Model predictive control of PWM AC/DC converters for ...

Model predictive control of PWM AC/DC converters for bi-directional power flow control in microgrids Xiaolong Shi1, Jianguo Zhu1, Li Li1, Yanqing Qu1 School of Electrical, Mechanical and Mechatronic Systems, University of Technology, Sydney, Australia [email protected]

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Abstract—The three-phase full-bridge converter has been popular for AC/DC conversion in microgrids, and various control methods have been employed to achieve low harmonic distortion of input currents, bi-directional power flow and high power factor, etc. Compared with the conventional control methods, the model predictive control (MPC) can be much more powerful and flexible for multiple control objectives. This paper presents a comparative study of the MPC-based direct power control (DPC) and the conventional DPC based on switching table with a focus on the steady-state and transient performance of bi-directional power flow control. The simulation results have shown that the MPC-based DPC has better performance, and thus is more suitable for AC/DC converter control in microgrids compared with the conventional DPC based on switching table. Index Terms—Direct power control, Model predictive control, Microgrids, Bi-directional power flow, AC/DC converter

driven by the sinusoidal pulse width modulation (PWM) scheme, as shown in Fig.1, have been commonly utilized for bi-directional power flow control. Compared with the uncontrolled AC/DC converters, this type of converters have several advantages, such as low harmonic distortion of input currents, bi-directional power flow, high power factor, stable DC-link voltage, and reduced DC filter capacitor size [3]. Idc

ea eb

Ia R Ib

ESS/DC Bus Va

C

Vb Ic

ec

L

Vdc Vc

I. INTRODUCTION

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owadays, renewable energy based microgrids are a better way for more efficient utilization of renewable power. Various kinds of renewable energy can be integrated into microgrids, such as photovoltaic (PV) and wind energy, fuel cell and battery system, etc. The output power of renewable energy sources varies with time, depending on the weather and ambient environment, and thus is intermittent and sometimes discontinuous. Therefore, the peaks of power demand do not necessarily coincide with the generation peaks [1]. To overcome the problems related to power fluctuation and the risk of voltage sags, it is necessary to use energy storage systems (ESS) to stabilize the grid, for example the recent battery product, Tesla Powerwall. In microgrids, ESS are often interfaced with a common AC bus or the utility through DC/AC converters. While the power flows from the renewable sources or the utility to ESS, it supplies power to charge ESS through the AC/DC converter which works in rectifier mode. When the power stored in ESS flows to the common AC bus for additional power supply or power feedback, ESS can be discharged by the AC/DC converter which works in inverter mode. It is important to achieve high power quality and excellent steady-state and transient performance through bi-directional power flow between the AC grid and the ESS system [2]. Thus an advanced control strategy to control the bi-directional power flow becomes more and more important in microgrids. In microgirds, three-phase full bridge AC/DC converters

Fig.1 Three-phase full bridge AC/DC converter used in a DC bus micrgrid

Various control strategies have been proposed in recent years for this type of PWM converters. The most popular one is the so-called direct power control (DPC). It has no internal current loops and the converter switching states are appropriately selected by a switching table based on the instantaneous errors between the commanded and estimated values of active and reactive power, and the voltage vector position [4],[5]. Besides, the space vector modulation control, voltage oriented control (VOC), model predictive control (MPC) and fuzzy logic based direct power control, etc., also have raised much interest in the last few years, especially the MPC because of its outstanding advantages [6],[7],[8],[9]. However, a proper comparative study between the MPC and the conventional direct power control is required on both the steady-state and transient performances for bi-directional power flow control in microgrids. The objective of this paper is to present such a study using a simple example of MPCbased DPC. The main advantages of the proposed predictive DPC in comparison to the conventional DPC based on switching table will be presented and discussed. The paper is organized as follows. Section II presents the mathematical model of the AC/DC converter. In section III, the proposed MPC for bi-directional power flow control in microgrids is discussed. The simulation results are shown in Section IV. Finally, the conclusions of this paper are given in

Section V. ESS /DC bus

II.

Inverter/Rectifier R Vbus

PCC L

MODELING OF AC/DC CONVERTER

Consider the three-phase two-level AC/DC converter for power conversion in microgrids as shown in Fig.1. Three IGBT half-bridge units are connected to the main grid via a choke consisting of three series-connected inductors L and resistors R. On the DC side, an energy storage system or a DC bus are connected to the IGBT bridge with a capacitor C in parallel, where ea, eb, ec are the three-phase power-source voltages, va, vb, vc the AC terminal voltages of the PWM rectifier, and ia, ib, ic the three-phase line currents. In the stationary reference frame, the power-source voltage vector and current vector in the αβ-coordinate system are given by the following transformation: e  1 2   a   e  2 1 1 2 e      (1)  eb 3 2  3 2   e  3 0  ec 

