The Discrete Time Control of a Three Phase 4 Wire PWM Inverter with Variable DC Link Voltage and Battery Storage for PV Application

Dipl. Ing. Said El-Barbari            and                  Prof. Dr. W. Hofmann

 

CHEMNITZ UNIVERSITY OF TECHNOLOGY Department of Electrical Machines and Derives

 

Abstract

The discrete time control of a three phase 4 wire PWM inverter with variable DC link voltage for simultaneously supply of three phase and single phase load in transformerless stand alone photovoltaic application with battery energy storage (BES) and LC output filter is described. The whole system consists of a photovoltaic array, a battery energy storage, two step up boost converter and three phase PWM voltage source inverter with a LC output Filter. The first boost converter is controlled in such a way so that the battery will be always charged at the maximum power point (MPP) when changes in the insulation or temperature are occurred. The second step up boost converter is connected in series between the Battery energy storage and the DC link capacitor of the PWM inverter. It controls the DC link capacitor voltage. The mathematical model of the linearized system is first obtained. The discretized state space equation of the whole system is derived. A new control method based on the dead beat control algorithm is implemented to control both the output voltage of the LC filter and dc link capacitor voltage so that disturbance of the output voltage due to load unbalances is eliminated. Simulation results for various operation conditions are presented to verify the validity of the control method.  

Summary  

Nowadays more attention is paid to PV system and their related technology for domestic application as well as in large central power stations. PV systems are advantageous because they are abundant, pollution free and distributed through the earth. The only draw back is that the initial installation cost is considerably high.

Figure 1 stand alone photovoltaic system with 3 phase 4 wire PWM voltage source inverter

Since the power generated by an array of PV panels is direct-current, it may be transformed, either into a power with constant voltage for dc applications or into ac power. In both cases it is important to draw as much energy as possible from the PV panel. The output power of PV generators vary extensively with the weather conditions such as solar insulation, temperature and cloudy skies. To obtain the maximum power from such an array under any weather condition it is necessary to connect the PV array to a converter that can adapt itself to the changing V-I characteristic of the PV generator (MPPT). In the system illustrated in Figure 1 this is provided by the DC/DC2. In this way the battery will be always charged at the Maximum Power Point. The goal of the system illustrated in figure 1 is to supply three as well as single phase loads of any art with constant amplitude sinusoidal voltage and constant frequency. For this propose the neutral point of the LC output filter and load is connected to the midpoint of the DC link capacitor bank. Due to load unbalances an intruding current flows throw the impedance between the neutral point and midpoint and a voltage drop occurs which distorts the symmetrical output voltage. To solve this problem the following measurements were taken

• a zero sequence current and voltage control is implemented

• a DC/DC converter is used to control the DC link voltage according to load unbalances

In this way the symmetry of the output voltage is achieved and the linear region of the PWM modulator of the DC/AC VSI (Voltage Source Inverter) is extended.

 

Figure 2 principle of the control method

Since the dead beat control strategy for single phase inverter was discussed in [4], [6] and [8] and for three phase inverters in [1], [2], [3], [5] and [7], the dead beat control in [1] and [2] is adopted and extended to mach for three phase 4 wire VSI. The control proposed of the VSI is illustrated in Figure 2. It contains the current minor loop, voltage major loop, the DC link reference estimation and the DC link voltage control loop. Here only a brief description of the current and voltage as well as dc link control is intended since to describe them in details will exceed the limits of the summary. The control of the VSI is designed in the synchronized dq0 frame. Equation (1) and (2) describe the discrete system in the synchronized dq0 frame.

 

     (1)  

     (2)

 
, 
, 

,
,

 
, 
,
, 

, 
 

Equation (3) and (4) describe the system in vector form

 
                             (3)

             (4)

 

Form these equations one can see that the d and the q variables are coupled with each other whereas the 0 sequence is decoupled. To enhance the performance of the control loop the capacitor voltage is fed forward as seen in figure 3. To control 
and 
separately the coupling elements b and d are decoupled by the matrixes F_dc and A_Idc so that 
and 
depend only on a and c. After removing the couplings, the dead beat controller G_IC is provided.

 
                                                   (5)

 

 

Figure 3 principle of the current control loop

Since the inverter must quickly supply the load current I_L to compensate the disturbance of the load, the prediction of the load current is implemented, as shown in figure 2, so that the predicted load current is given by ([1], [2])

                                 (6)

In this way the target value of the load current is provided and thus the computation time delay is compensated. The voltage major loop is constructed in the same manner. The same dead beat control is also applied to the 0-scequence of currents and voltages except that, in the 0 control loop no decouplings are needed.

