A New PWM-Based Control Method to Balance the Output Voltage of Two-Level Inverters Considering the

International Journal of Automation and Control Engineering (IJACE) Volume 3 Issue 3, August 2014 doi: 10.14355/ijace.2014.0303.01

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A New PWM-Based Control Method to Balance the Output Voltage of Two-Level Inverters Considering the Variations of dcLink Voltage Amir Behzadnia, Ebrahim Babaei Faculty of Electrical and Computer Engineering, University of Tabriz, Tabriz, Iran Amir_b220@yahoo.com, e-babaei@tabrizu.ac.ir Abstract In case of oscillation in the dc-link in two-level inverters, the ac voltage produced will be extremely unbalanced. Since in most of cases it is almost impossible to eliminate or even reduce the oscillation produced in the dc-link, an attempt must be made to minimize the effects of dc-link voltage oscillation on the ac side. In this paper, a new PWM-based control method is proposed to deal with the problem.

Changing the reference values, the proposed method helps to balance the generated voltage and the current. To prove the accuracy of the proposed control method simulation results using PSCAD/EMTDC are presented. For the sake of validity, both static and dynamic loads were applied in the simulation process.

Keywords Two-level Inverter; Unbalanced Voltage; Dc-link; PWM

Introduction With the advancement of semiconductor industry, power electronic inverters are much more economical to buy today which is the reason why power electronic inverters have gained such great popularity nowadays.

One of the most popular types of power electronic inverters used today is two-level inverters with PWM modulations (Holmes & Lipo, 2006) and (Hwang & Lehn, Aug. 2010). Two-level inverters have several applications among which induction motors and static loads are the most significant. To be more precise, power electronic inverters are used in induction motors and static loads to change the amplitude and frequency. Similarly, a two-level inverter is responsible for supplying the energy needed through a dc-link (Kazmierkowski, Krishnan, & Blaabjerg, 2002. The dclink energy can be supplied in different ways such as by fuel cells, PVs and power rectifiers. The dc-link voltage should be constant. Dc-link voltage oscillation

can result in serious problems on the ac side such as an increase in machine losses, machine heating up, efficiency losses and constant trembling of the machine shaft which can shorten the average life of the machine.

There are various factors that cause dc-link voltage oscillation in inverters. The most important one is unbalanced input voltage in power rectifiers that supply the energy of inverters dc-links. Distribution networks periodically experience high unbalanced voltage (Kretschmar & Nee, 1998). As a result there will be oscillation in inverters dc-link that their energy is supplied through rectifiers connected to distribution network. As unbalanced input voltage in power rectifiers causes dc-link voltage oscillation in (Liu, Xu, Zhu, Blaabjerg, & Chen, July 2013) a method proposed in order to reduce the negative impact of voltage unbalance on dc-link voltage. In this method, rectifier controller calculates the inverter active power based on inverter current and voltage references. This requires that the rectifier and inverter controller should be integrated into one controller, which causes high controller complexity. To deal with stated problem various control methods presented (Woolley & Milanovic, July. 2012) and (Woolley & Milanovic, July.

2012). In (Sudhoff, Corzine, Glover, Hegner, & Robey, Mar. 1998) a single-input space vector is used to regulate a grid-connected converter under generalized unbalanced condition in order to eliminate dc-link voltage oscillation and in (Woolley & Milanovic, July.

2012) a current control loop is added to the conventional rectifier current control loop hence dclink voltage would not be oscillating .The goal of all methods presented in (Liu, Xu, Zhu, Blaabjerg, & Chen, July 2013), (Sudhoff, Corzine, Glover, Hegner, & Robey, Mar. 1998) and (Woolley & Milanovic, July.

2012) is to produce constant dc-link voltage in

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International Journal of Automation and Control Engineering (IJACE) Volume 3 Issue 3, August 2014

T

unbalanced voltage condition, So these methods are efficient only if dc-link energy is supplied by rectifiers.

Although large capacitors can considerably reduce oscillations, they can result in a bulky system and can cost too much. Different methods can be used to reduce oscillations in the dc-link without having to resort to a large capacitor such as those presented in (Wu, 2006) and (Yao, Li, Liao, & Chen, May 2008).

