# Photovoltaic Integrated Shunt Active Power Filter with Simpler ADALINE Algorithm for Current Harmonic Extraction

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## Abstract

**:**

## 1. Introduction

## 2. Single-Phase Photovoltaic Shunt Active Power Filter

_{L}, which comprises harmonic component I

_{H}, within the source current I

_{S}. An injection current I

_{inj}is generated after the SAPF is connected; this compensates for the harmonic current, leaving only the fundamental component I

_{1}, as shown below.

_{inj}will comprise a combination of the capacitor charging current I

_{dc}, inverter current I

_{inv}, and PV current I

_{PV}.

_{inv}; second, the maximum power point tracking (MPPT) algorithm is used to control the PV current I

_{PV}; third and finally, the DC voltage control algorithm is used to control the capacitor charging current I

_{dc}. For the capacitor charging current I

_{dc}, there is possibility it is supplied from the grid or the capacitor with both directions. Its value and sign depend on the voltage of the DC link capacitor as when the voltage is overshot, its sign will be positive (discharging) in order to reduce the voltage, and when the voltage is undershot, its sign will be negative (charging) for voltage to increase. The capacitor charging current I

_{dc}is equal to zero when the desired voltage is on point.

_{inv}and the capacitor charging current I

_{dc}**,**respectively. The Adaptive Perturb and Observe (P&O)–Fuzzy algorithm is implemented as the MPPT algorithm [28], due to the fact that it can perform with fast response time and high accuracy. Proportional–integral (PI) was used as the current control algorithm for controlling the steady-state error of the reference current signal [29]. For this particular research work, the unified ADALINE-based fundamental voltage extraction algorithm is used as the synchronizer [30].

## 3. Simpler ADALINE-Based Current Harmonics Extraction

_{s}in digital operation with assigned fundamental frequency ω can be depicted by the nonlinear load current I

_{L}[18,31,32], or

_{an}and W

_{bn}. By rearranging Equation (3) in vector form, the following equations holds:

_{L}, the algorithm is used. The Widrow–Hoff (W-H) method is used because of its updating algorithm that is the main feature of this extraction algorithm [18]. Weight is used as the learning factor in the Widrow–Hoff (W-H) method. However, to reduce complexity of the normal ADALINE, the Modified W-H ADALINE has been proposed. This only uses the first order of the harmonic component as opposed to the n-many harmonic components in the normal Windrow–Hoff ADALINE, as depicted in Figure 3a [18]. It is independent of number of harmonic orders due to the need to only update the two weights of the fundamental component. However, a learning rate α is introduced as a by-product because of the large average square error e produced in this method [18]. Therefore, the weight updating equation becomes

_{H}can be produced as below [19]:

_{s}) represents the fundamental sine component multiplied by its weight factor W. To reimburse harmonic distortion, the inverter current I

_{inv}is used; this is inversely proportional to the harmonic current I

_{H}. Although it is capable of reducing THD below 5%, The Modified W-H ADALINE algorithm still has disadvantages that may lead to the current harmonics extraction being slowed. Extracting current harmonics has basic requirements that it has to fulfil and the unnecessary characteristics that it has do not represent them. Hence, it can be further simplified and improved. The first simplification is made by discarding the periodic signal cosine component. According to the symmetrical theory of AC power systems, the odd function of periodic signals is of the sine component only. This is because odd functions are inversely symmetrical about the y axis. In Equation (3), when W

_{bn}is made equal to zero (W

_{bn}= 0), odd functions are of the sine components only. The sum of elements is automatically removed when the cosine component is removed. As a result, the average square error e is removed in large magnitudes, making this the second improvement.

_{f}, or

_{inv}as further elaborated below.

_{inv}is the actual value used later (by removing its negative sign) for the amount of current to be injected by the SAPF. A new updating technique called the Fundamental Active Current (FAC) updating technique is formed by the average square error to the negative inverter current and weight learning factor to the fundamental active current I

_{f}, or

_{f}sin(kωt

_{s}). It is generated by multiplying I

_{f}with the unity sine function.

