Research on Deadbeat Control of a Three-level Grid- connected Inverter Based on αβ Transform Academic research paper on "Electrical engineering, electronic engineering, information engineering"

Available online at www.sciencedirect.com

Procedia Engineering

ELSEVIER

ProcediaEngineering23 397 - 402

www.elsevier.com/locate/procedia

PEEA neil Shaczhac

Research oc Daadbaat Coctrol of p Thraa-laval Grid-coccactad Icvartar Basad oc aß Transform

Ha JucpicgP9 Yi LaiP, Wacg XuasocgP9 Wacg JipcP, p*

aShenzhen Graduate School, Harbin Institute of Technology, Shenzhen, 518055, China

Abstract

In distributed grid-connected power system, the control strategy of grid-inverter influences the quality of its output power. An improved method based on a-p transformation of deadbeat control algorithm is proposed for a three-level photovoltaic grid-connected inverter. This new control method overcomes the shortcoming of complicated dynamic phase angle compensation and is easily to combine with SVPWM strategy to realize a fast control of inverter grid-connected power. The paper firstly established the control model of a three-level inverter grid-connected system and subsequently proposed the computation method of forecasted link of voltage and current. A MATLAB simulation model is built up. Simulation and experiment results indicate that this new control algorithm simplifies the control and a good static and dynamic performance is achieved.

© 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of PEEA Keywords: ap transform; deadbeat control; three-level inverter; grid-connected control

1. Introduction

Renewable energy is an important solution to overcome today's global energy shortage and a photovoltaic grid-connected generation system has been becoming a key part of renewable power. The control technology of grid-connected inverter has received more attention in recent years[1'2]. Currently, hysteresis current loop and PID are two main control methods in a grid-connected inverter. But hysteresis current control has some shortcomings, such as no fixed switch frequency and the difficulty to design a EMI filter[3]. Although PID control is simple and easy to implement, steady-state error of output current maybe exists at some time[4]. Deadbeat control method has little phase delay and can complete the

*Ha Jucpicg. Tal.: +86-755-26032452. E-mail addrass: hajucpicg@hitsz.adu.cc.

1877-7058 © 2011 Published by Elsevier Ltd. doi:10.1016/j.proeng.2011.11.2520

regulation of output current within a control period, which makes system in good dynamic and static performance. Therefore, deadbeat control is increasingly paid attention in inverter grid-connected generation[5-7].

Particularly, the deadbeat control combined with SVPWM has been applied rapidly in grid-connected inverter[89]. The common deadbeat control conducts operations based on dq coordinate[5'8], however, SVPWM modulation reference vector is a rotating voltage vector, so it is necessary to transform the reference signal calculated by deadbeat control into ap coordinate. In the process of coordinate transformation, the phase angle of inverter output voltage vector is needed, but the phase angle is changing with the output current changing, then it has to calculate the phase angle using feedback compensation in real time. So, this transformation greatly increases the complexity of control. In order to solve this deficiency, this paper proposed a deadbeat control methods based on ap coordinate, which can make the output of the deadbeat control be directly used for rotating vector of SVPWM modulation. This simplifies the coordinate transformation, avoids complex phase angle compensation link and makes deadbeat control easier to realize. This paper firstly obtains the deadbeat control algorithm based on ap transform by theoretical derivation and designs the prediction method of the output voltage and current. Then the system control principle block diagram is built up. Subsequently, MATLAB simulation and experiment results verified the effectiveness of the algorithm proposed.

2. Principles and design of deadbeat control based on ap transform for a grid-connected inverter

-.1 Principles ef agid-neaaented iaverteg depdbept neatrel based ea afi tgpasfegm

This paper adopts a diode-clamped three-level inverter as object of study for its high utilization of DC bus voltage, small switch voltage stresses and lower switching frequency. Figure 1 shows the main circuit of this grid-connected inverter system. In this figure, leftmost cell Vdn indicates the output voltage of photovoltaic cell array. The middle part is the three-level inverter, in which Si-Si2 are IGBT switches, and Di-D6 are clamped-diodes, and L is output filter inductance of inverter, and R is the equivalent resistance of filter inductor and output cables. Rightmost UgA, UgB, UgC are the three-phase voltages of a grid. Output three-phase currents iA, iB, iC and their positive directions are shown in the figure too.

For the inverter generation system above, the principle of the deadbeat control algorithm is derived as follows. Firstly, the system state space can be described by equation 1 in static three-phase coordinate system.

