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A new control strategy for active power line conditioner (APLC) using adaptive notch filter
Electrical Power and Energy Systems 47 (2013) 31–40
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Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes
A new control strategy for active power line conditioner (APLC) using adaptive notch filter Abbas Ketabi a,⇑, Mohammad Farshadnia a, Majid Malekpour a, Rene Feuillet b a b
Department of Electrical Engineering, University of Kashan, Kashan, Iran Laboratoire d’Electrotechnique de Grenoble, INPG/ENSIEG, Grenoble, France
a r t i c l e
i n f o
Article history: Received 29 July 2011 Received in revised form 30 July 2012 Accepted 27 October 2012 Available online 5 December 2012 Keywords: Shunt active filter Unbalanced conditions Harmonics Adaptive notch filter Power flow control Power quality
a b s t r a c t This paper proposes a new adaptive control algorithm for a three-phase current-source shunt active power-line conditioner (APLC) operating under unbalanced and distorted network conditions. This control scheme aims at compensation of network’s reactive power, elimination of active power’s oscillating components, compensation of network current and voltage harmonic contents resulting in sinusoidal waveforms, and equilibrating the drawn power from the source evenly between the three-phases. Unlike many of the existing methods, the proposed strategy does not require any coordinate transformations or complicated calculations. The reference signals for the hysteresis-band current controlled voltage-source converter (HBCC-VSC) are generated by passing the measured current and voltage signals through two layers of modified adaptive notch filters (ANFs). To ensure superb performance and minimum total harmonic distortion (THD) level of the power system, parameters of the HBCC-VSC are obtained using differential evolution (DE) optimization algorithm. The proposed strategy is simple, easily implementable, and robust against uncertainty or variations of power system parameters and loads. The effectiveness of the proposed control scheme is validated by simulation results of a selected network under various load and power system conditions. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction Growing use of nonlinear equipments and in particular power electronic devices has led to intense propagation of harmonic contents in power systems. If this harmonic pollution is left unattained, the quality of the supplied power will dramatically reduce. Many papers have addressed this issue and have proposed methods for compensating harmonics [1–3]. According to IEEE Standard 519-1992 [4], the maximum allowable total harmonic distortion (THD) for distribution lines, i.e. 69 kV and below, is 5%. Another significant problem in power systems, especially transmission lines is reactive power. Various types of compensators have been developed for resolving this issue and setting the power factor near unity [1,5,6]. The author in [6] has reviewed the most general concepts of power factor correction for polyphase systems. In addition to reactive power, elimination of active power’s oscillating component is also crucial. This is to draw a non-oscillating amount of instantaneous active power from the source [7]. Facing unbalanced loads, another objective in the three-phase power systems is equilibrating the transferred energy evenly between the three phases of the transmission lines, leading to a three-phase balanced set [7,8]. ⇑ Corresponding author. Tel.: +98 3615555333; fax: +98 3615559930. E-mail address: [email protected] (A. Ketabi). 0142-0615/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijepes.2012.10.063
The ability of active power filters (APFs) and active power line conditioners (APLCs) in achieving one or all of the above mentioned objectives and their performance quality directly depends on their control method, i.e. reference signal generating algorithm. These control schemes are mainly based on the instantaneous reactive power theory also known as the p–q theory, first introduced by Akagi in 1984 [5], the improved instantaneous active and reactive current component theory [9,10] the modified p–q theory [2,11], the d–q or park transformation [12], the p–q–r reference frame [13], and the synchronous reference frame theory [14]. All these methods use coordinate transformations in order to generate the required reference signals. A comparative study on these control methods is carried out in [15]. Despite the massive and complex calculations of these methods, their resultant THD level can rise up to 10% which is higher than the maximum allowable values according to IEEE Standard 519-1992 [4]. Moreover, in general unbalanced and non-sinusoidal conditions, special considerations must be taken into account. Other advanced techniques used to improve the performance of APLCs and APFs are wavelet theory, fuzzy logic, resonant controllers, artificial neural networks (ANNs), hybrid APFs, and prediction control based schemes [3,16–20]. In [16], the fundamental components of voltages and currents are extracted using wavelet-transform decomposition. The required reference signals for a UPQC active filter are then generated using the positive sequence of these
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A. Ketabi et al. / Electrical Power and Energy Systems 47 (2013) 31–40
voltages and currents. The drawbacks of this strategy are its complexity and the requirement for two voltage source converters (VSCs) rather than one. The authors in [17] have applied Takagi–Sugeno type fuzzy controller to an APF for power quality improvements and reactive power compensation, however despite the achieved improvements, it is not applicable to practical systems since the three-phase voltages are assumed to be balanced and sinusoidal. Resonant-type compensators are another type of current control methods that require a careful and complicated design. A resonant-type controller for a Shunt APF is designed using genetic optimization algorithm in [18]. This approach is capable of compensating the harmonic contents of the current. However, the resultant THD, although below 5%, is near the maximum allowable boundary, which is quite high comparing to other methods. Moreover it requires other considerations in order to compensate reactive power and other common distortions of the power system. Another promising method for reference signal generation is utilization of ANNs. An example of this type of APF is represented in [3] where an Adaline ANN is trained to generate the required voltage component for recovering the system voltage to a balanced set, and another Adaline ANN extracts the current’s harmonic contents. The required reference signals for the APF are then generated using these outputs. Hybrid shunt APF is another topology in which the APF is connected to the network thorough a passive filter. Reduction of VSC voltage magnitude and thus utilizing lower rated and cheaper switching devices are the main advantages of hybrid shunt APFs [19]. Prediction control based reference signal generating schemes have also been addressed in the literature as effective control strategies for APFs, where the reference current signal is calculated based on the predicted current value of the system [20]. These schemes require the load to have slow dynamics and are not applicable to systems with rapidly varying or unpredictable loads, thus are not suitable for practical networks. An approach for extraction of active and reactive currents and harmonic components of a single-phase system using two enhanced phase-locked loops (EPLLs) is presented in [21]. Inspired by this work, a new signal generating approach for APFs operating in unbalanced and distorted three-phase networks is proposed here. The main objectives of this approach are compensation of the reactive power, elimination of active power’s oscillating component, compensation of the harmonic contents of currents and voltages, and equilibration of the transferred energy through the transmission lines evenly between the three phases in order to obtain a three-phase sinusoidal balanced set. The proposed strategy consists of two layers of adaptive notch filters (ANFs), connected in series, such that the outcome of the second layer is the input reference signal to a hysteresis-band current controlled voltagesource converter (HBCC-VSC). In addition, in order to acquire optimum results, internal parameters of the ANFs are tuned globally using differential evolution (DE) optimization algorithm. The parameters of the HBCC-VSC are also obtained using DE algorithm in order to have the least THD level in the compensated network.
This paper is organized as follows. In Section 2, a brief overview on ANF is presented and it is globally tuned using DE optimization algorithm. The proposed compensation strategy is presented in Section 3. Section 4 is dedicated to describing HBCC-VSC and the procedure of obtaining its parameters using DE optimization algorithm. In Section 5, simulation results on a realistic power system model under different conditions and loads are presented. Finally Section 6 is devoted to the conclusions. 2. Adaptive notch filter 2.1. Overview Notch filter is a linear time-invariant structure that multiplies its input signal in a gain equal to unity in all frequencies except the notch frequency, in which the gain is null. Therefore, all frequencies except the notch frequency will exist in the frequency spectrum of the filter’s output signal. If the filter becomes capable of locking the notch frequency on the fundamental frequency of the input signal and tracking it accordingly, it is then called an adaptive notch filter (ANF) [22]. Here, a modified version of the lattice-based discrete-time ANF [22,23] with the following dynamic behavior is employed:
€x þ h2 x ¼ 2nheðtÞ h_ ¼ cxheðtÞ
ð1Þ
eðtÞ ¼ uðtÞ x_ where u(t) is the input signal, h is the estimated angular frequency, and n and c are real positive numbers that determine the performance of the ANF in terms of accuracy and convergence speed, respectively. Note that there is always a trade-off between these two parameters. The block diagram of the introduced ANF is shown in Fig. 1. Stability analysis of the ANF characterized by (1) and its convergence to a unique periodic orbit are presented in [22–24]. For a sinusoidal input u(t) = A sin (xt + u), i.e. the measured voltage or current of the network, the presented dynamic system converges to a unique periodic orbit as follows [22,23]:
0 1 0 A 1 x x cosðxt þ uÞ B C B C O ¼ @ x_ A ¼ @ A sinðxt þ uÞ A h
ð2Þ
x
In the above equations, A is the input signal amplitude, x is the angular frequency, and u is the phase. According to (2), the amplitude of the input signal fundamental component can be obtained by
A¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi _ 2 þ ðhxÞ2 ðxÞ
ð3Þ
The system described by (2) is robust against noise, disturbances, distortions, and other pollutions of the power system and can successfully follow fundamental frequency variations of the input signal [24]. 2.2. Parameter tuning
Fig. 1. Block diagram of the modified ANF.
The values of ANF’s internal parameters, n and c, depend on its application and desired output. Here, fast and accurate extraction of the input signal fundamental component is desired. In order to have the best performance the internal parameters have to be determined with extra care. Therefore, DE optimization algorithm is employed to obtain their optimum values. In order to tune the ANF, a distorted signal with a wide range THD, as depicted in Fig. 2a, is considered as the input. The cost function of the optimization procedure is defined as the weighted
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A. Ketabi et al. / Electrical Power and Energy Systems 47 (2013) 31–40
Input Signal
Section 1
Section 2
Table 1 DE optimization algorithm parameters.
