consistency of three phases, only phase a is given in detail. In phase a, there are 2N cascaded sub modules, and 2 valve reactors La which are used to suppress the circulating current in normal operation and to limit the rate of rising of DC short circuit current. The neutral point of phase a is connected to grid through grid reactor Lsa. There are 3 operation states of a half bridge sub module: 1) Blocking state, the pulses of IGBT T1 and T2 are blocked in this state. 2) IN state, T1 is switched off and T2 is switched on. In this state, the output voltage uSM=uC, the current through capacitor iC=iSM, where uc is capacitor voltage and ism is output current of the sub module. 3) OUT state, T1 is switched on and T2 is switched off. In this state, uSM=0, iC=0. By controlling the IN and OUT states of each sub

†

Corresponding Author: ABB (China) Corporate Research Center, Beijing, China * ABB (China) Corporate Research Center, Beijing, China ** ABB (US) Corporate Research Center, Raleigh, USA Received: December 26, 2013; Accepted: March 11, 2014

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Average Modeling and Control of Module Multilevel Converter

where upa and ipa represent upper arm voltage and current of phase a. By replacing the sub-modules with controllable voltage sources in equation(3), the average model of MMC can be obtained as shown in Fig. 2, and the corresponding mathematic model can be described by:

module, the sinusoidal output voltage can be fitted by adding output voltages of sub modules. In steady state operation, DC side current Id is equally distributed to 3 phases, and AC side current ia, ib and ic are equally distributed in upper and down arms of respective phase.

di pk ⎧1 ⎪ 2 Vdc = u pk + Lk dt + uNO ⎪ ⎪1 di ⎨ Vdc = unk + Lk nk − uNO dt ⎪2 ⎪ dik ⎪⎩usk = uNk − Lsk dt

(4)

where uNk is the voltage of neutral point of phase a, and k=a,b,c. When the system is symmetrical, uNO=0. Fig. 1. Topology of MMC. Vdc 2

3. Average model 3.1 Average modelling of sub module

Vdc 2

According to the operation states of a sub module, switching function S can be used to represent IN (S=1) and OUT (S=0) states of a sub module:

⎧uSM = S ⋅ uC ⎨ ⎩ iC = S ⋅ iSM

(1)

Fig. 2. Average model of MMC. Comparing with 2-level VSC, one difference is that there exists the circulating current path inside MMC. The circulating current is defined as the current between positive DC line and negative DC line or the current among three phases [15]. The circulating current is used to not only transfer active power between AC side and DC side, but also transfer reactive power among three phases. As mentioned before, the AC side current in each phase is equally distributed in upper and down arms in steady state, then upper and down arms currents ipk, ink can be described by:

In one switching period, assuming the duration when S=1 is d, using state space average method, the average model of a sub module is:

⎧uSM = d ⋅ uC ⎨ ⎩ iC = d ⋅ iSM

(2)

3.2 Average modeling of MMC As shown in Fig. 1, either upper or down arm is composed of N cascaded sub modules. Taking upper arm of phase a as an example, combining with equation(2), average model of this arm can be described by: N ⎧ u = ⎪ pa ∑ d i uCi i =1 ⎨ ⎪ i =di i pa ⎩ Ci

1 ⎧ i = i + ik pk Zk ⎪⎪ 2 ⎨ ⎪ink = iZk − 1 ik ⎪⎩ 2

(5)

(3) where iZk is the circulating current in phase k. iZk can be deduced from power conservation law: 152

GuoJu Zhang, Yao Chen, Lisa Qi, Rongrong Yu and Jiuping Pan

⎧ ⎪i = A ⎡cos ϕ + cos ( 2ωt − ϕ ) ⎤ ⎣ ⎦ ⎪ Za ⎪⎪ 2π ⎡ ⎛ ⎞⎤ − ϕ ⎟⎥ ⎨iZb = A ⎢cos ϕ + cos ⎜ 2ωt + 3 ⎝ ⎠⎦ ⎣ ⎪ ⎪ 2π ⎡ ⎛ ⎞⎤ − ϕ ⎟⎥ ⎪iZc = A ⎢ cos ϕ + cos ⎜ 2ωt − 3 ⎝ ⎠⎦ ⎪⎩ ⎣

where upk1* and unk1* are modulation waves of upper and down arms in phase k. GIR(s) can be transfer function of a PI controller or proportional resonant (PR) controller. And the circulating current control equations:

