# Enhanced Instantaneous Power Theory with Average Algorithm for Indirect Current Controlled Three-Level Inverter-Based Shunt Active Power Filter under Dynamic State Conditions

Authors: Yap Hoon; Mohd Amran Mohd Radzi; Mohd Khair Hassan; Nashiren Farzilah Mailah
Journal: Mathematical Problems in Engineering
 (2016)

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## Abstract

An enhanced harmonics extraction algorithm based on Instantaneous Power (PQ) Theory is proposed for indirect current controlled (ICC) three-level neutral point diode clamped (NPC) inverter-based shunt active power filter (SAPF). SAPF is famous in current harmonics mitigation for its flexibility in dealing with dynamic state conditions. As for its controller, PQ Theory has served the major role in harmonics extraction algorithm due to its simple implementation features. However, it suffers from serious time delay due to its dependency on sluggish numerical filters. Furthermore, the algorithm is mostly designed to suit the operation of direct current controlled (DCC) SAPF which requires the knowledge of actual SAPF current (injection current). This leads to inaccurate mitigation as the injection current does not possess the exact information on actual source current which suffers from switching ripples problems. Therefore, two major modifications are introduced involving the development of mathematical average algorithm to replace numerical filter for fundamental real power computation and the formation of mathematical current relationship to change DCC to ICC based operation. The proposed algorithm is developed and evaluated in MATLAB/Simulink. From the simulation results, significant improvement in terms of Total Harmonic Distortion (THD) and response time is presented in comparison to conventional algorithm.


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## Body

## 1. Introduction

The proliferation of nonlinear loads such as adjustable speed drives, power converters, and switched mode power supplies, as well as other power electronics products has posted significant power quality problems in power distribution system. These problems are commonly related to electrical equipment breakdown caused by voltage, current, or frequency deviations [1]. As one of the most hazardous power quality problems, current harmonics generated by the nonlinear loads cause equipment overheating, voltage quality degradation, excessive transmission power losses, and malfunction of sensitive devices [2, 3]. Moreover, they also decrease overall system efficiency and worsen power factor (PF) performances. Therefore, it is crucial to mitigate the harmonics level of a power system. Shunt active power filter (SAPF) [4, 5] is designed specifically for this purpose. Additionally, it also provides reactive power compensation meant for power factor correction.Most SAPFs utilize a standard two-level inverter configuration in their design. However, multilevel inverters have recently proven to possess significant advantages over conventional two-level inverters [6, 7]. Their ability to produce stepwise output with higher voltage level reduces the harmonics contents of the output signals and simultaneously minimizes the power losses. However, in the context of APFs, the multilevel inverters employed are mostly restricted to three-level [8, 9] due to complexity in controller design which involves larger number of switching states and greater severity of voltage imbalance to the capacitors as the number of level increases. In three-level neutral point diode clamped (NPC) inverter, voltage across the split capacitors has to be maintained as half of the overall DC-Bus voltage.The effectiveness of SAPFs in power quality mitigation strictly depends on their control strategies. Specifically, the controller comprises three main algorithms, namely, harmonics extraction algorithm, voltage control algorithm, and current control or switching algorithm. Among these algorithms, the harmonics extraction algorithm is deemed to be the most crucial part that leads SAPF to achieve its optimal performance [10, 11]. Accurate and efficient harmonics extraction leads to proper and fast reference current generation which further controls the SAPF to generate the required injection current for harmonics mitigation.In recent years, various research works on this particular algorithm have been reported in the literature including Synchronous Reference Frame (SRF) [12, 13], Instantaneous Power (PQ) Theory [11, 14–18], DQ-axis with Fourier (DQF) [19], Fast Fourier Transform (FFT) [20], Synchronous Detection (SD) [21, 22], wavelet-based approach [23], and Artificial Neural Network (ANN) [24, 25]. Among all the existing algorithms,PQ Theory has advantages over the others such as simple design, increased speed, and fewer calculations, making it more likely to be implemented practically.However, the latest trend inPQ Theory algorithm is still applying numerical filters such as low pass filter (LPF) [14, 16–18], both LPF and high pass filter (HPF) [11], and band reject filter (BRF) [15] to detect the desired real power signal for reference current generation. The dependency on these sluggish numerical filters is the main factor that limits the harmonics extraction performance which in turn degrades the overall harmonics mitigation result. Moreover, the performance of numerical filters strictly depends on their tuned cutoff frequency where the tuning is normally realized through tedious approach. Furthermore, a good trade-off between cutoff frequency and the order of filter is difficult to be attained, but it is required to ensure optimum performance.Besides that, another weakness of the conventionalPQ Theory algorithm is related to the characteristic of its generated reference current. To date, the nonsinusoidal reference current is mainly derived from the extracted current harmonics [11, 14–18] and thus forces the SAPF to operate based on direct current controlled (DCC) scheme [26–28] where the knowledge of actual SAPF injection current is required in generating the desired PWM switching signals to control the switching activities of SAPF for harmonics mitigation.From the literature [4, 28, 29], it is revealed that switching activities of SAPF produces ripples in the source current. In the field of harmonics mitigation, it is important to address switching ripples problems as the THD performance of the mitigated source current is degraded. A DCC scheme which operates based on comparison of measured injection current with its nonsinusoidal reference current counterpart does not possess accurate information on the characteristic of the actual source current. Therefore, even if the source current is polluted by switching ripples, the DCC scheme will not be able to mitigate the ripples due to the lack of necessary information.Although indirect current controlled (ICC) scheme which operates based on the comparison of the actual source current with its sinusoidal reference current counterpart [26–29] has been proven to overcome the weakness of DCC scheme, there is still no work onPQ Theory which has been conducted together with ICC scheme. In fact, it is the characteristic of conventionalPQ Theory algorithm itself that makes it not suitable to be applied in ICC scheme.On top of that, the key parameters that determine the performance of SAPF are the THD value, PF, and dynamic response. Basically, the previous literatures [11, 16–18] reported that SAPF which operates based onPQ Theory successfully performed within the limit (THD < 5%) set by IEEE Standard 519-2014 [30] with PF close to unity. Meanwhile, the best response time achieved is within 0.05 s which corresponds to 2.5 cycles of 50 Hz signal [11, 16]. However, further improvement can still be done especially in reducing the unnecessary delay resulting from inefficient harmonics extraction algorithm which will surely improve the dynamic performance of SAPF.Therefore, this paper presents an enhanced version ofPQ Theory algorithm known as EnhancedPQ with average algorithm that suits the operation of ICC based SAPF in which the reference current is derived from fundamental active current instead of the current harmonics. Moreover, a mathematical average algorithm is proposed to overcome the drawbacks of the sluggish numerical filters. The design concept and the effectiveness of the proposed algorithm are verified using MATLAB/Simulink. For performance comparison, the conventionalPQ Theory algorithm is developed, and both the algorithms are tested under steady and dynamic state conditions.The rest of the paper is organized as follows. In Section2, the proposed SAPF with its control strategies is explained. In Section 3, the details of the proposed current harmonics extraction algorithm are presented with clear illustration. In Section 4, simulation results are presented and discussed showing the effectiveness of the proposed algorithm in comparison to the conventional algorithm. The paper ends with a brief conclusion in Section 5 by summarizing the significant contributions of this work.