Section 3
1
Population size (Np)
Step size (s)
Crossover rate (CR)
0
100
0.5
0.7
-1 Table 2 Boundaries and optimum values of n and c.
Fundamental Component
(a) 1
n
c
0
Maximum value
Optimum value
0.0 50.0
2.0 10000.0
0.1675 178.3672
-1
FðtÞ ¼ F h ðtÞ þ F f ðtÞ
(b) Harmonic Component
Minimum value
1 0 -1 0
0.05
0.1
0.15
0.2
Time (s)
(c) Fig. 2. Performance of the ANF with its internal parameters set to the optimal values obtained by DE method: (a) input signal with a wide range THD, (b) extracted fundamental component, (c) extracted harmonic content.
sum of the output THD values. These values are measured 1.8 cycles after occurrence of each change of THD in the input signal. The associated weights to the THD values in the cost function are 2, 1.5 and 1, respectively as the THD of the input signal reduces. The chosen DE parameters for this optimization problem are shown in Table 1. In addition, a boundary should be defined for each tuning parameter. These boundaries are chosen based on experience and are shown in Table 2 along with the obtained optimum values of n and c. Performance of the optimally tuned ANF for an input signal with the wide range THD is illustrated in Fig. 2. THD of the input signal in sections 1, 2, and 3 are 48.342%, 28.738%, and 12.115%, respectively. The associated steady-state THDs of the extracted fundamental component at these sections are 4.474%, 3.412%, and 1.417%, respectively, which are satisfactory. Note that since in the proposed control method, the input signal passes through two layers of ANFs, the resultant THD will become smaller, as will be seen in Section 5. 3. Proposed compensation strategy The proposed compensation strategy provides the HBCC-VSC with the required reference signal for compensating the power system. This reference signal is generated using two signal processing layers, as explained in the follows. The first layer’s duty is to extract the so-called active current of each phase according to the extracted voltage and current fundamental components. This is the required current in order to have zero reactive power. The second layer’s duty is to equilibrate the drawn power by unbalanced loads evenly between the three phases, which will result in a threephase balanced set as well as elimination of active power’s oscillating part caused by unbalanced situations. The inputs to the first layer are the measured voltages and currents of the power system, and its outputs are the inputs to the second layer. It has to be noted that both layers effectively use ANFs to calculate the outputs. The measured power system quantities, i.e. current and voltage, can be decomposed into two components, the harmonic component and the fundamental component, as
ð4Þ
in which F(t) denotes the measured power system quantity, Fh(t) is its harmonic component, and Ff(t) is its fundamental component. This decomposition is performed using ANFs. The fundamental component of each phase’s line-current, if(t), can be further decoma posed into two other components, namely the active current, if ðtÞ, r and the reactive current, if ðtÞ: a
r
if ðtÞ ¼ if ðtÞ þ if ðtÞ
ð5Þ
The active and reactive currents in the above equation can be obtained using the following expressions [21] a
if ðtÞ ¼ I cosð/i /v Þ sinð/v Þ r
if ðtÞ ¼ I sinð/i /v Þ cosð/v Þ
ð6Þ
where I is the amplitude of if(t), /i is the total phase of if(t) and /v is the total phase of the relative phase-to-ground voltage fundamental component. Rearranging (6), we get a
if ðtÞ ¼ I cosð/i cos /v Þ þ I sinð/i Þ sinð/v Þ sinð/v Þ r
if ðtÞ ¼ I sinð/i Þ cosð/v Þ I cosð/i Þ sinð/v Þ cosð/v Þ
ð7Þ
According to (2), the above equations are in the perfect form for being implemented using two ANFs, one for the voltage and one for the current, as illustrated in Fig. 3. In this figure, i(t) and v(t) are the measured line-current and phase-to-ground voltage, respectively. The proposed APLC control scheme is based on the extracted active current, hence only the active current extraction section of Fig. 3 is required. The first layer consists of three sets of this active current extraction unit in order to simultaneously extract the active currents of all phases. The second layer has the duty of equilibrating the drawn power from the source evenly between the three phases and shaping the system’s current waveforms as a three-phase balanced set. Since the power system is assumed to be three-wire, this is easily done by eliminating the negative sequence of the three-phase active currents. The positive sequence of the three-phase active currents are obtained by
Fig. 3. Block diagram of the active and reactive current extractor using two ANFs.
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A. Ketabi et al. / Electrical Power and Energy Systems 47 (2013) 31–40
a;P 1 0 if ;A 1 B a;P C 1 B B i C ¼ @ a2 @ f ;B A 3 a;P a if ;C
0
a 1 a2
10
a
1
if ;A a C CB B a A@ if ;B C A a 1 if ;C
a2
ð8Þ
where the subscripts A, B, and C denote the different phases of the system, the superscript P denotes positive sequence component, and a is a 120° phase shift and can be expressed as the sum of a constant gain and a 90° phase-shift [25]: 2p
a ¼ ej 3
pffiffiffi 1 3 ¼ þj 2 2
ð10Þ
In (9) and (10), j is the imaginary unit and acts as a 90° phaseshifter. Substituting (9) and (10) in (8) yields
1 a a a a 16 if ;B þ if ;C þ 2pj ffiffi3 if ;B if ;C B C C B a;P C B a;P a;P C Bi C ¼ B þ I I f ;A f ;C C @ f ;B A B @ A a;P a a a a j ffiffi 1 a 1 if ;C p i 6 if ;A þ if ;B þ 2 3 if ;A if ;B 3 f ;C 0
a;P
if ;A
1
0
ifek > HB ) Gkþ ¼ 1; Gk ¼ 0
ð13Þ
ifek < HB ) Gkþ ¼ 0; Gk ¼ 1 ref
ð9Þ
Similar to (9), a2 can be expressed as
pffiffiffi 1 3 2p a2 ¼ ej 3 ¼ j 2 2
its input reference signal always remains within a specific tolerance band, i.e. the hysteresis band (HB). Fig. 5a demonstrates the basic configuration of a HBCC-VSC connected to the grid through three single-phase transformers, and Fig. 5b illustrates VSC’s output current waveform. The switching logic can be expressed as follows
1 a i 3 f ;A
where k = A, B, C indicates the phase, ek ¼ ik Imeas is the error bek tween the reference value and the measured output current Imeas , k Gk+ and Gk- are the generated IGBT gate signals, and HB is the value of the hysteresis band. Advantages and disadvantages of HBCC strategy and its comparison with other methods are reviewed in [26]. As it is realizable form Fig. 5, performance of the HBCC-VSC is directly affected by the choices of L, Cdc, and HB. Hence, extra care should be taken when specifying their values. Similar to the tuning procedure of ANFs in Section 2, these values are determined using DE algorithm as described in the follows.
ð11Þ 4.2. Determining L, Cdc, and HB
The system described by (11), constructs the second layer using three more ANFs, as illustrated in Fig. 4. These ANFs also act as three necessary low-pass filters at the entrance of the second layer. The generated positive sequence signals in the output of the second layer are then subtracted from the measured currents in order to produce the required reference signals by the HBCC-VSC:
Optimal values of L, Cdc, and HB, should be obtained based on the nominal MVA of the system and the minimum THD level of the three-phase network. Similar to the tuning procedure of the ANFs, the chosen cost function for the optimization algorithm is the weighted sum of voltage and current THDs at different instants, and is given by
8 ref meas a;P > iA ¼ iA if ;A > > > > < ref meas a;P iB ¼ iB if ;B > ref meas a;P > iC ¼ iC if ;C > > > :
CF ¼ W 1 THDv ðt 1 Þ þ W 2 THDi ðt 2 Þ þ W 3 THDi ðt3 Þ ð12Þ
In (12), the superscript ref identifies the reference currents, and the superscript meas denotes the measured currents. 4. APLC structure 4.1. Principles of an HBCC-VSC Hysteresis-band current control (HBCC) method is a procedure of instantaneously controlling the output current of a VSC. This is done by instantaneously comparing the VSC’s output current with its input reference signal and changing the switching sequence of the VSC in accordance. The error between the output current and
ð14Þ
where the subscripts v and i denote voltage and current, t1, t2, and t3 are the moments at which the value of THD is considered, W1, W2, and W3 are weights equal to 1, 2, and 2.5, respectively. The chosen cost function aims at decreasing the THD level as much as possible. t1, t2, and t3 are 1.8 cycles after the moments at which extreme disturbances happen in the network. Note that the associated weights to the measured THDs in (14) are relevant to the level of the occurred disturbance in the system. Since harmonic and unbalanced load currents are the main cause of voltage unbalances and harmonic voltage drops, they have a higher priority in the optimization procedure. Therefore, the associated weights to the current THDs are larger than that of the voltage THD. Tuning of the APLC using the explained procedure will be carried out in Section 5. 5. Simulation results In this Section the proposed compensation strategy will be evaluated under common situations of the power system, i.e. balanced nonlinear loads, unbalanced nonlinear loads, unbalanced unpredictable nonlinear loads, and change of the power supply thevenin equivalent impedance, Z. Fig. 6 illustrates the schematic diagram of the simulated power system. In the simulations, PI line model is used to characterize the transmission line behavior. The proposed compensation strategy is validated in terms of the resultant voltage and current THDs, three phase active and reactive powers, power factor, and voltage and current unbalance factors (VUF and CUF), given by:
Unbalance factor ¼
Fig. 4. Block diagram of positive sequence extractor using three ANFs.
negativ e sequence component 100 positiv e sequence component
ð15Þ
In order to tune the APLC’s parameters as described in the previous section, a balanced nonlinear load is applied to the system. Afterward, parameters of the APLC, i.e. HB, L, and Cdc, are tuned
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A. Ketabi et al. / Electrical Power and Energy Systems 47 (2013) 31–40
Current
(a)
Time
(b) Fig. 5. HBCC-VSC: (a) basic configuration, (b) the output current in the 20% hysteresis band.
using DE algorithm such that (14) becomes minimum. The DE algorithm internal parameters are as shown in Table 1. The obtained optimal APLC parameters for the nonlinear load of case-study 1 are shown in Table 3. Note that although these parameters are obtained for the balanced nonlinear load of case-study 1, they are applicable to other loads of the system, as it is clearly seen in case-studies 2 and 3.