## 4. Self-Charging with Step Size Error Cancellation Algorithm

_{inj}is properly generated for compensating harmonics. Therefore, the charging capacitor current I

_{dc}is an important factor to be controlled as such change to it may affect the performance of the DC link capacitor. Interestingly, I

_{dc}may also affect the performance of the PV array in supplying I

_{PV}, besides the existing role carried out by the MPPT algorithm. Considering an analysis of the circuit’s connection between the DC link capacitor and the inverter as shown in Figure 1, the effective amount of I

_{PV}injected to the grid depends on the condition of I

_{dc}. Therefore, a new parameter named the capacitor–PV current I

_{CPV}is introduced, by combining I

_{PV}and I

_{dc}as follows:

_{dc}may affect the delivery of I

_{PV}, which has to be used for keeping the DC link capacitor voltage at a certain level, rather than to be used for injection. Therefore, it is critical to control I

_{dc}, not only to ensure that the voltage of the DC link capacitor is maintained at its desired value, but also to ensure a fast and optimum supply of I

_{PV}.

_{dc}. The charging capacitor current I

_{dc}is determined by the energy conversion law mathematical equation in relation to the DC link capacitor. The DC link capacitor voltage always fluctuates from the desired voltage value during the charging process. The energy stored in the DC link capacitor is forced to change as a result. Hence, the self-charging equations [27] are

_{dc}

_{1}is the desired DC link capacitor voltage, V

_{dc}

_{2}is the instantaneous DC link capacitor voltage, and the period of the supply frequency is given by T. The difference between V

_{dc}

_{1}and V

_{dc}

_{2}can be represented as voltage error e, or

_{dc}, and, thus, it should be controlled accordingly. To realize control of e, the PI technique has been implemented [19]; with rapid growth of artificial intelligence techniques, especially Fuzzy Logic Control (FLC) [19], better control of voltage error e can be achieved, as shown in Figure 4. However, from the figure it is noticeable that the e is controlled directly, where the FLC has to perform and act accordingly based on whatever its value (including zero). Thus, the capability of the self-charging algorithm is still limited, especially for dynamic operation.

_{new}[27], or

_{new}provides an appropriate value to minimize such drastic changes due to change of the capacitor’s voltage. Thus, the charging current I

_{dc}[27] becomes

## 5. Simulation Results

^{2}(low irradiance), 600 W/m

^{2}(medium irradiance), and 1000 W/m

^{2}(high irradiance). For comprehensive evaluation, performance of the Simpler ADALINE algorithm in reducing THD level was evaluated with the Modified W-H ADALINE algorithm, by fixing the self-charging with step size error cancellation algorithm. In addition, the performance of the self-charging with step size error cancellation algorithm was compared with that of the Direct Fuzzy-based Self-charging algorithm by fixing the simpler ADALINE algorithm. Among the major parameters which were evaluated, besides THD, were overshoot, undershoot, response time, and energy losses. The simulation sampling time was set at about 6.67 µs, while the learning rate of 0.0001 was configured for both proposed and existing algorithms of current harmonics extraction. The duty cycle to boost up the PV voltage to 400 V

_{dc}was set to 0.46. The PV module used was a SHARP NT-180UI (Sharp Electronics Corporation, Huntington Beach, CA, USA) its characteristics are as shown in Table 1. Table 2 shows the main parameters and components used in this work. The configuration of the proposed PV SAPF is based on a voltage source inverter (VSI) which is considered as a conventional inductor-based converter. According to Middlebrook’s extra element theorem [33], to avoid instability, the input impedance of the converter should be much higher than the output impedance of the filter. For the PV SAPF configuration, the switching frequency was set at high frequency—around 20 kHz. The inductive element inside the PV SAPF increases the input impedance for the high switching frequency; therefore, Middlebrook’s condition is verified and the filter does not affect the stability of the proposed PV SAPF.