## 2. Proposed SAPF with Control Strategies

The proposed SAPF connected at point of common coupling (PCC) between three-phase source and nonlinear load and its control strategies are shown in Figures1 and 2, respectively. A three-phase three-level NPC inverter is employed to function as the SAPF, and the nonlinear load consists of a bridge rectifier which is considered as the worst source of harmonics in electrical system [31, 32].Figure 1
The proposed SAPF connected at PCC.Figure 2
The proposed SAPF controller showing the harmonics extraction algorithm and all the other associated algorithms.Meanwhile, the controller is composed of harmonics extraction algorithm, DC-Bus voltage control algorithm, synchronizer algorithm, neutral point voltage control algorithm, and current control (switching) algorithm.The proposed controller is designed to perform the following functions.(1)
Fundamental Real Power Detection. The source voltage vS and load current iL are sensed to obtain their corresponding real power P. The fundamental component of the calculated real power is then detected and reconverted back to fundamental active current i1L.(2)
DC-Bus Voltage Regulation. Instantaneous DC current idc is calculated and drawn by the proposed SAPF to maintain DC-Bus voltages (Vdc, Vdc1, and Vdc2) at desired level.(3)
Reference Current Generation. The proposed controller utilizes both i1L and idc to generate the reference source current signal iS,ref.(4)
Minimization of Neutral Point Voltage Deviation. The differences between Vdc1 and Vdc2 are taken to generate an incremental time interval Δt which adjusts the time distribution of the switches. This approach ensures equal inflow and outflow of the current at the neutral pointZ, thus reducing the deviation.(5)
Regulation of Instantaneous Current. The source current iS is regulated through proper switching activities of SAPF controlled by the generated switching signals S1-4.Based on Figure1, it is clear that the current expression before connecting SAPF can be written as(1)iS=iL=i1L+iH,where iH is the current harmonics generated due to nonlinearity characteristic of nonlinear loads. Under the presence of nonlinear loads, the source current iS is polluted by the addition of iH and causes it to displace away from vS.The installation of parallel connected SAPF at PCC as the proposed current harmonics mitigation as well as reactive power compensation strategy has introduced additional signal meant to mitigate the effect ofiH. The mitigation process is accomplished by injecting the required injection current iinj to cancel iH during operating state of SAPF and drawing the necessary idc to regulate the switching losses during nonoperating state of SAPF. Therefore, the new current expression is now written as(2)iS=i1L+iH+idc-iinjwhich can be further simplified as(3)iS=i1L+idcwhen iinj is made equivalent to iH.According to (3), the mitigated iS is presumed to have recovered its pure sinusoidal shape and is in phase with vS.This paper focuses mainly on harmonics extraction algorithm. A synchronizer is utilized to provide sinusoidal referencing signal to the voltage control algorithm governed by self-charging technique [33, 34]. Meanwhile, the switching control is realized through 25 kHz Space Vector PWM (SVPWM) [8, 35–38] switching algorithm with the help from the neutral point voltage control algorithm [38–40] adjusting the switching time according to the behaviour of the instantaneous DC-Bus voltages.


