Current Balancing Control of High Power Parallel-Connected AFE with

Current Balancing Control of High Power Parallel-Connected AFE with Small Current Ripples 1

Xinbo Cai1? , Zhenbin Zhang1? , Liang Cai2 , Ralph Kennel1 , Senior Member, IEEE Institute of Electrical Drive Systems and Power Electronics, Technische Universit¨at M¨unchen 2 STEP Electric Corporation, Shanghai, China Arcisstr. 21, D-80333, Munich, Germany Phone: +49 (89) 289-28445, Fax: +49 (89) 289-28336 Email: {xinbo.cai, james.cheung, ralph.kennel}@tum.de, URL: http://www.eal.ei.tum.de

Abstract—Parallel connected Active Front End (AFE) voltage converters are widely employed in high-power grid interfaces for renewable energy applications. With parallel connected two level power converters, the power rating of the system can be easily increased with higher stability and less control efforts than multilevel power converter based solutions. However, due to unmatched modules, unbalanced currents inevitably happen to different modules of the same phase, which seriously impacts the efficiency and performances of the converter. This paper presents an improved current balancing control methods for a high power (600 kVA) parallel connected AFE for wind energy applications. The proposed current balancing method is integrated within a well-known Voltage Oriented Control Scheme with few implementation efforts. The simulation results show that with the proposed strategy the current ripples of each parallelconnected converter leg decrease evidently and the THDs are therefore decreased. Moreover, the effectiveness of the proposed method is also confirmed by experimental results with a grid-code compatible testing set-up. Index Terms—High Power AFE, Current Sharing Control of Parallel-Connected AFE, Voltage Oriented Control, PMSG wind turbine system, Non-linear control

I. I NTRODUCTION Variable-speed wind turbine systems are drawing increasing interests globally. A multi-pole permanentmagnet synchronous generator (PMSG) with an activefront-end back-to-back (AC/DC/AC) converter offers several advantages compared to passive-front-end AC/DC/AC converter [1]. With an active-front-end AC/DC/AC converter, a bi-directional power flow is feasible and higher potential for fault ride-through and grid voltage support ability is achieved. Power ratings of PMSG wind turbine system has been seeing a great increase. Currently 7.5 MW units are available in the market and numerous research efforts have been done 1 This publication was made possible by the National High Technology Research and Development Program of China (863 Program, No.: 2014BAF08B05) and the Deutsche Forschungsgemeinschaft (DFG) Project (No.: KE817/32-1). Authors with ? contributed equally. Corresponding author: Zhenbin Zhang, e-mail: [email protected]).

for large systems, targeting 5-10MW level for offshore applications [2]–[4]. This increase in power rating will require high power converter/inverter topologies to meet grid codes and to guarantee low total harmonic distortion. In particular, compared with multi-level back-to-back converters, parallel connected two level converters are interested to the industrial. It allows for high voltage and power levels, but the required control, installation and maintenance efforts are drastically less than for multilevel converters [3], [5]. A typical parallel connected back-to-back PMSG wind turbine system is shown in Fig. 1. This work focuses on the grid side control of a parallel-connected AFE. As can be seen from Fig. 1, a parallel-connected AFE contains three main parts: (i) parallel connected two-level converter modules, (ii) passive current balancing inductance, (iii) DC-link. The control targets for controlling a parallel connected AFEs are: (I) DC-link voltage control, i.e., maintaining a constant DC-link voltage against different load side conditions; (II) grid side power factor and power (current) quality control; (III) maintain the phase currents on different modules x2 balanced (i.e., keep ix1 n = in , where x can a, b, or c, represents the phases of the grid side converter). And to fulfill (I) and (II), the control schemes in general can be divided into four groups [6]–[8]: (i) Vector control with modulator, (ii) direct control with look-up table; (iii) direct control with modulator, (iv) predictive control (direct and continuous predictive control [9]– [13]). Vector control is dominating the most industrial applications. Especially, due to its intuitiveness and effectiveness, Voltage Oriented Control (VOC) is widely applied. In practice, the cells (See Figure. 1, Cell-A and Cell-B) cannot be (perfectly) matched. This imperfect matching is mainly caused by: different parameters of the power switches and passive balancing inductances 1 and L2 in Fig. 1), or different lengths (delays) (Lcb cb of drive paths of the gate signals for Cell-A and B. These imperfect matching of the cells leads to unmatched currents of same phase on different cells,