_{s}, injection current I

_{inj}, voltage V

_{s}, and load current I

_{L}for the nonlinear load. Figure 8 shows the simulation results of harmonic spectra for different irradiances (including without PV) for the Simpler ADALINE algorithm. The simulation results of harmonic spectra for the Modified W-H ADALINE algorithm are shown in Figure 9. From Figure 7, Figure 8 and Figure 9, the source current I

_{s}is properly compensated for by both current harmonics extraction algorithms. Specifically, for THD, with irradiance of 0 W/m

^{2}, the values are 1.48% and 2.12% for Simpler ADALINE and Modified W-H ADALINE algorithms, respectively. At irradiance of 200 W/m

^{2}, the THDs are 1.62% and 2.25% for the Simpler ADALINE and Modified W-H ADALINE algorithms. After irradiance is increased to 600 W/m

^{2}, the THD recorded using Simpler ADALINE is 1.93%, while for Modified W-H ADALINE, it is around 2.57%. Lastly, at irradiance of 1000 W/m

^{2}, the Simpler ADALINE algorithm gives a THD of about 2.28% and Modified W-H ADALINE algorithm gives a THD of about 2.85%.

_{PV}. The source current I

_{s}is decreased with the increase of I

_{PV}where the load is depending more on power from the PV. Another point to take note of from the findings is during the operation of the normal SAPF, when PV is in the off condition and there should be no additional active power flow to the grid. Only when the PV is in the on condition will additional active power flow to the grid, affecting the injection and source currents. In addition, according to the previous works on SAPF, operation of the normal SAPF compensates only the reactive component, which means it only has the effect of removing harmonics from the grid [34,35]. Therefore, it is confirmed that PV is the main source of producing active power. In comparing both algorithms, Simpler ADALINE clearly shows much better performance over the Modified W-H ADALINE. The significant reduction of THD values shows that the performance of the SAPF is better with the algorithm that is proposed, with or without PV connectivity. Meanwhile, the power factor is improved from 0.89 to almost unity, which directly confirms the effectiveness of the proposed current harmonics extraction algorithm to perform power correction, too.

^{2}, as it is considered as medium irradiance in the Malaysia climate [36]. The performances of both DC link capacitor voltage control algorithms and both harmonic extraction algorithms during off–on operation between PV and SAPF are shown in Figure 10. Consideration is given to evaluate both current harmonics extraction algorithms which were simulated together with the DC link capacitor voltage control algorithm. The self-charging with step size error cancellation algorithm performs at a much lower overshoot (0.5 V) and fast response time (0.1 s), as compared to the direct control where it has high overshoot (4.5 V) with slow response time (1.5 s). Meanwhile, both current harmonics extraction algorithms respond well during off–on dynamic operation, but Simpler ADALINE performs with a much better response time of only 15 ms, as opposed to the Modified W-H ADALINE algorithm which needs 40 ms to respond.

_{loss-Cdc}can be calculated as below:

_{dc}is the steady-state power of the DC link capacitor that should be obtained after change, t

_{1}is the starting time of change, and t

_{2}is the end time of change before achieving steady state. However, considering that the change is linear, the calculation of energy can be performed as follows:

## 6. Experimental Results

_{ac}. Hence, the voltage was put to 200 V

_{dc}, which is the desired voltage of the DC link capacitor. To execute all the control strategies for the single-phase PV SAPF, the DSP TMS320F28335 board was programmed and configured. These strategies include the current harmonics extraction, current control, DC link capacitor voltage control, MPPT, and synchronizer. As in the simulation for dynamic operations, the proposed Simpler ADALINE was compared with the established Modified Widrow–Hoff ADALINE algorithm by using the self-charging with step size error cancellation algorithm as the DC link capacitor voltage control algorithm. All the algorithms were evaluated to validate their performance practically in real-time applications. All the measured waveforms were taken by using an oscilloscope Tektronix TBS1000 (Tektronix, Inc., Beaverton, OR, USA) with 4 channels, 150 MHz bandwidth, and 1 GS/s sample rate. The PV simulator Chroma 62100H-600S (Chroma Ate Inc., Kuei-Shan Hsiang, Taoyuan, Taiwan) was the main PV source used for this experiment. It has a voltage range of 0–1.5 kV with output power up to 15 kW.