## 3. Proposed EnhancedPQ with Average Algorithm

In order to provide better understanding of the proposed algorithm and at the same time show proper comparison, the details of the existing algorithm, namely, conventionalPQ Theory algorithm, are first presented serving as a benchmark for improvement. Next, with reference to the conventionalPQ Theory algorithm, the proposed algorithm known as EnhancedPQ with average algorithm is elaborated highlighting the improvements made.


### 3.1. ConventionalPQ Theory Algorithm

The overall harmonics extraction process flow based on conventionalPQ Theory is shown in Figure 3. Basically, the extraction process is realized through a series of mathematical calculations of Instantaneous Power in a balanced three-phase system. The calculations are conducted in α-β coordinates where all the three-phase signals involved are first translated into α-β domain via a mathematical transformation represented by matrix [M] given as(4)M=23cos⁡θ1tcos⁡θ2tcos⁡θ3tsin⁡θ1tsin⁡θ2tsin⁡θ3t,where(5)θpht=θt-2π3ph-1,ph=1,2,3and θt is an angular arbitrary function representing the phase angle of each signal.Figure 3
The conventionalPQ Theory algorithm operating with DCC scheme.Consequently, thePQ Theory applies this matrix to transform the three-phase voltages and currents into their respective representation in α-β coordinates by means of Clarke-transformation [41] which can be expressed as the following matrix relation:(6)vαvβ=231-12-12032-32vavbvc,(7)iαiβ=231-12-12032-32iaibic,where va, vb, and vc and ia, ib, and ic are the three-phase voltages and currents, respectively.Inα-β coordinates, the complex power S can be represented as(8)S=P+jQ=vαβiαβ∗=vα-jvβiα+jiβ=vαiα+vβiβ+jvαiβ-vβiα,where P and Q represent the instantaneous real and reactive power, respectively, and ∗ represent a complex conjugate.Hence, the instantaneous real powerP is given by(9)P=vαiα+vβiβ.Meanwhile, the instantaneous reactive powerQ is given by(10)Q=vαiβ-vβiα.Equations (9) and (10) can be rewritten as(11)PQ=vαvβ-vβvαiαiβ.However, under the influences of nonlinear loads, the actualP and Q values are polluted by additional disturbances resulting in the formation of new Instantaneous Power relationship given as(12)PQ=Pdc+PacQdc+Qac,where Pdc and Pac represent the fundamental (dc) and distorted (ac) components of instantaneous real power, respectively. Similar relation holds for reactive powers, Qdc and Qac.For the purpose of harmonics extraction, onlyPac is required to generate the current harmonics iHαβ. The Pac components are obtained by removing the Pdc component from the original P value. This approach can be represented as follows:(13)Pac=P-Pdc.Previously, the fundamental componentPdc detection is mostly accomplished by using Butterworth-type tuned numerical LPF [11, 14, 17, 42]. However, the tuning of cutoff frequency and the selection of filter’s order are quite difficult tasks. Generally, LPF with higher cutoff frequency provides a fast dynamic response, but some unwanted components remain (as ripples) in the filtered signal while lower cutoff frequency provides a smoother filtered signal (less ripples) but slow dynamic response. On the other hand, a low order LPF provides fast dynamic response but poor filtering effect (more ripples). Meanwhile, high order LPF has a good filtering effect (less ripples), but it suffers from longer time delay [13, 42]. Therefore, a good trade-off between cutoff frequency and order of filter is crucial for optimum performance, but this is a tough decision to be made.From the literature, in order to achieve a balance between dynamic response and filtering performance, the best cutoff frequency is reported to be in the range of 5 Hz to 35 Hz [11, 13, 14], and meanwhile the order of filter is limited to the second order as the higher order filter imposes great computational burden to the controller [13, 17, 42]. However, no matter how good the trade-off has been done to the numerical LPF, it is still not a promising solution to achieve fast and smooth filtering performance.Once thePdc component is subtracted from the original P value, (11) can be rewritten as (14)PacQ=vαvβ-vβvαiHαiHβ,where iHα and iHβ  represent the current harmonics components in α-β coordinates.From (14), the inverse matrix is taken to generate the required current harmonics in α-β coordinates and is expressed as follows:(15)iHαiHβ=1det⁡PQvα-vβvβvαPacQ,where det⁡PQ=vα2+vβ2.Inverse Clarke-transformation as shown in (16) is then performed to transform iHαβ in α-β coordinates back to three-phase current harmonics iHabc which is then used to derive the required reference injection current iinj,ref. Consider(16)iHaiHbiHc=2310-1232-12-32iHαiHβ.The reference injection current is derived based on the following equation:(17)iinj,ref=iHabc+idc.The nonsinusoidaliinj,ref forces the subsequent switching signals S1-4 to be generated based on DCC scheme which operates by requiring the measurement of actual injection current iinj.