Applying the methods to (Wu, 2006) and (Yao, Li, Liao, & Chen, May 2008), we can reduce the effects of transient oscillations as well as dampen the oscillations in the dc-link. In case of permanent oscillations the methods in (Wu, 2006) and (Yao, Li, Liao, & Chen, May 2008) will not be efficient.

To deal with the problem, the present study attempts to change the reference value voltage by a compensating term in cases of permanent or transient oscillations in the dc-link in order for the inverter to produce balanced ac voltage, also the proposed method will be efficient in all of two-level-inverters regardless of how the dc-link energy is produced. In the control method presented here, the sinusoidal reference signal amplitude varies in relation to the voltage ripple in the dc-link. To prove the accuracy of the method presented, the results were tested through simulation in the PSCAD/EMTDC software.

Voltage

2 T 3

1 T 3

Ton

0

t2

t1

t3

Time

FIG. 2 APPLIED VOLTAGE TO PHASES IN A TWO LEVEL INVERTER WITH OSCILLATING DC-LINK VOLTAGE

Control Algorithm In case voltage oscillation in the dc-link, the voltage and the current produced by the two-level inverter (Fig. 1) will be unbalanced. Fig. 2 shows a dc-link with oscillated voltage. As shown in the Fig. 2 a sinusoidal wave has been added to the dc-link voltage.

FIG. 3 BLOCK DIAGRAM OF THE PROPOSED CONTROL METHOD

The major reason for the unbalanced generation of voltage in the ac side when dc-link voltage is oscillated is the fact that the power switches are turned on and off based on balanced conditions. That is, as can be seen from fig 1 and 2, if s1 switch is turned on at t 1 for a period ofT on , and dc-link voltage is at phase A, s 3 in 1 t2 = T 3

FIG. 1 A TWO-LEVEL INVERTER

64

and

s5

2 3

in t 3 = T will be switched on to

create a balance in the function of the switches, and the dc-link voltage will be on phases b and c for a period of time equal to T on . However, as can be seen in Fig. 2,

International Journal of Automation and Control Engineering (IJACE) Volume 3 Issue 3, August 2014

while the dc-link voltage might be at its highest at t 1 , it may not be at its highest at t 2 and t 3 . In the worst case scenario, it even may be at its lowest at t 2 and t 3 .

Therefore, the input voltage will be different in different phases. The present paper suggests an algorithm to balance the voltage in the two level inverter output so that the ac voltage produced in different phases is balanced when the dc-link voltage is oscillating. In this algorithm, as can be seen from Fig. 3, the index modulation moves in an inverse direction to the dc-link voltage in order to keep a balance between the voltages produced in different phases. In other words, in cases where the dc-link voltage is at its highest or its lowest level, the sinusoidal reference voltage is decreased or increased in order for the input voltages into the loads to reduce or increase so that three-phase voltage and current are balanced. In this algorithm, the dc-link voltage is measured to determine its oscillating part. Subsequently, the amplitude ( v m ) and frequency ( ωo ) of the oscillation have been measured. The compensating signal amplitude, K , is determined by the amplitude of oscillation, and moves up and down in relation to it.

And the frequency must equal the compensating signal frequency. When a compensating signal with amplitude equal to K and a frequency equal to ωo is produced, this signal is removed from the reference signal and creates a new reference signal. The new reference signal is used to produce voltage using a PWM method.

The voltage oscillation in the dc-link has a certain frequency which determines the amplitude of the reference signal. If we assume the dc-link voltage as follows:

v dc = V DC + v m cos (ωo + φ1 )

(1)

Where v dc is the instantaneous dc-link voltage, V DC is the dc component of dc-link voltage, v m is the dc-link oscillation amplitude, ωo is the dc-link oscillation frequency, and φ1 is the dc-link oscillation term phase.

In equation (1), first term and second term are average voltage and oscillating voltage of dc-link respectively.

The reference signal in phase a is as follows:

V ref − A = V sin(ωt )

(2)

where V is the index modulation (the reference signal amplitude), ω is the reference signal frequency and V ref − A is the reference signal.

