stability analysis and simulation of a single-phase voltage source...

EUROPEAN TRANSACTIONS ON ELECTRICAL POWEREuro. Trans. Electr. Power 2008; 18:29–49Published online 12 January 2007 in Wiley InterScience
(www.interscience.wiley.com) DOI: 10.1002/etep.160
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Stability analysis and simulation of a single-phase voltagesource UPS inverter with two-stage cascade output filter

Jawad Faiz1,*,y, Ghazanfar Shahgholian2 and Mehdi Ehsan3

1Department of Electrical and Computer Engineering, Faculty of Engineering, University of Tehran, Tehran, Iran2Department of Electrical Engineering, Islamic Azad University, Science and Research Branch, Tehran, Iran

3Department of Electrical and Computer Engineering, Faculty of Engineering, Sharif University of Technology,Tehran, Iran

SUMMARY

The primary role of an uninterruptible power supply (UPS) systems is to produce sinusoidal output voltage withminimum total harmonic distortion (THD) and fast dynamic response. This paper investigates the performance oftwo-stage cascade output filter for single-phase voltage source UPS inverter and it is compared with an LC outputfilter. The simulation result shows harmonic reduction of output voltage of the inverter due to using multiple-filter.Both THD of the low output voltage and good voltage utilization can be achieved by the proposed filter scheme.The THD of the output voltage in various load condition are all less than 4%. A good agreement between thesimulation and experimental results is achieved. Copyright # 2007 John Wiley & Sons, Ltd.

key words: voltage source inverter; filter; harmonic reduction; root locus; pulse width modulation

1. INTRODUCTION

In recent years, extensive use of power electronic devices offers nonlinear loads to the power systems.

On the other hand, there is an increasing demand for high quality and reliable power supply for the

above-mentioned equipment. Thus having a stable and high reliability supply has been important issue

in industry and business. An uninterruptible power supply (UPS) system is frequently used where the

losses and damage of the power interruption are higher than the expense of the UPS system. An ideal

UPS system delivers a sinusoidal output voltage with low total harmonic distortion (THD) and fast

dynamic response to linear and nonlinear loads, and also provides seamless transition when a failure

occurs. Consequently, a closed loop regulated pulse width modulation (PWM) inverter is required to

achieve a good dynamic response and high quality output voltage [1,2].

To improve and enhance the capability of a power supply, the UPS systems have been widely used

for sensitive and critical loads which are generally nonlinear loads. Such loads include: life support

rrespondence to: Jawad Faiz, Department of Electrical and Computer Engineering, Campus No. 2, North Kargar Avenue, Poste 1439957131, University of Tehran, Tehran, Iran.mail: [email protected]

pyright # 2007 John Wiley & Sons, Ltd.

30 J. FAIZ, G. SHAHGHOLIAN AND M. EHSAN

equipment, instrumentation plants, satellite, hospital equipment, industrial controllers, telecommu-

nication systems, computers, and constant frequency power supply [3,4].

Development of a high-performance control method for PWM inverters of UPS is one of the major

subjects in the area of power electronics [5]. PWM inverter is widely used in variable speed induction

motors, emergency power supplies, active filter, power factor correction converter, induction furnaces,

andUPSs.Many controllers have been proposed to obtain an output voltagewith lowTHD for application

in UPS inverter, under both transient and periodic load disturbances. Various techniques have been so far

presented to improve the performance, to achieve the ideal characteristics and to introduce different

circuits for UPS. When a PWM inverter is used to feed the load, a LC low pass filter is employed to

eliminate the switching frequency or harmonic components of the output voltage.When a filter is inserted

at the output of the inverter, the load voltage control methods include: repetitive control [6], sliding mode

control [7], multi loop control [8], and deadbeat control [9]. Average current mode control technique,

based on a compensator circuit for a three-phase full bridge inverter inserted between an arbitrary

renewable power source and the utility grid has been presented in Reference [10]. In Reference [11], a full

digital deadbeat controller for series parallel line interactive UPS is designed and implemented. Analysis

and design of a current regulated voltage controlled for single-phase voltage source UPS inverters, with a

second order filter has been presented in Reference [5]. In Reference [12], a second-order filter design

technique for output of a UPS has been proposed, and dependency of the amplitude of harmonic

components on the capacitance and inductance of the filter and also dependency of the switching

frequency with output voltage control are shown. Two improved SPWM control techniques for

single-port and double-port inverters have been proposed to eliminate harmonics [13].