_{s}, injection current I

_{inj}, load current I

_{L}, and source current I

_{s}, for different irradiance levels. The outcomes of harmonic spectra with different irradiances (including without PV) for the Simpler ADALINE algorithm are shown in Figure 16 while Figure 17 shows the results of harmonic spectra for the Modified W-H ADALINE algorithm. Figure 18 shows the experimental results of the self-charging with step size error cancellation algorithm with Simpler ADALINE and Modified Widrow-Hoff ADALINE current harmonics extraction algorithms with off–on operation between PV and SAPF. The results of the self-charging with step size error cancellation algorithm with Simpler ADALINE and Modified Widrow–Hoff ADALINE current harmonics extraction algorithm under low to high irradiance operation of PV are shown in Figure 19. Figure 20 shows the energy losses using the self-charging with step size error cancellation DC link capacitor voltage control algorithm for both dynamic operations.

^{2}, 2.54% at 200 W/m

^{2}, 2.8% at 600 W/m

^{2}, and lastly 3.2% at 1000 W/m

^{2}. The THDs obtained are almost the same as in the simulation work. The proposed current harmonics extraction algorithm is proven to work well to compensate current harmonics to below than 5% THD under any level of PV irradiance. The power factor has been improved from 0.86 to almost unity. This confirms the productiveness of the proposed algorithm to accomplish power factor corrections as well. By referring to Figure 18 and Figure 19, the self-charging with step size error cancellation algorithm performs with low overshoot (0.5 V) for off–on operation between PV and SAPF, and only 1 V for change of irradiance. The self-charging with step size error cancellation algorithm also produces a fast response time within 0.3 s for the off–on operation between PV and SAPF, and within 0.4 s for the change of irradiance. The same also applies to the proposed harmonic extraction algorithm where for both dynamic operations, the Simpler ADALINE algorithm achieved a fast response time of only 20 ms. The established Modified Widrow–Hoff ADALINE algorithm produces a slow response time of about 40 ms—about 20 ms slower than the proposed algorithm. This really shows that the proposed current harmonic extraction algorithm performs well with good THD values under various irradiances and fast response times under various dynamic operations. Referring to Figure 20, under the first dynamic operation which involves off–on operation between the PV and SAPF, the self-charging with step size error cancellation algorithm produces low energy losses of only 54 J. The self-charging with step size error cancellation algorithm produces an energy loss of around 112 J for the second dynamic operation of the adjustment of irradiance between low and high irradiance levels.

## 7. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## Nomenclature

ω | Angular frequency |

α | Learning rate |

t_{s} | Sampling period |

e | Average square error |

e(k) | Digital time-varying average square error |

I_{L} | Load current |

I_{L}(k) | Digital time-varying load current |

I_{1} | Fundamental current |

I_{S} | Source current |

I_{S}(k) | Digital time-varying source current |

W | Weight learning factor |

W(k + 1) | Matrix of next iteration weight |

I_{f}(k + 1) | Matrix of next iteration fundamental active current |

W_{an} | Amplitude of the sine component |

W_{bn} | Amplitude of the cosine component |

n | Harmonic order |

N | Maximum harmonic order |

Sin (k ωt_{s}) | Sine function |

V_{dc} | DC link capacitor voltage |

V_{dc1} | Desired DC link capacitor voltage |

V_{dc2} | Instantaneous DC link capacitor voltage |

V_{s} | Source voltage |

Y(k) | Matrix of sine and cosine function |

I_{H} | Harmonic current |

I_{H}(k) | Digital time-varying harmonic current |

I_{f} | Fundamental active current |

I_{inj} | Injection current |

I_{est}(k) | Digital time-varying estimation current |

I_{PV} | PV current |

I_{inv} | Inverter current |

I_{dc} | Capacitor charging current |

I_{CPV} | Capacitor–PV current |

E_{ac} | Charging energy of AC |

P | Real power |

t_{c} | Charging time of the capacitor |

V_{rms} | RMS value of the supply voltage |

I_{dc,rms} | RMS value of the charging capacitor current |

V | Peak value of the supply voltage |

T | Period |

Ө | Phase angle |

∆E | Energy differential |

∆e | Step size error |

e_{new} | New voltage error |

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**Figure 3.**Block diagrams of (