25kV/600V Z 25kV/60Hz 10MVA
70 Km Line
A 25kV/600V
S1
Nonlinear load#1
Nonlinear load#2
25kV/600V
APLC Fig. 6. Schematic diagram of the simulated three-phase power system.
5.1. Case-study 1 – balanced nonlinear loads In this part, performance of the proposed APLC is studied in presence of nonlinear loads. For better demonstration of the performance, a sudden change in the load is happened after t = 0.05 s. Fig. 7 shows the instantaneous active power, reactive power, current, and voltage waveforms measured at point A of Fig. 6 whilst switch S1 is open. Since the load is assumed to be balanced, voltage and current waveforms of a single phase is only represented here. By activating the APLC and closing switch S1, the three-phase system is compensated. Fig. 8 demonstrates the characteristics of the compensated system. Variations of the power factor before and after the compensation are illustrated in Fig. 9. Voltage profile of the APLC’s DC-link is also shown in Fig. 10. Comparing Figs. 7 and 8, one can see that using the proposed compensation strategy, oscillations of the active power is
Table 3 Boundaries and optimum values of HB, L and Cdc.
HB L (H) Cdc (F)
Minimum value
Maximum value
Optimum value
0.005 1e7 1e6
0.5 1e2 1e1
0.1079 9.0093e5 0.04843
Voltage (kV)
A. Ketabi et al. / Electrical Power and Energy Systems 47 (2013) 31–40
Voltage (kV)
36
20 0 -20
20, 0 -20,
(a) Current (A)
Current (A)
(a) 10 0 -10
10 0 -10
(b) p(t) (MW)
p(t) (MW)
(b) 0.4 0.2
0.4 0.2 0
0
(c) 0.3
0.3
q(t) (MVar)
q(t) (MVar)
(c) 0.2 0.1 0
0
0.05
0.1
0.15
0.2 0.1 0 0
0.2
0.05
Time (s)
5.2. Case-study 2 – unbalanced nonlinear loads In this case-study the nonlinear load is assumed to be unbalanced. Similar to the previous case-study, a sudden change in the
0.2
Power Factor
Fig. 8. Compensated system with balanced nonlinear loads: (a) voltage of phase A, (b) current of phase A, (c) instantaneous active power, (d) instantaneous reactive power.
1 0.9 0.8 0.7
Power Factor
(a) 1 0.998 0.996 0
0.05
0.1
0.15
0.2
Time (s)
(b) Fig. 9. Power factor of the system with balanced nonlinear loads: (a) before the compensation, (b) after the compensation.
DC-link Voltage (V)
effectively damped and the reactive power is effectively compensated such that power factor is near unity, Fig. 9. Moreover the harmonic content of voltage and current is eliminated and their waveforms have become smoother and sinusoidal. Table 4 lists voltage and current THDs of the network before and after the compensation in comparison with the performance of the conventional p–q theory-based scheme. As it is evident, using the proposed strategy, THDs of both current and voltage have reduced to a great extent such that voltage THD value has reduced from 10.96% and 11.262% to 0.153% and 0.758%, respectively. Current THD has also reduced from 9.427% and 16.781% to 0.5% and 1.58%, respectively. These resultant THDs are much lower than the maximum allowable THD for distribution systems. The maximum CUF and VUF have also reduced from 4.547% and 0.638% to 1.57% and 0.184%, respectively. According to Table 4, compared to the performance of the conventional p–q theory-base scheme, the proposed scheme represents superior performance in case of both current and voltage THD correction, and CUF and VUF reduction. The same statement can be made about achieving smoother and non-oscillating instantaneous active power. The conventional scheme has a better performance in case of compensating the reactive power oscillations in the instant of the sudden change in the load, such that a smoother characteristic is achieved, but the resultant average reactive power is almost the same. In case of power factor, the conventional scheme represented almost the same results as that of the proposed scheme.
0.15
(d)
(d) Fig. 7. Uncompensated system with balanced nonlinear loads: (a) voltage of phase A, (b) current of phase A, (c) instantaneous active power, (d) instantaneous reactive power.
0.1
Time (s)
820 800 780 760 0
0.05
0.1
0.15
Time (s) Fig. 10. APLC’s DC-link voltage in case-study 1.
0.2
37
A. Ketabi et al. / Electrical Power and Energy Systems 47 (2013) 31–40 Table 4 THDs of currents and voltages of the system of case-study 1.
Uncompensated system THD of voltage (%) THD of current (%) Maximum VUF (%) Maximum CUF (%)
Before t = 0.05 s
After t = 0.05 s
10.96 9.427
11.262 16.781 0.638 4.547
Compensated system using the proposed strategy THD of voltage (%) 0.153 THD of current (%) 0.5 Maximum VUF (%) Maximum CUF (%)
0.758 1.58 0.184 1.57
Compensated system using the conventional p–q theory-based strategy THD of voltage (%) 8.854 1.853 THD of current (%) 10.352 3.154 Maximum VUF (%) 0.398 Maximum CUF (%) 4.024
5.3. Case-study 3 – change of the power supply thevenin equivalent impedance under unbalanced unpredictable nonlinear loads Since APLCs are commonly installed permanently, their performance has to be robust against variations of power system param-
Voltage (kV)
Voltage (kV)
load happens after t = 0.05 s. The three-phase current and voltage of the uncompensated system is shown in Fig. 11. This system is compensated by the same APLC used in case-study 1, and the results are shown in Fig. 12. Table 5 lists the associated current and voltage THD values. This table implies that the proposed APLC has effectively eliminated the current and voltage harmonic contents, such that the maximum THD of the compensated voltage is 0.16% which is near ideal. The maximum THD of the current is also 2.37% which represents a satisfactory value. In addition to currents and voltages, comparing Figs. 11 and 12, one can see that using the proposed APLC, the active power’s oscil-
lating component is eliminated. Likewise, the reactive power of the network is also compensated such that the resultant power factor is near unity, Fig. 13. Moreover, the proposed APLC has successfully equilibrated the load evenly between the three phases, thus resulting in a three phase balanced set: the maximum CUF and VUF has reduced from 49.02% and 1.742% to 2.831% and 0.073%, respectively. The voltage characteristics of the APLC’s DC-link is also illustrated in Fig. 14. Table 5 also includes the achieved results by the conventional p–q theory-based scheme. These results indicate that the proposed scheme has a far superior performance compared to the conventional scheme in case of both current and voltage THD correction, and CUF and VUF reduction. Unlike the proposed method, because of the conventional scheme’s lack in complete correction of current and voltage THDs, CUF and VUF, the resultant instantaneous active power includes oscillations but with lower amplitudes compared to the uncompensated system. The same statement can be made about the instantaneous reactive power, however it has a zero average value with oscillation amplitude of below 10 KVar which is negligible. In case of power factor, the conventional scheme represented slightly lower results compared to the proposed scheme, but is still satisfactory and above 0.98.
20 0 -20
20 0 -20
(a) Current (A)
Current (A)
(a) 10 0 -10
10 0 -10
(b) p(t) (MW)
p(t) (MW)
(b) 0.3 0.2 0.1
0.3 0.2 0.1 0
0
(c)
(c) 0.3
q(t) (MVar)
q(t) (MVar)
0.3 0.2 0.1 0 -0.1 0
0.05
0.1
0.15
0.2
0.2 0.1 0 -0.1 0
0.05
0.1
Time (s)
Time (s)
(d)
(d)
Fig. 11. Uncompensated system with unbalanced nonlinear loads: (a) three phase voltage, (b) three-phase current, (c) instantaneous active power, (d) instantaneous reactive power.
0.15
0.2
Fig. 12. Compensated system with unbalanced nonlinear loads: (a) three phase voltage, (b) three-phase current, (c) instantaneous active power, (d) instantaneous reactive power.
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A. Ketabi et al. / Electrical Power and Energy Systems 47 (2013) 31–40
Table 5 THDs of currents and voltages of the system of case-study 2.