It is important that inverter incorporates a high stability and reliability as well as fast dynamic

response, particularly under nonlinear loads [14].Themechanism of output waveform distortion of a high

frequency PWM voltage source inverter, with an LC filter and rectifier load has been revealed through a

theoretical analysis [7]. Amethod for individual harmonic control using overriding current controllers for

UPS with nonlinear loads has been presented in Reference [15]. The most desirable feature of an UPS is

using an inverter with filter providing a perfect sinusoidal output waveform for load changing case. A

number of harmonic components are transferred to load through a low pass filter. In order to reduce the

ripple of the load voltage, a second filter can be inserted between the first filter and the load.

This paper describes the design procedure for inverter having two-stage cascade output filters. In such

inverter, the output voltagewaveform can be sinusoidal under nonlinear load, no-load, or light load. This

paper is organized as follows. Section 2 presents a theoretical analysis using the switching function of

the harmonics in the output voltage of a single-phase PWM inverter. Section 3 describes the output

impedance principle of the plant. Section 4 gives state space equation of the system and shows the open

loop frequency response. Finally, simulation results are reported and discussed for operation with mono-

and multiple-filter under nonlinear load in Section 5. Simulations results are presented under different

loading conditions in order to demonstrate the suitability of the proposed filter. Applying multiple-filter

also improves the transient of system and its robustness to the load fluctuations. Simulation and

experimental results are compared in Section 6. Section 7 concludes the paper.

2. MATHEMATICAL ANALYSIS AND MODELING OF THE PWM INVERTER

Mathematical model and linearization technique are used to design controller of a nonlinear system.

State equations are commonly used in the simulation procedure. Single-phase voltage source PWM

inverters are commonly used in low and medium power UPSs. Low output voltage distortion and fast

Copyright # 2007 John Wiley & Sons, Ltd. Euro. Trans. Electr. Power 2008; 18:29–49

DOI: 10.1002/etep

Figure 1. Single-phase UPS inverter with multiple filters.

SINGLE-PHASE VOLTAGE SOURCE UPS INVERTER 31

dynamic response are key requirements for single-phase UPS inverter. The most important role of an

inverter in the system is regulating the output voltagewaveform, such that the voltage and frequency are

kept fixed and independent of the load change and supply voltage. The inverter output waveform is

nonsinusoidal and contains harmonic components. These components may be reduced using different

switching techniques and diminished their effects by a filter [16,17]. Any nonsinusoidal alternating

waveform can be shown as infinite number of sinusoidal functions with related harmonics using Fourier

series. It is clear that the main component has the fundamental frequency and frequencies of the

remaining harmonic components are multiple of the fundamental frequency. The period of the resultant

waveform is always equal to the period of the basewaveform. The voltagewaveform of the real inverter

is nonsinusoidal and having the orders and amplitudes of its harmonic components can be very helpful

in the filter design and selection of proper switching techniques.

Figure 1 shows a single-phase full bridge voltage source PWM inverter used in an UPS system. It

consists of dc supply Vdc, filter inductors LF1 and LF2, filter capacitors CF1 and CF2, equivalent series

resistance of the filters RF1, RF2,RC1 and RC2, power switches Q1–Q4, and inductive load with resistance

RL and inductance LL. In practice, the equivalent series resistance of the filter capacitor is so small that

it has little effect on the mathematical model.

The output voltage of inverter, UI, is directly proportional to the commanded duty cycle of the

inverter and dc supply. The voltagewaveform of the actual inverter is nonsinusoidal. Harmonic analysis

was used for carrying out the system planning, filter design, and output voltage inverter controlling. The

most important technique for controlling the output voltage of the inverter is PWM. Various PWM

techniques can largely improve the output voltage which leads to a low THD. Advantages of PWM

techniques include low cost, easy implementation, and high reliability. A PWM inverter with higher

switching frequency enables to reduce the LC filter size. However, switching frequency is generally

limited and the switching loss increases with the elevation of the switching frequency [9]. The LC filter

is usually designed using the Fourier series of the inverter output voltage waveform. Similar to a linear

system, the ac voltage of the inverter output can be expressed as components of the input voltage; the

transferred harmonics are defined via the inverter. Using the switching function theory, the detailed

relationship between the input and output variables can be obtained. If S(vt) is the transfer function of

the single-phase inverter, the output voltage of the inverter is as follows:

UIðvtÞ ¼ UdcSðvtÞ ¼ Udcma sinðvotÞ þ Udc

X1k¼3;5;7;...