### 3.2. Proposed Modifications

Based on Figure4, it is clear that two major modifications are applied to the conventionalPQ Theory algorithm to implement the EnhancedPQ with average algorithm.Figure 4
The proposed EnhancedPQ with average algorithm operating with ICC scheme.The first modification is implemented aiming at overcoming two major drawbacks of tuned numerical LPF which includes tedious tuning workload and significant delay inPdc detection. For this purpose, a mathematical average algorithm is proposed which replaces the tuned numerical LPF in Pdc detection. The proposed mathematical average algorithm is given as(18)Pdc=Paverage=1T∫0TPdt,where Paverage is the average value of P and T is the period of the signal.The mathematical average algorithm eliminates the need of filtering, thus removing the tuning workload as well as the possibility of inaccurate and inefficientPdc detection due to improper tuning.Next, the second modification is implemented aiming at solving the switching ripples problems, existing in source current which cannot be eliminated through DCC based operation. For this purpose,PQ Theory algorithm that suits ICC based operation is proposed. In order to realize this modification, the characteristic of the generated reference current needs to be changed. Instead of deriving the reference current from iHabc, the proposed algorithm makes it possible to derive the reference current from fundamental active current i1Labc.The fundamental active currenti1Labc is made available by modifying the output of iHabc generated from the conventionalPQ Theory algorithm through an additional mathematical expression given as(19)i1Labc=iLabc-iHabc,where iLabc is the load current and iHabc is the current harmonics that resulted from (16).The reference source currentiS,ref is now derived based on (3). The sinusoidal iS,ref enables the subsequent switching signals S1-4 to be generated based on the measurement of iS instead of iinj. In other words, it changes the DCC based operation to ICC based operation. In contrast to DCC based operation, ICC based operation which possesses the exact information on switching ripples, existing in the source current, eliminates any unnecessary problem caused by switching activities of SAPF.Therefore, operating under ICC scheme is capable of ensuring the current harmonics to efficiently be mitigated, resulting in lower THD value of source current.


## 3.1. ConventionalPQ Theory Algorithm

The overall harmonics extraction process flow based on conventionalPQ Theory is shown in Figure 3. Basically, the extraction process is realized through a series of mathematical calculations of Instantaneous Power in a balanced three-phase system. The calculations are conducted in α-β coordinates where all the three-phase signals involved are first translated into α-β domain via a mathematical transformation represented by matrix [M] given as(4)M=23cos⁡θ1tcos⁡θ2tcos⁡θ3tsin⁡θ1tsin⁡θ2tsin⁡θ3t,where(5)θpht=θt-2π3ph-1,ph=1,2,3and θt is an angular arbitrary function representing the phase angle of each signal.Figure 3
The conventionalPQ Theory algorithm operating with DCC scheme.Consequently, thePQ Theory applies this matrix to transform the three-phase voltages and currents into their respective representation in α-β coordinates by means of Clarke-transformation [41] which can be expressed as the following matrix relation:(6)vαvβ=231-12-12032-32vavbvc,(7)iαiβ=231-12-12032-32iaibic,where va, vb, and vc and ia, ib, and ic are the three-phase voltages and currents, respectively.Inα-β coordinates, the complex power S can be represented as(8)S=P+jQ=vαβiαβ∗=vα-jvβiα+jiβ=vαiα+vβiβ+jvαiβ-vβiα,where P and Q represent the instantaneous real and reactive power, respectively, and ∗ represent a complex conjugate.Hence, the instantaneous real powerP is given by(9)P=vαiα+vβiβ.Meanwhile, the instantaneous reactive powerQ is given by(10)Q=vαiβ-vβiα.Equations (9) and (10) can be rewritten as(11)PQ=vαvβ-vβvαiαiβ.However, under the influences of nonlinear loads, the actualP and Q values are polluted by additional disturbances resulting in the formation of new Instantaneous Power relationship given as(12)PQ=Pdc+PacQdc+Qac,where Pdc and Pac represent the fundamental (dc) and distorted (ac) components of instantaneous real power, respectively. Similar relation holds for reactive powers, Qdc and Qac.For the purpose of harmonics extraction, onlyPac is required to generate the current harmonics iHαβ. The Pac components are obtained by removing the Pdc component from the original P value. This approach can be represented as follows:(13)Pac=P-Pdc.Previously, the fundamental componentPdc detection is mostly accomplished by using Butterworth-type tuned numerical LPF [11, 14, 17, 42]. However, the tuning of cutoff frequency and the selection of filter’s order are quite difficult tasks. Generally, LPF with higher cutoff frequency provides a fast dynamic response, but some unwanted components remain (as ripples) in the filtered signal while lower cutoff frequency provides a smoother filtered signal (less ripples) but slow dynamic response. On the other hand, a low order LPF provides fast dynamic response but poor filtering effect (more ripples). Meanwhile, high order LPF has a good filtering effect (less ripples), but it suffers from longer time delay [13, 42]. Therefore, a good trade-off between cutoff frequency and order of filter is crucial for optimum performance, but this is a tough decision to be made.From the literature, in order to achieve a balance between dynamic response and filtering performance, the best cutoff frequency is reported to be in the range of 5 Hz to 35 Hz [11, 13, 14], and meanwhile the order of filter is limited to the second order as the higher order filter imposes great computational burden to the controller [13, 17, 42]. However, no matter how good the trade-off has been done to the numerical LPF, it is still not a promising solution to achieve fast and smooth filtering performance.Once thePdc component is subtracted from the original P value, (11) can be rewritten as (14)PacQ=vαvβ-vβvαiHαiHβ,where iHα and iHβ  represent the current harmonics components in α-β coordinates.From (14), the inverse matrix is taken to generate the required current harmonics in α-β coordinates and is expressed as follows:(15)iHαiHβ=1det⁡PQvα-vβvβvαPacQ,where det⁡PQ=vα2+vβ2.Inverse Clarke-transformation as shown in (16) is then performed to transform iHαβ in α-β coordinates back to three-phase current harmonics iHabc which is then used to derive the required reference injection current iinj,ref. Consider(16)iHaiHbiHc=2310-1232-12-32iHαiHβ.The reference injection current is derived based on the following equation:(17)iinj,ref=iHabc+idc.The nonsinusoidaliinj,ref forces the subsequent switching signals S1-4 to be generated based on DCC scheme which operates by requiring the measurement of actual injection current iinj.