The mathematical model of the DC/DC converter in the continuos conduction mode is established and linearized ([9], [10]). The digital control is implemented [11] so that the DC link voltage will follow a certain reference voltage which is given by

                     (7)

where 
is given by
                                     (8)

and K is a correction factor.

 

 

Figure 4 inverter current and capacitor voltage of the output filter with unbalanced load (R_u=R_v=20 ,R_w=2000 ) and uncontrolled DC link voltage

 

Figure 4 shows the simulation results of the dead beat control for unbalanced load with uncontrolled dc link voltage. The distortion in the inverter currents occur when the control signals exceed the linear region of the PWM modulator due to load unbalances. As a result, the capacitor voltage of the output filter is also distorted. Figure 5 shows the simulation results when the DC-link voltage is controlled. It shows the capacitor voltage of the output filter when the load changes from (R_u=R_v=60 , R_w=2000 ) to (R_u=R_v=20 , R_w=2000 ) as indicated by an arrow in the lift hand sub diagram. This shows the high dynamic performance of the introduced dead beat control method as the disturbance of the output voltage is quickly compensated. The distortion of the output voltage reduces gradually as a result of the controllable dc link voltage as indicated in the right hand sub diagram.

Figure 5 capacitor voltage of the output filter with unbalanced load and controlled DC link voltage

 

Figure 6 DC link Voltage

Diagram 6 shows the dc link voltage when the load changes and distortion in the output voltage occurs. The dc link voltage increases to reduce the output voltage distortion. The oscillations in the dc link voltage are due to the filter effect in the DC link reference estimation given by equation (8). However; the oscillation portion is relatively small compared to the dc voltage portion, so that it does not affect the output voltage.

References

[1]    Takao Kawabata, Takeshi Miyashita and Yushin Yamamoto, "Digital Control of three-Phase Inverter with LC Filter", IEEE Transactions on Power Electronics, Vol. 6, No. 1, January 1991, pp. 62-72.

[2]    Takao Kawabata, Takeshi Miyashita and Yushin Yamamoto, "Dead Beat Control of three-Phase PWM Inverter", IEEE Transactions on Power Electronics, Vol. 5, No. 1, January 1990, pp. 21-28.

[3]    Osman Kükrer, "Deadbeat Control of a Three-Phase Inverter with an Output LC Filter", IEEE Transactions on Power Electronics, Vol. 11, No. 1, January 1996, pp. 16-23.

[4]    Chihchiang Hua and Richard G. Hoft, "Hight Performance Deadbeat Controlled PWM Inverter using a Current Source Compensator for nonlinear loads", IEEE/PESC 23rd Anual, Toledo, Spain 1992, pp. 443-450.

[5]    Tomoki Yokoyama and Atsuo Kawamura, "Disturbance Observer Based Fully Digital Controlled PWM Inverter for CVCF Operation", IEEE Transactions on Power Electronics, Vol. 9, No. 5, September 1994, pp. 473-480.

[6]    Atsuo Kawamura and Tomoki Yokoyama, "Comparison of Five Control Methods for Digitally Feedback Controlled PWM Inverters", EPE Firenze 1991, Vol. 2, pp. 35-40.

[7]    Youichi Ito and Shoichi Kawauchi, "Microprocessor-Based Robust Digital Control for UPS with Three -Phase PWM Inverter", IEEE Transactions on Power Electronics, Vol. 10, No. 2, March 1995, pp. 196-204.

[8]    Atsuo Kawamura, Toshimasa Haneyoshi and Richard G. Hoft, "Deadbeat Controlled PWM Inverter with Parameter Estimation Using Only Voltage Sensor", IEEE Transactions on Power Electronics, Vol. 3, No. 2, April 1988, pp. 118-125.

[9]    P. R. K. Chetty "Current Injected Equivalent Circuit Approach to Modeling and Analysis of Current Programmed Switching DC-DC Converters (Discontinuous Inductor Conduction Mode)", IEEE Transactions on Industrial Applications, Vol. IA-18, No. 3, May/June 1982, pp. 295-299.

[10]    Francisco Guinjoan, Javier Calvente, Alberto Poveda and Luis Martinez, "Large-Signal Modeling and Simulation of Switching DC-DC Converter", IEEE Transactions on Power Electronics, Vol. 12, No. 3, May 1997, pp. 485-494.

[11]    F. Al-Hosini, ABB Corporate Research, Sweden, "An Aproximate Dead-Beat Control stratigy for the disign of functions regulators in DC/DC Converters", EPE Trondheim 1997, Vol. 3, pp. 155-160.

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