Ak sinðkvotÞ (1)


DOI: 10.1002/etep

Table II. Switching patterns and output voltage of unipolar PWM inverter.

Q1 Q2 Q3 Q4 UI(t)

ON OFF OFF ON Udc

OFF ON ON OFF �Udc

ON ON OFF OFF 0OFF OFF ON ON 0

Table I. Switching patterns and output voltage of bipolar PWM inverter.

Q1, Q4 Q2, Q3 UI(t)

ON OFF Udc

OFF ON �Udc


For full bridge inverter, there are bipolar and unipolar switching techniques. As shown in Figure 1,

there are two and four possible combinations of on and off for the power switches in the bipolar PWM

(BPWM) and unipolar PWM (UPWM), respectively. The combinations and output voltage of inverter

in terms of dc supply voltage are shown in Table I and Table II. Figures 2–5 show the simulation results

in terms of ma for frequency modulation ratio (mf) variation for bipolar and UPWM. As seen in

Figures 2 and 4, the value of THD and distortion factor (DF) in UPWM is less than that of the BPWM.

UPWM method has lower switching loss and it offers the advantage of effectively doubling the

switching frequency of the inverter voltage. A unipolar SPWM technique is selected for the control,

since the undesired harmonics in the technique are shifted to a frequency around double the carrier

frequency (Figure 5), which is much higher than the reference sinusoidal frequency, the output filter is

Figure 2. Change of THD and DF in terms of ma for mf variation in a bipolar PWM.


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Figure 3. Simulation results of bipolar PWM inverter for ma¼ 0.8 and mf¼ 9.

Figure 4. Change of THD and DF in terms of ma for mf variation in unipolar PWM.

Figure 5. Simulation results for unipolar PWM inverter with ma¼ 0.8 and mf¼ 9.


DOI: 10.1002/etep



smaller and it is easier to implement. A PWM control minimal filtering is required, which minimizes

the filter cost, size, weight, and loss.

3. OUTPUT IMPEDANCE PRINCIPLE

Figures 6 and 7 show the system block diagram of the single-phase inverter with output mono-filter and

multiple-filter which has two inputs. The output voltage is:

UOðsÞ ¼ HUðsÞUI � HIðsÞIO (2)

whereHU(s) is tracking characteristic andHI(s) is the output impedance. No-load or light load cases has

no effect on the stability of the UPS system, therefore sensitivity of the load change has little effect on

the inverter output impedance. Equation 2 shows that the output voltage harmonics depend on both the

harmonics generated by the inverter output voltage (UI) and load current (IO). The transfer functions for

mono-filter are independent of the load (Figure 6) and they can be obtained ignoring RC1 and RC2 as

follows:

HUðsÞ ¼UOðsÞUIðsÞ

��Io¼0

¼ 1

LF1CF1s2 þ RF1CF1sþ 1(3)

HIðsÞ ¼UOðsÞIOðsÞ

��UI¼0

¼ LF1sþ RF1

LF1CF1s2 þ RF1CF1sþ 1(4)

For multiple filters case, the transfer functions of Figure 7 are as follows:

HUðsÞ ¼Uo

UI

��IO¼0

¼ NUðsÞDðsÞ (5)

HIðsÞ ¼Uo

Io

��UI¼0

¼ NIðsÞDðsÞ (6)

Figure 6. Block diagram of a UPS system with mono-filter.

Figure 7. Block diagram of the proposed filter for UPS system.


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where:

NUðsÞ ¼1

LF1LF2CF1CF2

(7)

NIðsÞ ¼1

CF2

s3 þ RF1

LF1þ RF2

LF2

� �s2 þ RF1RF2

LF1LF2þ LF2

LF1CF1

þ LF1

LF2CF1

� �sþ RF1 þ RF2

LF1LF2CF1

� �(8)

DðsÞ ¼ s4 þ RF2

LF2þ RF1

LF1

� �s3 þ 1

LF1LF2CF1CF2

ðLF2CF2 þ RF1RF2CF1CF2 þ LF1CF2 þ LF1CF1Þs2

þ 1

LF1LF2CF1CF2

ðRF2CF2 þ RF1CF2 þ RF1CF1Þsþ1

LF1LF2CF1CF2

(9)

The Bode plot of the output impedance and the tracking characteristics for LF1¼ 0.3mH, LF2¼0.15mH, CF1¼ 60mF, CF2¼ 40mF, RF1¼ 0.7V and RF2¼ 0.35V are shown in Figures 8 and 9,

respectively. Conforming to Figure 8, the width band of HI(s) in the multiple filters is less than the

mono-filter and it has less sensitivity to the change of the load.