I  1 2   a   I  2  1  1 2 I      (2)  Ib 3 2  3 2    I   3 0  I c  For a balanced three-phase system, the line current equation can be represented in the stationary reference frame as follows dI a e  L  RI a  V (3) dt dV 3 (4) C dc   I S  I  S   I L dt 2 where eαβ, Vαβ, Iαβ, IL are the three-phase input voltage vector, the converter input voltage vector, the line current vector, and load current, respectively. The active and reactive power exchanged with the grid can be calculated as  P  3  e e   I  (5)   Q   2  e     e   I  

Switching Table

φVg

dq

dp

S1

e

I

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~

Power and Grid Voltage Estimation

Q

Q* P P*

Fig.2. Block diagram of conventional DPC-based power regulation for microgrids TABLE I. SWITCHING TABLE OF DPC dP 1 0

dQ

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Im V2(110)

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ESS /DC bus

Re

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Fig.3 Position of voltage vectors Inverter/Rectifier PCC Grid R L Vbus S I e 1

~

Best Vector Selection

Pk+1 Model Based Power

Qk+1 Prediction Vαβ

P*

Q*

Vdc

III. MODEL BASED PREDICTIVE DIRECT POWER CONTROL The conventional DPC scheme is based on the instantaneous active and reactive power control loops. As shown in Fig. 2, the switching states of the PWM AC/DC converter are selected by a predefined switching table illustrated in Table I [5]. The power control is based on the digitized signals Sp and Sq for tracking errors of active and reactive power, respectively, and implemented by two fixed band hysteresis comparators and the power source voltage vectors in the α–β plane as shown in Fig. 3.

Fig.4.Block diagram of MPC-based power regulation for microgrids

Fig.4 illustrates a block diagram of the MPC-based DPC for micrgrids. The aim of MPC is to predict the power of the (k+1)th time instant for different voltage vectors. The one that yields the minimum power ripple is applied. The derivatives of active and reactive power can be obtained by substituting (3) and (4) into (5) and then taking derivatives on both sides as d  P  3  d  e  dI   I   dt Q  2  dt e  dt

 e  d  e  dI   e   e   I      dt  e  dt  e    

(6) Assuming sinusoidal and balanced three-phase line voltages,





   

(9)

where Vi is the typical space vector representation. For each converter switching state and its corresponding space vector, the values of Vi and Vi components can be calculated as follows 1    Sia  2 ( Sib  Sic )  Vi  2  V   Vdc   3   i  3 ( S  S ) ic  2 ib 

(10)

where S ia , S ib and S ic are the converter switching states. If the tracking error of the DC-bus voltage is assumed constant over two successive sampling periods, the instantaneous active power command at the (k+1)th sampling time instant can be estimated using a linear extrapolation. Therefore, the predicted power at the end of sampling period Ts for each converter switching state can be expressed as





*   2 k  Pi k 1   Qi k  3  e  Re eVi R  Pi    k 1   Ts    k     k   Qi   Pi  2 L   Im eVi*  L Qi   





 

 Pi k     Qi k   

(11) Then the system can evaluate the effects of each converter switching state on active and reactive power, and select the one producing the least power ripple according to a specific cost function defined as (12) J i  ( P*  Pi k 1 )2  (Q*  Qi k 1 )2 IV. SIMULATION RESULTS To verify the proposed bi-directional power flow, both the conventional and MPC-based DPC of the three-phase PWM converter for bi-directional power flow control in microgrids have been simulated using MATLAB/Simulink. The main electrical parameters used in the simulation are listed in Table II. The simulation are conducted with pure sinusoidal powersource voltages.

40 I(A),E(V)



I(A)



*  2  Qi  3  e  Re eVi d  Pi  R  Pi            P  dt  Q i  L Q i   i  2 L   Im eV *i 

Ea/4

20 0

Ia

-20 -40 0.06 40 20 0 -20

0.07

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0.14 Ic Ib Ia

-40 0.06 0 P(W)

one obtains the following expression  e  d  e  (8) e       dt     e  The instantaneous active and reactive power derivatives can be calculated by substituting (1) and (8) and into (6) as

