Harmonics Minimisation in Non-Linear Grid System Using an Intelligent Hysteresis Current Controller Operated from a Solar Powered ZETA Converter

Abstract

Due to the non-linear load characteristics in the domestic three-phase grid system, the quality of power transmission is a challenge for researchers. In this paper, the harmonics injected in a three-phase grid system due to the non-linear loads and a solution for harmonics minimisation using the hysteresis current controller (HCC) is presented. The proposed work consists of switched dc loads such as personal computers, SMPS, etc., connected to the three-phase grid system through the rectifier unit. These loads connected with other AC loads inject harmonics in the power lines. The total harmonic distortion (THD) at the power line is therefore increased. A ZETA embedded three-phase inverter using an artificial neural network-based HCC (ANN-HCC) is used to minimise the voltage and the current THDs. To ease the power consumption, a solar photovoltaic system (SPV) is used to power the ZETA embedded three-phase inverter. The output of the SPV is regulated using the ZETA dc/dc converter. However, the hysteresis bands (U_upper and U_lower) are selected using the ANN with respect to the actual value compared with the calculated current error. The vector shifts to the next based on the previous vector applied, and thereby the process repeats following the same pattern. The back propagation (BP)-based neural network is trained using the currents’ non-linear and differential functions to generate the current error. The neural structure ends when the value hits the hysteresis band. Simultaneously, the PWM control waveform is tracked by the neural network output. The proposed system is mathematically modelled using MATLAB/Simulink. An experimental setup of a similar prototype model is designed. The voltage and the current harmonics are measured using a Yokogawa CW240 power quality meter and the results are discussed.

1. Introduction

Distributed generations (DGs) have become a striking choice for integrating power distribution systems due to their cost-effective, technical, and ecological benefits [1,2,3]. Additionally, the advancement in the three-phase power distribution system has introduced the dc/dc converters for their contribution to the power quality improvements. The power quality parameters such as active power flow direction, reactive power, harmonics, and power factor play an essential role in the grid power system [4]. In recent studies, non-linear loads are more commonly found and produce disturbances to other loads in the grid systems that are weak or remote systems. Consequently, the grid connecting both three-phase and single-phase domestic or residential appliances is affected due to the injection of current harmonics in the line, which lowers the power quality of the overall system. The total harmonic distortion (THD) is a series of issues emerging from the non-linear loads connected in the grid system.

The origin of the power system harmonics is due to the characteristic behaviour of the non-linear loads such as uninterrupted power supply (UPS), TVs, computers, printers, adjustable speed drives, fluorescent lighting, arc furnaces, and transformers [5]. These non-linear devices used in residential homes generate current harmonics injected into the grid system that affect other loads. These non-linear distorted waves are identical to the 3rd, 5th, and 7th harmonics that are referred to as the harmonic impedances associated with the current harmonics [6]. The harmonics sources at the point of common coupling are planned with harmonic distortion limits, quality of electric supply, equipment performances, and utilities [7]. When non-linear loads are connected in the distribution system, the performance of the system deviates outside the desired standard value. Hence, the harmonics are to be monitored in the distribution system involving non-linear loads. The harmonics monitoring management is carried out based on the international and national standards [8,9]. The current and voltage harmonic distortions have different standards to maintain depending on the type of load. However, most loads need to have lower current harmonics and within limits during operation.

Several works reported the effectiveness of the converting techniques and their controllers adapted for power quality improvement using sophisticated approaches. Authors also proposed a model predictive control (MPC) method for microgrids that maintains the power quality by regulating the converters to attain the required criteria [10]. These approaches are adopted successfully for interconnected and islanded systems. Further, to overcome the power quality degradation, artificial neural networks (ANNs) and hybrid differential evolution (HDE) are involved in reinstating the frequency and voltage considering the disturbances [11]. Some works proposed a chopper, two PI controllers, and an inverter to improve a fuel cell’s power quality interconnected with the power system network [12]. Each PI controller was tuned using three different evolutionary programs: electromagnetic field optimisation (EFO), modified flower pollination algorithm (MFPA), and harmony search (HS).

