Application of Generalized Instantaneous Reactive/ Non

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Application of Generalized Instantaneous Reactive/
Non-active Power Theories in the Control of Shunt
Active Power Line Conditioners: Practical Evaluation
under Nonideal Voltage and Unbalanced Load
Mihaela Popescu, Alexandra Pătraşcu, and Mircea Dobriceanu
University of Craiova, Faculty of Electrical Engineering, Decebal Bd. 107,
200440 Craiova, Romania
{mpopescu,apatrascu,mdobriceanu}@em.ucv.ro
Abstract. This paper is focused on the practical evaluation of two generalized
theories of powers in phase coordinate system, namely generalized
instantaneous reactive power and generalized instantaneous non-active power,
by their implementation in the real time control of a three-phase three-wire
shunt active power line conditioner through a dSPACE-based platform. Based
on each theory concepts, specific blocks for reference current generation to
achieve the global compensation were conceived first. Then, experimental tests
were conducted to prove the ability of the active filtering system to compensate
a nonlinear distorted and unbalanced load under nonideal voltage conditions.
The good dynamics behaviour of the compensating system is illustrated too.
Keywords: Active power line conditioner, Generalized instantaneous nonactive power theory, Generalized instantaneous reactive power theory, Nonlinear
load.
1
Introduction
For quite a long time, the compensation of the nonlinear and distorted load in electric
power systems is an important topic in the field of power quality improvement due to
the increasingly use of such loads.
Clearly, recent advances in power electronics devices and control make the socalled shunt active power line conditioners (APLCs) or active power filters (APFs)
the more flexible and efficient solution to eliminate the current harmonic distortion
and to compensate both the reactive power and load unbalance.
In order to obtain unity power factor or perfect harmonic cancellation after
compensation irrespective of the supply voltage waveform, many methods of
reference compensating current generation have been adopted until now. Most of
them are time domain based and provide either the current to be compensated or the
desired supply current after compensation.
While the most common approaches involve the transformation from phase
coordinate system to stationary or rotating two-phase system in order to apply the p-q
V.M. Mladenov and P.C. Ivanov (Eds.): NDES 2014, CCIS 438, pp. 125–133, 2014.
© Springer International Publishing Switzerland 2014
126
M. Popescu, A. Pătraşcu, and M. Dobriceanu
theory of the instantaneous reactive power concepts [1], [2] or the id-iq method [3],
[4], there are different approaches whose implementation does not require any
reference frame transformation. This last set refers to the theories such as FryzeBuchholz-Depenbrock (FBD) [5], the generalized instantaneous reactive power [6]
and generalized instantaneous non-active power [7].
The attention in this paper is directed to the two above mentioned generalized
theories and their practical implementation for total compensation in a shunt
compensator through a dSPACE based control system operating together with
Matlab/Simulink software. After a brief description of the compensating system, the
reference current generation algorithms and the associated developed Simulink blocks
are presented. Section 4 refers to the experimental setup and the results achieved
under nonideal voltage and unbalanced load, in order to prove the high performance
of the developed APLC system. At the end, some conclusions are pointed out.
2
APLC System Structure
A shunt APLC including its control system has been developed for experimental
testing. As depicted in Fig. 1, the voltage source inverter is connected to the point of
common coupling (PCC) by an inductive filter.
Power
source
u
Rectifier
load
is PCC
AC controller
load
iL
LC
uDC
iF
Acquisition u
iL
system
iF
APL
C
Nonlinear
load
uDCref
DC
iFlos
voltage
control
Compensating iFref
current
calculation
Current
control
IGBTs’ gating
Control system
Fig. 1. Single-phase block diagram of shunt APLC system
Based on the sensed load currents and supply voltages, the compensating current
calculation block generates the reference currents (iFref) by the real time
implementation of the adopted algorithm. To keep the DC-voltage at its prescribed
value in order to cover the power system losses, the additional compensating current
iFloss, which is an active current, is generated by the DC-voltage control block. The
ability of the current controller to ensure the accurate tracking of the resulting
reference current gives the compensation system efficiency.
Application of Generalized Instantaneous Reactive/ Non-active Power Theories
3
127
Reference Current Generation
The compensation goal taken into consideration in the reference current generation is
to eliminate the load generated harmonics, the load unbalance, as well as the reactive
power. Depending on the current decomposition method, the reference compensating
current supplied to the current controller (iFref) can be provided either directly from
the expression of load current decomposition, or by subtracting the load current (iL)
from the desired (reference) supply current (isref), as follows in the vectorial writing:
i Fref = i sref − i L ,
(1)
where the vector of the line currents is defined as:
i = [i a (t ) ib (t ) ic (t )]T .