Figure 8. Bode diagram of the output impedance.

Figure 9. Bode diagram of the tracking characteristics.


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4. SYSTEM OF EQUATIONS AND OPEN LOOP FREQUENCY RESPONSE

By comparing the simulated performance of the system, the suitable pole location can be selected.

When an LC filter is used between the load and the first filter (in state space form), as shown in Figure 1,

the time state matrix equations and characteristic equation of the system, neglecting the equivalent

series resistance of the filter, will be as follows:

d

dt

uF1uF2iF1iF2iO

266664

377775 ¼

0 0 1CF1

� 1CF1

0

0 0 0 1CF2

� 1CF2

� 1LF1

0 � RF1þRC1

LF1

RC1

LF10

1LF2

� 1LF2

RC1

LF2� RC1þRC2þRF2

LF2

RC2

LF2

0 1LL

0 RC2

LL� RC2þRL

LL

2666664

3777775

uF1uF2iF1iF2iO

266664

377775þ

0

01LF10

0

266664

377775 uI½ � (10)

uOiC2iF1

" #¼

0 1 0 RC2 �RC2

0 0 0 1 �1

0 0 1 0 0

24

35 uF1 uF2 iF1 iF2 io½ �T (11)

DðsÞ ¼ s5 þ RL

LLs4 þ 1

CF1

1

LF1þ 1

LF2

� �þ 1

CF2

1

LF2þ 1

LL

� �� s3

þ RL

LL

1

LF1LLþ 1

LF2CF1

þ 1

LF2CF2

� �s2 þ 1

LF1CF1LF2CF2LLsþ RL

LF1CF1LF2CF2LL(12)

The transient response and relative stability are directly related to the location of the closed loop

roots of the characteristic equation in the s-plane. Several open loop system properties must be known

before the controller can be designed. The transfer function describes the dynamics of the system under

consideration. From the state equations, the plant control to output transfer function is:

HUOðsÞ ¼UOðsÞUIðsÞ

¼ 1

DðsÞ �1

LF1LF2CF1CF2

sþ RL

LL

� �(13)

HICðsÞ ¼IC2ðsÞUIðsÞ

¼ 1

DðsÞ �1

LF1LF2CF1

sþ RL

LL

� �s (14)

where IC2 is the capacitor current of the second filter. The transfer functions with mono-filter are as

follows:

HUOðsÞ ¼UOðsÞUIðsÞ

¼ 1

LF1CF1s2 þ RF1CF1sþ 1sþ RL

LL

� �(15)

HICðsÞ ¼IC1ðsÞUIðsÞ

¼ CF1

LF1CF1s2 þ RF1CF1sþ 1sþ RL

LL

� �s (16)


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where IC1 is the capacitor current of the mono-filter. If an LCL filter is used at the output of inverter,

characteristic equation of the system will be as Equation (17).

DLCLðsÞ ¼ s3 þ RC1 þ RF1

LF1þ RC1 þ RF2 þ RL

LF2 þ LL

� �s2

þ 1

CF1

1

LF1þ 1

LF2 þ LL

� �þ RF1ðRC1 þ RL þ RF2Þ þ RC1ðRL þ RF2Þ

LF1ðLF2 þ LLÞ

� �s

þ RF1 þ RF2 þ RL

LF1ðLF2 þ LLÞCF1

(17)

Figure 10 shows the root locus of the output voltage due to incremental change of the modulation

index for the multiple-filter at the output of the inverter. Figure 11 shows the root locus of the output

voltage due to incremental change of duty cycle for the LCL filter in the output inverter. An UPS

inverter operates over a wide impedance ranges from resistive to inductive and capacitance load.

Variation of the load impedance changes the system transfer characteristic and the output voltage value.

Figure 10. Root locus plot with multiple-filter.

Figure 11. Root locus plot with LCL filter.