Uncompensated system Phase A THD of voltage THD of current Phase B THD of voltage THD of current Phase C THD of voltage THD of current Maximum VUF (%) Maximum CUF (%)
(%) (%) (%) (%) (%) (%)
Before t = 0.05 s
After t = 0.05 s
6.678 31.188 4.401 25.412 5.605 8.027
8.825 69.117 5.484 16.52 7.328 47.687 1.742 49.02
proposed strategy (%) 0.124 (%) 0.804 (%) 0.102 (%) 0.791 (%) 0.16 (%) 0.791
Compensated system using the Phase A THD of voltage THD of current Phase B THD of voltage THD of current Phase C THD of voltage THD of current Maximum VUF (%) Maximum CUF (%)
conventional p–q theory-based strategy (%) 5.443 5.627 (%) 13.415 15.073 (%) 12.589 4.492 (%) 18.491 13.486 (%) 11.356 4.422 (%) 18.328 23.645 0.703 20.98
0.085 2.032 0.076 2.37 0.086 2.296 0.073 2.831
1 0.8
Voltage (kV)
0.6
Power Factor
(a) 1
20 0 -20
0.995
(a)
0.99 0
0.05
0.1
0.15
0.2
Time (s)
(b)
Current (A)
Power Factor
Compensated system using the Phase A THD of voltage THD of current Phase B THD of voltage THD of current Phase C THD of voltage THD of current Maximum VUF (%) Maximum CUF (%)
Here, a 25% increase in Z is considered and performance of the proposed APLC is evaluated. Such increase in Z, causes the shortcircuit level of the source to decrease by 20%. Therefore, the resultant short-circuit level of the source would become 8 MVA. Unlike the previous case-studies, the aggregated load of this case-study does not vary on a regular basis and is not predictable. Note that parameters of the APLC used in this case-study are similar to those of case-studies 1 and 2. Fig. 15 shows the characteristics of the uncompensated system and Fig. 16 illustrates those of the compensated system. Note that after t = 0.03 s, the aggregated load is randomly varying. The values of voltage and current THDs in certain randomly chosen cycles after t = 0.03 s for both uncompensated and compensated systems are listed in Table 6. These values show that the proposed APLC has effectively eliminated the harmonic content of currents and voltages. According to Figs. 15 and 16, the APLC has also successfully compensated the reactive power and set the power factor near unity as it is illustrated in Fig. 17. Moreover the oscillating part of the active power is eliminated. The outcome is a set of perfectly balanced sinusoidal waveforms such that the maximum CUF has reduced from 21.917% to 2.207%, Likewise maximum VUF has reduced from 1.327% to 0.115%. It is evident that the proposed APLC can effectively compensate unbalanced unpredictable nonlinear loads and is immune to reduction of the network’s short-circuit level. For better comparison between the case-studies, the DClink voltage profile is also shown in Fig. 18. A comparison between the proposed method and the conventional p–q theory-base scheme can be made by looking at Table 6. It can be seen that unlike the proposed strategy, in very distorted situations, i.e. 7th cycle after t = 0.03 s, the conventional scheme is unable to improve current and voltage THDs, CUF and VUF. The
20 0 -20
Fig. 13. Power factor of the system with unbalanced nonlinear loads: (a) before the compensation, (b) after the compensation.
(b) p(t) (MW)
880 830
0.4 0.2 0
(c)
780 0
0.05
0.1
0.15
0.2
Time (s) Fig. 14. APLC’s DC-link voltage in case-study 2.
eters over time. The thevenin equivalent impedance, Z, of the power supply is a parameter that can vary due to expansion of the power system, or because of some transmission lines getting disconnected, i.e. in case of faults or maintenance. Small changes in Z can affect the performance of the connected APLC. Performance of a perfectly designed APLC should be immune to such parameter variations in the power system.
q(t) (MVar)
DC-link Voltage (V)
0.6
0.4 0.2 0 0
0.03
0.08
0.14
0.2
Time (s)
(d) Fig. 15. Uncompensated system of case-study 3: (a) three phase voltage, (b) threephase current, (c) instantaneous active power, (d) instantaneous reactive power.
39
Power Factor
Voltage (kV)
A. Ketabi et al. / Electrical Power and Energy Systems 47 (2013) 31–40
20 0 -20
1 0.8 0.6
(a)
20
Power Factor
Current (A)
(a)
0 -20
1 0.997 0.994 0
(b)
0.03
0.08
0.2
(b)
0.6
p(t) (MW)
0.14
Time (s)
0.4
Fig. 17. Power factor of the system in case-study 3: (a) before the compensation, (b) after the compensation.
0.2
DC-link Voltage (V)
0
q(t) (MVar)
(c) 0.4 0.2 0 0
0.03
0.08
0.14
950 900 850 800 0
0.03
Time (s)
0.08
0.14
0.2
Time (s)
0.2
Fig. 18. APLC’s DC-link voltage in case-study 3.
(d) Fig. 16. Compensated system of case-study 3: (a) three phase voltage, (b) threephase current, (c) instantaneous active power, (d) instantaneous reactive power.
Table 6 THDs of currents and voltages of the system of case-study 3. Number of cycles after t = 0.03 s Uncompensated system Phase A THD of voltage THD of current Phase B THD of voltage THD of current Phase C THD of voltage THD of current Maximum VUF (%) Maximum CUF (%)
(%) (%) (%) (%) (%) (%)
6. Conclusion
2
7
10
16.346 20.806 9.943 17.754 21.498 23.149
20.905 23.351 12.204 22.34 23.569 21.943 1.327 21.917
20.219 18.966 22.332 16.299 36.589 14.6
0.231 1.655 0.19 1.621 0.226 1.986 0.115 2.207
0.391 1.024 0.421 1.312 0.437 0.797
Compensated system using the proposed strategy Phase A THD of voltage (%) 0.208 THD of current (%) 1.359 Phase B THD of voltage (%) 0.278 THD of current (%) 1.922 Phase C THD of voltage (%) 0.347 THD of current (%) 0.988 Maximum VUF (%) Maximum CUF (%)
still represents satisfactory performance in compensating the reactive power and power factor, such that its result is almost the same with those achieved by the proposed strategy.
Compensated system using the conventional p–q theory-based strategy Phase A THD of voltage (%) 7.982 12.211 8.441 THD of current (%) 13.552 27.875 10.493 Phase B THD of voltage (%) 4.972 5.474 4.016 THD of current (%) 15.346 22.028 7.598 Phase C THD of voltage (%) 6.179 14.349 3.817 THD of current (%) 19.94 32.491 11.879 Maximum VUF (%) 0.796 Maximum CUF (%) 18.05
oscillations in the resultant instantaneous active power, however reduced, won’t be fully compensated. The conventional scheme
In this paper, a new ANF-based reference signal generating scheme for a shunt active power line conditioner was introduced. Simple arithmetic structure of ANFs, their fast and accurate response, and intrinsic robustness against disturbances and frequency variations has made the proposed method exceptionally suitable for power system applications. To ensure optimal performance, the ANFs were globally tuned using DE optimization algorithm. Moreover parameters of the hysteresis-band current controlled VSC were also obtained by DE algorithm to acquire the minimum possible THD level. Simulation results and comparison of the proposed scheme with the conventional p–q theory-based method validated the exceptional superiority of the proposed scheme in case of: – Elimination of current and voltage harmonic contents. – Elimination of active power’s oscillating content. – Balancing the three-phase currents and voltages.
The proposed scheme demonstrated satisfactory performance similar to the conventional scheme in case of: – Reactive power compensation. – Power factor correction. Moreover, robustness of the proposed scheme against power supply impedance variations and its satisfactory performance in weak grids were confirmed.
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References [1] Moran LA, Dixon JW, Wallace RR. A three-phase active power filter operating with fixed switching frequency for reactive power and current harmonic compensation. IEEE Trans Ind Electron 1995;42:402–8. [2] Fang Zheng P, Ott Jr GW, Adams DJ. Harmonic and reactive power compensation based on the generalized instantaneous reactive power theory for three-phase four-wire systems. IEEE Trans Power Electron 1998;13:1174–81. [3] Abdeslam D, Wira P, Merckle M, Flieller D, Chapuis Y. A unified artificial neural network architecture for active power filters. IEEE Trans Ind Electron 2007;54:61–76. [4] IEEE recommended practices and requirements for harmonic control in electrical power systems. IEEE std 519-1992; 1993. [5] Akagi H, Kanazawa Y, Nabae A. Instantaneous reactive power compensators comprising switching devices without energy storage components. IEEE Trans Ind Appl 1984;IA-20:625–30. [6] Montano JC. Reviewing concepts of instantaneous and average compensations in polyphase systems. IEEE Trans Ind Electron 2011;58:213–20. [7] Herrera RS, Salmeron P. Instantaneous reactive power theory: a reference in the nonlinear loads compensation. IEEE Trans Ind Electron 2009;56:2015–22. [8] Mishra MK, Karthikeyan K. An investigation on design and switching dynamics of a voltage source inverter to compensate unbalanced and nonlinear loads. IEEE Trans Ind Electron 2009;56:2802–10. [9] Zaveri T, Bhalja BR, Zaveri N. Load compensation using DSTATCOM in threephase, three-wire distribution system under various source voltage and delta connected load conditions. Int J Electr Power Energy Syst 2012;41:34–43. [10] Zaveri N, Chudasama A. Control strategies for harmonic mitigation and power factor correction using shunt active filter under various source voltage conditions. Int J Electr Power Energy Syst 2012;42:661–71. [11] Fang Zheng P, Jih-Sheng L. Generalized instantaneous reactive power theory for three-phase power systems. IEEE Trans Instrum Meas 1996;45:293–7. [12] Esfandiari A, Parniani M, Mokhtari H. A new control strategy of shunt active filters for power quality improvement of highly and randomly varying loads. In: Proceedings of IEEE international symposium on industrial electronics; 2004. p. 1297–302. [13] Hyosung K, Blaabjerg F, Bak-Jensen B, Jaeho C. Instantaneous power compensation in three-phase systems by using p–q–r theory. IEEE Trans Power Electron 2002;17:701–10.