which seriously impacts converter performances and efficiency. Moreover, unmatched currents also cause different amounts of heat production on different modules of the converter legs. It thus makes the heat-sink design more difficult and will even shorten the lifespan of the whole converter. Therefore, research on effective and robust current balancing control (i.e, control target (III)) strategies for parallel connected high power AFE is of great necessity. Recently, some publications can be found on this topic [14]–[18], and in general it can be divided into two branches: (a) passive current balancing methods and (b) active current balancing methods. Passive current balancing method highly depends on the accuracy of the balancing inductance, and is of great limitation due to the inductance producing accuracy. Therefore, most of the recent researches are focusing on active current balancing methods, which can be further divided into two sub-methods, namely, MasterSlave based control methods (See i.g. [15], [17] for instance.) and adaptive droop control methods (See i.g. [14] for instance). These two methods are in general very effective for controlling the RMS values of the unbalanced currents, however, the unbalanced currents cannot be balanced instantaneously. Theoretically, for active current balancing control methods, the bandwidth of the (inner) current balancing control loop is the bottle-neck for reaching a high performance control [19]. Therefore high or large bandwidth active current balancing controller is a precondition for reaching high control performance. Hence, hysteric band based nonlinear controller with fast dynamics to adjust the final duty-cycles for the same phases of the parallel connected modules is of interests. However, big ripples and therefore bad THDs are observed at the phase current output of each module. In this work, an improved current balancing method with high dynamics, but much smaller current ripples is proposed. The proposed control method is combined with the wellknown VOC scheme, with which a fast and effective active current balancing control performance is reached but few implementation efforts are required. The contributions of this paper are: (i) Simulation analysis of the causes for unmatched currents in parallel connected AFE is given. (ii) An improved current balancing (sharing) control scheme combined with a well-known VOC scheme with Space Vector Modulator (SVM) is proposed. (iii) The proposed method is verified by both simulation and experimental data using a low cost but grid-code compatible testing configuration. This paper is outlined as follows: In Sec. 2, a complete description of a parallel connected AFE with Voltage Oriented Control scheme is introduced. In Sec. 3, the reasons causing unmatched currents in different modules of the parallel connected AFE is verified with simulation results. After revisiting a conventional bang-bang controller based scheme, an

improved current balancing control scheme with high dynamics meanwhile smaller current ripples is proposed. Finally, in Sec. 4, simulation comparison with the conventional bang-bang controller based current balancing control scheme is provided. Then with an intelligent testing configuration a high power parallel connected AFE set-up is configured and the experimental data which further confirms the effectiveness of the proposed control method is presented and analyzed. Sec. 5 summarizes the paper. II. PARALLEL C ONNECTED AFE S WITH VOLTAGE O RIENTED C ONTROL In this section, a parallel connected AFE (left part of Figure 1) with Voltage Oriented Control scheme is introduced. At low frequency domain, a LCL filter shown in Figure 1 can be simplified as a L filter. Assuming the gate signals are simultaneously reaching the switches, 1 = L2 = L , the system can be modeled in and Lcb cb cb direct-quadrature frame (rotating with the grid side voltage vector ~en at a frequency of ωn ) as: didn = edn − vdn − Rn · idn + ωn · Lnq · iqn dt q din Ln = eqn − vqn − Rn · iqn − ωn · Lnd · idn dt

