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IEEE International Conference on
Power Engineering, Energy and
Electric al Orives
POWERENG2*H. Ha* H-13- T«ireM*l¡B«S, Málaga, SpaÍB
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IEEE Catalog Number: CFP1197B-USB
ISBN; 978-1-4244-9843-7

Proceedings of the 2011 International Conference on Power Engineering, Energy and Electrical Drives Torremolinos (Málaga), Spain. May 2011
S. P. Litrán, P. Salmerón, R.S. Herrera
Departamento de Ingeniería Eléctrica y Térmica. Escuela Técnica Superior de Ingeniería. Universidad de Huelva
E-mail: salvador@uhu.es; patricio@uhu.es; reyes.sanchez@die.uhu.es
AbstractThe configuration of a series active power filter (APF) and a parallel passive filter (PPF) has proven to be an efficient system for nonlinear load compensation. Different compensation strategies have been proposed to control the series APF. The most effective strategy determines the APF reference voltage as addition of two terms. The first one is proportional to source current harmonics and the second one is opposite to the load voltage harmonics. The control strategy has been analyzed from the state model of the single phase equivalent circuit. The resulting model analysis provides the information needed to establish design criteria for the control strategy, both in terms of harmonic filtering and the system stability. The design criteria have been applied to load type of current source harmonics
(CSH). Finally, results of an experimental prototype developed for this purpose allowed the proposed analysis to be verified.
The filtering equipment has been contrasted in two different situations: sinusoidal supply voltages and distorted supply voltages.
I.
I NTRODUCTION
The increase of harmonic pollution in electric network has attracted the attention of the power system engineers. As result, adjustable dynamic solutions have been developed to mitigate the quality problems of electric power. Many of these solutions include active power filters or also called
Active Power Line Conditioners, APLC [1-3]. Since 1970 numerous contributions of parallel connection active filters have published and implemented [4-8]. This topology type has been effective for the elimination of harmonics and reactive power compensation of nonlinear loads of harmonic current source type, HCS. This is because traditional sources of harmonics were due mainly to cycloconverter and controlled rectifiers, which can be considered as charges of this kind [1].
On the other hand, it is usually to find loads that include a rectifier with a capacitor at the dc side, which behave as a source voltage harmonics, HVS. For these loads the parallel connection active filters can not completely cancel the harmonics. This equipment can even cause problems such as increased voltage ripple at the dc side and high currents at the rectifier dc side. For these load types, it possible uses a series connection active filter and thereby eliminating voltage harmonics and compensating reactive power of HVS loads
[9]. However, in power systems HCS or HVS loads are rare and in some cases in the presence of other charges may have a different behavior. As an example, a HCS type load connected at a point near a capacitor bank or LC filters may have different behavior than expected. Therefore, in this situation a parallel connection compensator will be less effective. Others topologies have been proposed which incorporate series and parallel configurations of hybrid and active filters including an active power filter with a passive filter which can be applied to any load types [10-12].
The topology of active filter connected in series with the source and passive filter connected in parallel to the load
(Series Active Filter and Parallel Passive Filter, SAPPF) has been effective for eliminating voltage and current harmonics generated by the load (Fig. 1) [13-19]. Three strategies have been proposed to control the active filter in such settings:
• Source current detection (SCD). In this strategy, the series APF generates a voltage proportional to the source current harmonics [13,14].
• Load voltage detection (LVD). In this strategy the series APF generates a voltage opposite to the load voltage harmonics.
• Current and voltage detection (CVD). This strategy combines the source current detection and the load voltage detection.
The functionality of these strategies have been analyzed from a steady state model and from the point of view of performance; but this analysis do not specify design criteria for each compensation strategy. Furthermore, this theoretical development is not suitable to study the system stability or to determine the proportionality constant value.
Among these strategies, the current and voltage detection
(CVD) has been proven as the most effective [8]. In this paper the theoretical analysis of a hybrid filter constituted by a series APF and shunt passive filter is carried out. For this, the state model equations are obtained from its single phase equivalent circuit.
The resulting model allows to establish the control specifications to ensure system stability and to eliminate the source current harmonics. For this purpose a simulation platform based on MATLAB has been developed.
978-1-4244-9843-7/11/$26.00 ©2011 IEEE

