Evaluation of Power Quality Parameters of
Microgeneration Systems
Sérgio Lopes, Instituto Superior Técnico, UTL.

Abstract - The growing interest and use of
microgenerators has brought some attention to the
evaluation of their impact on Power Quality, namely to the
Total Harmonic Distortion (THD) on the current and on
the grid voltage, as well as on the Power Factor and
Displacement Factor. Also, the use of microgenerators to
mitigate some Power Quality problems, acting as Active
Power Filters (APF), is becoming more attractive.
This paper presents and evaluates two possible
solutions for microgenerators grid connection: through a
first order or through a third order filter. For each one of
these solutions, linear and nonlinear controllers are
designed for the current injected into the low voltage grid.
The proposed solutions are simulated in Matlab/Simulink
and the obtained results are compared to those obtained
for the existing equipment and to the maximum values
admissible by international standards.
A microgeneration solution with a third order
filter in the connection to the low voltage grid and
guaranteeing simultaneous reactive power compensation
(Active Power Filter) is proposed.
Keywords - Microgeneration, Power Quality, Inductive
Filter, LCL Filter, Harmonic Distortion, Power Factor.
I.
INTRODUCTION
Usually, microgenerators (µG) have voltage source
inverters (VSI) for grid connection. However, due to the high
switching frequency of the VSI, it is necessary to use an
adequate filter to connect the inverter to the electrical grid,
guaranteeing the compliance with international standards.
The wide use microgenerators will have an impact on
Power Quality (PQ), particularly in the voltage and current
total harmonic distortion (THD). The aim of this work is to
evaluate the solution - filter topology + controller which
introduces less impact on PQ. To meet that goal, two different
filters are sized: L filter and LCL filter, and two types of
controllers are designed: a) nonlinear control by sliding mode,
b) linear Proportional Integral (PI) control and polynomial
control.
Then it is created a more complete model that allows the
compensation of power factor. With this model is intended to
inject in the grid the maximum active power consumed by
nonlinear loads.
With these guidelines, is built a model of a µG which is
subsequently included in a model of small test grid. Thus it is
possible to analyze the PQ in operating conditions closer to
reality. PQ parameters that are compared for the different
solutions are:
 total harmonic distortion of voltage;
 total harmonic distortion of current;
 Power Factor.
The results are evaluated and compared.
II. POWER QUALITY PARAMETERS (PQ)
In an electrical system has the power supplied has quality
when is guaranteed the proper functioning of electrical
equipment without significant changes in performance.
The three-phase voltage in Portugal is characterized by
three sinusoidal voltages, lagged of 120°, with effective value
and frequency defined by the norm NP50160 [1]. When there
are significant changes from these features there is a
consequent degradation of PQ.
In the last decades has been a high growth in the use of
electronic equipment, connected to the grid trough power
electronic converters, regularly rectifiers with diodes. These
devices, while allowing more efficient use of electricity, have
a nonlinear behavior, causing distortions in the waveforms of
the current, and consequently in the tension, contributing
significantly to the decline in quality of power supplied.
A. Total Harmonic Distortion - THD
Harmonics are voltages or currents with multiple
frequencies of the fundamental component (50 Hz).
Considering the values of the most significant harmonics,
can be calculated one indicator of PQ, the total harmonic
distortion (THD) (1).
(1)
1
The increase of the THD is reflected in the increase of
Joule losses, losses by skin effect, the proximity effect and the
increase in neutral currents[1].
the semiconductors command variable γ can take three values,
depending on the value of the error:
(5)
B. Power Factor
The harmonics of grid currents and the resulting harmonics
of grid voltage produced by nonlinear loads increase losses,
usually leading to oversized transformers and equipment
connected to the grid. The power factor is defined as the ratio
between the Active Power (power delivered to loads) and
Apparent Power (installed power) [2] [3]:
Considering continuous conduction, the inverter’s output
voltage
is directly dependent on the semiconductor
conduction intervals, so the transfer function
of the
modulator+inverter association can be write as (6) [3]
(2)
Fig.2 shows the grid voltage and current when it is used a
sliding mode strategy to control the current
(6)
And can be writhed as a function of the total harmonic
distortion:
Grid Voltage [V/10]
Injected Current [A]
40
30
(3)
20
10
0
III. CONVENTIONAL G
-10
The connection of the G to the grid is made through a
single-phase inverter and a filter that provides attenuation of
high frequency current harmonics the electrical network. In
this chapter is introduced the model of the single phase
voltage inverter and is dimensioned two types of filter: one of
first order (L) and a third order (LCL) filter. For both types of
filtering used are sized for sliding mode controllers and linear
controllers.