Ln

q

(1) (2)

q

where vdn , vn , edn and en are the the converter and grid q side voltage vectors in dq frame (edn and en can be obtained by using a Phase Lock Loop (PLL)); idn and q in are the filter currents near the converter side in dq frame (See Figure 1), Ln = Ln1 + Ln2 + 0.5Lcb is the overall equivalent inductance, Rn is the sum of the self resistance of the grid side inductances (Ln1 , Ln2 and Lcb ). After rearranging, the voltage that the converter should output can be put in the following form: didn − Rn · idn + ωn · Ln · iqn dt q din vqn = eqn − Ln − Rn · iqn − ωn · Ln · idn dt

vdn = edn − Ln

q

(3) (4)

q

Regarding ωn · Ln · in in equation (3), and ωn · Lnd · d in in equation (4) as coupling terms, one can get the following controller: didn d − Rn · idn + ωn · Ln · iqn vd∗ n = en − Ln dt | {z } | {z } PId

d−Coupling

q din

q vq∗ − Rn · iqn − ωn · Ln · idn n = en − Ln dt | {z } | {z } PIq

(5)

(6)

q−Coupling q∗

The voltage references vd∗ n and vn are then transβ∗ formed into αβ frame as vα∗ n and vn with the knowledge of the grid side voltage vector position obtained β∗ from a PLL. vα∗ n and vn can be assigned to a Space Vector Modulator (SVM) to control the converters. The outer loop, i.e., the DC-link voltage control loop, is done through a Proportional Integration (PI)

Unit

Parallel Connected AFEs v

v

Figure 1: Circuit of direct-drive permanent-magnet synchronous generator (PMSG) wind turbine system with parallel connected back-to-back power converter.

PI

PLL

PI

PI

Figure 2: Voltage oriented control of parallel connected AFEs.

controller due to its simplicity and effectiveness. Its output serves as a reference (id∗ n ) for the direct current controller (also a PI controller). The quadrature current q∗ reference (in ) is usually set to 0 to achieve a unit power factor. So the whole control scheme can be described by the block diagram in Figure 2. III. U NMATCHED C URRENTS AND C URRENT BALANCING C ONTROL In this section the analysis of the unbalanced currents for the same phase on different modules is introduced and verified by simulations. Afterward, an active current control scheme with a bang-bang controller is revisited. Then, an improved current balancing control scheme combined with a modified SVM is proposed.

same value, while the gate transformation delay for cell-2 is set as 0.2 µs; Test (d) saturation voltages of the power switches in cell − B is in 0.1v bigger than that in cell − A, and all the other conditions are set as the same. The results are shown in Figure 3. Clearly, it can be found from Figure 3 that, (i) unmatched passive inductances, (ii) different paths of gate drive lines, or (iii) unmatched power switches can all lead to unbalanced currents. Especially (iii) and (i), in practice, after long time of operation it is easy to change its characteristic parameters. And a slight change may introduce remarkable unbalanced currents. B. Current Balancing Control with Bang-Bang Controller As is analyzed in the last sub-section, the current unbalancing is inevitable in a parallel connected converters. Therefore, current balancing control, especially active current balancing control is necessary. And, given a control scheme as shown in Figure 2. Basically, one can achieve the balanced currents by giving different on-duty times of the gate signals to the relevant paralleled modules, which originally output unbalanced currents. Based on this concept, a bang-bang controller which directly output the on-duty differences taking the current differences as input are introduced firstly. The idea is depicted in Figure 4, where ixi n is the current

A. Unmatched Current Analysis The unmatched currents are usually caused by (i) different balancing inductance values, (ii) different drive signal delay time, or (iii) unmatched power switches (saturation voltages). These reasons are often stated in part of the recent publications, but seldomly verified by certain proof. In the following of this section, four scenarios of testing are carried out by simulation to investigate this: Test (a) passive balancing inductances are set with the same value of 15 µH (i.e., 1 = L2 = 15µH), and no gate transformation delay. Lcb cb 1 is set as 11.25 µH, Test (b) passive inductance of Lcb 2 and Lcb = 15µH, and no gate transformation delay; Test (c) passive balancing inductances are set with the

Figure 4: Block diagram of a bang-bang controller based current balancing control method .

on x phase (x ∈ {a, b, c} represents the phase of the converter output) of paralleled module i (i ∈ {1..k} is the paralleled module number, here k = 2); δDxi n,

0 ia1 n

ia1 n

-500

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

Current [A]

Current [A]

500

500

0 ia1 n

0.04

0

0.005

0.01

0.015

Time [s]

ia1 n

ia1 n

-500

0.015

0.02

0.025

0.03

0.035

0.04

Current [A]

Current [A]

0

0.01

0.025

0.03

0.035

0.04

(b) Currents with unmatched passive inductances.