3.1
(2)
Generalized Instantaneous Reactive Power Theory-Based Approach
The foundation of the generalized instantaneous reactive power (GIRP) theory for
three-phase power systems, which was introduced by Peng and Lai in 1996, is the
decomposition of the current vector into the instantaneous active component (ip) and
the instantaneous reactive component (iq) [6].
When used to decompose the load current vector (iL), the associated expression is:
i L = i Lp + i Lq .
(3)
Following the GIRP’s theory concepts, the active and reactive current vectors are
expressed by using the instantaneous active power (pL) and the instantaneous reactive
power vector (qL), whose definitions make use of the dot product ( · ) and cross
product ( x ) of voltage and current vectors, i.e.
i Lp = p L (u ⋅ u ) ⋅ u ;
pL = u ⋅ i L ;
i Lq = (q L × u ) (u ⋅ u ) ;
qL = u × iL .
(4)
(5)
The vector u in (4) and (5) corresponds to the three-phase supply voltages system,
u = [u a (t ) u b (t ) u c (t )]T .
(6)
After making evident the average (PL) and oscillatory (pL~) components of pL,
expression (3) of the load current can be written as follows:
i L = PL (u ⋅ u ) ⋅ u − [− p L ~ (u ⋅ u ) ⋅ u − (q L × u ) (u ⋅ u )] .
(7)
Thus, for total compensation, the reference current vector to be extracted from
PCC is:
128
M. Popescu, A. Pătraşcu, and M. Dobriceanu
i Fref = − ( p L − PL ) (u ⋅ u ) ⋅ u − (q L × u ) (u ⋅ u ) .
(8)
The associated block diagram shown in Fig. 2 was created in Matlab/Simulink and
further used for the experimental implementation on a dSPACE-based platform.
Fig. 2. Block diagram for total compensation strategy based on the GIRP theory concepts
As the quantity in the denominator of the active current given in (4) is not constant
when the voltage waveform is distorted, it is expected that the supply current
waveform will be more different compared to the voltage waveform as the voltage
distortion is higher.
3.2
Generalized Instantaneous Non-active Power Theory-Based Approach
The proposal of a generalized decomposition of the load current vector in poly-phase
circuits into the instantaneous active component (iLp) and the so-called instantaneous
non-active component (iLq) belongs to Peng and Tolbert [7]. From the very beginning,
the applicability in shunt compensation was envisaged.
Neglecting the compensator power losses, the active power at the supply side (P)
during an averaging interval TC is equal to the load active power (PL).
As only the active current expression is actually defined and the remaining current
is the non-active component, the calculation of the reference compensating current is
performed by imposing the desired supply current, as required by (1).
The flexibility in implementing the generalized instantaneous non-active power
(GINAP) theory for shunt compensation of the load current comes from the general
expression of the supply active current,
 1
i sref = P U P2 ⋅ u p = 
 TC

u(τ ) ⋅ i L (τ )dτ 
t −TC


t
 1

T
 C

u p (τ ) ⋅ u p (τ )dτ  ⋅ u p ,
t −TC


t
(9)
where the imposed reference voltages in vector up give the resulting waveforms of the
supply line currents.
Thus, when unity power factor (UPF) is the compensation goal, up must be the
voltage vector itself. But, in order to obtain sinusoidal supply currents and unity
displacement power factor, up must contain the fundamental components of u.
In the associated Simulink block diagram shown in Fig. 3, the unity power factor
strategy is implemented and the equivalent conductance is highlighted.
Application of Generalized Instantaneous Reactive/ Non-active Power Theories
129
Moreover, by imposing a proper averaging interval TC in (9) in relation to the
fundamental period of the supply voltage (T), both periodic and non-periodic currents
can be compensated [8], [9].