-20
-30
-40
0
0.005
0.01
0.015
0.02
time [s]
0.025
0.035
0.04
Fig. 2. Experimental result obtained using sliding mode
The current
injected into the network can also be
controlled using a PI controller (Fig.3):
A. G with Inductive Filter
RL
One approach to control the output filter current
is
using the sliding mode control (Fig. 1), since it is a robust and
easy to implement controller.
0.03
i0ref
Linv
i0
Amp
i
+
+
C(s)
Modulator
+ Inverter
-
VPWM
VR
Req
i
RL
i0ref
i
+
e
+
-
Linv
Fig. 3. Equivalent diagram of the inverter connected to the network through an
inductive filter with PI control.
i0
Amp
+
+
Modulator
+Inverter
VPWM
VR
i
Fig. 1. Equivalent diagram of the inverter connected to the network through an
inductive filter with sliding mode control.
Considering the effect of non-ideal disturbance introduced
by the network voltage, the transfer function of current
injected into the grid by the inverter is given by (7):
(7)
The error of current is given by the difference between the
reference current and the inverter output current:
(4)
Is necessary to design the compensator
that
guarantees the tracking of reference current. Since it is
intended to have a null static error the compensator must have
integral action (I). However, if the compensator has only
2
integral action the system becomes sluggish. For this reason is
introduced proportional action (P) that enables a faster system
response.
(8)
The transfer function in closed loop of current controller is
given by:
To control the current
to inject into the network, is
studied the sliding mode control, control with PI compensator
and polynomial control.
To dimension the current controller for sliding mode it is
assumed that the voltage of the capacitor is approximately
equal to the grid voltage. Under these conditions, the design of
the controller for sliding mode is identical to that performed
for the inductive filter.
L1
R1
L2
i1
R2
Amp
(9)
iref
i
+
Modulator
+ Inverter
+
+
+
-
C
V12
VPWM
VR
RC
i
Grid Voltage [V/10]
Injected Current [A]
40
Fig. 6. Equivalent diagram of the inverter connected to the network through an
LCL filter with sliding mode control.
30
Fig.7 shows the grid voltage and current when it is used a
sliding mode strategy to control the current and a LCL filter
20
10
0
40
-10
30
-20
20
-30
10
-40
Grid Voltage [V/10]
Injected Current [A]
0
0
0.005
0.01
0.015
0.02
time [s]
0.025
0.03
0.035
0.04
-10
Fig. 4. Experimental result obtained using a PI control strategy.
-20
-30
B. G with LCL filter
-40
To obtain a greater attenuation of high frequency
harmonics is necessary to consider a higher order filter. In this
work was considered an LCL filter that allows a reduction of
the THD at lower switching frequencies, which is a big
advantage for higher power applications [4]. However, the use
of a higher order filter requires the design of a current
controller more complex and more susceptible to disruption
and distortion in the waveform of the grid.
L1
VPWM
R1
0.005
0.01
0.015
0.02
time [s]
L2
R2
RC
0.03
0.035
0.04
In a second approach is considered to make the current
control with a PI compensator. Again, it is considered that the
voltage on the capacitor is approximately equal to the network
voltage and in this case is controlled the inverter’s output
current. The block diagram and layout of the filter are shown
in Fig. 8.
i2
iC
C
0.025
Fig. 7. Experimental result obtained using sliding mode whit a LCL filter.
L1
i1
V12
0
R1
L2
i1
R2
Amp
iref
VR
i
+
C(s)
+
Modulator
+ Inverter
-
C
V12
VPWM
VR
Req
RC
Req
i
Fig. 8. Equivalent diagram of the inverter connected to the network through
Fig. 5. Schematic of the G filter connected to the grid.
an LCL filter with PI control.