500

0.005

0.02

Time [s]

(a) Currents with perfectly matched modules (cells).

0

ia1 n

-500

500

0 ia1 n

0

0.005

0.01

0.015

Time [s]

(c) Currents with unmatched gate signal drive paths.

0.02

0.025

0.03

0.035

where ka > 0, H > 0, are tunable parameters. This idea is quite simple but effective in balancing the current. However, due to the bang-bang switching nature, to achieve fast current balancing performance, high gain of the hysteresis is required and thus big ripples are inevitably observed (See Figure 8). C. Improved Current Balancing Control with Modified Space-Vector Modulation

(d) Currents with unmatched switches (saturation voltage).

(on − o f f states)) should be modified to include the current balancing controller output. To integrate the proposed current balancing control method, the duty cycle has to be modified before it is transformed into on − o f f states. And the final modified SVM (named as M − SV M in the following) combined with the current balancing (sharing) controller (CSC) is illustrated by Figure 6:

M

SVM

CSC

PWM

...

kb (8) 1 + e−kc x where kb , kc > 0, are tunable parameters. Clearly, equation (8), in stead of outputting the true(ka ) or f alse(−ka ) -like discrete actuating signals, produces continuous triggering duty-differences. Thus, it may improve the short-coming of big current ripples for bang-bang controller scheme, but remains the high dynamic nature of the bang-bang controller. The method is shown in Figure 5. Note that, when involving the active current balancing control methods, no matter a bang-bang controller or the proposed sigmoid switching function based scheme is used, conventional Space Vector Modulator (whose output is directly the switching signals

Figure 5: Block diagram of a sigmoid switching function based current balancing control method.

...

This work, proposed an improved current balancing method by changing the discrete switching function into a sigmoid function based switching

0.04

Time [s]

Figure 3: [Simulation data:] Current unbalance test. xi Dxi n (VOC) and Dn are the output signal of the hysteresis switching function, on-duty time processed by the VOC controller (achieved by using the part of a modified SVM, for which, please refer to Figure 6), and the final on-duty time to be assigned to the relevant leg of the converter, respectively. Here the switching function is defined as:   x>H ka (7) Y (x) = 0 −H ≤ x ≤ H   −ka x < −H

ia1 n

-500

Y (x) =

Figure 6: Block diagram of a modified space vector modulator with current balancing control.

IV. R ESULTS AND A NALYSIS In this section the proposed control method will be firstly illustrated by simulations using Matlab/Simulink as a first proof of concept. The improvement is seen through comparison with the conventional control method. And afterward, the control method is further confirmed by experimental data. All simulation and experimental parameters are collected in Table I.

Table I: System Configuration Symbol

Parameter

Unit

Simulation

Experiment

ea,b,c n ωn Ln1 Ln2 R1n Cn1 Lcb fs ka H kb kc

Grid-side Phase Voltages (peak) Grid-side Voltage Frequency Grid-side Inductance of LCL IGBT-side Inductance of LCL Resistor of LCL Capacitor of LCL Sharing Inductance Switch Frequency Tuning Parameter Bang-bang Tuning Parameter Bang-bang Tuning Parameter Sigmoid Tuning Parameter Sigmoid

[V] [Hz] [H] [H] [Ohm] [F] [H] [Hz] [1] [A] [1] [1]

311 50 38e−6 100e−6 75e−3 400e−6 15e−6 4000 0.001 5 0.001 0.007

311 50 38e−6 100e−6 0 400e−6 15e−6 4000 non non 0.001 0.007

Grid Vol.[V]&Cur.[A]

DC Voltage [V]

800 ∗ Udc Udc

750

700 0

0.05

0.1 Time [s]

0.15

0.2

(a) Performance of DC-Link voltage control.