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Figures 12 and 13 exhibit the Bode diagram of time-dependent output voltage for resistance and

inductive load, with power factor equal to 0.1 where two filters at the inverter output are employed. As

seen, changing the two-filter to mono-filter has insignificant effect. Figures 14 and 15 show the Bode

diagram of the output voltage and inner current under inductive load for different filter at the output

Figure 12. Bode diagram of the open loop transfer function of the outer voltage loop––multiple-filter.

Figure 13. Bode diagram of the open loop transfer function of the capacitor current—multiple-filter.

Figure 14. Bode diagram of the open loop transfer function of the output voltage for different output filter underinductive load.


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Figure 15. Bode diagram of the open loop transfer function of the inner current for different output filter underinductive load.


inverter of the UPS system. The Figures show that the inner current exhibits a band pass and output

voltage, a low pass filter-like characteristics.

The main objective of feedback application in the control systems is improvement of the dynamic

response and reduction of sensitivity of the system against parameters variations and undesirable

disturbances. Application of the feedback in control systems leads to the increase of number of

elements and its complexity and this may cause instability. Generally, for systems with input that also

has undesirable disturbances, integral control with the constant gain state feedback is used. The

major role of an UPS is maintaining a stable voltage and alternative reserving for critical loading

under any nonlinear loading conditions or load change without taking into account the input supply.

Minimization of the harmonic components in the output of the inverter can improve the dynamic

response of the UPS system for load changes, and also decrease the output filter size and finally

reduces the cost [18,19]. In a UPS system, selecting the feedback scheme, not only depends on the

control method, but also other factors such as system cost, protection, and availability of the current

sensors. If there are two filters in the output of the inverter, only one output voltage feedback is used

for load voltage control. So:

UOðsÞ ¼KPWMNUðsÞ

DðsÞ þ KPWMGOðsÞLF1CF1LF2CF2

URðsÞ �NIðsÞ

DðsÞ þ KPWMGOðsÞLF1CF1LF2CF2

IOðsÞ (18)

Where UR is the reference voltage, Io is the load current, KPWM is the effective gain of the inverter,

and NI(s) and NU(s) have been given by Equations (7) and (8). Control of Go(s) is carried as follows:

GOðsÞ ¼ KPU þ KDUsþKIU

s(19)

where KPU, KDU ,and KIU are proportional coefficient, derivative, and integrator, respectively. By

application of the suitable controller and ignoring the resistance of the filters, the characteristic

equation is as follows:

DðsÞ ¼ s4 þ ðLF1 þ LF2ÞCF2 þ LF1CF1

LF1CF1LF2CF2

s2 þ 1þ KPWMKPU

LF1CF1LF2CF2

(20)


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Increasing the capacitance of the filters reduces the load voltage fluctuations and the output

waveform tends to a sinusoidal wave with low harmonic distortion. Also when the capacitance of

the first filter is higher than that of the second, the voltage error in the transient mode will be

lower.

The LC filter fundamental cutoff frequency is dependent on the load impedance and elements of the

passive filter (LF1, CF1, LF2, and CF2). The simplest design approach is to assume a nonload condition.

Using multiple-filter, the resonance frequency given by Equation (21), depends only to values of the

filter components.

LF1LF2CF1CF2v4 � ðLF1CF1 þ LF2CF2 þ LF1CF2Þv2 þ 1 ¼ 0 (21)

If two are identical filters, the resonance frequency is 1.618vo, where vo is the resonance frequency

in the mono-filter case.

5. SIMULATION RESULTS

Key parameters of the single-phase full bridge UPWM inverter are listed in Table III. Simulations are

performed using the Matlab Simulink toolbox. The simulation results are given and discussed for

operation with a resistive, inductive, and nonlinear load. Figure 16 shows a nonlinear or rectifier load.

In the steady-state, the rectifier bridge turns on and off periodically. The full bridge diode rectifier is an

uncontrolled system involving resistor, inductor, and capacitor.

Figures 17 and 18 show the simulated waveforms of output voltage and output current of the inverter

system with resistive load and with a full wave rectified resistive load (10V), where DC side capacitor

filter (10mF) is employed. The THD of the voltage in Figure 17 is 1.89% and the regulation is 2.9%.

For nonlinear load, the load current is highly distorted and the output voltage is only slightly

distorted, the THD of the output voltage is 2.3% and the regulation is 2.7%. Figures exhibit that the load

Table III. System parameters.