## 3.2. Proposed Modifications

Based on Figure4, it is clear that two major modifications are applied to the conventionalPQ Theory algorithm to implement the EnhancedPQ with average algorithm.Figure 4
The proposed EnhancedPQ with average algorithm operating with ICC scheme.The first modification is implemented aiming at overcoming two major drawbacks of tuned numerical LPF which includes tedious tuning workload and significant delay inPdc detection. For this purpose, a mathematical average algorithm is proposed which replaces the tuned numerical LPF in Pdc detection. The proposed mathematical average algorithm is given as(18)Pdc=Paverage=1T∫0TPdt,where Paverage is the average value of P and T is the period of the signal.The mathematical average algorithm eliminates the need of filtering, thus removing the tuning workload as well as the possibility of inaccurate and inefficientPdc detection due to improper tuning.Next, the second modification is implemented aiming at solving the switching ripples problems, existing in source current which cannot be eliminated through DCC based operation. For this purpose,PQ Theory algorithm that suits ICC based operation is proposed. In order to realize this modification, the characteristic of the generated reference current needs to be changed. Instead of deriving the reference current from iHabc, the proposed algorithm makes it possible to derive the reference current from fundamental active current i1Labc.The fundamental active currenti1Labc is made available by modifying the output of iHabc generated from the conventionalPQ Theory algorithm through an additional mathematical expression given as(19)i1Labc=iLabc-iHabc,where iLabc is the load current and iHabc is the current harmonics that resulted from (16).The reference source currentiS,ref is now derived based on (3). The sinusoidal iS,ref enables the subsequent switching signals S1-4 to be generated based on the measurement of iS instead of iinj. In other words, it changes the DCC based operation to ICC based operation. In contrast to DCC based operation, ICC based operation which possesses the exact information on switching ripples, existing in the source current, eliminates any unnecessary problem caused by switching activities of SAPF.Therefore, operating under ICC scheme is capable of ensuring the current harmonics to efficiently be mitigated, resulting in lower THD value of source current.


## 4. Simulation Results

The proposed three-phase three-level NPC inverter-based SAPF utilizing the EnhancedPQ with average algorithm as the proposed harmonics extraction algorithm is tested and evaluated in MATLAB/Simulink. Simulation work is conducted under both steady and dynamic state conditions which involve two types of nonlinear loads. The first nonlinear load is constructed using a three-phase uncontrolled bridge rectifier feeding a 50 Ω resistor and 2200 μF capacitor connected in parallel (capacitive), while the second nonlinear load is developed using similar rectifier feeding a series connected 30 Ω resistor and 50 mH inductor (inductive). Furthermore, the conventionalPQ Theory algorithm is also tested for comparison purpose. The details of the proposed parameters are summarized in Table 1.Table 1
The proposed parameters for SAPF.
Parameter
Value
Voltage source
400 Vrms, 50 Hz
DC-Bus capacitor
3300μF (each)
DC-Bus reference voltage
880 V
Limiting inductor
5 mH
Switching frequency
25 kHzUnder steady state condition, three key parameters are used in analyzing the performance of each harmonics extraction algorithm which includes percentage of ripple power, THD value, and power factor. The percentage of ripple power%RP is a newly proposed parameter and is defined as the ratio of peak-to-peak fundamental real power Pdc,pp to the desired fundamental real power Pdc,desired as given in the following equation:(20)%RP=Pdc,ppPdc,desired×100.Meanwhile, under dynamic state condition, the performance parameters involved are undershoot, overshoot, and response time. For this analysis, two dynamic state conditions are created by changing the nonlinear load from capacitive to inductive and from inductive to capacitive loads, respectively.