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If dc-link voltage does not vary, V will be constant. But in case the voltage is oscillating, the compensating signal will be deduced from it which is indicative of the dc-link voltage change. In other words, V will include two components. The first component is the reference signal amplitude and the second component is the compensating signal with a frequency and amplitude equal to those of the dc-link voltage, respectively. In other words:

V new = V old − K cos (ωo + φ1 )

(3)

where V new is the reference signal amplitude of the phase a after compensating, and V old is the reference signal amplitude of the phase a before compensating.

Therefore, if K is controlled, voltage in the phases can be balanced. K must be adjusted in such a way that the first component of the voltage in all the three phases be equal. Moreover, V new must not exceed 1 in order for the modulation not to exceed the linear region. In case the dc-link voltage is fixed, the first components of the three-phase voltage will be equal. In other words: 1 V a1 = V b1 = V c1 = f ( x ) ⋅ cos ( nx ) ⋅ dx T ∫T

(4)

where V a1 , V b 1 and V c 1 are the first components of the voltage in the phases a , b and c respectively.

The reasons why the first components of the threephase voltage is equal are the time period during which the switches are turned on and off are equal for all the phases and also that the dc-link voltage is fixed at all times.

In case the dc-link voltage is not fixed, it is impossible to keep the main voltage components and the current equal simply by keeping the switches on for the same time duration in all the three phases. In the method presented here, the compensation signal is used to adjust the turning on and switching off of switches in such a way that the first components of the threephase voltage be equal.

Simulation Results The simulation results using PSCAD/EMTDC software are presented for static and dynamic loads. In the first simulation, the dc-link average voltage is 125 kV, and in the dynamic load simulation the average voltage is 600 V both of which bear oscillations with a 120Hz frequency. For the purposes of this paper, pulse width modulation has been used. Changing the sinusoidal

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International Journal of Automation and Control Engineering (IJACE) Volume 3 Issue 3, August 2014

reference signal, pulse width modulation improves the inverter’s performance in case the dc-link voltage is oscillated. In the proposed control method, a sinusoidal signal with 120 Hz frequency and amplitude proportionate to the dc-link ripple has been deduced from the reference signal amplitude.

Static Load The link ripple equals 70kV in this stage. The simulation process takes place in 1 second where L = 0.1H and R = 2â„Ś for the load. It was simulated first with the common PWM method, and then with the proposed control method.

Fig.4. indicates the three-phase current of the load before the implementation of the control method suggested in this article. As can be seen, the voltage and the load current are extremely unbalanced. Fig.5 indicates the three-phase current of the load after the implementation of the control method suggested in this article. As can be seen, the voltage and the load current are perfectly balanced after the implementation of the new method. A comparison of the two methods well indicates the efficiency of the control method presented in this article. Similarly, Fig. 6 indicates the reference signal before the implementation of the new control method (the conventional PWM method) where the sinusoidal reference signal has a fixed frequency and amplitude.

In Fig. 7 the amplitude of the sinusoidal reference signal is variable where the amplitude varies in proportion to the dc-link voltage oscillation variations.

That is, when the dc-link voltage exceeds its normal range, the reference signal amplitude will decrease to lessen the effect of the dc-link voltage increase. The K factor here is equal to 0.35. Fig. 8 indicates the dclink voltage. It is clear that the dc-link undergoes extreme oscillations. Figs. 9 and 10 indicate the active power of the load. The active power of the load was extremely oscillating before the implementation of the new control method, as can be seen from Fig. 9. Fig. 10 suggests that these oscillations are perfectly balanced after the application of the new control method. To be more precise, oscillations have decreased from 3MW in Fig. 9 to 1MW in Fig. 10. It is worth mentioning that the high frequency oscillations in Figs. 9 and 10 are due to the turning on and off the switches and not to be attributed to the dc-link oscillations. That is, even in cases where the dc-link voltage is fixed, these high frequency oscillations exist. Figs. 11 and 12 indicate the reactive power of the load. A comparison of the two figures well suggests the efficiency of the new control

66

method presented in this article. Reactive power oscillations have been reduced from 4MVAr to 1MVAr after the implementation of the new control method.

