Output Voltage Control for PWM Inverterwith Electric Double Layer Capacitor as DC
Power Supply
Y. Nakata*, K. Fujiwara**, M. Yoshida**, J. Itoh*, Y. Okazaki*** Nagaoka University of Technology, 1603-1, Kamitomioka, Nagaoka, Niigata, Japan** Kochi National College of Technology, 200-1, Monobe Otsu, Nankoku, Kochi, Japan
Abstract--In general, chopper circuits are necessary forthe inverter system whose input voltage fluctuates such as
solar power energy, wind power energy, capacitor energy
and so on. Therefore, the inverter system becomes larger,
the energy losses of power converter increase, and control
circuit is complicated. In this paper, to overcome theseproblems, a control scheme of PWM inverter to get theconstant R.M.S. AC voltage on inverter output without
chopper circuit is proposed.
At first, R.M.S. value calculation method and feedback
control procedure are investigated to realize proposedsystem. Next, the simulation results of the system are shownand characteristics of power converter using proposed
control scheme are discussed. At last, experimental resultsof proposed control system using fluctuating voltage source
are shown. Finally, availability of the newly developed
system is confirmed.
Index Terms--PWM inverter, R.M.S. value calculator,
Electric double layer capacitors, Output voltage regulation

I. INTRODUCTION

II. CONTROL SYSTEM
Fig.1 shows the outline of the conventional inverter
system which output the constant voltage value. In thisfigure, chopper circuit is connected between electric
double layer capacitors (EDLCs) which are used as DC
voltage source and PWM inverter circuit. In this case, themodulation ratio of the PWM inverter is kept constant,and the output voltage of chopper circuit is controlled as
constant value for fluctuation of the input voltage of thechopper circuit. This scheme is easy to construct because
the feedback control value is DC value. However, thiscontrol scheme needs both chopper circuit and inverter
circuit.

ControlcircuitLC
Filter

Reference value

Fig. 1. Configuration of the conventional control system.

LoadV

Inverter

EDLC +Chopper

In recent years, new energy resources such as
photovoltaic generation, wind force power generation andfuel cell have been developed. They generate DCpower[1]. Such a voltage type inverter and its control
technique are necessary to convert into AC power for
power source[2]. Energy storage approaches have beenstudied to smooth power generated by new energy
resources. Electric double layer capacitors have been paid
attention as the electrical energy charge devices which
are kind to the global environment. Therefore, they havebeen applied to some newly produced equipments such as
hybrid EV and UPSs and so on[3][4].
However, the voltage of capacitor falls down whenelectrical power is supplied to load. Usually, dc-dc
converter such as step-up or down type chopper circuit isapplied for this system to keep constant voltage of
inverter input voltage. However, this method need both
chopper circuit and inverter circuit, therefore it isconcerned that power conversion efficiency is decreased,
circuit sizes are too much larger and control system
becomes complicated.
When output voltage of inverter is controlled, PI
control with sine-wave target value is used. However, it
is impossible to control of high precision by only thisway, because error by phase shifting is caused. D-qtransformation is effective for three-phase system, but it

is not adaptive single-phase system[5]. Consequently,
control method of single-phase inverter with Hilberttransformation is suggested[6]. It is a control method with
the DC target value. Therefore, it is possible to control
the system without stationary error. However, it iscomplicated because this method require more than one
control system.
In this paper, to solve these problems, the control
scheme which compensates a drop-down of the capacitor
voltage only with inverter is suggested, and it is intended
to realize a power conversion circuit keeping a constant
output voltage of the inverter. A feedback control method
and operation circuit which calculates the R.M.S value ofinverter output voltage in real time are considered torealize these system[7].
At first, the theory to detect as DC voltage value from
R.M.S. value of inverter output voltage was suggested,
and the effectiveness of proposed method was confirmed
by using simulation analysis. Next, the circuit parameterof this control system is determined by simulation
analysis, and the effectiveness of power conversion
circuit which designed by using proposed scheme wasconfirmed by experimental results.

reference voltage Vref. Modulation ratio m of the PWM
inverter is determined with feedback control which iscalculated from PI controlled value of the error e which isthe difference of Vrms and Vref. Here, m is obtained fromthe ratio of carrier wave amplitude and modulating wave
amplitude. R.M.S. value of PWM inverter output voltage
is adjustable by using m[8].
III. R.M.S. VALUE CALCULATOR
Fig. 2. Configuration of the proposed control system.

