1. Jun. 30 IJASCSE Vol 1 Issue 1 2012
GRID CONNECTED PV SYSTEM: Use of Single phase Inverter
1
K. Kartikaye, 2Aruna R.
Abstract because of shortage of fossil fuels and
greenhouse effect. Among various types
This paper presents a single-phase five- of renewable energy sources, solar
level photovoltaic (PV) inverter topology energy and wind energy have become
for grid-connected PV systems with a very popular and demanding due to
novel pulsewidth-modulated (PWM) advancement in power electronics
control scheme. Two reference signals techniques. Photovoltaic (PV) sources
identical to each other with an offset are used today in many applications as
equivalent to the amplitude of the they have the advantages of being
triangular carrier signal were used to maintenance and pollution free. Solar-
generate PWM signals for the switches. electric-energy demand has grown
A digital PID control algorithm is consistently by 20%–25% per annum
implemented in Microcontroller to keep over the past 20 years, which is mainly
the current injected into the grid due to the decreasing costs and prices.
sinusoidal and to have high dynamic This decline has been driven by the
performance with rapidly changing following factors:
atmospheric conditions. The inverter
offers much less total harmonic 1) An increasing efficiency of solar cells;
distortionand can operate at near-unity 2) Manufacturing technology
power factor. The proposed system is improvements; and
verified through simulation and is 3) Economies of scale [1]. PV inverter,
implemented in a prototype, and the
experimental results are compared with Which is the heart of a PV system, is
that with the conventional single-phase used to convert dc power obtained from
three-level grid-connected PWM PV modules into ac power to be fed into
inverter. the grid. Improving the output waveform
Index Terms— grid connected, of the inverter reduces its respective
photovoltaic (PV), proportional–integral harmonic content and, hence, the size of
(PI) current control, pulse width the filter used and the level of
modulated (PWM) inverter. electromagnetic interference (EMI)
generated by switching operation of the
I. INTRODUCTION inverter [2]. In recent years, multilevel
inverters have become more attractive
The demand for renewable energy has for researchers and manufacturers due
increased significantly over the years to their advantages over conventional
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reduced. This inverter topology uses two
reference signals, instead of one
three-level pulse width-modulated reference signal, to generate PWM
(PWM) inverters. signals for the switches. Both the
reference signals Vref1 and Vref2 are
They offer improved output waveforms, identical to each other, except for an
smaller filter size, lower EMI, lower total offset value equivalent to the amplitude
harmonic distortion (THD), and others of the carrier signal Vcarrier, as shown in
.The three common topologies for multi Fig. 1.
level inverters are asfollows:
1) diode clamped (neutral clamped
2) capacitor clamped (flying capacitors)
3) cascaded H-bridge inverter
In addition, several modulation and
control strategies have been developed
or adopted for multilevel inverters,
including the following: multilevel Ease of Use: The inverter is used in a
sinusoidal (PWM), multilevel selective PV system, a proportional– integral (PI)
harmonic elimination, and spacevector current control scheme is employed to
modulation A typical single-phase three- keep the output current sinusoidal and to
level inverter adopts full-bridge have high dynamic performance under
configuration by using approximate rapidly changing atmospheric conditions
sinusoidal modulation technique as the and to maintain the power factor at near
power circuits. The output voltage then unity. Simulation and experimental
has the following three values: zero, results are presented to validate the
positive (+Vdc), and negative (−Vdc) proposed inverter configuration.
supply dc voltage (assuming that Vdc is
the supply voltage). The harmonic
FIVE-LEVEL INVERTER
II.
components of the output voltage are
TOPOLOGY AND PWM LAW
determined by the carrier frequency and
switching functions.Therefore, their
harmonic reduction is limited to a certain The proposed single-phase five-level
degree [4].To overcome this limitation, inverter topology is shown in Fig. 2. The
this paper presents a five-level PWM inverter adopts a full-bridge configuration
inverter whose output voltage can be with an auxiliary circuit [4]. PV arrays are
represented in the following five levels: connected to the inverter via a dc–dc
zero, +1/2Vdc, Vdc, −1/2Vdc, and −Vdc. boost converter. Because the proposed
As the number of output levels inverter is used in a grid-connected PV
increases, the harmonic content can be system, utility grid is used instead of
load. The dc–dc boost converter is used
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Figure 2 Configuration of the
proposed single-phase five-level
to step up inverter output voltage Vinv to PWM inverter.
be more than √2 of grid voltage Vg to
ensure power flow from the PV arrays
into the grid [19]. A filtering inductance Lf
is used to filter the current injected into
the grid. The injected current must be
sinusoidal with low harmonic distortion.
In order to generate sinusoidal current,
sinusoidal PWM is used because it is
one of the most effective methods.