Oscillations in the active and reactive powers applied can have detrimental effects on the loads. Moreover, the purpose is for the load to utilize a certain degree of power considering the fact that oscillations in the active and the reactive power can affect the efficacy of the load.

2.00 1.50 1.00 0.50 0.00 -0.50 -1.00 -1.50 -2.00

I load [kA] Ib

Ic

ib

0.920

0.900

0.940

Ia

ia

ic

0.960

1.000

0.980

FIG. 4 UNSYMMETRICAL OUTPUT CURRENTS BEFORE IMPLEMENTATION OF THE PROPOSED CONTROL METHOD

2.00 1.50 1.00 0.50 0.00 0.50 1.00 1.50 2.00 0.900

I load [kA] Ib

Ic

ib

0.920

0.940

Ia

ic

0.960

ia

0.980

1.000

FIG. 5 SYMMETRICAL OUTPUT CURRENTS AFTER IMPLEMENTATION OF THE PROPOSED CONTROL METHOD

1.00 0.80 0.60 0.40 0.20 0.00 0.20 0.40 0.60 0.80 1.00 0.900

Voltage_reference

0.920

0.940

0.960

0.980

1.000

FIG. 6 REFERENCE SIGNAL BEFORE IMPLEMENTATION OF THE PROPOSED CONTROL METHOD

International Journal of Automation and Control Engineering (IJACE) Volume 3 Issue 3, August 2014

Voltage reference 1.00 0.80 0.60 0.40 0.20 0.00 0.20 0.40 0.60 0.80 1.00 0.900

0.920

0.940

0.960

0.980

1.000

FIG. 7 REFERENCE SIGNAL AFTER IMPLEMENTATION OF THE PROPOSED CONTROL METHOD

200 180 160 140 120 100 80 60 40 20 0.900

dc Link Voltage [kV]

0.920

0.940

0.980

0.960

1.000

FIG. 8 DC-LINK VOLTAGE

8.0 7.0 6.0 5.0 4.0 3.0 2.0 1.0 0.0 -1.0 0.900

0.900

0.900

Reactive Power [MVAr]

0.920

0.940

0.960

0.980

1.000

FIG. 11 LOAD REACTIVE POWER BEFORE IMPLEMENTATION OF THE PROPOSED CONTROL METHOD

70.0 69.0 68.0 67.0 66.0 65.0 64.0 63.0 62.0 61.0 60.0 59.0 58.0 0.900

Active Power [MW]

Reactive Power [MVAr]

0.920

0.940

0.960

0.980

1.000

FIG. 12 LOAD REACTIVE POWER AFTER IMPLEMENTATION OF THE PROPOSED CONTROL METHOD

Dynamic Load In this section, a 900 kV induction motor has been used to examine the proposed control method. The induction motor applied is fully described in TableI.

0.925

0.950

0.975

1.000

FIG. 9 LOAD ACTIVE POWER BEFORE IMPLEMENTATION OF THE PROPOSED CONTROL METHOD

8.0 7.0 6.0 5.0 4.0 3.0 2.0 1.0 0.0 -1.0

70.0 69.0 68.0 67.0 66.0 65.0 64.0 63.0 62.0 61.0 60.0 59.0 58.0

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Active Power [MW]

0.925

0.950

0.975

1.000

FIG. 10 LOAD ACTIVE POWER AFTER IMPLEMENTATION OF THE PROPOSED CONTROL METHOD

Also, dc-link voltage oscillation has a frequency of 120 Hz, and the induction motor supply frequency is 50 Hz. The simulation process takes place in 3 seconds.