**a**) Modified Widrow–Hoff adaptive linear neuron (ADALINE) and (

**b**) Simpler ADALINE algorithms.

**Figure 5.**Indirect control in self-charging algorithm: (

**a**) block diagram and (

**b**) details of Fuzzy Logic Control.

**Figure 6.**Membership functions for change of voltage error, previous voltage error, and step size error.

**Figure 7.**Simulation results which cover source voltage V

_{s}, load current I

_{L}, injection current I

_{inj}, and source current I

_{s}using both current harmonics extraction algorithms for (

**a**) 0 W/m

^{2}(without PV), (

**b**) 200 W/m

^{2}, (

**c**) 600 W/m

^{2}, and (

**d**) 1000 W/m

^{2}.

**Figure 8.**Simulation results of harmonic spectra for inductive load using Simpler ADALINE algorithm with (

**a**) no active power filter and at (

**b**) 0 W/m

^{2}(without PV), (

**c**) 200 W/m

^{2}, (

**d**) 600 W/m

^{2}, and (

**e**) 1000 W/m

^{2}.

**Figure 9.**Simulation results of harmonic spectra for inductive load using the Modified W-H ADALINE algorithm at (

**a**) 0 W/m

^{2}(without PV), (

**b**) 200 W/m

^{2}, (

**c**) 600 W/m

^{2}, and (

**d**) 1000 W/m

^{2}.

**Figure 10.**Simulation results of DC link capacitor voltage under off–on operation between PV and SAPF by using (

**a**) step size error cancellation and (

**b**) direct control in self-charging algorithms; (

**c**) performance of current harmonics extraction algorithms.

**Figure 11.**Simulation results of DC link capacitor voltage under low to high irradiance using (

**a**) step size error cancellation and (

**b**) direct control in self-charging algorithms; (

**c**) performance of current harmonics extraction algorithms.

**Figure 12.**Simulation results of DC link capacitor power under off–on operation between PV and SAPF using (

**a**) step size error cancellation and (

**b**) direct control in self-charging algorithms.

**Figure 13.**Simulation results of DC link capacitor power under low to high irradiance using (

**a**) step size error cancellation and (

**b**) direct control in self-charging algorithms.

**Figure 15.**Experimental results which cover source voltage V

_{s}(200 A/div), load current I

_{L}(5 A/div), injection current I

_{inj}(5 A/div), and source current I

_{s}(5 A/div) using the Simpler ADALINE current harmonics extraction algorithm for (

**a**) 0 W/m

^{2}, (

**b**) 200 W/m

^{2}, (

**c**) 600 W/m

^{2}, and (

**d**) 1000 W/m

^{2}.

**Figure 16.**Experimental results of harmonic spectra for inductive load using the Simpler ADALINE algorithm at (

**a**) 0 W/m

^{2}(without PV), (

**b**) 200 W/m

^{2}, (

**c**) 600 W/m

^{2}, and (

**d**) 1000 W/m

^{2}.

**Figure 17.**Experimental results of harmonics spectra for inductive load using the Modified W-H ADALINE algorithm at (

**a**) 0 W/m

^{2}(without PV), (

**b**) 200 W/m

^{2}, (

**c**) 600 W/m

^{2}, and (

**d**) 1000 W/m

^{2}.