Parameter Symbol Nominal value Unit

dc input voltage Udc 180 VSwitching frequency FSW 5 kHzSampling time TS 5 msReference sine frequency fO 50 HzOutput voltage amplitude UO,rms 100 VRated output power SO 1 kVARated output current IO,rms 10 AFirst filterInductor LF1 0.3 mHResistance RF1 0.7 V

Second filterInductor LF2 0.15 mHResistance RF2 0.35 V

First filter capacitor CF1 60 mFSecond filter capacitor CF2 40 mFLoad power factor cosu 0.8 Lag


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Figure 16. Nonlinear load.

Figure 17. Simulation results under full load and output multiple-filter (load voltage and power spec-trum––current second filter).


voltage of multiple-filter is nearly sinusoidal and it means that it provides stable response at any

load type and value. Table IV lists the measured THD and regulation of output voltage under various

load conditions. Figure 19 depicts the output voltage transient response for input voltage variations,

from 180 to 200Vand back to 180V. Figure 20 shows the transient response of the output voltage and

the output current for load changes from 10 to 5V and back to 10V. Theses results point out the

robustness of the output voltage for load current variations and input voltage disturbances. The THD of

the voltage in Figures 19 and 20 is 1.63 and 1.48% and the regulation is 2.6 and 3.1%, respectively. The

system performance for step change in the load from no load to full load is shown in Figure 21. The

output voltages with multiple-filter under no load and variable load are more stable than that of other

filters. It is seen that the transient dies out quickly and the voltage error remains almost unchanged

during the load fluctuation. UPS may face no load or light load conditions, thus proper operation of

system must be maintained. Figures 22 show results simulation of the system under no load with

multiple-filter. As seen, response with multiple-filter is stable. The THD of the output voltage with

mono and multiple filters is 1.6 and 1.2%, respectively.


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Figure 18. Simulation results under nonlinear load and output multiple-filter (Load voltage and power spec-trum––current load and filters).

Table IV. Regulation and THD of output voltage in different load conditions.

Different Loads Regulation (%) THD (%)

100% Load (R¼ 10V) 2.9 1.8950% Load (R¼ 20V) 2.7 2.58200% Load (R¼ 5V) 3.3 1.83Nonlinear load (rectifier) 2.7 2.30RL Load (8V–19mH) 4.0 2.37


6. EXPRIMENTAL RESULTS

When loads connected at the output of the inverter are nonlinear in nature, the load currents consists of

harmonics in addition to the fundamental frequency component. The advantages of multiple-filter are

reduction of devices size and voltage ratings for the switches, more attenuation in harmonics, less

voltage loss, and the improvement of control response. Also, the THD reduces with load voltage,

because the harmonics reduced by going for multiple filters. The overall system as shown in Figure 23,


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Figure 19. Transient response for input voltage variation (from 180 to 200V and back to 180V).

Figure 20. Transient response for load variation step changes (from 10 to 5V and back to 10V).


consists of two parts namely controller part and power circuit. The controller part includes the

micro-controller running the control algorithms and driver circuits. The power circuit part includes the

full bridge inverter, filter, and dc voltage. To show the validity of the proposed output filter and control

method, a small experimental system with the scheme as shown in Figure 24 was built and operated in

the laboratory. The controller circuit and PWM pulse generation circuit for switches are shown in

Figures 25 and 26, respectively. The experimental results were obtained for the same system


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Figure 21. Simulation results of the dynamic response of the UPS system for a 100% step change in the load.(a) Load suddenly turned on (b) load suddenly turned on.


parameters as the computer simulation results. The system has an inverter consisting of a single-phase

MOSFET full bridge with a switching frequency of 8KHz and multiple output filters, with

LF1¼ 90mH, LF2¼ 10mH, CF1¼CF2¼ 100mF and dc voltage 50Vand output voltage 38Vat 50Hz.

The experimental results corresponding to the simulated cases are presented in Figures 27 and 28.


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Figure 22. Simulation results of the system under nonload.

Figure 23. The simplified block diagram of the experimental setup.


Figure 27 shows the output voltage and filter inductive currents, respectively. Figure 28 shows the

output voltage and load current with a nonlinear load. Simulation and experimental results demonstrate

the effectiveness of the proposed control scheme. If dc voltage increases, we will to obtain higher

output voltage, because inverter output voltage is proportional with dc voltage. The reason that the

THD of experimental result is higher than the simulation is: (1) in the simulation, the inverter switching

devices are assumed as ideal switches, but SPWM modulation is not an ideal amplification including

dead time and conducting resistance of device, (2) the state observer cans also generator error, and (3)

the simulation is achieved under the dc source voltage is ripple free and constant.