(6)

* ⎧u*pk 2 = −GCR ( s ) ( iZk − iZk ) ⎪ ⎨ * * ⎪⎩unk 2 = −GCR ( s ) ( iZk − iZk )

where A=M·Ism/4, M is the modulation ratio, Ism is the peak value of AC side current, φ is power factor angle. In summary, equations (3), (4), (5) and (6) represents the average model of MMC. The developed average model is used in the simulation study in Section 5.

where upk2* and unk2* are modulation waves of upper and down arms in phase k. GCR(s) can be transfer function of a PI controller or PR controller. As shown in equation(6), there exist DC component and nd 2 harmonic component in the circulating current. The DC component is related to active power transferring through MMC, summation of DC components in three phases is Id which cannot be eliminated by control method. The 2nd harmonic component, which is used to transfer active power among three phases for energy balancing, is related with capacitor charging and discharging. In steady state, the energy should be distributed equally in three phases. Based on the analysis above, the circulating current reference izk* can be described by:

4. Control strategy and modulation method The mathematical model of MMC in section 3 is analyzed in order to develop appropriate control strategies. Based on equations (4) and (5), upk and unk can be described by:

⎧ 1⎛ dik ⎞ diZk ⎪u pk = 2 ⎜Vdc − Lk dt ⎟ − Lk dt ⎪ ⎝ ⎠ ⎨ ⎪u = 1 ⎛V + L dik ⎞ − L diZk k ⎟ k ⎪⎩ nk 2 ⎜⎝ dc dt ⎠ dt

(9)

(7)

* = iZk

Id + GZR ( s ) ( ucp _ ref − ucpk _ avg ) 3

∑k (u cpak + u cpbk + u cpck )

(10)

2N

where u cp _ ref =

As shown in equation(7), there exist two components in upk and unk: one is related with AC side current ik, and the other is related with circulating current iZk. There are different control strategies applicable to MMC due to different applications. For examples, DC voltage and unit power factor control can be adopted when a MMC is used as a rectifier; PQ control can be adopted when a MMC is used as an inverter. One common point in these applications is that the output of out loop is the AC side current reference, which means that different control strategies is realized by controlling of fast current inner loop. According to equation(7), the AC side current control equations in abc phases static coordinates can be described by:

1 ⎧ * * ⎪⎪u pk 1 = 2 Vdc − GIR ( s ) ( ik − ik ) ⎨ 1 * ⎪unk = V + GIR ( s ) ( ik* − ik ) ⎪⎩ 1 2 dc

=1

denotes

the

3

average energy stored in each phase,

u

cpk _ avg

=

∑k

2N

u

=1 cpak

is energy stored in phase k, GZR(s) is transfer function of a PI controller. For high-power multilevel converters, the most commonly used modulation methods include direct modulation (DM), selective harmonic elimination PWM (SHEPWM), multicarrier PWM, phase-shift carrier PWM (PSCPWM), etc. Among them, PSCPWM can realize high equivalent switching frequency using low physical switching frequency and automatically suppress all loworder harmonics; these advantages make PSCPWM a good choice of modulation strategy for MMC in MVDC applications. Due to parameters’ differences among different sub modules in one arm, the capacitor voltages are different respectively, which adversely influences output voltage quality. In order to eliminate this adverse influence, one method is to sort sub modules according to the capacitor voltage, and then decide IN or OUT state of each sub

(8)

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Average Modeling and Control of Module Multilevel Converter

module according to the direction of arm current. However, this method needs extra resources for comparison and selection, which makes IGBTs switch on and off with high frequency and thus causes higher switching loss [16]. According to the operation principles of sub module, the charging or discharging duration in one switching period can be adjusted by changing IN or OUT duration time. Based on this, a component uC* for balancing capacitors voltages is added to the control strategy: * uCi = K ( uCref − uCi ) ⋅ sign ( iSMi )

1.5MVA, motor rated speed 1500rpm. The square torque load representing pump/fan load characteristic is modeled. The simulation results from both detailed model and average model are shown in Fig. 5 and Fig. 6 for comparison. Sequentially in each figure, they are capacitor voltages (a), DC line voltage (b), active and reactive power of rectifier (c), rotor speed of M1 (d), electrical and load torque of M1 (e). At t=5s, load of M1 is reduced and its rotor speed also reduces from 1500rpm to 1000rpm accordingly. It can be observed the behavior of average model is consistent with that of detailed model under both normal operation and load change scenario, which veried the correctness of the proposed average modeling method developed in Section 3. Besides, during the load change, the DC line voltage kept unchaged through outler loop control, and the fluctuation of capacitor voltage reduces along with the active power as expected, which demonstrate the effectiveness of the control strategy discussed in Section 4.

