Design and Implementation of a Single Phase Inverter With Sine Wave Tracking Method for Emergency...

8/11/2019 Design and Implementation of a Single Phase Inverter With Sine Wave Tracking Method for Emergency Power Sup

1/6

Design and Implementation of a Single Phase Inverter with

Sine Wave Tracking Method for Emergency Power Supply

with High Performance Reference

H. R. Karshenas1, M. Niroomand21Department of Electrical and Computer Engineering, Isfahan University of Technology, Iran

2Department of Electrical and Computer Engineering, Isfahan University of Technology, Iran

Abstract Uninterruptible Power Supplies (UPS) play

an important role in supplying critical loads. The

majority of UPS systems employ batteries as a mean of

energy storage. Since typical loads are supplied by ac

voltage, an inverter is an indispensable part of a UPS

to convert dc voltage to ac. Conventional control

methods for single phase inverters suffers from manydrawbacks like slow dynamic/transient response,

oscillatory no-load behavior and distorted waveform

in presence of non-linear loads. This paper in

concerned with the control loop design for a

single-phase voltage source inverter when employed in

UPS applications. The regulation of the output voltage

is done based on reference tracking to ensure good

steady-state and dynamic performance. The control

loop is designed taking into consideration the low

damping during light loads. Three control strategies

are proposed. The first is based on modified PID

controller which demonstrated moderate performance

and is suitable for low cost applications. The secondmethod is based on an additional current control loop

which has the benefit of inherent inverter protection.

The last method is based on the theory of "Internal

Model Controller" which gives nearly ideal

steady-state regulation. Key points in implementing

controllers with digital controllers are addressed. An

experimental system is built to verify the validity of

theoretical results.

I. INTRODUCTION

Nowadays Uninterruptible Power Supplies (UPSs)

are widely used in industry and wherever a clean and

uninterrupted power is required. The majority of these

systems employ batteries as a mean of energy storage,

thus a dc/ac inverter is an inherent part of their structure.

Conventional inverters lack many features required by

modern UPSs like fast transient and dynamic

response and good steady-state performance.Furthermore, many modern sensitive loads which are

supplied by UPS systems are non-linear loads with

non-sinusoidal current waveform. Conventional inverters

which use half-cycle averaging for regulation show high

output voltage distortion in presence of non-linear loads.

As a result, the inverter stage of a modern UPS needs

more advanced control scheme to fulfill the above

mentioned requirements [1],[2].

In this paper, tracking method is used to force the

inverter output voltage to follow a sinusoidal reference as

closely as possible. High switching frequency, which is

easily obtainable with modern power switching

devices, enables us to use a controller with highbandwidth and achieve fast transient response. It is shown

that conventional PI controllers cannot be used due toinherent instability of output LC filter, and other

structures like PID controller or current mode control

must be used. To achieve the optimum steady-state

performance, the concept of Internal Model Controllers is

proposed to reduce the steady-state error to zero without

affecting dynamic response. Theoretical and experimentalverifications are used to show the validity of analysis.

II. INVERTEROPEN-LOOPCHARACTERISTIC

Fig. 1 shows a single phase bridge inverter commonly

used in the output stage of a single phase UPS. Usingaveraging techniques, the switching stage is modeled by a

gain [3],[4], and thus the transfer function of the inverterincluding LC filter is given by:

])/1/(

[)(2 LCRCssLC

VsT i

++

=

It can be clearly seen that at light loads the output

filter becomes oscillatory, as shown by the root locus of

Fig. 2. Also shown in Fig. 3 is the output waveform at

light loads. This is one of the problems associated with

inverter output LC filter.As stated in the introduction, presently the majority

of sensitive loads are nonlinear loads. Such loads are

normally characterized by non-sinusoidal current due toinput rectifier with capacitive filter, as shown in Fig. 4.

When the diodes are conducting, the inverter is exposed

to a large filter capacitor, and when they are not

conducting, the inverter is practically in no load

condition. Therefore, the inverter repeatedly faces two

totally different loading conditions which happen twice a

cycle.

Fig. 5 shows the open-loop response of an inverter toa typical diode-capacitor load. The inverter controller

must be able to correctly regulate output voltage withminimum distortion.

(1)

1232


2/6

Fig.1. A single phase bridge inverter

Some standards have been published to specify the

maximum distortion of a static UPS in presence of

non-linear loads. A UPS manufacturer must carefully

follow these standards [5],[6].