The simulation was first carried out through the conventional PWM method and then using the new control method presented in this article. Fig. 13 indicates the three-phase current of the load before the implementation of the new control method while Fig. 14 indicates the three-phase current after the new method has been implemented. A comparison of the two methods suggests the efficiency of the new method. Also, due to the switching of the power electronic elements the high frequency oscillations are evident. However, using a more inductive induction motor can decrease the oscillations. Figs.15 and 16 indicate the reference signal input to the PWM comparator before and after the implementation of the new control method, respectively. The dc-link voltage can be seen in Fig. 17. An unbalanced supply in the

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International Journal of Automation and Control Engineering (IJACE) Volume 3 Issue 3, August 2014

dynamic loads can result in numerous problems such as fluctuations in the electromagnetic torque and the rotational speed, heating-up of the machine and machine losses all of which can have a negative impact on the performance and the life of the machine. Thus, it can be concluded that it is absolutely necessary to balance the supply voltage in electrical machines. For this reason, a new control method to achieve this was presented in this article. Figs. 18 and 19 indicate the electromagnetic torque before and after the implementation of the new control method. A comparison of the two figures suggests that the stress on the shaft has considerably reduced after the implementation of the new control method which is indicative of the method’s efficiency. Figs. 20 and 21 indicate the machine’s speed. The machine’s speed is not constant before the new method is implemented and the machine’s speed fluctuation frequency is equal to the dc-link oscillation frequency (120 Hz). After the new method was implemented, however, the machine’s speed has become almost constant (Fig. 21).

Fig. 22 indicates the induction motor’s active power before the new control method is implemented. Active power consumption is extremely oscillated with an oscillation frequency of 120 Hz. After the suggested control method was implemented, the oscillations dramatically decreased from 40 kW to only 500 W in Fig. 23. Figs. 24 and 25 indicate the reactive power consumption before and after the new control method was implemented. As can be seen, reactive power oscillations have dramatically decreased, too. In general, as shown in the simulation results, and as suggested by the figures in this study, the new control method proved quite efficient in all phases of the experiment.

TABLE 1 CHARACTERISTICS OF INDUCTION MOTOR

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Nominal power

900 kVA

Nominal voltage

380 V

Frequency

50 Hz

Inertia

1

Dampening

0.1 pu

Stator resistance

0.093 pu

Rotor resistance

0.009 pu

Stator leakage inductance

0.126 pu

Rotor leakage inductance

0.116 pu

Mutual inductance

1 pu

I Load[kA] Ib

Ic

3.0 2.0 1.0 0.0 -1.0 -2.0 -3.0 -4.0

Ia

ib 2.920

2.900

ia

ic 2.960

2.940

2.980

3.000

FIG. 13 UNSYMMETRICAL OUTPUT CURRENTS BEFORE THE PROPOSED CONTROL METHOD

I Load [kA] Ib

Ic

3.0 2.0 1.0 0.0 -1.0 -2.0 -3.0 -4.0

ib

2.900

2.920

2.940

Ia

ic

ia

2.960

2.980

3.000

FIG. 14 SYMMETRICAL OUTPUT CURRENTS AFTER IMPLEMENTATION OF THE PROPOSED CONTROL METHOD

1.00

Voltage reference

0.50 0.00 -0.50 -1.00 2.900

2.920

2.940

2.960

2.980

3.000

FIG. 15 REFERENCE SIGNAL BEFORE IMPLEMENTATION OF THE PROPOSED CONTROL METHOD

1.00

Voltage reference

0.50 0.00 -0.50 -1.00 2.900

2.920

2.940

2.960

2.980

3.000

FIG. 16 REFERENCE SIGNAL AFTER IMPLEMENTATION OF THE PROPOSED CONTROL METHOD

International Journal of Automation and Control Engineering (IJACE) Volume 3 Issue 3, August 2014

Rotor mechanical speed [p.u]

dc Link Voltage[kV]

0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00

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0.9933 0.9930 0.9927 0.9924 0.9921 0.9918 0.9915 0.9912

2.925

2.900

2.975

2.950

2.900

3.000

2.920

2.940

2.960

2.980

3.000

FIG. 21 MACHINE ROTATIONAL SPEED BEFORE IMPLEMENTATION OF THE PROPOSED CONTROL METHOD

FIG. 17 DC-LINK VOLTAGE

Electromagnetic Torque [p.u]

Active Power[MW]