2000 ias ean

0

-2000 0

0.05

0.1 Time [s]

0.15

0.2

(b) Grid side current and voltage (Power factor performance).

Figure 7: [Simulation data:] DC-link voltage control and grid side power factor control performances with VOC.

A. Simulation verification of the proposed control method For verifying the control performances of VOC controller, and the current balancing controller, simulation verifications are carried out using Matlab/Simulink. The DC-link voltage and grid side power factor control performances are depicted by Figure 7: Figure 7 (a) shows the DC-link control performances during reference step change, and load changes (from no load to rated load (600VA) change), and clearly the DClink voltage is controlled nicely in both situations. In figure 7 (b), the unit power factor control is shown. Clearly, with the proposed control scheme, a unit power factor is maintained (See time instance of [0.15, 0.2]s, and the phase shifting during beginning intervals is due to the reactive current flowing in the LCL filter). In Figure 8, an overall control comparison between the conventional bang-bang controller based method and the proposed sigmoid function based method is shown. It is clearly seen that the currents ripples with the proposed method are greatly reduced. And to investigate the detailed improvement, in Figure 9 the current quality in terms of Total Harmonic Distortions (THDs) is illustrated. An obvious improvement is seen (with the proposed method, the THDs are reduced from 7.07% to 4.32%). B. Experimental verification of the proposed control method In practice, in order to ease the grid side reactive power requirement (it is required from the local government, one cannot produce or withdraw too much reactive power from the grid), in this paper, an intelligent testing configuration is proposed as is shown in

Figure 10. Using this configuration, seeing from the grid side, only little power (both active and reactive) will be consumed (due to the filter resistance and power converter imperfect efficiency). The energy is therefore just flowing in between the two test units (Unit-A and Unit-B, each of which is exactly the same as the shadowed part of Figure 1). It is thus allowable to set the reactive power reference with a big value without polluting the grid. It is already verified by the the simulation results that very big ripples (will potentially make the home constructed set-up under great risks) will be produced by using bang-bang controller based method. And it is already clear, the proposed method outperforms the conventional one. Therefore, to lower the risks for the real experimental testing (with a power rating of 600VA), the authors are focusing on testing the proposed method with the as-described experimental set-up. In Figure 11, the overall performance of the current (positive reactive for Unit-A, and negative reactive for Unit-B) is shown, where the grid side current (~is in Figure 1) obtained simultaneous is also illustrated. As expected, even the current in both Unit-A and B are very big (peak value roughly reaches 900A), the current in the grid side is still quite small (with a mean value of roughly 20A, caused by the cooling systems, resistors and converter lost), which confirms the effectiveness of the testing set-up, and which also means the proposed testing configuration can be used as a good example for testing high power converters. Experimental verification of the proposed current balancing control method is shown in Figure 12. Clearly, it can be confirmed that the proposed current

ia1 n

Current [A]

Current [A]

ia1 n

500

0

-500

500

0

-500 ia1 n

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0

0.01

0.02

0.03

0.04

Time [s]

ia1 n

0.05

0.06

0.07

0.08

Time [s]

(a) Current balancing control with bang-bang controller activated at 0.04s

(b) Current balancing control with proposed controller activated at 0.04s

Current (ia1 n ) [A]

Current (ia1 n ) [A]

Figure 8: [Simulation data:] Current balancing control performance comparison. 500

0

-500 0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

500

0

-500 0

0.08

0.01

0.02

0.03

0.04

Mag (% of Fundamental)

Mag (% of Fundamental)

3

2

Fundamental (50Hz) = 626.7 , THD= 7.07%

1

1000

2000

3000

4000

5000

6000

7000

8000

9000

0.06

0.07

Fundamental (50Hz) = 625.4 , THD= 4.32%

2 1.5 1 0.5 0

10000

0

1000

2000

3000

4000

Frequency (Hz)

5000

6000

7000

8000

9000

(b) Current balancing control with proposed controller activated at 0.04s

Figure 9: [Simulation data:] Current quality comparison.

UnitA

UnitB

Figure 10: Configuration of the experimental test-bench.