Next, the configuration of the proposed control scheme
in this paper is shown in Fig.2. In this case, PWM
inverter circuit and EDLCs are directly connected, andoutput voltage of the inverter is controlled to constant
R.M.S. value only with the modulation ratio of the PWM
inverter. In this scheme, detection of the R.M.S. value ofthe inverter output voltage is necessary to control themodulation ratio to the target value. However, output
voltage of the PWM inverter is AC voltage, therefore it isdifficult to detect the R.M.S. value from theinstantaneous value of the inverter output voltage.
Therefore, a new calculation method of R.M.S. value
using the instantaneous value of inverter output voltage
has been proposed in chapter 3.
The operation circuit realizing this newly proposed
calculation method is named an "R.M.S. value
calculator". The DC voltage value Vrms which iscalculated by "R.M.S. value calculator" is compared with

The calculation of the R.M.S. value of the inverter
output voltage is necessary for controlling the modulation
ratio of the PWM inverter to get settled voltage on
inverter output.
In this paper, we propose a new way to have R.M.S.
value of the inverter output voltage as a DC value. TheR.M.S. value is calculated from the sinusoidal
instantaneous value of the inverter output voltage byusing analog operational circuit shown as R.M.S. value
calculation circuit in Fig.2.
If the instantaneous value of v1 (t ) = 2V sin (ωt + θ ) andv2 (t ) = 2V cos (ωt + θ ) are known, then the R.M.S. value ofthe inverter output voltage V is calculated by using
trigonometric function, shown in equation (1).

{ 2V sin(ωt + θ )} + { 2V cos(ωt + θ )} = ( 2V ) (1)22

When the inverter output voltage v1 (t ) = 2V sin (ωt + θ ) is{ 2V sin(ω t + θ )}2v (t ) = 2Vrms sin(ω t + θ )

Vrms

rms

12{ddtd{v(t )} = ω 2Vrms cos(ω t + θ )dt} {}

221⎡
2Vrms sin(ω t + θ ) + 2Vrms cos(ω t + θ ) ⎤⎥⎦2 ⎢⎣22= Vrms sin 2 (ω t + θ ) + cos 2 (ω t + θ ) = Vrms

{1ω2}

{ 2V cos(ω t + θ )}2rms

2Vrms cos(ω t + θ )Fig. 3. Block diagram for calculating R.M.S. value of the inverter output voltage.

Fig. 4. Simulation circuit.

sensed by the circuit shown in Fig.2, then the voltage
v2 (t ) = 2V cos (ωt + θ ) can be calculated by differentiating
v1(t) and dividing by ω. Therefore, the R.M.S. value isobtained by the following equation.

V=21 ⎧⎪ 2 ⎛ 1 dv(t ) ⎞ ⎪⎫+⋅vt()⎜⎟⎨⎬2 ⎪⎩⎝ ω dt ⎠ ⎪⎭(2)Equation (2) shows that the R.M.S. value of the inverter
output voltage V is calculated from the instantaneous
value of v1(t). A detailed block diagram of R.M.S. value
calculation circuit is shown in Fig.3.
IV. SIMULATION RESULTS
The proposed feedback control system is simulatedusing PSIM. This simulation is implemented under thecondition of Table 1. The simulated circuit is indicated inFig.4 and the result is shown in Fig.5.
TABLE ISIMULATION CONDITION
Output voltage frequency
Sampling frequency
Proportional gainIntegration gain
LoadValue
60 [Hz]
10 [kHz]0.05
0.002
500 [W]

Fig. 6. Picture of inverter and control circuit.

value calculator is configured by analog devices. For
example, operational amplifier is used for differentiation,amplification and addition. Multiplication IC is used for
multiplication and square root extraction. Here, it isimportant that designing of differentiation andamplification circuit, and adjustment of the offset ofoperational amplifier.
B. Characteristics of R.M.S. Value Calculator
Fig.7 shows the output waveforms of the R.M.S. valuecalculator indicated in Fig.2 in case that input R.M.S.
value of the sinusoidal waveform is 5 [V]. From thisoutput waveforms, it is understood that DC value which
depends on the R.M.S. value is obtainable from the ACwaveform.

Fig. 5. Simulation results.

From this result, it is understood that the output
voltage is kept at constant R.M.S. value in case that theinput capacitor voltage decreases. Therefore, proposed
control system is effective to control the output voltage toconstant.

Fig. 7. The input and output voltage waveforms ofR.M.S. value calculation circuit.(Vout=5.00 [V], Vrms=5.00 [V])V. EXPERIMENTAL RESULTS
The effectiveness of the proposed control system isconfirmed from the simulation results in chapter 4. Next,
it is considered whether the output value of the PWM
inverter kept to constant R.M.S. value in experimental
setup.
A. Experimental Circuit
The appearance of the experimental setup is shown inFig.6. The inverter part of this experimental setup is
configured by PWM inverter and control circuit. IGBTs
are used as switching devices of this inverter. The R.M.S.

Fig. 8. Input-output characteristic of R.M.S. value calculation circuit.