'A 1 n A 1 U0A R 'a

'b nB naB 'b

= L L L

_ 'C _ _ nc _ _nac . _ 'c _

Where, [A B C ] — output current from inverter [ ]T

A "B "C' — output voltage from inverter

[ugi ugB "gc ] — grid voltage L — filter inductance

R — equivalent resistance between inverter and grid Because a normal three-level inverter uses SVPWM modulation, this means the input command of inverter is a rotating voltage vector. So, it needs to convert the state space equation 1 into ap coordinate system in order to control and calculate conveniently. After transforming grid voltage and output current signals of inverter in equation 1 to ap coordinate system, the state space equation of inverter generation system in ap coordinate system is obtained as equation 2.

d ia 1 Ua 1 a ga R ia

dt L L L if>

Where, [ ^ ] — ap transformation of inverter output current [u up]T — ap transformation of inverter output voltage [u u ] — ap transformation of grid voltage Let control-period be T, and discrete equation 2, then the formula below can be obtained:

1* — 1 * — i + i*

a a _ * r) a a

La a _ * r)

-— aa— a ra — R--/51

T a 2 (3)

h a * a

L-— u n — u on — R

Where, t'a (i*) — given reference current ia (t n) — the initial current of control period T u'a (u p) — the output voltage of inverter u ga (u gP ) — the mean value of grid voltage in control period T For controlled sampling frequency is high enough normally, the currents in T period can be considered changing linearly, then (ia+1<*)/2 is the mean value of current in T. Then output variables of deadbeat control can be gotten using equation 4. By the way, each variable of formula 4 has the same specific meaning with the equation 3.

i + i' i' — i ■ D a a . j a a

+ R~T~ + ~ (4)

; + r1P + + T —

It can be seen from equation (4) that the reference vector value of next period needs some signal values, such as grid mean voltage value, initial output current value and reference current value. Except the reference current value, the grid average voltage value and initial output current are both needed to be estimated.

2.2 Fast pri-istimntid method of grid voltage vnlai nod initial current vnlai

It is well known that deadbeat control method predicts the output of next control cycle in present control cycle. Further more, the needed variables of deadbeat control used in equation 4 should be the

value of next control cycle. Therefore, it is necessary to pre-estimate the initial current and grid voltage values fast and accurately to reduce delay produced by control and sampling and improve accuracy of control.

This paper proposes a new forecasting method to meet the requirements above and the new pre-estimated method is introduced below. Figure 2 shows the sampling-point distribution and output voltage approximate waveform in two control cycles. Because output vector of SVPWM modulation is usually symmetric small vector, the inverter output voltage is then symmetrical around the central point of PWM cycle[5'6]. Suppose the n-th cycle to be the present control cycle, the controller is required to calculate out (n+1)-th inverter output reference voltage in the n-th cycle. The detail pre-estimated process is explained as follows. This paper makes the sampling cycle be 1/4T and then A, B, C, D point in the n-th cycle and E, F, G, H point in the n+1-th cycle are shown in figure 2. In one control cycle, the grid voltage is considered changing linearly, then the grid average voltage of the (n+1)-th cycle can be replaced by the instantaneous voltage of G point. Further more, because the grid voltage changes slowly, it can be thought that the voltage in A, D and G point is changing linearly too. Then the equation 5 can be gotten.

uG = 2uD - uA (5)

Similarly, it is considered that the output current in A, C, E point is changing in a linear relationship, then the initial current iE of the (n+1) cycle can be derived from equation 6.

iE = 2iC - iA (6)

Then grid average voltage value and output current initial value in the (n+1)th cycle can be estimated fast and accurately. After taking these two signals into equation 4, the output reference vector of the inverter in the (n+1)th cycle can be obtained too. The whole deadbeat control and calculation process can be completed between D point and E point before the (n+1)th cycle.

2.3 The framework design of improved deadbeat control system

According to the proposed algorithm above and combining with SVPWM modulation method of a three-level inverter, the principle block diagram of deadbeat control inverter based on ap transform is designed as shown in figure 3. The main work process is explained briefly in the bellow.

Fig.3 Control block of grid-connected inverter system

The reference currents is given using *, q in dq coordinate. In order to get the reference current t'a, in aß coordinate, dq/ABC and ABC/aß transformation are conducted on ¿*, f firstly. During above transformation, the phase angle 0=0+A0 is used. 0 is the phase angle at the end of next control cycle, 0 is the initial phase angle in current control cycle, and A0 is the phase angle changes between these two control cycle, that is 2mT. After aß transforming of inverter output current iA, iB, iC obtained by sampling, current vectors ia, iß in aß coordinate are obtained. Then ■ , ■ initial current vector of the next control

cycle can be forecasted using current pre-estimated algorithm above. Similarly, after ap transforming of grid voltage uA, uB, uC obtained by sampling, voltage vectors u«, up are obtained, and then the grid voltage average value Uia, u of the next control cycle can be obtained using voltage pre-estimated algorithm above. Finally, the required output ua, u* of the inverter is calculated out using equation 4. The SVPWM block then produces PWM pulse for this three-level inverter accordingly and the inverter generates output current waveform required.