analyze both the steady-state and transient performance for each control strategy, the active power reference value steps down from -5,000 W to -2,000 W at 0.1 s while the reactive power is maintained to be zero. The simulation results of the conventional and MPC-based DPC are depicted in Figs. 5(a) and (b), respectively. Under the conventional DPC based on switching table, the input currents are distorted (THD=4.66%) because the instantaneous reactive power is poorly controlled during some sectors and peaks of reactive power, Q, appear periodically as shown in Fig.5(a). The active power ripple is 420 W and the reactive power ripple 1,200 VAR. In comparison, under the MPC-based DPC, the instantaneous active power and instantaneous reactive power track their references with good accuracy and stability during all sectors of the main period as shown in Fig.5(b). The input currents have nearly sinusoidal waveforms (THD = 3.15%) and are in phase with the line voltages. Unity power factor operation of the converter is successfully achieved by maintaining the reactive power close to zero. The active power ripple is 410 W and the reactive power ripple is 450 VAR, much less than that obtained under the conventional DPC. After a very short transient at 0.1 s with a step change of the load demand, the MPC-based DPC strategy shows excellent dynamic response and better references tracking capability than that of the conventional DPC as can be observed in Figs. 5(a) and (b). The active power tracks its reference with good approximation and stability, and the reactive power is successfully reduced and maintained close to zero. The input currents have nearly sinusoidal waveforms. It can be concluded from these simulation results that the proposed MPC-based DPC is much better than the conventional DPC based on switching table in both steady and transient states.

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(7)

500 0 -500 -1000 0.06 Mag (% of Fundamental)

e  e  je | e | e jt

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Fundamental (60Hz) = 19.36 , THD= 4.66%

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Power Flow from ESS/DC Bus to Utility Grid When the power flows from the ESS to the grid, the AC/DC converter works in inverter mode (for convenience, the current flows from grid to ESS is referenced to be positive). To A.

I(A),E(V)

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TABLE II. ELECTRICAL PARAMETER OF POWER CIRCUIT Resistance of reactor R 450 mΩ Inductance of reactor L 4.5 mH DC-bus capacitor C 1000 uF Load resistance RL 50 Ω Line to line ac Voltage e 150 V(rms) Source voltage frequency f 60 Hz DC-bus voltage Vdc 300 V

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Selected signal: 12 cycles. FFT window (in red): 11 cycles 20 10 0 -10 -20 0

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For bi-directional power flow between the ESS and the utility grid, the AC/DC converter works in either rectifier or inverter mode depending on the direction of power flow.

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(b) MPC-based DPC Fig.5. Power flows from ESS to grid.

40

I(A),E(V)

Power Flow from Utility Grid to ESS/DC Bus When the power flows from the utility grid to the ESS, the three-phase AC/DC converter works in rectifier mode. To analyze both the steady-state and transient performance under each control strategies, the active power reference value steps up from 2,000 W to 5,000 W at 0.1 s while the reactive power keeps at zero. The simulation results of the MPC-based and conventional DPC are shown in Figs. 6(a) and (b), respectively. Similarly, it can be concluded that the MPC-based DPC also has more excellent performance compared with that of the conventional DPC based on switching table in both the steady and transient states. As shown in Fig. 6, the input currents have nearly sinusoidal waveforms (THD = 2.44%) under the MPC-based DPC while it is distorted (THD = 3.15%) under the conventional DPC. Also, the reactive power ripple decreases from 950 VAR under the conventional DPC to 410 VAR under the MPC-based DPC. It can also be seen that the MPC-based DPC strategy shows better dynamic response and better reference tracking capability than that of the conventional DPC when the active power reference value steps up from 2,000 W to 5,000 W at 0.1 s where the active power tracks its command in less than 10 ms. B.

I(A),E(V)

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Selected signal: 12 cycles. FFT window (in red): 11 cycles

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Fundamental (60Hz) = 18.14 , THD= 3.15% 25 20

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(b) MPC-based DPC. Fig.7. Bi-directional power flows.

The dynamic behavior under a step change of the load is shown in Figs.7(a) and (b). The ESS starts to feed the active power of 4,000 W to the grid at 0.04 s while the reactive power keeps at zero. Then from 0.08 s to 0.12 s, the ESS supplies 2,000 VAR reactive power to the grid while the active power keeps steady. At 0.12 s, the grid supplies the active power of 5,000 W to the ESS while the reactive power keeps steady at 0 VAR. It can be seen that both the conventional and MPC-based DPC work well for bidirectional power flow. Again, the MPC-based DPC yields better performance with the advantages of good dynamic response and lower THD during the whole simulation period. V. CONCLUSION

10000

Ia

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(a) Conventional DPC.

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This paper proposes an MPC-based DPC strategy for threephase AC/DC converters for bi-directional power flow control in microgrids. Using the Simulink models, the conventional and MPC-based DPC strategies are compared for bidirectional power flow control between the grid and the ESS. The simulation results show that the proposed MPC-based DPC strategy yields much better performance than that of the conventional DPC strategy in both transient and steady states. Therefore, the proposed MPC-based DPC strategy would be more suitable for power flow control in microgrids.

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(b) MPC-based DPC. Fig.6. Power flows from grid to ESS.

C.

Ea/4

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Bi-directional Power Flow between ESS and Utility Grid

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