### 4.1. Steady State Condition

Figures5 and 6 show the performance of each harmonics extraction algorithm in detecting the fundamental real power Pdc for capacitive and inductive loads, respectively. Both algorithms detect the fundamental real power well, but they differ in terms of percentage of ripple power. The proposed EnhancedPQ with average algorithm provides accurate fundamental real power detection without any ripple for both nonlinear loads. In contrast, the conventionalPQ Theory algorithm produces fundamental real power with ripple powers of 10 W (%RP = 0.17%) and 1.5 W (%RP = 0.02%) for capacitive and inductive loads, respectively.Figure 5
Fundamental real powerPdc detected by each harmonics extraction algorithm for capacitive load.Figure 6
Fundamental real powerPdc detected by each harmonics extraction algorithm for inductive load.The findings prove that the proposed mathematical average algorithm is able to detect the desired fundamental real power component with higher accuracy compared to the tuned numerical LPF.On the other hand, Figures7 and 8 show the three-phase waveforms of source voltage vS, load current iL, injection current iinj, and source current iS that resulted from the proposed EnhancedPQ with average algorithm for capacitive and inductive loads, respectively. Meanwhile, the THD values of source current iS mitigated by SAPF utilizing each harmonics extraction algorithm are summarized in Table 2.Table 2
THDs of mitigated source current obtained from each harmonics extraction algorithm for capacitive (RC) and inductive (RL) loads.
Harmonics extraction algorithm
Total Harmonic Distortion, THD (%)
Phase A
Phase B
Phase C
RC
RL
RC
RL
RC
RL
Before connecting SAPF
N/A
62.30
26.07
62.30
26.07
62.30
26.07
After connecting SAPF
ConventionalPQ Theory
2.10
1.24
2.08
1.25
2.12
1.24
EnhancedPQ with average
1.56
1.01
1.52
0.96
1.60
1.02Figure 7
Three-phase simulation waveforms for source voltagevS, load current iL, injection current iinj, and source current iS resulted from the proposed EnhancedPQ with average algorithm for capacitive load.Figure 8
Three-phase simulation waveforms for source voltagevS, load current iL, injection current iinj, and source current iS resulted from the proposed EnhancedPQ with average algorithm for inductive load.Both algorithms successfully control the SAPF to remove the generated current harmonics resulting in THD value below 5% which complies with the limit set by IEEE Standard 519-2014 [30]. However, the proposed EnhancedPQ with average algorithm shows superior performance in reducing the switching ripples existing in the source current iS by achieving a lower THD value for both capacitive and inductive loads compared to the conventionalPQ Theory algorithm. Furthermore, the mitigated source current iS seems to work in phase with the source voltage vS for both nonlinear loads which lead to almost unity power factor.


### 4.2. Dynamic State Condition

Figures9 and 10 show the dynamic behaviour of each harmonics extraction algorithm in detecting the fundamental real power Pdc for dynamic state conditions of capacitive to inductive and inductive to capacitive loads, respectively.Figure 9
Fundamental real powerPdc detected by each harmonics extraction algorithm for dynamic state condition of capacitive to inductive load.Figure 10
Fundamental real powerPdc detected by each harmonics extraction algorithm for dynamic state condition of inductive to capacitive load.For capacitive to inductive load, the proposed EnhancedPQ with average algorithm shows the best performance with response time of 0.025 s and no overshoot. Meanwhile, the conventionalPQ Theory algorithm performs poorly with response time of 0.12 s and high overshoot of 150 W.Similarly, for inductive to capacitive load, the proposed EnhancedPQ with average algorithm also shows the best performance with response time of 0.025 s and no undershoot. Meanwhile, the conventionalPQ Theory algorithm performs poorly with response time of 0.12 s and high undershoot of 150 W.The findings prove that, in terms of fundamental real power detection, the proposed algorithm shows superior dynamic performance by achieving a response time 4.8 times faster than the conventional algorithm.On the other hand, Figures11 and 12 show the dynamic behaviour of each harmonics extraction algorithm in current harmonics mitigation for dynamic state conditions of capacitive to inductive and inductive to capacitive loads, respectively.Figure 11
Phase A simulation waveforms for dynamic state condition of capacitive to inductive load for (a) source voltagevS, (b) load current iL, and (c) source current iS resulted from conventionalPQ Theory algorithm, and (d) source current iS resulted from EnhancedPQ with average algorithm.
(a)
(b)
(c)
(d)Figure 12
Phase A simulation waveforms for dynamic state condition of inductive to capacitive load for (a) source voltagevS, (b) load current iL, and (c) source current iS resulted from conventionalPQ Theory algorithm, and (d) source current iS resulted from EnhancedPQ with average algorithm.
(a)
(b)
(c)
(d)For both dynamic state conditions, the proposed EnhancedPQ with average algorithm shows the best performance with response time of 0.02 s. Meanwhile, the conventionalPQ Theory algorithm performs poorly with response time of 0.05 s.Thus, in terms of current harmonics mitigation, SAPF with the proposed algorithm shows superior dynamic performance by achieving a response time 2.5 times faster than the conventional algorithm.Furthermore, in order to study the effectiveness of the proposed SAPF, performance evaluation in terms of DC-Bus voltage control and neutral point voltage deviation control is also conducted.Figures13 and 14 show the simulation results obtained for the overall DC-Bus voltage Vdc, the split capacitor voltages (Vdc1 and Vdc2), and neutral point voltage deviation (Vdc1-Vdc2) for dynamic state conditions of capacitive to inductive and inductive to capacitive loads, respectively.Figure 13
Simulation waveforms of (a) overall DC-Bus voltageVdc, (b) upper capacitor voltage Vdc1, (c) lower capacitor voltage Vdc2, and (d) neutral point voltage deviation (Vdc1-Vdc2), for dynamic state condition of capacitive to inductive load.
(a)
(b)
(c)
(d)Figure 14
Simulation waveforms of (a) overall DC-Bus voltageVdc, (b) upper capacitor voltage Vdc1, (c) lower capacitor voltage Vdc2, and (d) neutral point voltage deviation (Vdc1-Vdc2), for dynamic state condition of inductive to capacitive load.
(a)
(b)
(c)
(d)The results show that all the DC-Bus voltages (Vdc, Vdc1, and Vdc2) of the proposed SAPF are properly controlled at desired value with response time of 0.3 s for both dynamic state conditions. Moreover, voltages across each split capacitor (Vdc1 and Vdc2) are successfully maintained as half of the overall DC-Bus voltage Vdc with the minimal neutral point voltage deviation. The findings prove the effectiveness of the DC-Bus voltage control algorithm and neutral point voltage control algorithm applied in the proposed SAPF.From all the simulation results obtained in both steady and dynamic state conditions, the improvements achieved by the proposed EnhancedPQ with average algorithm have revealed significant roles of applying the mathematical average algorithm and modifying the characteristic of generated reference current to suit ICC based operation. The implementation of the proposed algorithm has significantly improved the performances of the proposed SAPF.By providing accurate and fast fundamental real power detection together with the ability to generate sinusoidal reference current, significant improvements in terms of THD value and dynamic response in current harmonics mitigation are achieved. The THD value recorded by using the proposed algorithm is in better range that is within 0.96% to 1.60% as compared to the conventional algorithm which performs within the range of 1.24% to 2.12%. Most importantly, by using the proposed algorithm, the response time of two and half cycles (0.05 s) in harmonics mitigation which is achieved previously by using the conventional algorithm is now significantly reduced to one cycle (0.02 s).In addition, the successful control of all the DC-Bus voltages at desired value together with minimal neutral point voltage deviation has further verified the design concept and the effectiveness of the proposed SAPF in current harmonics mitigation.