Fig. 3. Block diagram for UPF compensation strategy based on the GINAP theory concepts
4
Experimental Setup and Results
The experimental tests were conducted on a three-phase 15 kVA laboratory prototype
consisting of an IGBT-based voltage source inverter with a DC-link capacitor of 1100
µF and an inductive filter of 4.4 mH on the AC side. Based on dSPACE DS1103 PPC
controller board with comprehensive I/O, the real-time control system was
implemented via Matlab/Simulink environment. The conceived Simulink model of
the control system illustrates the analog to digital conversion, the generation of the
prescribed currents, the DC-voltage and current control, the digital to analog
conversion and the output signals transfer to the digital I/O channels (Fig. 4). The
start-up process and the required protections are also taken into consideration.
Fig. 4. Compiled Simulink model for the real time control through dSPACE platform
The voltage controller of PI type was designed in accordance with the principle of
Modulus Optimum criterion [10], [11]. The DC-voltage prescribed value is 700 V.
130
M. Popescu, A. Pătraşcu, and M. Dobriceanu
By adopting a sampling time of 20 μs and a hysteresis band of 0.4 A for the current
controller, the IGBTs’ switching frequency was kept below their capability.
One of the nonlinear loads is an AC voltage controller manufactured by Nokian
Capacitors Ltd. and especially aimed for testing, which allows producing an
unbalanced current. It is connected in parallel with a controlled thyristor-bridge
rectifier and acts together as the three-phase nonlinear unbalanced load to be
compensated. A reactive power exists too.
The three-phase nonideal system of supply voltages has an low average harmonic
distortion of 2.4 % and an unbalance factor of about 1.4% (Fig. 5 and Fig. 6).
Fig. 5. The acquired waveforms in the Control Desk panel in the case of GIRP theory
implementation
Fig. 6. The acquired waveforms in the Control Desk panel in the case of GINAP theory
implementation for TC = T =20 ms
Table 1 summarizes the results of the experimental tests conducted for both GIRP
and GINAP based methods of reference current generation. As subharmonic and
interharmonic components exist in the current drawn by the line-commutated loads,
three values of the averaging interval were taken into consideration (i.e. TC = T/2, TC
= T and TC = 2T) for the GINAP based method.
Application of Generalized Instantaneous Reactive/ Non-active Power Theories
131
To quantify the compensation performance, besides the total harmonic distortion
factor (THD) on each phase and its average value (THDe), the three-phase rms value
of the line currents (Ie), the unbalance factor (UF) according to IEC definition,. the
global power factor (PF) and the displacement power factor (DPF) were calculated.
As it can be seen in Table 1 and results displayed in the conceived Control Desk
panel (Fig. 5 and Fig. 6), the compensating system is able to significantly improve the
power quality at the supply side in all experimental tests.
The good dynamics behaviour of the filtering system is shown in Fig. 7. The APLC
is charged for UPF compensation through the reference current calculation according
to GINAP theory for TC = 20 μs. The steady state regime is rapidly established in both
situations of partial coupling of the load and suddenly coupling of the filter.
Table 1. Summary of the compensation performance
ILa
(A)
GIRP
19.3
GINAP - T/2 19.4
GINAP - T 18.8
GINAP - 2T 19.4
GIRP
GINAP - T/2
GINAP - T
GINAP - 2T
ILb
(A)
17.5
17.7
17.2
17.6
ILc
(A)
14.3
14.4
14.2
14.6
ILe
(A)
17.1
17.3
16.8
17.3
Load side
PL THDLa THDLb THDLc THDLe
(W)
(%)
(%)
(%) (%)
8659.0 33.52 31.22 24.37 29.70
8789.1 33.68 30.91 24.63 29.74
8506.9 33.41 31.08 24.35 29.61
8779.3 33.04 30.57 24.67 29.43
Supply side after compensation
PS THDSa THDSb THDSc THDSe
ISa
ISb
ISc
Ise
(A)
(A)
(A)
(A)
(W)
(%)
(%)
(%)
(%)
14.0
14.3
13.9
14.3
14.1
13.8
13.5
14.1
14.4
14.6
14.3
14.7
14.2
14.2
13.9
14.4
9165.4
9281.1
8998.1
9267.3
4.92
5.29
4.69
5.13
5.69
6.21
6.53
6.38
5.58
5.44
5.16
5.56
5.40
5.65
5.46
5.69
(a)
PFL
0.7775
0.7768
0.7769
0.7827
DPFL UFL
(%)
0.8140 15.60
0.8131 15.61
0.8135 15.35
0.8185 15.08
PFS
DPFS UFS
(%)
0.9965
0.9967
0.9971
0.9971
0.9990
0.9987
0.9989
0.9989
1.83
2.93
2.95
2.90
(b)
Fig. 7. Experimental phase voltage and supply for GINAP theory implementation when TC = T
=20 ms: (a) APLC compensates the AC controller current and the rectifier is suddenly
connected; (b) APLC is suddenly connected to compensate the global load.