For the LCL filter, the transfer function is:
(10)
Assuming that the capacitor’s voltage is approximately
equal to the grid voltage, the transfer function is given (11)
where
is the inverter output current,
is the inverter
output voltage.
(11)
3
(14)
is given by (12):
(12)
Similar to the approach used for the inverter with inductive
filter, in this case is also used a PI compensator (8).
The transfer function in closed loop of current controller is
given by (15):
The experimental results obtained using this control
strategy is shown in Fig.9.
(15)
Fig. 11 shows the grid voltage and current obtained with a
µG with LCL filter when polynomial control is used.
Grid Voltage [V/10]
Injected Current [A]
40
30
20
10
0
-10
Fig. 9. Experimental result obtained using PI and a LCL filter.
-20
-30
To obtain a compensator a better dynamic response and
power factors closer to unity should be considered the
dynamics of the 3rd order LCL filter.
L1
R1
L2
-40
0
0.005
0.01
0.015
0.02
time [s]
0.025
0.03
0.035
0.04
Fig. 11. Experimental result obtained using polynomial control and a LCL
filter.
i2
R2
Amp
iref
i
+
C(s)
+
Modulator
+ Inverter
-
C
V12
VPWM
VR
Req
RC
The Power Quality Parameters obtain when these
Microgenators are connected to a ideal network are listed in
Table I.
i
TABLE I
Fig. 10. Equivalent diagram of the inverter connected to the network through
an LCL filter with polynomial control.
According to (10), the transfer function of the filter has
one zero
and three poles
e
, one real
and two complex conjugate (13) .
(13)
To compensate the effect introduced by the LCL filter, it is
assumed that the compensator is polynomial , with three zeros
(
e
) to cancel the three filter’s poles and a pole
coincident with the filter’s zero. To ensure a null static error in
response to the step is considered a pole at the origin. To avoid
increasing the excess of zeros/poles of the system, it is
introduced a third pole
in the compensator with a
frequency high enough to not interfere in the dynamics of the
system (14).
POWER QUALITY PARAMETERS WHEN Gs ARE CONNECTED TO IDEAL
GRID
Filter
L
L
LCL
LCL
LCL
Controller
Slindig Mode
PI
Sliding Mode
PI
Polynomial
Power
Factor
2,97
2,51
0,91
0,45
0,56
0,999
0,999
0,998
0,984
0,998
IV. COMPENSATED µG
In the last years the proliferation of power equipment with
non-linear load increase the disturbances in PQ, thus is
required a more efficient way to mitigate those effects [5].
The Active Power Filter (APF) consists in connecting a
capacitor to the VSI in order to reduce the THD and
simultaneously compensate the power factor, being a much
better solution than conventional approaches. The APF adjusts
4
the amplitude of the inverter’s output voltage o by pulse width
modulation or by the control of DC link, and thus cancel the
harmonics created by nonlinear loads [6] [7].
L1
CFAP
ipv
Inverter
R1
i1
L2
C
V12
VPWM
iµG
R2
(19)
irede
icarga
VR
RC
Non-linear
Load
Fig. 12. Schematic of the G with APF filter.
To verify the proposed model are simulated three different
cases. In the first case the microgenerator with a LCL filter is
connected to the grid with a parallel nonlinear load without the
APF. Then is introduced the APF in the model. And in the last
case is used an inductive filter instead of the LCL filter. The
gird voltage and current of each case is shown in Figs. 15, 16
and 17. And the corresponding THD obtained is listed in
Table II.
Considering the polynomial current control the controlled
system can be represented as a current source.
Grid Voltage [V/10]
Grid Current [A]
40
30
(16)
20
10
Considering the current source, the simplified model can
be represented as:
0
-10
ic
VCFAP
ipv
-20
CFAP
-30
i (s)
-40
1.9
1.91
1.92
1.93
1.94
1.95 1.96
time [s]
1.97
1.98
1.99
2
Fig. 15. Grid voltage and current, with non-linear load and conventional
microgenerator.
Fig. 13. Block diagram of the overall system, whereas the current source
represents the current control system.