Next, Fig.8 shows the input and output characteristicof R.M.S. value calculator. From this figure, it isunderstood that output voltage conforms to input value,and accords with ideal line when the range of input
voltage is from 0.6 to 1.0 [pu]. On the other hand, in therange except these, it is recognized that the characteristics
are incongruent from an ideal straight line. These causes
attribute the offset of operational amplifier and the errorof the calculation circuit. However, it is understood thatthe error near to 1.4 [pu] and 0.4 [pu] is no problems
when the target value of R.M.S. value calculator isdesigned around 1.0 [pu].
C. Low Output Voltage Characteristics
Fig.9 shows the inverter output voltage waveforms
when inverter input voltage changed. In this experiment,
target R.M.S. value of output voltage set to 10 [V].
When the input DC voltage is 40 [V] and 30 [V], it isunderstood that 10 [V] output voltage is obtainable from
PWM inverter, and control system operates according tothe design. However, in case that the input DC voltage is
20 [V], it is sure that 10 [V] output voltage is not
obtainable from PWM inverter. This feedback control
circuit has the output limitation so that output waveform
is not distorted. This limitation depends on PI gainlimitation. Therefore, in case that calculated PI gain ismuch larger than limitation value, modulation ratio of thePWM inverter is not conformed to desired value.
And, it is recognized that output waveform is distorted
around zero. This is considered to be influence of voltage
drop of switching devices and diodes because designed
output voltage is low as 10 [V].
Next, Fig.10 shows the output voltage waveform of(a) Input voltage of 40 [V] ( Vrms=10 [V] )(b) Input voltage of 30 [V] ( Vrms=10 [V] )(c) Input voltage of 20 [V] ( Vrms=7.8 [V] )Fig. 9. Experimental results of the output waveforms with reference
voltage of 10 [V].

(a) Input voltage decreases from 50 [V] to 40 [V](b) Input voltage increases from 40 [V] to 50 [V]Fig. 10. Input and output waveforms of inverter in the case of
decreasing and increasing input voltage.

PWM inverter when input voltage is increased from 40 to50 [V], and decreased from 50 to 40 [V]. In these results,
it is understood that the output voltage of PWM inverter
follows designed value 10 [V] in both cases.
D. Experiment for Output Voltage of 100 [V]
Fig.11 shows the case that the output voltage
waveform when the input voltage of the PWM inverter
was changed. In this experiment, the targeted value of theoutput voltage set 100 [V], and the load of inverter is 200[W] resistive load.
In case that the input voltage is 220 [V] and 210 [V], asine wave of actual value 100 [V] is provided the output
voltage, it is understood that the output voltage constantcontrol were realized.
However, in the case that input voltage was 190 [V],actual value of the output voltage was less than 100 [V],and the output voltage constant control was not realized.
This cause was the upper limitation of the modulation
ratio, for proposed feedback system is set to 0.7.
Therefore, the lower limitation value of the input DC
voltage was 200 [V]. If the limitation of this feedback
control system could be removed, it was considered thatoutput voltage was provided from lower voltage than 200[V]. In addition to this, the distortion around zero voltage
which is appeared in low voltage experiment was notobserved. It was considered that the effect of forward
voltage drop is vanishingly lower than that of low voltage
experiment.
Next, Fig.12 shows the output voltage waveform ofPWM inverter when input voltage is increased from 220to 240 [V], and decreased from 240 to 220 [V]. In theseresults, it is understood that output voltage of PWM
inverter follows designed value 100 [V] in both cases.

(a) Input dc voltage of 220 [V] ( f=60 [Hz], Vrms=100 [V] )(b) Input dc voltage of 210 [V] ( f=60 [Hz], Vrms=100 [V] )(a) Input voltage decreases from 240 [V] to 220 [V](c) Input dc voltage of 190 [V] ( f=60 [Hz], Vrms=93.5 [V] )Fig. 11. Experimental results of the output voltage waveforms withreference voltage of 100 [V].

(b) Input voltage increases from 220 [V] to 240 [V]Fig. 12. Input and output waveforms of inverter in the case of decreasing
and increasing input voltage.

VI. CONCLUSIONSIn this paper, a control method about the capacitor
source PWM inverter to stabilize the output voltage
without using the chopper circuit was described. A
R.M.S. value calculator was suggested to construct theproposed control scheme, and the effectiveness of thefeedback control law was inspected by simulation and anexperiment. As a result, it was confirmed that the stable
output voltage was provided from PWM inverter whenthe voltage of capacitor was dropped.
However, this proposed control system was not usefulwhen input DC voltage value is lower than the peak valueof the output AC voltage. Therefore, the energy of thecapacitor cannot be used effectively compared with thecase of using a boost chopper circuit.
To solve this problem, it is considered a method tochange the connection in parallel and series by value ofthe capacitor voltage. In this case, the input DC voltage
becomes step voltage, therefore the characteristics offeedback control system such as step response must bereconsidered to stabilize the output voltage. And thepower conversion efficiency of proposed control system
must be evaluated as compared with the control systemusing chopper circuit.
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