[14] Singh B, Jayaprakash P, Kothari DP. New control approach for capacitor supported DSTATCOM in three-phase four wire distribution system under non-ideal supply voltage conditions based on synchronous reference frame theory. Int J Electr Power Energy Syst 2011;33:1109–17. [15] Herrera RS, Salmeron P, Hyosung K. Instantaneous reactive power theory applied to active power filter compensation: different approaches, assessment, and experimental results. IEEE Trans Ind Electron 2008;55:184–96. [16] Forghani M, Afsharnia S. Online wavelet transform-based control strategy for UPQC control system. IEEE Trans Power Deliv 2007;22:481–91. [17] Bhende CN, Mishra S, Jain SK. TS-fuzzy-controlled active power filter for load compensation. IEEE Trans Power Deliv 2006;21:1459–65. [18] Lenwari W, Sumner M, Zanchetta P. The use of genetic algorithms for the design of resonant compensators for active filters. IEEE Trans Ind Electron 2009;56:2852–61. [19] Marques HS, Anunciada V, Borges BV. Power grid current harmonics mitigation drawn on low voltage rated switching devices with effortless control. Int J Electr Power Energy Syst 2010;32:87–99. [20] Zhou Z, Liu Y. Pre-sampled data based prediction control for active power filters. Int J Electr Power Energy Syst 2012;37:13–22. [21] Karimi-Ghartemani M, Mokhtari H, Iravani MR, Sedighy M. A signal processing system for extraction of harmonics and reactive current of single-phase systems. IEEE Trans Power Deliv 2004;19:979–86. [22] Mojiri M, Karimi-Ghartemani M, Bakhshai A. Time-domain signal analysis using adaptive notch filter. IEEE Trans Signal Process 2007;55:85–93. [23] Yazdani D, Bakhshai A, Joos G, Mojiri M. A nonlinear adaptive synchronization technique for grid-connected distributed energy sources. IEEE Trans Power Electron 2008;23:2181–6. [24] Mojiri M, Bakhshai AR. An adaptive notch filter for frequency estimation of a periodic signal. IEEE Trans Autom Control 2004;49:314–8. [25] Sang-Joon L, Jun-Koo K, Seung-Ki S. A new phase detecting method for power conversion systems considering distorted conditions in power system. In: Industry applications conference thirty-fourth IAS annual meeting, vol. 4; 1999. p. 2167–72. [26] Kazmierkowski MP, Malesani L. Current control techniques for three-phase voltage-source PWM converters: a survey. IEEE Trans Ind Electron 1998;45:691–703.
Contents lists available at SciVerse ScienceDirect
Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes
A new control strategy for active power line conditioner (APLC) using adaptive notch filter Abbas Ketabi a,⇑, Mohammad Farshadnia a, Majid Malekpour a, Rene Feuillet b a b
Department of Electrical Engineering, University of Kashan, Kashan, Iran Laboratoire d’Electrotechnique de Grenoble, INPG/ENSIEG, Grenoble, France
a r t i c l e
i n f o
Article history: Received 29 July 2011 Received in revised form 30 July 2012 Accepted 27 October 2012 Available online 5 December 2012 Keywords: Shunt active filter Unbalanced conditions Harmonics Adaptive notch filter Power flow control Power quality
a b s t r a c t This paper proposes a new adaptive control algorithm for a three-phase current-source shunt active power-line conditioner (APLC) operating under unbalanced and distorted network conditions. This control scheme aims at compensation of network’s reactive power, elimination of active power’s oscillating components, compensation of network current and voltage harmonic contents resulting in sinusoidal waveforms, and equilibrating the drawn power from the source evenly between the three-phases. Unlike many of the existing methods, the proposed strategy does not require any coordinate transformations or complicated calculations. The reference signals for the hysteresis-band current controlled voltage-source converter (HBCC-VSC) are generated by passing the measured current and voltage signals through two layers of modified adaptive notch filters (ANFs). To ensure superb performance and minimum total harmonic distortion (THD) level of the power system, parameters of the HBCC-VSC are obtained using differential evolution (DE) optimization algorithm. The proposed strategy is simple, easily implementable, and robust against uncertainty or variations of power system parameters and loads. The effectiveness of the proposed control scheme is validated by simulation results of a selected network under various load and power system conditions. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction Growing use of nonlinear equipments and in particular power electronic devices has led to intense propagation of harmonic contents in power systems. If this harmonic pollution is left unattained, the quality of the supplied power will dramatically reduce. Many papers have addressed this issue and have proposed methods for compensating harmonics [1–3]. According to IEEE Standard 519-1992 [4], the maximum allowable total harmonic distortion (THD) for distribution lines, i.e. 69 kV and below, is 5%. Another significant problem in power systems, especially transmission lines is reactive power. Various types of compensators have been developed for resolving this issue and setting the power factor near unity [1,5,6]. The author in [6] has reviewed the most general concepts of power factor correction for polyphase systems. In addition to reactive power, elimination of active power’s oscillating component is also crucial. This is to draw a non-oscillating amount of instantaneous active power from the source [7]. Facing unbalanced loads, another objective in the three-phase power systems is equilibrating the transferred energy evenly between the three phases of the transmission lines, leading to a three-phase balanced set [7,8]. ⇑ Corresponding author. Tel.: +98 3615555333; fax: +98 3615559930. E-mail address: [email protected] (A. Ketabi). 0142-0615/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijepes.2012.10.063
The ability of active power filters (APFs) and active power line conditioners (APLCs) in achieving one or all of the above mentioned objectives and their performance quality directly depends on their control method, i.e. reference signal generating algorithm. These control schemes are mainly based on the instantaneous reactive power theory also known as the p–q theory, first introduced by Akagi in 1984 [5], the improved instantaneous active and reactive current component theory [9,10] the modified p–q theory [2,11], the d–q or park transformation [12], the p–q–r reference frame [13], and the synchronous reference frame theory [14]. All these methods use coordinate transformations in order to generate the required reference signals. A comparative study on these control methods is carried out in [15]. Despite the massive and complex calculations of these methods, their resultant THD level can rise up to 10% which is higher than the maximum allowable values according to IEEE Standard 519-1992 [4]. Moreover, in general unbalanced and non-sinusoidal conditions, special considerations must be taken into account. Other advanced techniques used to improve the performance of APLCs and APFs are wavelet theory, fuzzy logic, resonant controllers, artificial neural networks (ANNs), hybrid APFs, and prediction control based schemes [3,16–20]. In [16], the fundamental components of voltages and currents are extracted using wavelet-transform decomposition. The required reference signals for a UPQC active filter are then generated using the positive sequence of these
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A. Ketabi et al. / Electrical Power and Energy Systems 47 (2013) 31–40
voltages and currents. The drawbacks of this strategy are its complexity and the requirement for two voltage source converters (VSCs) rather than one. The authors in [17] have applied Takagi–Sugeno type fuzzy controller to an APF for power quality improvements and reactive power compensation, however despite the achieved improvements, it is not applicable to practical systems since the three-phase voltages are assumed to be balanced and sinusoidal. Resonant-type compensators are another type of current control methods that require a careful and complicated design. A resonant-type controller for a Shunt APF is designed using genetic optimization algorithm in [18]. This approach is capable of compensating the harmonic contents of the current. However, the resultant THD, although below 5%, is near the maximum allowable boundary, which is quite high comparing to other methods. Moreover it requires other considerations in order to compensate reactive power and other common distortions of the power system. Another promising method for reference signal generation is utilization of ANNs. An example of this type of APF is represented in [3] where an Adaline ANN is trained to generate the required voltage component for recovering the system voltage to a balanced set, and another Adaline ANN extracts the current’s harmonic contents. The required reference signals for the APF are then generated using these outputs. Hybrid shunt APF is another topology in which the APF is connected to the network thorough a passive filter. Reduction of VSC voltage magnitude and thus utilizing lower rated and cheaper switching devices are the main advantages of hybrid shunt APFs [19]. Prediction control based reference signal generating schemes have also been addressed in the literature as effective control strategies for APFs, where the reference current signal is calculated based on the predicted current value of the system [20]. These schemes require the load to have slow dynamics and are not applicable to systems with rapidly varying or unpredictable loads, thus are not suitable for practical networks. An approach for extraction of active and reactive currents and harmonic components of a single-phase system using two enhanced phase-locked loops (EPLLs) is presented in [21]. Inspired by this work, a new signal generating approach for APFs operating in unbalanced and distorted three-phase networks is proposed here. The main objectives of this approach are compensation of the reactive power, elimination of active power’s oscillating component, compensation of the harmonic contents of currents and voltages, and equilibration of the transferred energy through the transmission lines evenly between the three phases in order to obtain a three-phase sinusoidal balanced set. The proposed strategy consists of two layers of adaptive notch filters (ANFs), connected in series, such that the outcome of the second layer is the input reference signal to a hysteresis-band current controlled voltagesource converter (HBCC-VSC). In addition, in order to acquire optimum results, internal parameters of the ANFs are tuned globally using differential evolution (DE) optimization algorithm. The parameters of the HBCC-VSC are also obtained using DE algorithm in order to have the least THD level in the compensated network.