Current [A]

1000 ianA ianB ias

500

0

-500

-1000 0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

Time [s] Figure 11: [Experimental data:] Current of grid and two units. 250

250 ia2 n

200

150

150

100

100

Current [A]

Current [A]

ia1 n

200

50 0 150 -50 100 -100

ia1 n ia2 n

50 0

150

-50

100

-100

50

50 -150

-150

0

-200

-50

0 -200 -50 -250 0

0.01

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10000

Frequency (Hz)

(a) Current balancing control with bang-bang controller activated at 0.04s

0

0.08

2.5

0 0

0.05

Time (s)

Time (s)

0.04

0.05

Time [s]

(a) Module current output without current balancing control.

-250 0

0.01

0.02

0.03

0.04

0.05

Time [s]

(b) Module current output with the proposed current balancing control.

Figure 12: [Experimental results:] Current balancing control performances.

control method is very effective. Note that, the relative big ripples of the current compared with the simulation results are caused by the sampling noises and also the dead-time in the real control. V. C ONCLUSION Parallel connected power converters can serve as a nice alternative for high or mid-power rating grid interfaces for renewable energy systems. Current unmatching in the same phase of different legs is one of the common issues. Within this work an effective current balancing control method combined within a well-known Voltage Oriented Control (VOC) scheme has been presented and verified. Within this work, the following has been achieved: (i) The current unmatching problems are verified by simulation; (ii) Based on a bang-bang control scheme, an improved current balancing method combined with a VOC control scheme with a modified SVM is proposed and verified. Compared with the conventional method, with the proposed one, both the current ripples on each module of the same phase have been greatly reduced, and THDs are also greatly lowered. (iii) An intelligent test configuration is proposed and with the proposed test set-up one can neglect the (reactive power consumption) effects to the grid. (iv) The proposed control scheme is verified by both simulation results and experimental data. Future work would focus on applying the proposed control method within predictive control scheme for a back-to-back parallel connected power converter for PMSG wind turbine systems. R EFERENCES [1] Z. Zhang, C. Hackl, F. Wang, Z. Chen, and R. Kennel, “Encoderless model predictive control of back-to-back converter direct-drive permanent-magnet synchronous generator wind turbine systems,” in Power Electron. Appl. (EPE), 2013 15th Eur. Conf., 2013, pp. 1–10. [2] Z. Song, C. Xia, and T. Liu, “Predictive current control of three-phase grid-connected converters with constant switching frequency for wind energy systems,” Industrial Electronics, IEEE Transactions on, vol. 60, no. 6, pp. 2451–2464, June 2013. [3] A. A. Daoud, S. S. Dessouky, and A. A. Salem, “Control scheme of PMSG based wind turbine for utility network connection,” in Environ. Electr. Eng. (EEEIC), 2011 10th Int. Conf., 2011, pp. 1–5. [4] M. Liserre, R. Cardenas, M. Molinas, and J. Rodriguez, “Overview of Multi-MW Wind Turbines and Wind Parks,” Ind. Electron. IEEE Trans., vol. 58, no. 4, pp. 1081–1095, 2011. [5] V. Yaramasu and W. Bin, “Three-level boost converter based medium voltage megawatt PMSG wind energy conversion systems,” in Energy Convers. Congr. Expo. (ECCE), 2011 IEEE, 2011, pp. 561–567. [6] H. M. Nguyen and D. S. Naidu, “Advanced control strategies for wind energy systems: An overview,” in Power Syst. Conf. Expo. (PSCE), 2011 IEEE/PES, 2011, pp. 1–8. [7] J. Rodriguez, M. P. Kazmierkowski, J. R. Espinoza, P. Zanchetta, H. Abu-Rub, H. A. Young, and C. A. Rojas, “State of the Art of Finite Control Set Model Predictive Control in Power Electronics,” Ind. Informatics, IEEE Trans., vol. 9, no. 2, pp. 1003–1016, 2013. [8] T. Geyer and D. E. Quevedo, “Multistep Finite Control Set Model Predictive Control for Power Electronics - Part 1: Algorithm,” Power Electron. IEEE Trans., vol. PP, no. 99, p. 1, 2014.

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