3. MATLAB simulation model and Experiment analysis

In order to test deadbeat control algorithms and block diagram proposed above, a MATLAB model of the three-level grid-connected inverter system is built up and a simulation is conducted using Simulation Link Toolbox. The main key-modules of simulation model are deadbeat control module and inverter SVPWM modulation module. The deadbeat control module is established according to figure 3. This SVPWM modulation uses five-phase pulse and its module mainly consists large sectors judge submodule, small triangles judge sub-module, action time calculation sub-module and trigger pulse forming sub-module[7]. Some main simulation parameters are as follows, input voltage Vdc=700V, grid voltage Ug=220V/50Hz, L=3mH, resistance R = 10Q.

Figure 4 and 5 show typical static and dynamic simulation performance of the inverter system using new algorithm. Fig.4 shows grid voltage waveform, inverter output current waveform of a phase under stable state of Id =7A, ^ =0A. Figure 5 shows output three-phase current response fast and accurately when Id steps up from 7A to 15A. Simulation results verify that the new deadbeat control is effective.

Fig.4 Phase grid voltage & inverter output current simulated

Fig. 5 Response performance of output current simulated

Figure 6 and 7 show some experiment results of a three-level grid-connected prototype inverter using new control. Fig.6 shows grid voltage waveform, inverter output current waveform of a phase under stable state ofId =2A, ^ =0A. Figure 7 shows two of three-phase output current waveform tested of inverter with load. It's clear that experiment results prove the feasibility of new deadbeat control.

Fig.6 Phase grid voltage & inverter output current tested

Fig.7 Inverter output stable current tested

4. Conclusion

This paper proposes a novel deadbeat control algorithm based on ap transformation to simplify computational complexity of traditional deadbeat control algorithms. Detail theoretical derivation of new algorithm is introduced. The control block diagram of three-level inverter system is designed and a MATLAB simulation model is built up accordingly. Simulation results show that the deadbeat control method proposed not only simplifies DSP calculation, but also posses a good static and dynamic performance. Experiment results also verify the new control achieves reliable, fast and accurate grid-connected generation. So, this deadbeat control algorithm based on ap transformation is helpful to improve performance of a distributed grid-connected generation application of renewable energy.

Acknowledgements

This project is supported by the National Natural Science Foundation of China under Grant No. 50877015 and the Doctor Subject Foundation of the Ministry of Education of China under Grant No. 200802131017.

References

[1] Kjaer S B, Pedersen J K, Blaabjerg F. A review of single-phase grid-connected inverters for photovoltaic modules[J]. IEEE Transactions on Industry Applications, 2005, 41(5):1292-1306

[2] Prodanovic M, Green T C. Control and filter design of three-phase inverters for high power quality grid connection[J]. IEEE Transactions on Power Electronics, 2003, 18(1): 373-380

[3] Gu He-rong, Yang Zi-long, Wu Wei-yang. Research on Hysteresis-band Current Tracking Control of Grid-connected Inverter. Proceedings of the CSEE, 2006, 26(9): 108-112

[4] Li Yongdong, Xiao xi, Gao yue. Principle, control & application of high capacity multi-level converter[M]. Beijing: Science Press, 2005

[5] Qingrong Zeng, Liuchen Chang. An advanced SVPWM-Based predictive current Controller for three-phase inverters in distributed generation systems[J]. IEEE Transactions on Industry Electronics, 2008, 3(3): 1235-1246

[6] V. S. Kumar and P. S. Kannan. Harmonic studies in space vector PWM inverter drive system[C], Proceeding of Power System Technology Conference, 2004, 123-127

[7] Luo Bei, He Junping, Wu Xuezhi. An Optimization SVPWM Method for Restraining the Common-Mode Voltage in a Photovoltaic Grid-connected Three-level Inverter[C], Proceedings of 18th annual conference of China power supply society,2009.11,124-127

[8] Hui Zhang, Hongwei Zhou, Jing Ren, et al. Three-phase grid-connected photovoltaic system with SVPWM current controller[C]. Power Electronics and Motion Control Conference, 2009, 2161-2164

[9] Moreno J.C, Huerta J.M.E, Gil, R.G, Gonzalez S.A A Robust Predictive Current Control for Three-Phase Grid-Connected Inverters [J]. IEEE Transactions on Industrial Electronics, 2009, 56(6): 1993-2004