This paper is organized as follows. In Section 2, a brief overview on ANF is presented and it is globally tuned using DE optimization algorithm. The proposed compensation strategy is presented in Section 3. Section 4 is dedicated to describing HBCC-VSC and the procedure of obtaining its parameters using DE optimization algorithm. In Section 5, simulation results on a realistic power system model under different conditions and loads are presented. Finally Section 6 is devoted to the conclusions. 2. Adaptive notch filter 2.1. Overview Notch filter is a linear time-invariant structure that multiplies its input signal in a gain equal to unity in all frequencies except the notch frequency, in which the gain is null. Therefore, all frequencies except the notch frequency will exist in the frequency spectrum of the filter’s output signal. If the filter becomes capable of locking the notch frequency on the fundamental frequency of the input signal and tracking it accordingly, it is then called an adaptive notch filter (ANF) [22]. Here, a modified version of the lattice-based discrete-time ANF [22,23] with the following dynamic behavior is employed:
€x þ h2 x ¼ 2nheðtÞ h_ ¼ cxheðtÞ
ð1Þ
eðtÞ ¼ uðtÞ x_ where u(t) is the input signal, h is the estimated angular frequency, and n and c are real positive numbers that determine the performance of the ANF in terms of accuracy and convergence speed, respectively. Note that there is always a trade-off between these two parameters. The block diagram of the introduced ANF is shown in Fig. 1. Stability analysis of the ANF characterized by (1) and its convergence to a unique periodic orbit are presented in [22–24]. For a sinusoidal input u(t) = A sin (xt + u), i.e. the measured voltage or current of the network, the presented dynamic system converges to a unique periodic orbit as follows [22,23]:
0 1 0 A 1 x x cosðxt þ uÞ B C B C O ¼ @ x_ A ¼ @ A sinðxt þ uÞ A h
ð2Þ
x
In the above equations, A is the input signal amplitude, x is the angular frequency, and u is the phase. According to (2), the amplitude of the input signal fundamental component can be obtained by
A¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi _ 2 þ ðhxÞ2 ðxÞ
ð3Þ
The system described by (2) is robust against noise, disturbances, distortions, and other pollutions of the power system and can successfully follow fundamental frequency variations of the input signal [24]. 2.2. Parameter tuning
Fig. 1. Block diagram of the modified ANF.
The values of ANF’s internal parameters, n and c, depend on its application and desired output. Here, fast and accurate extraction of the input signal fundamental component is desired. In order to have the best performance the internal parameters have to be determined with extra care. Therefore, DE optimization algorithm is employed to obtain their optimum values. In order to tune the ANF, a distorted signal with a wide range THD, as depicted in Fig. 2a, is considered as the input. The cost function of the optimization procedure is defined as the weighted
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A. Ketabi et al. / Electrical Power and Energy Systems 47 (2013) 31–40
Input Signal
Section 1
Section 2
Table 1 DE optimization algorithm parameters.
Section 3
1
Population size (Np)
Step size (s)
Crossover rate (CR)
0
100
0.5
0.7
-1 Table 2 Boundaries and optimum values of n and c.
Fundamental Component
(a) 1
n
c
0
Maximum value
Optimum value
0.0 50.0
2.0 10000.0
0.1675 178.3672
-1
FðtÞ ¼ F h ðtÞ þ F f ðtÞ
(b) Harmonic Component
Minimum value
1 0 -1 0
0.05
0.1
0.15
0.2
Time (s)
(c) Fig. 2. Performance of the ANF with its internal parameters set to the optimal values obtained by DE method: (a) input signal with a wide range THD, (b) extracted fundamental component, (c) extracted harmonic content.
sum of the output THD values. These values are measured 1.8 cycles after occurrence of each change of THD in the input signal. The associated weights to the THD values in the cost function are 2, 1.5 and 1, respectively as the THD of the input signal reduces. The chosen DE parameters for this optimization problem are shown in Table 1. In addition, a boundary should be defined for each tuning parameter. These boundaries are chosen based on experience and are shown in Table 2 along with the obtained optimum values of n and c. Performance of the optimally tuned ANF for an input signal with the wide range THD is illustrated in Fig. 2. THD of the input signal in sections 1, 2, and 3 are 48.342%, 28.738%, and 12.115%, respectively. The associated steady-state THDs of the extracted fundamental component at these sections are 4.474%, 3.412%, and 1.417%, respectively, which are satisfactory. Note that since in the proposed control method, the input signal passes through two layers of ANFs, the resultant THD will become smaller, as will be seen in Section 5. 3. Proposed compensation strategy The proposed compensation strategy provides the HBCC-VSC with the required reference signal for compensating the power system. This reference signal is generated using two signal processing layers, as explained in the follows. The first layer’s duty is to extract the so-called active current of each phase according to the extracted voltage and current fundamental components. This is the required current in order to have zero reactive power. The second layer’s duty is to equilibrate the drawn power by unbalanced loads evenly between the three phases, which will result in a threephase balanced set as well as elimination of active power’s oscillating part caused by unbalanced situations. The inputs to the first layer are the measured voltages and currents of the power system, and its outputs are the inputs to the second layer. It has to be noted that both layers effectively use ANFs to calculate the outputs. The measured power system quantities, i.e. current and voltage, can be decomposed into two components, the harmonic component and the fundamental component, as
ð4Þ
in which F(t) denotes the measured power system quantity, Fh(t) is its harmonic component, and Ff(t) is its fundamental component. This decomposition is performed using ANFs. The fundamental component of each phase’s line-current, if(t), can be further decoma posed into two other components, namely the active current, if ðtÞ, r and the reactive current, if ðtÞ: a
r
if ðtÞ ¼ if ðtÞ þ if ðtÞ
ð5Þ
The active and reactive currents in the above equation can be obtained using the following expressions [21] a
if ðtÞ ¼ I cosð/i /v Þ sinð/v Þ r
if ðtÞ ¼ I sinð/i /v Þ cosð/v Þ
ð6Þ
where I is the amplitude of if(t), /i is the total phase of if(t) and /v is the total phase of the relative phase-to-ground voltage fundamental component. Rearranging (6), we get a
if ðtÞ ¼ I cosð/i cos /v Þ þ I sinð/i Þ sinð/v Þ sinð/v Þ r
if ðtÞ ¼ I sinð/i Þ cosð/v Þ I cosð/i Þ sinð/v Þ cosð/v Þ
ð7Þ
According to (2), the above equations are in the perfect form for being implemented using two ANFs, one for the voltage and one for the current, as illustrated in Fig. 3. In this figure, i(t) and v(t) are the measured line-current and phase-to-ground voltage, respectively. The proposed APLC control scheme is based on the extracted active current, hence only the active current extraction section of Fig. 3 is required. The first layer consists of three sets of this active current extraction unit in order to simultaneously extract the active currents of all phases. The second layer has the duty of equilibrating the drawn power from the source evenly between the three phases and shaping the system’s current waveforms as a three-phase balanced set. Since the power system is assumed to be three-wire, this is easily done by eliminating the negative sequence of the three-phase active currents. The positive sequence of the three-phase active currents are obtained by
Fig. 3. Block diagram of the active and reactive current extractor using two ANFs.
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A. Ketabi et al. / Electrical Power and Energy Systems 47 (2013) 31–40
a;P 1 0 if ;A 1 B a;P C 1 B B i C ¼ @ a2 @ f ;B A 3 a;P a if ;C
0
a 1 a2
10
a
1
if ;A a C CB B a A@ if ;B C A a 1 if ;C
a2
ð8Þ
where the subscripts A, B, and C denote the different phases of the system, the superscript P denotes positive sequence component, and a is a 120° phase shift and can be expressed as the sum of a constant gain and a 90° phase-shift [25]: 2p
a ¼ ej 3
pffiffiffi 1 3 ¼ þj 2 2
ð10Þ
In (9) and (10), j is the imaginary unit and acts as a 90° phaseshifter. Substituting (9) and (10) in (8) yields
1 a a a a 16 if ;B þ if ;C þ 2pj ffiffi3 if ;B if ;C B C C B a;P C B a;P a;P C Bi C ¼ B þ I I f ;A f ;C C @ f ;B A B @ A a;P a a a a j ffiffi 1 a 1 if ;C p i 6 if ;A þ if ;B þ 2 3 if ;A if ;B 3 f ;C 0
a;P
if ;A
1
0
ifek > HB ) Gkþ ¼ 1; Gk ¼ 0
ð13Þ
ifek < HB ) Gkþ ¼ 0; Gk ¼ 1 ref
ð9Þ
Similar to (9), a2 can be expressed as
pffiffiffi 1 3 2p a2 ¼ ej 3 ¼ j 2 2
its input reference signal always remains within a specific tolerance band, i.e. the hysteresis band (HB). Fig. 5a demonstrates the basic configuration of a HBCC-VSC connected to the grid through three single-phase transformers, and Fig. 5b illustrates VSC’s output current waveform. The switching logic can be expressed as follows
1 a i 3 f ;A
where k = A, B, C indicates the phase, ek ¼ ik Imeas is the error bek tween the reference value and the measured output current Imeas , k Gk+ and Gk- are the generated IGBT gate signals, and HB is the value of the hysteresis band. Advantages and disadvantages of HBCC strategy and its comparison with other methods are reviewed in [26]. As it is realizable form Fig. 5, performance of the HBCC-VSC is directly affected by the choices of L, Cdc, and HB. Hence, extra care should be taken when specifying their values. Similar to the tuning procedure of ANFs in Section 2, these values are determined using DE algorithm as described in the follows.