## 4.1. Steady State Condition

Figures5 and 6 show the performance of each harmonics extraction algorithm in detecting the fundamental real power Pdc for capacitive and inductive loads, respectively. Both algorithms detect the fundamental real power well, but they differ in terms of percentage of ripple power. The proposed EnhancedPQ with average algorithm provides accurate fundamental real power detection without any ripple for both nonlinear loads. In contrast, the conventionalPQ Theory algorithm produces fundamental real power with ripple powers of 10 W (%RP = 0.17%) and 1.5 W (%RP = 0.02%) for capacitive and inductive loads, respectively.Figure 5
Fundamental real powerPdc detected by each harmonics extraction algorithm for capacitive load.Figure 6
Fundamental real powerPdc detected by each harmonics extraction algorithm for inductive load.The findings prove that the proposed mathematical average algorithm is able to detect the desired fundamental real power component with higher accuracy compared to the tuned numerical LPF.On the other hand, Figures7 and 8 show the three-phase waveforms of source voltage vS, load current iL, injection current iinj, and source current iS that resulted from the proposed EnhancedPQ with average algorithm for capacitive and inductive loads, respectively. Meanwhile, the THD values of source current iS mitigated by SAPF utilizing each harmonics extraction algorithm are summarized in Table 2.Table 2
THDs of mitigated source current obtained from each harmonics extraction algorithm for capacitive (RC) and inductive (RL) loads.
Harmonics extraction algorithm
Total Harmonic Distortion, THD (%)
Phase A
Phase B
Phase C
RC
RL
RC
RL
RC
RL
Before connecting SAPF
N/A
62.30
26.07
62.30
26.07
62.30
26.07
After connecting SAPF
ConventionalPQ Theory
2.10
1.24
2.08
1.25
2.12
1.24
EnhancedPQ with average
1.56
1.01
1.52
0.96
1.60
1.02Figure 7
Three-phase simulation waveforms for source voltagevS, load current iL, injection current iinj, and source current iS resulted from the proposed EnhancedPQ with average algorithm for capacitive load.Figure 8
Three-phase simulation waveforms for source voltagevS, load current iL, injection current iinj, and source current iS resulted from the proposed EnhancedPQ with average algorithm for inductive load.Both algorithms successfully control the SAPF to remove the generated current harmonics resulting in THD value below 5% which complies with the limit set by IEEE Standard 519-2014 [30]. However, the proposed EnhancedPQ with average algorithm shows superior performance in reducing the switching ripples existing in the source current iS by achieving a lower THD value for both capacitive and inductive loads compared to the conventionalPQ Theory algorithm. Furthermore, the mitigated source current iS seems to work in phase with the source voltage vS for both nonlinear loads which lead to almost unity power factor.