Moreover, a unique ANN-based control method that minimized the sag, swell, unbalancing, voltage deviation, frequency, and THD was demonstrated [13]. Further, some researchers recommended a shunt active power filter (SAPF) for microgrid systems encompassing solar, wind, and fuel cell-based distributed generation, and the influence of power quality hitches in an adopted standalone was explored [14]. An upgraded custom power device, namely a distributed power condition controller, was adapted to a multi-microgrid system with greater penetration of various distributed generators on the island and interconnected modes to increase the power quality [15]. An optimal control mechanism for a multi-level converter [16,17] was developed, and this control scheme alleviated the glitches caused by the conventional approaches. Authors also reported a solution to resolve the fast dynamic concerns and fixed-frequency operation using a whole, robust voltage control scheme and angle droop approaches [18]. It is also reported as a robust, fast, and dynamic PI resonance controller with a harmonic compensator (HC) and lead compensator (LC) feedback to manage the current of a 15-level neutral-point-clamped multi-level inverter [19]. In addition, a unified power quality conditioner was suggested as a consistent power quality conditioner for a nine-level structure [20].

Moreover, the most common concern is the accuracy of the harmonic measurements due to their complexity in design, so they are challenging to implement. Furthermore, the measure based on the active power flow, reactive power, and current–voltage ratio is still not accurate; each method has advantages and disadvantages. Various non-linear controllers are available that monitor and control the voltage and current harmonics in the three-phase line. Predictive control (PC), hysteresis current controller (HCC), and sliding mode controllers (SMCs) have been developed by researchers. Among the current controllers, the hysteresis current controller [21] (HCC) is most preferred for its simple design, fast response, and strong robustness to disturbances. However, a space vector-based hysteresis current controller [22,23] is designed for a fast response. In this method, the stator voltages along α and β axes are estimated using current error information and the steady state model of the induction machine. Consistently, the steady-state boundaries and the phase voltages are normalised, and the switching frequency is maintained constant.

Moreover, the zero-sequence current can be suppressed using a wide linear modulation range of zero-sequence voltage-based SVPWM [23]. This is performed by controlling the fundamental plane. The harmonics’ source can be estimated using key factors such as current cancellation due to phase angle diversity and the attenuation owing to system impedance. Certain digital controllers such as analogue-to-digital converters produce variable hysteresis controller bands that are insufficient to stabilise. A digital hysteresis current controller uses a mixed-level scheme [24,25] and prediction-based sampling method to estimate the switching frequency variations in the grid voltage and resolve the switching frequency, respectively. This provides greater comfort for the digital hysteresis current controller, ensuring stabilised switching frequency and high-quality grid-side filtered current.

In modern technology, the DC/DC converter plays a vital role in the dc micro-grid system. The non-linear load present is controlled by the dc/dc converters that provide non-linear bifurcation phenomena for the complex design. The analogue hysteresis controller exploits the oversampling [26], and DC to DC converters are used. Among the dc/dc converters, ZETA converters [27,28,29] are more efficient in operating in continuous conduction mode. Moreover, the converter can work both in buck and boost operation. ZETA converters have very low current harmonics and are usually preferred for drive applications. The proposed system thereby uses a power quality enhancement based on a ZETA converter for the PWM-based three-phase inverter. The current ripple is reduced and helps the inverter circuit regulate the bandwidth range of the hysteresis current controller. The variable band control of the HCC can be performed more efficiently by the intelligent controllers. The artificial neural network-based hysteresis current controller [30,31] has resulted in lower switching losses of the inverter and the ability to control the frequency constantly. Additionally, the bandwidth approaches the reference value to obtain the reduced THDs.

From the above literature survey, it is seen that the behaviour of the non-linear loads such as uninterrupted power supply (UPS), TVs, computers, printers, adjustable speed drives, fluorescent lighting, arc furnaces, and transformers causes the injection of harmonics into the grid system. This affects the overall performance. The proposed method deals with the modelling of the ANN-based HCC for the grid system.

2. Proposed Model

Since the globally increasing modernisation of infrastructure is one of the driving factors leading to the demand for electric power generation, the proposed system uses the solar photovoltaic system to power the dc/dc converter (Figure 1). The ZETA converter is used as the MPPT converter [32] for the solar PV. As discussed, the ZETA converter is in the buck–boost converter family, and a boundless region for maximum power point tracking (MPPT) is achieved. The proposed three-phase grid system has non-linear loads connected in parallel along with other loads. The voltage and the current harmonics injected into the three-phase grid voltages are analysed, and an intelligent controlled ZETA-based hysteresis current controller is proposed.

The proposed system involves the renewable energy distributed generation (REDG) system connected to a three-phase, four-leg inverter injecting the power back into the three-phase grid. The three-phase grid system is powering the sets of three-phase and single-phase loads. Multiple units of personal computers (SMPS loads) are connected along with other loads. We have considered this commercial utility as being primarily powered by a three-phase line through a delta-to-star-connected distribution transformer. The three-phase grid system is thus obtained for utility purposes. The modelling of the proposed system is described in the following sections.