0.72 0.60 0.48 0.36 0.24 0.12 0.00 -0.12 -0.24 -0.36

3280 3200 3120 3040 2960 2880 2800 2720

2.900

2.920

2.940

2.960

2.980

3.000

FIG. 18 MACHINE ELECTROMAGNETIC TORQUE BEFORE IMPLEMENTATION OF THE PROPOSED CONTROL METHOD

e

2.900

2.960

2.980

3.000

Active Power[MW] 3280 3200 3120 3040 2960 2880 2800 2720

2.920

2.940

2.960

2.980

3.000

FIG. 19 MACHINE ELECTROMAGNETIC TORQUE AFTER IMPLEMENTATION OF THE PROPOSED CONTROL METHOD

e

2.900

2.920

2.940

2.960

2.980

3.000

FIG. 23 MOTOR ACTIVE POWER AFTER IMPLEMENTATION OF THE PROPOSED CONTROL METHOD

Reactive Power[MVAr]

Rotor mechanical speed [p.u]

.3570 .3500 .3430 .3360 .3290 .3220 .3150

.9933 .9930 .9927 .9924 .9921 .9918 .9915 .9912 2.900

2.940

FIG. 22 MOTOR ACTIVE POWER BEFORE IMPLEMENTATION OF THE PROPOSED CONTROL METHOD

Electromagnetic Torque [p.u] 0.72 0.60 0.48 0.36 0.24 0.12 0.00 -0.12 -0.24 -0.36 2.900

2.920

2.920

2.940

2.960

2.980

3.000

FIG. 20 MACHINE ROTATIONAL SPEED BEFORE IMPLEMENTATION OF THE PROPOSED CONTROL METHOD

2.900

2.920

2.940

2.960

2.980

3.000

FIG. 24 MOTOR REACTIVE POWER BEFORE IMPLEMENTATION OF THE PROPOSED CONTROL METHOD

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International Journal of Automation and Control Engineering (IJACE) Volume 3 Issue 3, August 2014

REFERENCES

Reactive Power[MVAr] .3570 .3500 .3430 .3360 .3290 .3220 .3150 2.900

Holmes, D. G., & Lipo, T. (2006). Pulse Width Modulation for Power Converters. John Wiley & Sons. Inc. Hwang, J. G., & Lehn, P. (Aug. 2010). A single-input space vector for control of ac-dc converters under generalized unbalanced operating conditions. IEEE Trans. Power Electron, 2068–2081.

2.920

2.940

2.960

2.980

3.000

FIG. 25 MOTOR REACTIVE POWER AFTER IMPLEMENTATION OF THE PROPOSED CONTROL METHOD

Conclusion DC-link oscillations can cause serious problems. Due to the fact that dc-link voltage oscillations are mostly difficult to control, necessary measures must be taken to lessen the effects of dc-link voltage oscillations on the supplied load to prevent damages and losses. The present article attempted to suggest a PWM-based control method to deal with the problem. To prove the accuracy of the proposed method the simulation results using PSCAD/EMTDC software are presented.

For the sake of validity, both static and dynamic loads were applied in the simulation process. It was concluded that the new control method had a significant influence on balancing the voltage and on the static load current. To be more precise, it was indicated that active power oscillations and reactive power oscillations reduced from 3 MW and 4 MVAr to 1 MW and 1 MVAr, respectively. Also, dynamic loads as well as static load performances have significantly improved. That is, electromagnetic torque oscillations and active power reduced from 2.5 pu and 700 KVAr to 1 pu and 300 KVAr, respectively. Similarly, rotor speed oscillations and active power both reduced from 0.0017 pu and 40 KW to almost zero. In general, as shown in the simulation experiment, and as suggested by the figures in this study, the new control method proved quite efficient in all phases of the experiment.

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in

Power

Electronics

Selected

Problems.

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integral

motor.

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and

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Sudhoff, S. D., Corzine, K., Glover, S., Hegner, H., & Robey, H. (Mar. 1998). Link dc stabilized field oriented control of electric propulsion systems. IEEE Trans. Energy Convers, 27-33.

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Wu, B. (2006). High Power Converters and AC Drives. ohn Wiley & Sons. Inc. Yao, J., Li, H., Liao, Y., & Chen, Z. (May 2008). An improved control strategy of limiting the dc-link voltage fluctuation for a doubly fed induction wind generator. IEEE Trans.

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