v s
Finally, a SAPPF experimental prototype has been developed. The compensating strategy has been applied to the series APF, which has allowed the theoretical analysis to be contrasted.
II.
S TATE M ODEL OF H YBRID A CTIVE P OWER F ILTER
Fig. 1 shows a three-phase circuit with a voltage source that feeds a HCS type nonlinear load and a SAPPF hybrid filter. The source impedance is constituted by a resistance R
S
. The active power filter is connected in and an inductance L
S series with the source through a coupling transformer. The passive filter is connected in parallel with the load. It consists of two LC branches tuned to 5 th and 7 th current harmonics. v
S R
S
L
S
i
S
Three-phase source
v
PCC
L
F
+ v
C
-
C
F
v
L
L
5
L
7
V dc
C
5
Hybrid filter
Fig. 1. System with SAPPF filter and load type HCS
C
7
The circuit used to obtain the system state model is shown in Fig. 2. This circuit represents the equivalent single-phase network of Fig. 1 for any h order harmonic different of the fundamental harmonic. The active filter is modeled by a controlled voltage source, u . As load model the Norton equivalent has been used. It is defined by means of a resistor,
R
L
, in parallel with an inductance, L
L
, and a current source i
L
.
This current source will be zero for the fundamental harmonic. The passive filter consists of two LC branches tuned to the harmonics of interest. Each LC branch includes a resistance which models the resistive effect which is mainly present in the reactors. i s
R s
L
S u v
L v
PCC
R
5
R
7 i
LL i
5 i
7
L
5
L
7
R
L
L
L
+ + v
5
-
C
5 v
7
-
C
7
Passive filter Load
Fig. 2. Equivalent single phase circuit of the system of the Fig. 1 i
L
Considering the circuit in Fig. 2, the definition of the next state equation is possible
+
+
1
1
+
+
2
2
(1)
Where x is the state vector whose components are the state variables, u is the control variable, v the input vector and y the system output.
For the variables defined in Fig. 2 circuit, the state vector is composed of the currents through the inductances and the capacitors voltages x = [ i
S i
5 i
7 i
LL v
5 v
7
] T
(2)
The system matrix is given by
A =













 


−
(R
S
R
L
L
S
L
R
5
L
L
R
7
L
L
L
0
0
+ R
L
)
−
1
(R
L
L
S
+
−
−
R
L
C
L
R
5
L
L
R
7
L
L
1
L
0
5
R
5
)
−
−
R
−
L
S
R
(R
L
L
+
5
L
R
7
L
R
7
L
L
L
0
1
C
7
L
vector has the form
)
R
L
−
L
S
R
−
L
L
R
5
L
−
L
R
7
L
L
L
0
0
−
0
L
5
0
0
0
0
1
−
0
0
L
7
0
0
0
1
(3)
In this case the B















 
B
1


1
L
S
0 0 0 0 0


T
(4)
B
2
is defined by the matrix
B
2
=




1
L
S
R
L −
0
R
L −
0
R
L −
L
S
L
5
L
7
And the input vector takes the form v = [ v
S i
L
] T
0
R
L
0 0

0 0



T
L
L
(5)
(6)
The matrices C , D
1
and D
2
If the source current ( i
S matrices are as follows
depend on the selected output.
) is taken as an output signal, the
C = [
1 0 0 0 0 0
]
(7)

D
1
= D
2
= (8)
With the hybrid strategy, the active filter must generate a voltage waveform defined by means of u k i
S
− k v
L
(9)
Where k is the proportionality constant, i
S current, v
L
is the voltage at the load side and k instrumentation sensitivity. v
the source
models the
According to Fig. 2 circuit, the control signal can be calculated by u = ( − v L
)
S
+ k R i
5
+ k R i
7
+ k R i + k R i (10)
This is expressed in matrix form as follows
1
+
2
Where
K
1
= ( − v L
) k R
L k R
L k R
L
0 0

(12)
At the dc side are connected a resistance of 16.7 Ω in series with an inductance of 55 mH.
The first step is to obtain the model of the load. For this, the load is connected to a sinusoidal voltage source of 100 V rms and 50 Hz. The source resistance is R
S
=1.31 Ω and source inductance is L
S
=2.34 mH.
In this situation, the active power and reactive power consumed by the load are measured. Their values per phase are 0.38 kW and 0.15 kvar. With these data, the resistance and inductance of the Norton equivalent model of the load are determined. The results are 26.3 Ω for the resistance (R
L
) and
212 mH for the inductance (L
L
).
This load has odd current harmonics. The most significant harmonic is of 3 rd order with an rms value of 0.7 A. Table II shows the values of harmonics, THD and active and reactive powers.
The passive filter parameters are shown in Table I. It consists of two LC branches tuned at the frequencies of the
5 th and 7 th harmonics.
T ABLE I.
P ASSIVE E LEMENTS V ALUES
R
5
L
5
C
5
R
7
L
7
C
7
2.1 Ω 13.5 mH 30 µ F 1.1 6.75 mH 30 µ F
K
2
= [
0 k R
L
So, the state equation is defined by
]
(13)
With these data we can obtain the system matrix A’ as a function of the k v
(15).
and k parameters defined in the equation x = ( +
1
) + (
B
2
+ B K
2
) v
Here the system matrix is as follows
A ' = ( +
1 1
) =
=

