2.1. Modelling of the Solar PV

The ZETA embedded three-phase inverter is powered using the solar photovoltaic system. The size of the solar PV is slightly larger than the magnitude of the grid voltage in consideration of the losses. Hence, a solar maximum peak power, $P_{mpp}$ = 3.4 kW, is well sufficient to power slightly above the peak voltage in the three-phase grid. Vikram 280 W polycrystalline solar panels are selected for the SPV array of an appropriate size. The solar power, $P_m$ = 280 W, open circuit voltage, $V_{oc}$ = 38.70 V, voltage at maximum power, $V_m$ = 31.3 V, short-circuit current, $I_{sc}$ = 9.32 A, current at maximum power, $I_m$ = 8.94 A, are the specifications of the solar panel selected.

2.2. Modelling of ZETA Embedded Three-Phase Inverter

The ZETA dc/dc converter is capable of operating both in the buck and the boost mode by adjusting the duty ratio. Moreover, the efficiency and the voltage gain are better than a regular buck–boost converter. The ZETA embedded three phase inverter is the combination of the ZETA converter with a two-level inverter. In power flow between the AC grid and renewable energy systems (RESs) or any intermittent DC voltage levels, the intermediate circuit capacitor (dc-link) plays a vital role. Due to the variable nature of RESs, the variation in the current is subjected to peak values irregularly. An intermediate circuit capacitor of high value with the ability to withstand these variations and supply sufficient power is required. A typical ZETA converter with the dc-link capacitors is designed to have high values, which may be superimposed with high-frequency ripple voltages of 500 VDC to 1500 VDC. Figure 2 shows the ZETA embedded three-phase inverter.

The ZETA converter is a highly efficient converter operating in buck and boost mode. The output of the ZETA converter is responsible for the voltage across the dc-link. The components of the ZETA converter are designed to always operate in the continuous conduction mode (CCM). The design consists of input and the output inductors (L₁ and L₂) with an intermediate capacitor (C₁). The design of the ZETA converter is estimated from the duty cycle $\left(\delta \right)$.

$$\mathrm{Duty} \mathrm{Cycle}, \delta =\frac{V_{dc}}{V_{dc}+V_{mpp}}$$

(1)

where $V_{dc}$ is an average value of the ZETA output voltage and $V_{mpp}$ is the maximum peak to peak voltage of the solar panel. Under standard test conditions (STCs), for the given model of the solar panel, $V_{mpp}$ = 287.20 V and $I_{mpp}$ = 11.83 A.

For $V_{dc}$ = 300 V, the duty cycle from the Equation (1) is obtained as

$$\delta =\frac{300}{300+287.20}=0.51.$$

(2)

Let $I_{dc}$ be the average current that flows through the dc-link of the VSI. It is estimated as

$$I_{dc}=\frac{P_{mpp}}{V_{dc}}=\frac{3400}{300}=11.33 \mathrm{A}.$$

(3)

The value of the inductors (L₁, L₂) and capacitor (C₁) is estimated as

$$L_1=\frac{\delta V_{mpp}}{f_{sw}\Delta I_{L1}}=\frac{0.62\ast 287.20}{20000\ast 11.83\ast 0.06}=10 \mathrm{mH},$$

(4)

$$L_2=\frac{\left(1-\delta \right)V_{mpp}}{f_{sw}\Delta I_{L2}}=\frac{\left(1-0.62\right)\ast 287.20}{20000\ast 11.33\ast 0.06}=10 \mathrm{mH},$$

(5)

$$C_1=\frac{\delta I_{dc}}{f_{sw}\Delta I_{C2}}=\frac{\left(0.51\right)\ast 11.33}{20000\ast 300\ast 0.1}=9.6 \mathsf{\mu }\mathrm{F}.$$

(6)

2.3. ANN-Based HCC Model

The modelling of the hysteresis current controller (HCC) is done using the current vector components of the three-phase system. Consider a three-phase inverter with six switches. The switches are switched in complementary order such that no two switches in a single leg are turned ON at the same time. The pulse generated for each switch is restricted to turn ON the switches of the same leg. The HCC practically compares the current in each leg with the reference value. The HCC is designed to generate a hysteresis band (U_upper and U_lower). When the phase current exceeds the reference current, the lower switch is closed and, when it falls short, the upper switch is closed.