Sinusoidal PWM is obtained by Fig. 3. Basis of equivalence for
comparing a high-frequency carrier with sinusoidal PWM
a low-frequency sinusoid, which is the
modulating or reference signal. The
carrier has a constant period; therefore,
the switches have constant switching
frequency.
The switching instant is determined from
the crossing of the carrier and the
modulating signal. A. Sinusoidal PWM
Law A fundamental period in Fig. 3
consists of p pulses whose widths vary Fig. 4. Characterization of pulse.
sinusoidally throughout the cycle to give
the fundamental component of The switching period Δ and the
frequency. The basis of equivalence frequency modulation ratio p are,
between the desired sinusoid and the respectively, given by
actual pulsed waveform is taken to be Δ =2π/p (1)
volt–seconds, as shown in Fig. 3, i.e., p =fs/f1 (2)
As1 = Ap1 and As2 = Ap2. One of these where fs is the switching frequency and
pulses, the general kth pulse, is f1 is the fundamental frequency. The
characterized in detail in Fig. 4. quarter period of pulse δ0 is given as
δ0 = Δ/4. (3)
αk is the position from the origin of the
fundamental period of the midpoint of
the period Δ. The angles δ1k and δ2k
are the modulating angles which vary
throughout the cycle, and it is to
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As2 =Ap2. (18)
calculate these angles that a modulation By equating (12) and (14), and (13) and
law must be derived. (16)
Consider first the average voltages V 1k β1k = M sin(αk − δ0) (19)
and V 2k during the two halves of the and, similarly,
modulating pulse β2k = M sin(αk + δ0) (20)
V 1k =(Vs) {δ1k − (2δ0 − δ1k)} /2δ0 (4) where M is the “modulation index” and
∴ V 1k =(Vs)(δ1k − δ0)/δ0 (5) M = Vm/Vs. (21)
=(Vs)β1k (6)
where1k = (δ1k − δ0)/δ0 (7) Equation (21) can be expressed in terms
and, similarly of amplitude of carrier signal Vc by
replacing Vs with Vc. Because, in this
V 2k = (Vs)β2k (8) topology,two identical reference signals
Where are used, Vs = 2Vc and Vm =Vref1 =
Vref2. If M >1, higher harmonics in the
β2k = (δ2k − δ0)/δ0. (9) phase waveform are obtained.
Therefore, M is maintained between
The volt–second As1 is the half- zero and one. If the amplitude of the
pulsewidth of the sine wave and is given reference signal is increased to be
according to Fig. 4 by higher than the amplitude of the carrier
As1 = αkƒ signal, i.e., M >1, this will lead to
αk−2δ0 overmodulation. Large values of M in
Vm sinθ dθ (10) sinusoidal PWM techniques lead to full
=2Vm sin δ0 sin(αk − δ0). (11) overmodulation [20]. Fig. 6 shows the
However, sin δ0 → δ0 when δ0 is small carrier and reference signals for different
∴ As1 = 2δ0Vm sin(αk − δ0) (12) values of M. Equations (19) and (20)
and, similarly, define the modulation law, which is more
As2 = 2δ0Vm sin(αk + δ0). (13) M. (a)M = 0.3. (b)M = 0.5. (c)M = 0.7.
For the corresponding volt–second Ap1, (d)M = 1.2. commonly expressed in
in thePWMwaveform, terms of δ1k and δ2k, by
Ap1 =2δ0V 1k (14) substitutingfrom (7) and (9) to give
∴ Ap1 =2δ0β1k(Vs) (15)
and, similarly, δ1k =δ0 [1 +M sin(αk − δ0)] (22)
Ap2 = 2δ0β2k(Vs). (16)
For equivalence of volt–seconds from δ2k =δ0 [1 +M sin(αk + δ0)] . (23)
which the modulation law can be
derived, we require that Thus, the switching angles δ1k and δ2k
As1 =Ap1 (17) for the kth pulse can be calculated from
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Figure 5 Switching pattern for the
single-phase five-level
(22) and (23) in terms of modulation
inverter.
index M and angles αk and δ0 which
depend upon the fundamental frequency
and frequency ratio. B. Harmonic
Spectrum of Sinusoidal PWM Waveform
The voltage harmonics produced by the
sinusoidal PWM can be computed by
first calculating the harmonics due to the
kth pulse alone, Ank, and then
summating the harmonic contributions of
all p pulses
Switches S1–S3 will be switching at
the rate of the carrier signal frequency,
where as S4 and S5 will operate at a
frequency equivalent to the fundamental
Figure 6 single-phase five-level
inverter with PI controller.
The proposed single-phase five-
level inverter topology is shown in Fig. 6.