As the existing power supply in the laboratory provides a low degree of distortion
in the voltage waveform, there is little difference between the results related to GIRP
132
M. Popescu, A. Pătraşcu, and M. Dobriceanu
theory, which was conceived for sinusoidal voltage conditions, and those related to
GINAP theory applied for UPF strategy under distorted voltage conditions. The
implementation of the two strategies gets the supply currents to be almost sinusoidal
and balanced, with a power factor over 0.996. The filtering efficiency, in terms of
ratio of average harmonic distortion factors at the load and supply sides, the highest
value of 5.5 corresponds to GIRP theory, whereas the lowest value (about 5.17)
corresponds to GINAP theory in case of TC = 2T. The unbalance level of the supply
current is of about 5 times lower by implementing the GINAP theory are even over 8
times lower through GIRP theory implementation (Table 1). Though a small degree of
disturbance is identified in the electric power system, the choice of an averaging
interval other then the fundamental cycle does not improve the compensation quality.
5
Conclusions
The GIRP and GINAP theories, both of them associated with the phase coordinate
system, provide the necessary foundation to develop appropriate strategies for the
reference supply current generation in three-phase shunt active line conditioners, so
that the total compensation goal is achieved. The developed algorithms were
successfully tested by experimental tests on a dSPACE DS1103 platform in the case
of distorted and unbalanced load. The good dynamics during compensation is
highlighted too.
References
1. Akagi, H., Kanazawa, Y., Nabae, A.: Instantaneous Reactive Power Compensators
Comprising Switching Devices without Energy Storage Components. IEEE Trans. Ind.
Appl. IA-20(3), 625–630 (1984)
2. Akagi, H., Ogasawara, S., Kim, H.: The Theory of Instantaneous Power in Three-Phase
Four-Wire Systems: A Comprehensive Approach. In: Conf. Rec. IEEE-IAS Annu.
Meeting, pp. 431–439 (1999)
3. Soares, V., Verdelho, P., Marques, P.D.: Active Power Filter Control Circuit Based on
Instantaneous Active and Reactive Current id – iq Method. In: Proc. IEEE PESC, vol. 2,
pp. 1096–1101 (1997)
4. Soares, V., Verdelho, P.: An Instantaneous Active and Reactive Current Component
Method for Active Filters. IEEE Trans. Power Electron. 15(4), 660–669 (2000)
5. Depenbrock, M., Staudt, V., Wrede, H.: A Theoretical Investigation of Original and
Modified Instantaneous Power Theory Applied to Four-Wire Systems. IEEE Trans. Ind.
Appl. 39(4), 1160–1167 (2003)
6. Peng, F.Z., Lai, J.S.: Generalized Instantaneous Reactive Power Theory for Three-Phase
Power Systems. IEEE Trans. Instrum. Meas. 45(1), 293–297 (1996)
7. Peng, F.Z., Tolbert, L.M.: Compensation of Nonactive Current in Power SystemsDefinitions from a Compensation Standpoint, pp. 983–987. IEEE Power Eng. Society
Summer Meeting, Seattle (2000)
8. Xu, Y., Tolbert, L.M., Peng, F.Z., Chiasson, J.N., Chen, J.: Compensation-Based Nonactive Power Definition. IEEE Power Electronic Letters 1(2), 45–50 (2003)
Application of Generalized Instantaneous Reactive/ Non-active Power Theories
133
9. Tlusty, J., Svec, J., Sendra, J.B., Valouch, V.: Analysis of Generalized Non-active Power
Theory for Compensation of Non-Periodic Disturbances. In: International Conference on
Renewable Energies and Power Quality, Santiago de Compostela (2012)
10. Popescu, M., Bitoleanu, A.: Control Loops Design and Harmonic Distortion Minimization
in Active Filtering-Based Compensation Power Systems. Internat. Review Modelling and
Simulations 3(4), 581–589 (2010)
11. Popescu, M., Bitoleanu, A., Suru, V.: A DSP-based implementation of the p-q theory in
active power filtering under nonideal voltage conditions. IEEE Trans. Ind. Informat. 9(2),
880–889 (2013)
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