Grid Voltage [V/10]
Grid Current [A]
40
The capacitor voltage is given by:
30
(17)
20
10
It is used a PI compensator
defined as:
to control
, that can be
0
-10
(18)
The block diagram of capacitor voltage
in Fig. 14.
is represented
v
+
-
K
Kp  i
s
iref
Gi  i
sTdv  1
i
-30
-40
1.9
ipv
vcref
-20
+
-
1
sC
vc
1.91
1.92
1.93
1.94
1.95 1.96
time [s]
1.97
1.98
1.99
2
Fig. 16. Grid voltage and current, with non-linear load and compensated
microgenerator with LCL filter.
v
Fig. 14. Voltage controller of the capacitor voltage.
The response of the voltage disturbance introduced by the
panel is given by:
5
Grid Voltage
Grid Current
40
As Table III shows when the number of microgenerators
increase, the THD is much higher in cases which the inverter
has an inductive filter when compared with the inverters that
have a LCL filter.
Considering only G with LCL filter it appears that when a
PI controller is used the delay of the current’s first harmonic in
relation to the supply voltage is much larger than the other
cases, and consequently the power factor is never less than
0.984. Nevertheless this value of power factor still conforms
to the values defined by the standard [8].
30
20
10
0
-10
-20
-30
-40
1.9
1.91
1.92
1.93
1.94
1.95 1.96
time [s]
1.97
1.98
1.99
Fig. 17. Grid voltage and current, with non-linear load and compensated
microgenerator with L filter.
TABLE II
THD OF THE GIRD CURRENT WITH CONVENTIONAL AND COMPENSATED
MICROGENERATOR
Filter
LCL
L
LCL
Without APF
With APF
20,48
5.34
1,96
Fig.11 and Fig. 12 show that with a use of a compensated
microgenerator the grid current is sinusoidal in contrast to
what the case without the APF as shown in Fig. 10.
The Table II shows that the compensated microgenerator
with LCL filter gives a grater attenuation of THD.
V. EXPERIMENTAL RESULTS
To study the variation of the PQ parameters with the
increasing number of the µG in a network is considered the
models created in Chapter III and then is created a small low
voltage grid with a generator, a Power transformer, a power
line and a linear load.
TABLE III
COMPARATION OF THE 5 CASES STUDIED
Filter
Controller
µG
per
phase
L
Slindig
Mode
1
5
L
PI
LCL
Sliding
Mode
LCL
PI
LCL
Polynomial
1
5
1
5
1
5
1
5
Pwer
Factor
2,89
5,28
2,61
2,60
0,95
1,23
0,94
0,94
0,98
0,52
1,14
3,48
1,55
1,02
0,05
0,22
0,08
0,12
0,08
0,09
VI. CONCLUSION
2
0,999
0,999
0,999
0,999
0,998
0,998
0,984
0,981
0,998
0,998
This paper aimed to examine some of the indicators of PQ
that result from the introduction of Microgeneration in the
Low voltage network and suggest strategies to mitigate their
effects on quality of the electrical energy, namely in the total
harmonic distortion of voltage and current, as well as power
factor.
The microgenerator connection to the grid is done through a
filter, and is analyzed two different topologies for its
implementation: first-order filter (inductive) and third order
LCL filter. To control the current to inject into the network
two types of controllers are designed: nonlinear controllers
(sliding mode), and linear controllers – PI and polynomial. For
each case the results obtained for the total harmonic distortion
of current and power factor to verify the parameters given by
manufacturers and do not exceed the maximum values defined
by the standards.
By making the simulation of a microgenerator connected to
a nonlinear load proves the advantage of using the APF filter
in a low-voltage network. It allows to greatly reduction of the
current THD introduced by nonlinear loads. Comparing the
use of an LCL filter with an inductive filter it verifies that the
reduction in THD is even more pronounced for the higherorder filter.
All the proposed solutions were used in a small test
network. The results showed that, in general, for a network
with several microgenerators, the third-order filter allows to
obtain lower rates of harmonic distortion of current and
voltage. And with the increased number of G with LCL filter
there is no degradation of power quality parameters studied
unlike what happens with inductive filter.
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