The inverter adopts a full-bridge
configuration with an auxiliary circuit. PV
arrays are connected to the inverter via
a dc–dc boost converter. Because the
Table 1 Inverter Output Voltage proposed inverter is used in a grid-
during S1−S5 Switch on and off connected PV system, utility grid is used
instead of load. The dc–dc boost
converter is used to step up inverter
frequency. Table 1 illustrates the output voltage Vinv to be more than √2
level of Vinv during S1–S5 switch on of grid voltage Vg to ensure power flow
and off. Figure 5 shows Switching from the PV arrays into the grid. A
pattern for the single-phase five-level filtering inductance Lf is used to filter the
inverter. current injected into the grid. The
injected current must be sinusoidal with
low harmonic distortion. In order to
generate sinusoidal current, sinusoidal
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approximation is used to transform the
integral term into the discrete-time
PWM is used because it is one of the domain because it is the most
most effective methods. Sinusoidal straightforward technique. The
PWM is obtained by comparing a high- proportional term is directly used without
frequency carrier with a low-frequency approximation.
sinusoid, which is the modulating or P term : Kpe(t) =
reference signal. The carrier has a Kpe(k). (29)
constant period; therefore, the switches
have constant switching frequency.The Time relationship: t = k ∗ h
switching instant is determined from the where
crossing of the carrier and the h sampling period;
modulating signal. k discrete-time index: k = 0, 1, 2, . . ..
For simplification, it is convenient to
define new controller gains as
K_i = Ki h/2 (30)
from which one can construct the
discrete-time PI control
Fig. 7 PI control algorithm implemented
in PIC controller.
u(t) control signal;
e(t) error signal;
t continuous-time-domain time variable;
τ calculus variable of integration;
Kp proportional-mode control gain;
Ki integral-mode control gain.
Implementing this algorithm using a PIC
requires one to transform it into the
discrete-time domain. Trapezoidal sum
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Fig. 7. Fig shows grid current of the
circuit
B. ALGORITHM IMPLEMENTATION
V. SIMULATION RESULTS
Control signal saturation and
integral-mode antiwindup limiting are Let us consider the following
easily implemented in software. In this example, inverter circuit involving
work, the control signal itself takes the unipolar switching. It is connected with
form of PWM outputs from the PIC. an R Load as shown below.
Therefore, the control signal is saturated
at the value that corresponds to 100%
duty cycle for the PWM. An undesirable
side effect of saturating the controller
output is the integral-mode windup.
When the control output saturates, the
integral-mode control term (i.e., the
summation) will continue
to increase but will not produce a
corresponding increase in controller
output (and hence will not produce any
additional increase in plant response).
The integral can become quite large,
and it can take a long time before the
controller is able to reduce it once the
error signal changes sign. The effects of
windup Figure 8 Simulation Circuit
Diagram
Figure 9 five level Output
Waveform the inverter circuit
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modulation index M will determine the
shape of the inverter output voltage Vinv
and the grid current Ig shows Vinv and Ig
for different values of M. The dc-bus
voltage is set at 400 V (>√2Vg) in this
case, Vg is 240 V in order to inject
current into the grid. Vinv is less than
√2Vg due to M being less than 0.5.The
inverter should not operate at this
condition because the current will be
injected from the grid into the inverter,
rather than the PV system injecting the
current into the grid. Figure 9 shows five
Figure 10 filtered Output level Output Waveform the inverter
Waveform from the inverter circuit and Figure 10 shows the five level
output Waveform the inverter circuit.
In order to verify that the proposed
inverter can be practically implemented VI .CONCLUSION
in a PV system, simulations were
performed by using MATLAB SIMULINK. Improving the output waveform of
It also helps to confirm the PWM the inverter reduces its respective
switching strategy which then can be harmonic content and, hence, the size of
implemented in a PIC. It consists of two the filter used and the level of
reference signals and a triangular carrier electromagnetic interference (EMI)
signal. Both the reference signals are
generated by switching operation of the
compared with the triangular carrier
signal to produce PWM switching signals inverter. In recent years, multilevel
for switches S1−S5. Note that one leg of inverters have become more attractive
the inverter is operating at a high for researchers and manufacturers due
switching rate equivalent to the to their advantages over conventional
frequency of the carrier signal, whereas three-level Pulse Width Modulated
the other leg is operating at the rate of
(PWM) inverters. They offer improved
fundamental frequency (i.e., 50 Hz).
Figure 8 shows the Simulation Circuit output waveforms, smaller filter size,
Diagram The tch at the auxiliary circuit lower EMI, lower total harmonic
S1 also operates at the rate of the carrier distortion (THD).
signal. As mentioned earlier, the
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PESC, Jun. 17–21, 2001, vol. 3, pp.
1173–1178.
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