**Figure 18.**Experimental results of (

**a**) the self-charging with step size error cancellation DC link capacitor voltage control algorithm under off–on operation between PV and SAPF, with (

**b**) Simpler ADALINE and (

**c**) Modified Widrow–Hoff ADALINE current harmonics extraction algorithms covering load current I

_{L}(5 A/div), injection current I

_{inj}(5 A/div), and source current I

_{s}(5 A/div).

**Figure 19.**Experimental results of (

**a**) self-charging with step size error cancellation DC link capacitor voltage control algorithm under change of irradiance of PV, with (

**b**) Simpler ADALINE and (

**c**) Modified Widrow–Hoff ADALINE current harmonics extraction algorithms covering load current I

_{L}(5 A/div), injection current I

_{inj}(5 A/div), and source current I

_{s}(5 A/div).

**Figure 20.**Energy loss analyses for experimental results of the self-charging with step size error cancellation DC link capacitor voltage control algorithm under (

**a**) off–on and (

**b**) change of irradiance operations.

Electrical Characteristics | |
---|---|

Maximum power P_{max} | 180 W |

Short circuit current I_{sc} | 5.60 A |

Voltage at maximum power V_{mp} | 35.86 V |

Current at maximum power I_{mp} | 5.02 A |

Open circuit voltage V_{oc} | 44.8 V |

Type | Value |
---|---|

Switching frequency | 20 kHz |

Injection inductor | 10 mH |

DC link voltage | 450 V_{dc} |

Boost inductor | 600 µH |

PV voltage | 35.86 V_{dc} × 8 |

Line inductor | 2 mH |

DC link capacitor | 1600 µF |

Voltage source | 230 V_{ac} |

**Table 3.**Total Harmonics Distortions (THDs) of current harmonics extraction algorithms in simulation work with different irradiances.

Current Harmonics Extraction Algorithm | Total Harmonics Distortion (%) | |||
---|---|---|---|---|

0 W/m^{2} | 200 W/m^{2} | 600 W/m^{2} | 1000 W/m^{2} | |

Simpler ADALINE | 1.48 | 1.62 | 1.93 | 2.28 |

Modified W-H ADALINE | 2.12 | 2.25 | 2.57 | 2.85 |

**Table 4.**Overall performance of DC link capacitor voltage control algorithms for both dynamic operations.

DC Link Capacitor Control Algorithm | Off-On | Change of Irradiance | ||||
---|---|---|---|---|---|---|

Voltage Overshoot (V) | Response Time (s) | Energy Losses (J) | Voltage Overshoot (V) | Response Time (s) | Energy Losses (J) | |

Self-charging with step size error cancellation | 0.5 | 0.1 | 36 | 1 | 0.2 | 112 |

Direct fuzzy-based Self-charging | 4.5 | 1.5 | 540 | 4 | 1.6 | 896 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Mohd Zainuri, M.A.A.; Mohd Radzi, M.A.; Che Soh, A.; Mariun, N.; Abd Rahim, N.; Teh, J.; Lai, C.-M.
Photovoltaic Integrated Shunt Active Power Filter with Simpler ADALINE Algorithm for Current Harmonic Extraction. *Energies* **2018**, *11*, 1152.
https://doi.org/10.3390/en11051152

**AMA Style**

Mohd Zainuri MAA, Mohd Radzi MA, Che Soh A, Mariun N, Abd Rahim N, Teh J, Lai C-M.
Photovoltaic Integrated Shunt Active Power Filter with Simpler ADALINE Algorithm for Current Harmonic Extraction. *Energies*. 2018; 11(5):1152.
https://doi.org/10.3390/en11051152

**Chicago/Turabian Style**

Mohd Zainuri, Muhammad Ammirrul Atiqi, Mohd Amran Mohd Radzi, Azura Che Soh, Norman Mariun, Nasrudin Abd Rahim, Jiashen Teh, and Ching-Ming Lai.
2018. "Photovoltaic Integrated Shunt Active Power Filter with Simpler ADALINE Algorithm for Current Harmonic Extraction" *Energies* 11, no. 5: 1152.
https://doi.org/10.3390/en11051152