−
(
R s
+ R
L
L
S
R
L
L
5
R
L
L
7
R
L
L
L
0
0
(
1 − k v
) )
R
L
−
(
−
−
1
C
0
−
(R
L
L
S
+
L
5
R
L
L
7
R
L
L
1
L
5 k v
)
R
L
−
(
(R
−
L
S
R
L
L
L
5
+
−
1
L
7
R
L
L
0
1
−
L k v
)
R
L
(
1
0
0
−
−
L
S
R
L
−
L
5
R
L
−
L
7
R
L
L
L k v
)
−
0
L
0
0
0
0
1
5
−
0
0
L
0
0
0
1
7
















C
7
(15)
The CVD control strategy modifies the first row of the matrix and the matrix system that multiplies the input vector.
III.
E XPERIMENTAL P ROTOTYPE D ESIGN
This section describes the design procedure of CVD control strategy for active filter with the topology shown in Fig.1.
The design will be for a CSH type load. It consists of three single-phase rectifiers connected between phase and neutral. criterion is established that the system gain at frequencies between 150 Hz and 10 kHz is less than -40 dB. The k v
value is considered of 0.98 although the ideal value should be 1 it will be practically impossible due to the instrumentation sensitivity. From these data is possible to determine the k value which achieve the proposed control objective and ensure system stability.
Fig. 3 shows the system Bode gain without compensating and with filter SAPPF for values of k =20 and k =80. With the first value is found that in the case of an undistorted supply voltage the system gain is about -40 dB.
0
-10
From: vs
Bode Diagram
From: iL
-20
-30
-40
-50
-60
-70
-80
10
1
10
2
Without filters
10
3
10
4
10
1
Frequency (Hz)
With k=20
Fig. 3. Bode diagram
10
2
10
3
With k=80
10
4

k =20 is not enough to obtain a gain of less than -40 dB. This objective is found when k =80, as it is shown in the Bode diagram on the left of Fig 3.
Regarding the system stability, with k =20 and k =80 the system has all its poles and zeros in the right half plane, so that the system is stable.
On the other hand, when the supply voltage is distorted,
IV.
E XPERIMENTAL R ESULTS
An experimental prototype of the circuit shown in Fig. 1 has been implemented. The system is supplied by a programmable three-phase source, the California Instruments
4500-iL model. The source impedance is constituted by a resistor, R
S
=1.31 Ω and an inductance, L
S
=2.34 mH. The passive filter parameters are shown in Table I. The active filter consists of an IGBT bridge of three SKM50GB123 modules from Semikron. A source is connected at the inverter dc side to maintain the capacitor voltage at V dc
=100 V. The inverter output includes an LC filter to eliminate voltage ripple. The element values are: C
F
=50 µ F, L
F
=0.13mH.
The nonlinear load consists of three single-phase uncontrolled rectifier connected between phase and neutral wires. This is an IR 36MT60-type three-phase bridge with an inductance of 55 mH in series with a resistance of 16.7 Ω at the dc side.
Two types of tests have been considered: the first one using sinusoidal voltage source and the second one using nonsinusoidal voltage source. In the first test the voltage source generates a balanced sinusoidal waveform, 50 Hz frequency and phase voltage of 100 V. When the active and passive filters are disconnected, the waveforms shown in Fig.
4a are obtained. The voltage has a 5.1 % THD and the source current a 22.2% THD. a)
Voltage b)
Current
Current
Voltage
Fig. 4. Voltage and current, CSH load with sinusoidal voltage source: a) without filter; b) with filters. Voltage, 48V/div, current, 10 A/div
Both waveforms are characterized by presenting odd harmonics. The voltage rms value is 98.8 V and the current applied to the active filter. The k value is fixed to 20 according to previous analysis. The voltage THD at the point of common coupling is 0.9 % and the source current THD is
2.5 %. This strategy reduces the THD corresponding to both signals. The measured rms values are 100.0 V for the voltage and 4.1 A for the source current.
The active, reactive and apparent powers per phase are
P=0.40 kW, Q=0.09 kvar and S=0.70 kVA. This increase in active power is mainly due to the power consumed by the parallel passive filter. The power factor is 0.98 capacitive, since LC branch is capacitive at the fundamental frequency.
The current waveforms through the neutral wire before and after of the compensation are shown in Fig. 5. Without filters this current has an rms value of 0.4 A. The most significant harmonic is the 3 rd with 0.3 A of rms value. When the SAPPF is connected the neutral current is reduced to 0.1 A. rms value 4.2 A. The most significant harmonics are the 3
5 th and 7 rd th . The active, reactive and apparent powers per phase are: P=0.38 kW, Q=0.15 kvar and S=0.68 kVA. The load has a power factor of 0.93 inductive. The Table II shows the result obtained.
Fig. 4b shows the voltage waveform at point of common coupling and source current waveforms when the compensation equipment is connected. The CVD strategy is a) b)
Fig. 5. Neutral current, CSH load with sinusoidal voltage source: a) without filter; b) with filters. Current, 4 A/div
Table II summarizes the measured data in each experiment.
From the point of view of eliminating harmonics, when the supply voltage is sinusoidal
In the second test the SAPPF filter is connected to a distorted supply voltage. The load is the same as in the first test. The 4500-iL source is programmed to generate a 5 th harmonic of 12% of the fundamental harmonic. Fig. 5 shows the source current and the voltage at the point of common coupling waveforms before and after connecting the active filter.