Fig. 2. Root locus of inverter with light loads

Fig. 3. Output waveform at light loads

Fig. 4. Non-linear load input current

Fig. 5. Open-loop response of an inverter to a typical

diode-capacitor (non-linear) load.

III. CLOSEDLOOPSYSTEMDESIGN

Fig. 6 shows the block diagram of the closed-loop

system. The controller must be designed in such a way to

fulfill all dynamic and steady-state requirements. A

simple PI controller normally used in dc tracking systems

has many drawbacks in this application. Most

importantly, a PI controller cannot increase the system

phase margin adequately. Fig. 7 shows the system

response with a PI controller. It can be seen that properdamping with this structure is very difficult if not

impossible [7].

Fig. 6. Block diagram of the closed-loop system

1233


3/6

Fig. 7. System response with a PI controller

A PID controller, on the other hand, is able to provide

an acceptable performance. It has high gain at

low-frequencies, without affecting overall system phasemargin. By proper selection of the system bandwidth, an

adequate transient response is also achievable

IV.CASESTUDY

A 220V, 1.5KVA inverter with 48 Vdc input voltage

is considered in this work. A transformer with turn ratio

equal to 1:8 is used at the output for voltage matching.

The output inductor is integrated in this transformer, with

the value equal to 110uH as seen from the low voltage

side. The output capacitor seen from the low-voltage sideis equal to 100uF. The switching frequency is 25 KHz.

The PID controller is designed with corner frequency

equal to 4 KHz. This frequency is high enough to providefast dynamic response while does not interfere with

switching frequency. The phase margin is selected to beo52 , resulting in the following pole and zero:

sec/27331

sec/8545

1 radw

radw

P

Z

=

=

To improve the noise immunity, another pole at

sec/728852 radwP = is added, while a zero is placed at

sec/942radwL = to increase low frequency gain. Thus,

the complete transfer function is given by:

)/1)(/1(

)/1)(/1(.)(

21 pp

ZLC

wswss

wswsKsG

++

++=

Inserting the numerical values results in:

sss

sssGC

++

++=

)10258()10156(

1)0012.0()10124(.6000)(

62123

92

The gain is selected such that the dc gain at corner

frequency becomes unity. Fig. 8 shows the bode plot ofthe compensated system.

Fig. 8. Bode plot of the compensated system.

Fig. 9. Simulation results of the inverter as imposed

to a nonlinear load

Fig. 9 demonstrates the simulation results of the

inverter as imposed to a nonlinear load. The measured

THD is about 2.5%, which is below the given standards.

V.CURRENTMODECONTROLLER

Current mode control strategy is a well-knowntechnique particularly in motor drive applications. In this

control technique, the inverter output current is directly

controlled by a relatively fast inner control loop, and the

output voltage is regulated with a more sluggish outer

loop. Generally speaking, current mode controller design

is more straight-forward since the above mentionedcontrol loops can be decoupled. Another salient feature of

current mode control technique is that the inverter outputcurrent is directly controlled, making protection strategy

much more effective.

Fig. 10 shows the block diagram of the proposed

system with current mode control strategy [8]. Different

transfer functions can be obtained using this block

diagram. For example, transfer function from output

voltage to duty cycle is given by:

])/1/(

1[)(

2LCRCssLC

VsG ivd++

=

And the transfer function from inductor current toduty cycle is obtained as:

(2)

(3)

(4)

(5)

1234


4/6

])/1/(

1[)(

2 LCRCssLC

sRC

R

VsG iid

++

+=

Fig. 11 shows the simulation results obtained usingcurrent mode control method.

VI. INTERNALMODELCONTROLLER

From the control theory, a conventional PID

controller can never track a sinusoidal waveform ideally.

To illustrate this, one may consider the block diagram of

Fig. 6. It can be easily seen that an error must always existat the controller input to generate sinusoidal output and

consequently drive the inverter. This error is analogous to

steady-state error, which may not be acceptable.

High gain and bandwidth can improve tracking

performance, but other system parameters, specifically

dynamic characteristics, are limiting factors in increasing

gain.

From the block diagram of Fig. 6 one may suggeststhat if the controller can generate a sinusoidal output even

in the absence of input, then ideal tracking is achievable.

From the system point of view, a transfer function with

two conjugate poles at the working frequency can perform

this task [9]. This is in agreement with the Principle of

Internal Model Controller which states:

For proper asymptotic tracking, the loop transfer

function must contain and internal model of the

unstable poles of the reference signal.