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Figure 25. Controller circuit.

Figure 24. Set of practical test. (a) Hardware experimental setup; (b) multiple inverter output filters.

Figure 26. PWM pulse generation circuit for switches.


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Figure 27. Output voltage of the single inverter system operating with a pure resistance (voltage scale 20V/div,time scale 5milliseconds/div). (a) Experimental result (b) simulation result.

Figure 28. The results waveform of load current with nonlinear load (current scale 10A/div, time scale50milliseconds/div). (a) Experimental result; (b) simulation result.


7. CONCLUSION

In power electronic systems, the simulations are mainly performed to analyze and design the circuit

configuration and the applied control strategy. To confirm the performance of the system a simulationwas

carried out. UPSs are now commonly used to supply the critical loads which are often nonlinear. In this

paper, the open loop stability behavior of a single-phase inverter for different inverter output filter

topologies, using the Bode diagram and root locus is investigated. The simulation results show harmonic

reduction in output voltage inverter due to filters for full load, no load, and varied change. It is noted that

design and implementation of any new system needs study and simulation of the system. Fourier analysis

is used to predict the load voltage harmonic spectrum. To validate the theoretical analysis and simulation

an experimental prototype was build. Simulation and experimental results show that THD (less than 4%)

can be reduced further by using a second filter between the load and the first filter.

8. LIST OF SYMBOLS

Udc d

Copyright # 2

c input voltage

fO r
eference sine frequency
UI i
nverter output voltage
007 John Wiley & Sons, Ltd. Euro. Trans. Electr. Power 2008; 18:29–49

DOI: 10.1002/etep


mf f

Copyright # 2

requency modulation ratio

vo a
ngular frequency of main component
HU(s) t
racking characteristic
BPWM b
ipolar pulse width modulation
THD t
otal harmonic distortion
UO v
oltage load
iF1, iF2 fi
lter inductor current
CF1, CF2 fi
lter capacitance
KIV i
ntegral gain
KPWM i
nverter gain
iO l
oad current
RF1, RF2 e
quivalent series resistance of the filter inductance
RC1, RC2 e
quivalent series resistance of the filter capacitance
FSW s
witching frequency
SO r
ated output power
ma m
odulation index
DF d
istortion factor
Ak c
oefficient of Fourier series
HI(s) o
utput impedance
UPWM u
nipolar pulse width modulation
BW b
and width
vF1, vF2 fi
lter capacitor voltage
iC1, iC2 fi
lter capacitor current
LF1, LF2 fi
lter inductance
KPV p
roportional gain
KDV d
erivative gain
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AUTHORS’ BIOGRAPHIES

Jawad Faiz received his Ph.D. in Electrical Engineering from the University of Newcastleupon Tyne, England in 1988. He is now a Professor at Department of Electrical and ComputerEngineering, Faculty of Engineering, University of Tehran. He is the author of 215 publi-cations in international journals and conference proceedings. Dr Faiz is a senior member ofIEEE. He is also a member of Iran Academy of Sciences. His teaching and research interestsare switched reluctance and VR motors design, design and modeling of electrical machines,drives, and transformers.

Ghazanfar Shahgholian was born in Isfahan, Iran, in 1968. He graduated in electricalengineering from Isfahan University of Technology, Isfahan, Iran, in 1992. He received hisM.Sc. and Ph.D. in Electrical Engineering from University of Tabriz, Tabriz, Iran in 1994 andfrom Islamic Azad University, Science and Research Branch, Teheran, Iran in 2006,respectively. His research interests include application of control theory to power systemdynamics, power electronics, and power system simulation.

Mehdi Ehsan received his B.Sc. and M.Sc. in Electrical Engineering from Faculty ofEngineering, University of Tehran in 1963, Ph.D. and DIC from Imperial College, Universityof London in 1976. Since then, he has been with Electrical Engineering Department of SharifUniversity of Technology in different responsibilities. He has an extended cooperation withresearch centers in Iran and also abroad. Currently, he is a Professor in Electrical EngineeringDepartment of Sharif University. His research interests include power system simulation,dynamic and transient stability, application of expert systems in identification, operation,planning, and control of power system.


DOI: 10.1002/etep

stability analysis and simulation of a single-phase voltage source...

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