T ABLE II.
E XPERIMENTAL R ESULTS WITH S INUSOIDAL S OURCE AND CSH
T YPE L OAD .
(1) W ITHOUT F ILTERS ; (2) W ITH F ILTERS
THD
(%)
RMS H1 H3 H5 H7 H9 H11 H13
P
(kW)
V 5.1 98.8 97.9 2.4 2.2 2.0 1.8 1.5 1.2
I 22.2 4.2 4.1 0.7 0.4 0.3 0.2 0.1 0.1
Q
(kvar)
S
(kVA)
PF
0.38 0.15 0.41
0.93
Ind.
I n
0.4 0.1 0.3 0.0 0.0 0.1 0.0 0.0
V 0.9 100.0 100.0 0.3 0.1 0.1 0.2 0.2 0.2
I 2.5 4.1 4.1 0.1 0.0 0.0 0.0 0.0 0.0
I n
0.1 0.1 0.0 0.0 0.0 0.0 0.0 0.0
0.40 0.09 0.41
0.98
Cap.
Before the compensation the THD voltage at the point of common coupling is 11.5 % and its rms value is 97.9 V. The source current has a THD of 25.7 % and rms value of 4.2 A.
On the other hand, active, reactive and apparent power per phase are P=0.39 kW, Q= 0.15 kvar, S=0.42 kVA and the power factor is 0.94 inductive. a)
The compensation equipment is connected to the system and the CVD strategy is applied with k =80. This value was obtained from the analysis of the state model in previous section. The voltage and current waveform are shown in Fig.
6b. The THD voltage is 12.0 %. It is the same value as the supply voltage THD, which is distorted with a 5 th harmonic.
The source current THD is reduced to 3.3 %. So although the supply voltage is distorted it is possible to mitigate the source current harmonic with the proposed strategy. The voltage and current rms value are 100.0 V and 4.1 A respectively. b)
Voltage
Current
Current
Voltage
Fig. 6. Voltage and current, CSH load with nonsinusoidal voltage source: a) without filter; b) with filters. Voltage, 48V/div, current, 10
A/div
The current waveform through the neutral wire before the compensation is shown in Fig. 7a. The rms value is 0.4 A.
When the SAPPF is connected this current rms value is reduced to 0.1 and all the harmonics are null. a) b)
T ABLE III.
E XPERIMENTAL R ESULTS W ITH NO S INUSOIDAL S OURCE AND CSH
T YPE L OAD .
(1) W ITHOUT F ILTERS ; (2) W ITH F ILTERS
THD
(%)
RMS H1 H3 H5 H7 H9 H11 H13
P
(kW)
V 11.5 97.9 97.3 2.6 9.7 2.4 2.1 1.9 1.6
Fig. 7. Neutral current, CSH load with nonsinusoidal voltage source: a) without filter; b) with filters. Current, 4 A/div
Table III summarizes the most significant measured values:
THD, harmonics, powers and power factor. The strategy of current and voltage detection (CVD) reduce significantly the source current THD. The proposed design methodology has allowed to minimize the source current distortion for sinusoidal and nonsinusoidal supply voltage.
I n
V 12.0 100.0 99.2 0.2 11.9 0.1 0.0 0.1 0.1
I n
V.
C ONCLUSIONS
Q
(kvar)
S
(kVA)
PF
0.39 0.15 0.42
Ind.
A system dynamic analysis has been carried out by means of the state equations. It has allowed the design guidelines for the APF control to be established. Specifically, using the
CVD compensation strategy, the APF voltage is obtained by a combination of a term proportional to the source current harmonics and another term in opposite to the load voltage harmonics. This requires the specification of the proportionality constant in the first term and the sensitivity of the instrumentation in the second term. In this paper, the analysis has allowed the values of these parameters to be chosen from a reduction in harmonic distortion of source current specified by design.

Finally, the proposed methodology has been applied to an experimental SAPPF using the mentioned compensation strategies. The voltage and current waveforms and the measured results in terms of distortion and power, before and after compensation have been presented.
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