ð11Þ 4.2. Determining L, Cdc, and HB
The system described by (11), constructs the second layer using three more ANFs, as illustrated in Fig. 4. These ANFs also act as three necessary low-pass filters at the entrance of the second layer. The generated positive sequence signals in the output of the second layer are then subtracted from the measured currents in order to produce the required reference signals by the HBCC-VSC:
Optimal values of L, Cdc, and HB, should be obtained based on the nominal MVA of the system and the minimum THD level of the three-phase network. Similar to the tuning procedure of the ANFs, the chosen cost function for the optimization algorithm is the weighted sum of voltage and current THDs at different instants, and is given by
8 ref meas a;P > iA ¼ iA if ;A > > > > < ref meas a;P iB ¼ iB if ;B > ref meas a;P > iC ¼ iC if ;C > > > :
CF ¼ W 1 THDv ðt 1 Þ þ W 2 THDi ðt 2 Þ þ W 3 THDi ðt3 Þ ð12Þ
In (12), the superscript ref identifies the reference currents, and the superscript meas denotes the measured currents. 4. APLC structure 4.1. Principles of an HBCC-VSC Hysteresis-band current control (HBCC) method is a procedure of instantaneously controlling the output current of a VSC. This is done by instantaneously comparing the VSC’s output current with its input reference signal and changing the switching sequence of the VSC in accordance. The error between the output current and
ð14Þ
where the subscripts v and i denote voltage and current, t1, t2, and t3 are the moments at which the value of THD is considered, W1, W2, and W3 are weights equal to 1, 2, and 2.5, respectively. The chosen cost function aims at decreasing the THD level as much as possible. t1, t2, and t3 are 1.8 cycles after the moments at which extreme disturbances happen in the network. Note that the associated weights to the measured THDs in (14) are relevant to the level of the occurred disturbance in the system. Since harmonic and unbalanced load currents are the main cause of voltage unbalances and harmonic voltage drops, they have a higher priority in the optimization procedure. Therefore, the associated weights to the current THDs are larger than that of the voltage THD. Tuning of the APLC using the explained procedure will be carried out in Section 5. 5. Simulation results In this Section the proposed compensation strategy will be evaluated under common situations of the power system, i.e. balanced nonlinear loads, unbalanced nonlinear loads, unbalanced unpredictable nonlinear loads, and change of the power supply thevenin equivalent impedance, Z. Fig. 6 illustrates the schematic diagram of the simulated power system. In the simulations, PI line model is used to characterize the transmission line behavior. The proposed compensation strategy is validated in terms of the resultant voltage and current THDs, three phase active and reactive powers, power factor, and voltage and current unbalance factors (VUF and CUF), given by:
Unbalance factor ¼
Fig. 4. Block diagram of positive sequence extractor using three ANFs.
negativ e sequence component 100 positiv e sequence component
ð15Þ
In order to tune the APLC’s parameters as described in the previous section, a balanced nonlinear load is applied to the system. Afterward, parameters of the APLC, i.e. HB, L, and Cdc, are tuned
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A. Ketabi et al. / Electrical Power and Energy Systems 47 (2013) 31–40
Current
(a)
Time
(b) Fig. 5. HBCC-VSC: (a) basic configuration, (b) the output current in the 20% hysteresis band.
using DE algorithm such that (14) becomes minimum. The DE algorithm internal parameters are as shown in Table 1. The obtained optimal APLC parameters for the nonlinear load of case-study 1 are shown in Table 3. Note that although these parameters are obtained for the balanced nonlinear load of case-study 1, they are applicable to other loads of the system, as it is clearly seen in case-studies 2 and 3.
25kV/600V Z 25kV/60Hz 10MVA
70 Km Line
A 25kV/600V
S1
Nonlinear load#1
Nonlinear load#2
25kV/600V
APLC Fig. 6. Schematic diagram of the simulated three-phase power system.
5.1. Case-study 1 – balanced nonlinear loads In this part, performance of the proposed APLC is studied in presence of nonlinear loads. For better demonstration of the performance, a sudden change in the load is happened after t = 0.05 s. Fig. 7 shows the instantaneous active power, reactive power, current, and voltage waveforms measured at point A of Fig. 6 whilst switch S1 is open. Since the load is assumed to be balanced, voltage and current waveforms of a single phase is only represented here. By activating the APLC and closing switch S1, the three-phase system is compensated. Fig. 8 demonstrates the characteristics of the compensated system. Variations of the power factor before and after the compensation are illustrated in Fig. 9. Voltage profile of the APLC’s DC-link is also shown in Fig. 10. Comparing Figs. 7 and 8, one can see that using the proposed compensation strategy, oscillations of the active power is
Table 3 Boundaries and optimum values of HB, L and Cdc.
HB L (H) Cdc (F)
Minimum value
Maximum value
Optimum value
0.005 1e7 1e6
0.5 1e2 1e1
0.1079 9.0093e5 0.04843
Voltage (kV)
A. Ketabi et al. / Electrical Power and Energy Systems 47 (2013) 31–40
Voltage (kV)
36
20 0 -20
20, 0 -20,
(a) Current (A)
Current (A)
(a) 10 0 -10
10 0 -10
(b) p(t) (MW)
p(t) (MW)
(b) 0.4 0.2
0.4 0.2 0
0
(c) 0.3
0.3
q(t) (MVar)
q(t) (MVar)
(c) 0.2 0.1 0
0
0.05
0.1
0.15
0.2 0.1 0 0
0.2
0.05
Time (s)
5.2. Case-study 2 – unbalanced nonlinear loads In this case-study the nonlinear load is assumed to be unbalanced. Similar to the previous case-study, a sudden change in the
0.2
Power Factor
Fig. 8. Compensated system with balanced nonlinear loads: (a) voltage of phase A, (b) current of phase A, (c) instantaneous active power, (d) instantaneous reactive power.
1 0.9 0.8 0.7
Power Factor
(a) 1 0.998 0.996 0
0.05
0.1
0.15
0.2
Time (s)
(b) Fig. 9. Power factor of the system with balanced nonlinear loads: (a) before the compensation, (b) after the compensation.
DC-link Voltage (V)
effectively damped and the reactive power is effectively compensated such that power factor is near unity, Fig. 9. Moreover the harmonic content of voltage and current is eliminated and their waveforms have become smoother and sinusoidal. Table 4 lists voltage and current THDs of the network before and after the compensation in comparison with the performance of the conventional p–q theory-based scheme. As it is evident, using the proposed strategy, THDs of both current and voltage have reduced to a great extent such that voltage THD value has reduced from 10.96% and 11.262% to 0.153% and 0.758%, respectively. Current THD has also reduced from 9.427% and 16.781% to 0.5% and 1.58%, respectively. These resultant THDs are much lower than the maximum allowable THD for distribution systems. The maximum CUF and VUF have also reduced from 4.547% and 0.638% to 1.57% and 0.184%, respectively. According to Table 4, compared to the performance of the conventional p–q theory-base scheme, the proposed scheme represents superior performance in case of both current and voltage THD correction, and CUF and VUF reduction. The same statement can be made about achieving smoother and non-oscillating instantaneous active power. The conventional scheme has a better performance in case of compensating the reactive power oscillations in the instant of the sudden change in the load, such that a smoother characteristic is achieved, but the resultant average reactive power is almost the same. In case of power factor, the conventional scheme represented almost the same results as that of the proposed scheme.
0.15
(d)
(d) Fig. 7. Uncompensated system with balanced nonlinear loads: (a) voltage of phase A, (b) current of phase A, (c) instantaneous active power, (d) instantaneous reactive power.
0.1
Time (s)
820 800 780 760 0
0.05
0.1
0.15
Time (s) Fig. 10. APLC’s DC-link voltage in case-study 1.
0.2
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A. Ketabi et al. / Electrical Power and Energy Systems 47 (2013) 31–40 Table 4 THDs of currents and voltages of the system of case-study 1.
Uncompensated system THD of voltage (%) THD of current (%) Maximum VUF (%) Maximum CUF (%)
Before t = 0.05 s
After t = 0.05 s
10.96 9.427
11.262 16.781 0.638 4.547
Compensated system using the proposed strategy THD of voltage (%) 0.153 THD of current (%) 0.5 Maximum VUF (%) Maximum CUF (%)
0.758 1.58 0.184 1.57
Compensated system using the conventional p–q theory-based strategy THD of voltage (%) 8.854 1.853 THD of current (%) 10.352 3.154 Maximum VUF (%) 0.398 Maximum CUF (%) 4.024
5.3. Case-study 3 – change of the power supply thevenin equivalent impedance under unbalanced unpredictable nonlinear loads Since APLCs are commonly installed permanently, their performance has to be robust against variations of power system param-
Voltage (kV)
Voltage (kV)
load happens after t = 0.05 s. The three-phase current and voltage of the uncompensated system is shown in Fig. 11. This system is compensated by the same APLC used in case-study 1, and the results are shown in Fig. 12. Table 5 lists the associated current and voltage THD values. This table implies that the proposed APLC has effectively eliminated the current and voltage harmonic contents, such that the maximum THD of the compensated voltage is 0.16% which is near ideal. The maximum THD of the current is also 2.37% which represents a satisfactory value. In addition to currents and voltages, comparing Figs. 11 and 12, one can see that using the proposed APLC, the active power’s oscil-
lating component is eliminated. Likewise, the reactive power of the network is also compensated such that the resultant power factor is near unity, Fig. 13. Moreover, the proposed APLC has successfully equilibrated the load evenly between the three phases, thus resulting in a three phase balanced set: the maximum CUF and VUF has reduced from 49.02% and 1.742% to 2.831% and 0.073%, respectively. The voltage characteristics of the APLC’s DC-link is also illustrated in Fig. 14. Table 5 also includes the achieved results by the conventional p–q theory-based scheme. These results indicate that the proposed scheme has a far superior performance compared to the conventional scheme in case of both current and voltage THD correction, and CUF and VUF reduction. Unlike the proposed method, because of the conventional scheme’s lack in complete correction of current and voltage THDs, CUF and VUF, the resultant instantaneous active power includes oscillations but with lower amplitudes compared to the uncompensated system. The same statement can be made about the instantaneous reactive power, however it has a zero average value with oscillation amplitude of below 10 KVar which is negligible. In case of power factor, the conventional scheme represented slightly lower results compared to the proposed scheme, but is still satisfactory and above 0.98.