(11)

where uCi* is the capacitor voltage of sub module i, sign(iSMi) is sign of current iSMi, K is proportional gain. Based on control equations above, the control block diagram of MMC is shown in Fig. 3which is also implemented in the simulation study in Section 5.

Fig. 4. MVDC distribution system.

Vcaps /kV

1.5 1 0.5

Fig. 3. Control strategy block diagram of MMC.

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5. Simulation verification

10 5

PQ /MVA

In order to verify the effectiveness of the average MMC model and the control strategy thereof, both detailed and average MMC models are implemented in a MVDC distribution system model shown in Fig. 4. The simulation environment is Matlab/Simulink/SimPowerSystems. In Fig. 4, there exists one rectifier, two motor drives and other loads in the MVDC distribution system. DC voltage is controlled by the rectifier and DTC control method is adopted in motor drive. The parameters of MMC converters system are: AC grid line to line voltage 11kV; transformer rated capacity 6MVA and voltage ratio 11kV/6.3kV; rectifier rated capacity 5MVA, DC voltage 10kV; line resistor 0.03 Ohm; inverter rated capacities 2.7MVA and

6 4 2 0 -2

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2000 1000

Te& Tload /Nm

0

2

4 x 10

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1 0 -1

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Fig. 5. simulation results of detail model.

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GuoJu Zhang, Yao Chen, Lisa Qi, Rongrong Yu and Jiuping Pan

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[8]

Fig. 6. simulation results of average model. [9]

6. Conclusions This paper presented the average modeling method of MMC, and based on which elaborated the control mechanism for circulating current suppression and capacity voltage balancing. Taking a MVDC distribution system as an example, the simulation results of the MMC detail and average models are compared and analyzed to verify the effectiveness of the developed average MMC model and control. This example also indicates feasibility of MMC for MVDC applications.

[10]

[11]

[12]

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Average Modeling and Control of Module Multilevel Converter

[16] Zhao Xin, Zhao Chengyong, Li Guangkai, et al. Submodule Capacitance Voltage Balancing of Module Multilevel Converter Based on Carrier Phase Shifted SPWM Technique[J]. Proceedings of the CSEE, 2011, 21(31) : 48-55.

Environment at Virginia Tech USA. His expertise includes power system modeling and analysis, HVDC transmission, power system planning and energy market, power plant engineering, T&D asset management.

GuoJu Zhang received Ph.D. degree in electrical engineering from Institute of Electrical Engineering, CAS in 2011. His main interests include grid automation, power system modeling and simulation, power system dynamic and stability analysis, power electronics applications.

Yao Chen received her Ph.D. degree in Electrical Engineering in 2008 from Beijing Jiaotong University of China. She is currently a Senior R&D Engineer with ABB China, Corporate Research. Her research interests include power conversion technology of new energy and electric vehicle integration, MV drive based energy efficiency solution in Electrical Balance of Plant (EBoP), advanced generator control strategy and power plant stability studies.

Li Qi received the B.Eng degree from Xian Jiaotong University, China, the M.Sc. degree from Zhejiang University, China, and the Ph.D. degree from Texas A&M University, College Station. All in electrical engineering. She is currently a principal R&D Engineer with ABB Corporate Research (U.S. Center), Raleigh, NC. Her expertise and research interests include power system modeling and simulation, power system dynamic and stability analysis, power system protection, dc grid, power electronics applications.

Rongrong Yu received her Ph.D. degree in Electrical Engineering in 2011 from Beijing Jiaotong University of China. Her main interests include grid automation, electric vehicle integration, system reliability.

Jiuping Pan received B.S. and M.S. in electric power engineering from Shandong University, China and Ph.D. in electrical engineering from Virginia Tech, USA. He is currently a Principal R&D Engineer with ABB US Corporate Research Center. Prior to joining ABB, He was with the faculty of Electric Power Engineering Department of Shandong University in China. From 1993 to 1995, He was a visiting scholar at the Center of Energy and Global

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