## 4.2. Dynamic State Condition

Figures9 and 10 show the dynamic behaviour of each harmonics extraction algorithm in detecting the fundamental real power Pdc for dynamic state conditions of capacitive to inductive and inductive to capacitive loads, respectively.Figure 9
Fundamental real powerPdc detected by each harmonics extraction algorithm for dynamic state condition of capacitive to inductive load.Figure 10
Fundamental real powerPdc detected by each harmonics extraction algorithm for dynamic state condition of inductive to capacitive load.For capacitive to inductive load, the proposed EnhancedPQ with average algorithm shows the best performance with response time of 0.025 s and no overshoot. Meanwhile, the conventionalPQ Theory algorithm performs poorly with response time of 0.12 s and high overshoot of 150 W.Similarly, for inductive to capacitive load, the proposed EnhancedPQ with average algorithm also shows the best performance with response time of 0.025 s and no undershoot. Meanwhile, the conventionalPQ Theory algorithm performs poorly with response time of 0.12 s and high undershoot of 150 W.The findings prove that, in terms of fundamental real power detection, the proposed algorithm shows superior dynamic performance by achieving a response time 4.8 times faster than the conventional algorithm.On the other hand, Figures11 and 12 show the dynamic behaviour of each harmonics extraction algorithm in current harmonics mitigation for dynamic state conditions of capacitive to inductive and inductive to capacitive loads, respectively.Figure 11
Phase A simulation waveforms for dynamic state condition of capacitive to inductive load for (a) source voltagevS, (b) load current iL, and (c) source current iS resulted from conventionalPQ Theory algorithm, and (d) source current iS resulted from EnhancedPQ with average algorithm.
(a)
(b)
(c)
(d)Figure 12
Phase A simulation waveforms for dynamic state condition of inductive to capacitive load for (a) source voltagevS, (b) load current iL, and (c) source current iS resulted from conventionalPQ Theory algorithm, and (d) source current iS resulted from EnhancedPQ with average algorithm.
(a)
(b)
(c)
(d)For both dynamic state conditions, the proposed EnhancedPQ with average algorithm shows the best performance with response time of 0.02 s. Meanwhile, the conventionalPQ Theory algorithm performs poorly with response time of 0.05 s.Thus, in terms of current harmonics mitigation, SAPF with the proposed algorithm shows superior dynamic performance by achieving a response time 2.5 times faster than the conventional algorithm.Furthermore, in order to study the effectiveness of the proposed SAPF, performance evaluation in terms of DC-Bus voltage control and neutral point voltage deviation control is also conducted.Figures13 and 14 show the simulation results obtained for the overall DC-Bus voltage Vdc, the split capacitor voltages (Vdc1 and Vdc2), and neutral point voltage deviation (Vdc1-Vdc2) for dynamic state conditions of capacitive to inductive and inductive to capacitive loads, respectively.Figure 13
Simulation waveforms of (a) overall DC-Bus voltageVdc, (b) upper capacitor voltage Vdc1, (c) lower capacitor voltage Vdc2, and (d) neutral point voltage deviation (Vdc1-Vdc2), for dynamic state condition of capacitive to inductive load.
(a)
(b)
(c)
(d)Figure 14
Simulation waveforms of (a) overall DC-Bus voltageVdc, (b) upper capacitor voltage Vdc1, (c) lower capacitor voltage Vdc2, and (d) neutral point voltage deviation (Vdc1-Vdc2), for dynamic state condition of inductive to capacitive load.
(a)
(b)
(c)
(d)The results show that all the DC-Bus voltages (Vdc, Vdc1, and Vdc2) of the proposed SAPF are properly controlled at desired value with response time of 0.3 s for both dynamic state conditions. Moreover, voltages across each split capacitor (Vdc1 and Vdc2) are successfully maintained as half of the overall DC-Bus voltage Vdc with the minimal neutral point voltage deviation. The findings prove the effectiveness of the DC-Bus voltage control algorithm and neutral point voltage control algorithm applied in the proposed SAPF.From all the simulation results obtained in both steady and dynamic state conditions, the improvements achieved by the proposed EnhancedPQ with average algorithm have revealed significant roles of applying the mathematical average algorithm and modifying the characteristic of generated reference current to suit ICC based operation. The implementation of the proposed algorithm has significantly improved the performances of the proposed SAPF.By providing accurate and fast fundamental real power detection together with the ability to generate sinusoidal reference current, significant improvements in terms of THD value and dynamic response in current harmonics mitigation are achieved. The THD value recorded by using the proposed algorithm is in better range that is within 0.96% to 1.60% as compared to the conventional algorithm which performs within the range of 1.24% to 2.12%. Most importantly, by using the proposed algorithm, the response time of two and half cycles (0.05 s) in harmonics mitigation which is achieved previously by using the conventional algorithm is now significantly reduced to one cycle (0.02 s).In addition, the successful control of all the DC-Bus voltages at desired value together with minimal neutral point voltage deviation has further verified the design concept and the effectiveness of the proposed SAPF in current harmonics mitigation.


## 5. Conclusion

This paper has presented an EnhancedPQ Theory algorithm which is applicable in ICC based SAPF. The following points summarize the major contributions of this work.(1)
Mathematical average algorithm is proposed to replace sluggish numerical filter in fundamental component detection. It provides accurate and fast detection ability and at the same time eliminates the needs of dull and tedious tuning workload.(2)
A mathematical current relationship is added to the proposed algorithm which provides the ability to generate sinusoidal reference current. By using this approach, thePQ Theory algorithm can now be implemented in ICC based SAPF which was previously only applicable in DCC based SAPF. Consequently, such technique indirectly improves the THD value of the mitigated source current through the elimination of switching ripples.The analysis in both steady and dynamic state conditions is conducted to evaluate the performance of the proposed algorithm. Moreover, comparative evaluation with the conventional algorithm is also conducted to verify the improvement achieved by the proposed algorithm. In steady state condition, the proposed algorithm is not only able to control the SAPF in mitigating the current harmonics with lower THD value for both capacitive and inductive nonlinear loads, but also able to eliminate ripples that remained in the detected fundamental component. On the other hand, significant improvement can be observed during dynamic state conditions where the proposed algorithm has successfully performed with fast response time, no undershoot, and no overshoot.The comprehensive findings of this work clearly show the advantages of the proposed EnhancedPQ with average algorithm over the conventionalPQ Theory algorithm especially in dealing with dynamic state conditions.



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*Source: 9682512-2016-03-17.xml*