20 0 -20
20 0 -20
(a) Current (A)
Current (A)
(a) 10 0 -10
10 0 -10
(b) p(t) (MW)
p(t) (MW)
(b) 0.3 0.2 0.1
0.3 0.2 0.1 0
0
(c)
(c) 0.3
q(t) (MVar)
q(t) (MVar)
0.3 0.2 0.1 0 -0.1 0
0.05
0.1
0.15
0.2
0.2 0.1 0 -0.1 0
0.05
0.1
Time (s)
Time (s)
(d)
(d)
Fig. 11. Uncompensated system with unbalanced nonlinear loads: (a) three phase voltage, (b) three-phase current, (c) instantaneous active power, (d) instantaneous reactive power.
0.15
0.2
Fig. 12. Compensated system with unbalanced nonlinear loads: (a) three phase voltage, (b) three-phase current, (c) instantaneous active power, (d) instantaneous reactive power.
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A. Ketabi et al. / Electrical Power and Energy Systems 47 (2013) 31–40
Table 5 THDs of currents and voltages of the system of case-study 2.
Uncompensated system Phase A THD of voltage THD of current Phase B THD of voltage THD of current Phase C THD of voltage THD of current Maximum VUF (%) Maximum CUF (%)
(%) (%) (%) (%) (%) (%)
Before t = 0.05 s
After t = 0.05 s
6.678 31.188 4.401 25.412 5.605 8.027
8.825 69.117 5.484 16.52 7.328 47.687 1.742 49.02
proposed strategy (%) 0.124 (%) 0.804 (%) 0.102 (%) 0.791 (%) 0.16 (%) 0.791
Compensated system using the Phase A THD of voltage THD of current Phase B THD of voltage THD of current Phase C THD of voltage THD of current Maximum VUF (%) Maximum CUF (%)
conventional p–q theory-based strategy (%) 5.443 5.627 (%) 13.415 15.073 (%) 12.589 4.492 (%) 18.491 13.486 (%) 11.356 4.422 (%) 18.328 23.645 0.703 20.98
0.085 2.032 0.076 2.37 0.086 2.296 0.073 2.831
1 0.8
Voltage (kV)
0.6
Power Factor
(a) 1
20 0 -20
0.995
(a)
0.99 0
0.05
0.1
0.15
0.2
Time (s)
(b)
Current (A)
Power Factor
Compensated system using the Phase A THD of voltage THD of current Phase B THD of voltage THD of current Phase C THD of voltage THD of current Maximum VUF (%) Maximum CUF (%)
Here, a 25% increase in Z is considered and performance of the proposed APLC is evaluated. Such increase in Z, causes the shortcircuit level of the source to decrease by 20%. Therefore, the resultant short-circuit level of the source would become 8 MVA. Unlike the previous case-studies, the aggregated load of this case-study does not vary on a regular basis and is not predictable. Note that parameters of the APLC used in this case-study are similar to those of case-studies 1 and 2. Fig. 15 shows the characteristics of the uncompensated system and Fig. 16 illustrates those of the compensated system. Note that after t = 0.03 s, the aggregated load is randomly varying. The values of voltage and current THDs in certain randomly chosen cycles after t = 0.03 s for both uncompensated and compensated systems are listed in Table 6. These values show that the proposed APLC has effectively eliminated the harmonic content of currents and voltages. According to Figs. 15 and 16, the APLC has also successfully compensated the reactive power and set the power factor near unity as it is illustrated in Fig. 17. Moreover the oscillating part of the active power is eliminated. The outcome is a set of perfectly balanced sinusoidal waveforms such that the maximum CUF has reduced from 21.917% to 2.207%, Likewise maximum VUF has reduced from 1.327% to 0.115%. It is evident that the proposed APLC can effectively compensate unbalanced unpredictable nonlinear loads and is immune to reduction of the network’s short-circuit level. For better comparison between the case-studies, the DClink voltage profile is also shown in Fig. 18. A comparison between the proposed method and the conventional p–q theory-base scheme can be made by looking at Table 6. It can be seen that unlike the proposed strategy, in very distorted situations, i.e. 7th cycle after t = 0.03 s, the conventional scheme is unable to improve current and voltage THDs, CUF and VUF. The
20 0 -20
Fig. 13. Power factor of the system with unbalanced nonlinear loads: (a) before the compensation, (b) after the compensation.
(b) p(t) (MW)
880 830
0.4 0.2 0
(c)
780 0
0.05
0.1
0.15
0.2
Time (s) Fig. 14. APLC’s DC-link voltage in case-study 2.
eters over time. The thevenin equivalent impedance, Z, of the power supply is a parameter that can vary due to expansion of the power system, or because of some transmission lines getting disconnected, i.e. in case of faults or maintenance. Small changes in Z can affect the performance of the connected APLC. Performance of a perfectly designed APLC should be immune to such parameter variations in the power system.
q(t) (MVar)
DC-link Voltage (V)
0.6
0.4 0.2 0 0
0.03
0.08
0.14
0.2
Time (s)
(d) Fig. 15. Uncompensated system of case-study 3: (a) three phase voltage, (b) threephase current, (c) instantaneous active power, (d) instantaneous reactive power.
39
Power Factor
Voltage (kV)
A. Ketabi et al. / Electrical Power and Energy Systems 47 (2013) 31–40
20 0 -20
1 0.8 0.6
(a)
20
Power Factor
Current (A)
(a)
0 -20
1 0.997 0.994 0
(b)
0.03
0.08
0.2
(b)
0.6
p(t) (MW)
0.14
Time (s)
0.4
Fig. 17. Power factor of the system in case-study 3: (a) before the compensation, (b) after the compensation.
0.2
DC-link Voltage (V)
0
q(t) (MVar)
(c) 0.4 0.2 0 0
0.03
0.08
0.14
950 900 850 800 0
0.03
Time (s)
0.08
0.14
0.2
Time (s)
0.2
Fig. 18. APLC’s DC-link voltage in case-study 3.
(d) Fig. 16. Compensated system of case-study 3: (a) three phase voltage, (b) threephase current, (c) instantaneous active power, (d) instantaneous reactive power.
Table 6 THDs of currents and voltages of the system of case-study 3. Number of cycles after t = 0.03 s Uncompensated system Phase A THD of voltage THD of current Phase B THD of voltage THD of current Phase C THD of voltage THD of current Maximum VUF (%) Maximum CUF (%)
(%) (%) (%) (%) (%) (%)
6. Conclusion
2
7
10
16.346 20.806 9.943 17.754 21.498 23.149
20.905 23.351 12.204 22.34 23.569 21.943 1.327 21.917
20.219 18.966 22.332 16.299 36.589 14.6
0.231 1.655 0.19 1.621 0.226 1.986 0.115 2.207
0.391 1.024 0.421 1.312 0.437 0.797
Compensated system using the proposed strategy Phase A THD of voltage (%) 0.208 THD of current (%) 1.359 Phase B THD of voltage (%) 0.278 THD of current (%) 1.922 Phase C THD of voltage (%) 0.347 THD of current (%) 0.988 Maximum VUF (%) Maximum CUF (%)
still represents satisfactory performance in compensating the reactive power and power factor, such that its result is almost the same with those achieved by the proposed strategy.
Compensated system using the conventional p–q theory-based strategy Phase A THD of voltage (%) 7.982 12.211 8.441 THD of current (%) 13.552 27.875 10.493 Phase B THD of voltage (%) 4.972 5.474 4.016 THD of current (%) 15.346 22.028 7.598 Phase C THD of voltage (%) 6.179 14.349 3.817 THD of current (%) 19.94 32.491 11.879 Maximum VUF (%) 0.796 Maximum CUF (%) 18.05
oscillations in the resultant instantaneous active power, however reduced, won’t be fully compensated. The conventional scheme
In this paper, a new ANF-based reference signal generating scheme for a shunt active power line conditioner was introduced. Simple arithmetic structure of ANFs, their fast and accurate response, and intrinsic robustness against disturbances and frequency variations has made the proposed method exceptionally suitable for power system applications. To ensure optimal performance, the ANFs were globally tuned using DE optimization algorithm. Moreover parameters of the hysteresis-band current controlled VSC were also obtained by DE algorithm to acquire the minimum possible THD level. Simulation results and comparison of the proposed scheme with the conventional p–q theory-based method validated the exceptional superiority of the proposed scheme in case of: – Elimination of current and voltage harmonic contents. – Elimination of active power’s oscillating content. – Balancing the three-phase currents and voltages.
The proposed scheme demonstrated satisfactory performance similar to the conventional scheme in case of: – Reactive power compensation. – Power factor correction. Moreover, robustness of the proposed scheme against power supply impedance variations and its satisfactory performance in weak grids were confirmed.
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