Fig. 10. Block diagram of the proposed system withcurrent mode control strategy

Fig. 11. Simulation results using current mode control method

Using internal model controller one can effectively

decouple the steady-state and dynamic performance,making the controller design more flexible.

Fig. 12 shows different waveforms obtained using

PID controller with high and low gain and also with

internal model controller. It can be observed that thesteady-state error with internal model controller is

practically equal to zero, while it is not zero and depends

on controller gain in PID controller.

VII. DIGITALCONTROLLER

Recent advances in fast microcontrollers and DSPshave opened a new perspective for power electronics

designers. Using digital controller extremely increase the

system design flexibility. Time consuming computations

are now less restricting factors due to high performance

controllers available in the market.

Fig. 12. Different waveforms obtained using PID controller with highgain(top) and low gain(middle) and also with internal model

controller(bottom)

(6)

1235


5/6

In designing a system with digital controllers, the

delays associated with sampling and computation timemust be properly considered. The sampling delay due to

the input zero-order-hold is equal to Ts/2, where Ts is the

sampling period, while the computation delay is generally

equal to one sampling time, Ts. The above delays are

added together and included in the original continuoussystem model. Then, the controller is designed and

digitized using existing methods, like Euler or Tustin

methods.Using this approach, the controller is re-designed for

implementation by a digital controller. The controller

transfer function is then given by:

205.077.0025.0

102.0128.01.129.)(

23

23

+=

zzz

zzzzGdig

The digitization is done controller using Tustin

method and sampling frequency equal to switchingfrequency (25 KHz). Simulation results are shown

in Fig 13.

IX.EXPERIMENTALVERIFICATIONS

Fig. 14 shows the inverter used in experimental

verifications. At this stage, only the analogue controller

was implemented using op-amps and other relevant

components. The inverter output waveform whenimposed to a non-linear load is shown in Fig 15. Table I

shows the harmonic spectrum of the output voltage.

Fig. 13. System response with a digital controller

Fig14. Inverter used in experimental system

Fig. 15. Inverter output waveform when imposed toa non-linear load

Table I. Harmonic spectrum of the output voltage

X. CONCLUSION

A single phase inverter used at the output stage of

UPS systems is considered. Various requirements of suchinverter are stated. It is shown that conventional

controllers can not fulfill the necessary requirements

particularly when the inverter is supplying a non-linear

load. A PID controller is designed based on given

specifications. Current mode control technique is also

used to design a controller with desired dynamic

performance and inherent current limiting capability. It is

shown that the concept of Internal Model Controller canbe used to design a controller with zero steady-state error.

Controller design using digital controllers is shown and

some aspects associated with the existing time delays are

addressed.

REFERENCES

[1] M.J. Ryan, W.F. Brumsikle and R.D. Lorenz, Control topology

options for single-phase UPS INVERTERS, Industry Application,

IEEE Transaction on power electronics, Vol. 33, 1997[2] N.M. ABdel- Rahim, analysis and design of a multiple feedback

loop control strategy for single-phase voltage-sourse UPS invert-

ers, IEEE Transaction on power electronics,Vol. 11, No. 4, 1996.[3] Kassakian, M.F.Schlecht, and G.C. Vergese, Principles of Power

electronic, Addison-wesley, 1991

(7)

1236


6/6

[4] D.N. Mitchell, DC-DC Switching regulator analysis, Mc Graw Hill,1998.

[5] International Engineering Consortium (IEC), IEC 1000-2-2, 1990.

[6] European Committee for Electrotechnical Standardization(CENELEC), EN 50091-1, 1990.

[7] A. Moriama, I. Ando, and I. Takahashi, Sinusoidal Voltage Controlof a single phase uninterruptible power supply by a high gain PI

circuit, Industrial Electronics Society,IECON 9,. Proceedings of

24th Annual Conference of the IEEE, 1998.

[8] R.W. Erickson, and D. Maksimovic, Fundamentals of powerelectronics, Second Edition, Colorado, 2001.

[9] J. C. Dolye, B. A. francis, and A. R. Tannenbaum, Feedback

Control theory, Maxwell Macmilian International, 1992

1237

Design and Implementation of a Single Phase Inverter With Sine Wave Tracking Method for Emergency...

Documents

Transcript of Design and Implementation of a Single Phase Inverter With Sine Wave Tracking Method for Emergency...