The d-axis reference current is set to zero $\left(i_d^{\ast }\right)$. According to the Park’s transformation, $i_d^{*}$, $i_q^{*}$, and the phase angle ${\phi }_e$ are transferred to the reference phase currents $\left(i_{abc}^{*}\right)$ = $\left[i_a^{*},i_b^{*},i_c^{*}\right]$. The matrix representation is given as

$$\left[\begin{array}{c}{i}_a^{*}\\ i_b^{*}\\ i_c^{*}\end{array}\right]=\left[\begin{array}{cc}\cos \left({\phi }_e\right)& \sin \left(-{\phi }_e\right)\\ \cos \left({\phi }_e-{120}^o\right)& \sin \left({120}^o-{\phi }_e\right)\\ \cos \left({\phi }_e-{240}^o\right)& \sin \left({120}^o-{\phi }_e\right)\end{array}\right]\left[\begin{array}{c}{i}_d^{*}\\ i_q^{*}\end{array}\right].$$

(7)

The third phase current can be obtained from the measured phase currents $i_A$ and $i_B$ and is given as

$$i_c=-\left(i_a+i_b\right).$$

(8)

The reference current $i_{abc}^{*}$ and the phase currents $i_{abc}$ are compared with the hysteresis comparator. The novel hysteresis current controller uses an artificial neural network to obtain the switching states of phase A, B, and C. The switching states are represented as $k_{abc}$ = $\left[k_a,k_b,k_c\right]$. At each stage of the switching, the back propogation methodology finds the minimum value of the error function in weighted space. On obtaining the minimum error function, the value of the switching states is fixed using the below equations:

$$k_p=\{\begin{array}{c}1, \Delta i_p>+H\\ 0, \Delta i_p<-H\end{array}$$

(9)

where $\Delta i_p$ is the phase current error, H is the hysteresis band. The band limit is obtained as $U_{upper}=+H$ and $U_{lower}=-H$. The phase switching state $k_p$ is unchanged when the current error $\Delta i_p$ is well defined within the limit. Thus, the current distortions are controlled within the limit. Figure 3 shows the hysteresis band across the measured current traced with a bandwidth of 2 H (i.e., BW = +H − (−H)). The point $P_2$ is found to be within the range, hence the value of $k_p$ is freely implemented. This region is called the free region. For the point $P_1$, the value outside the range (unfree region) has to be enforced to bring the point within the range so as to satisfy Equation (9).

The ANN-based hysteresis current controller (ANN–HCC) is shown in Figure 4. The ANN is applied through the PMW mechanism to regulate the grid current. By setting the amplitude of the triangular waveform to 1, the ratio of the output current to the ANN output is determined. This is the gain of the PWM that must equal the current error $\Delta i_p$, approximately close to zero. For the points occurring outside the free region, the approximation is calculated from the state space model.

The ANN controls the band limit and enforces the points that are away from the free region. The ANN is trained to minimise the time taken to bring the point outside the free region. By using the back propagation algorithm, the initial switching states are set with respect to the weight vector of the three-phase current.

The back propagation functions in two steps. The first step is to set the initial switching state of the current vector. The value of $k_p$ is set such that the band (U_lower and U_upper) is within the range.

The time required for the training typically depends on the amount of the training data. The determination of network size involves conciliation between output accuracy, preparation time, and ANN speculation capacities. There is no broad methodology for deciding the right ANN size for a particular issue. The nested loop structure has a slower outer loop formed by the faster inner loop—the three-layered feed-forward NN and the four-layered feed-backward NN form the back propagation technique. The proposed ANN consists of 3 hidden layers of 6 nodes each (Figure 5).

3. Simulation Results

The proposed three-phase solar interfaced grid system is initially verified mathematically using MATLAB/Simulink. The grid system powers various sets of loads. The solar output is inverted using a four-leg inverter and back supplied to the three-phase grid. The dc-link voltage is found to be constant throughout the work. The set of non-linear SMPS loads measures the load voltage and the current. The harmonics injected into the three-phase grid are measured. The system is thereby modelled with a closed-loop ANN-HCC to verify the harmonic levels. The waveforms of the input side grid voltages ($V_r, V_y, V_b$), input side grid currents ($I_r, I_y, I_b$), load side grid currents ($I_{lr}, I_{ly}, I_{lb}$), inverter currents ($I_{r\_inv}, I_{y\_inv}, I_{b\_inv}$), and dc-link voltages are shown in Figure 6.

The peak significance of grid current and voltages at the input side is measured as I_peak = 60 A and V_peak = 500 V, respectively (Figure 6a,b). The system is connected to the non-linear load that injects the harmonics into the grid. The load side peak value of grid current is I_load = 60 A (Figure 6c). The inverter current obtained from the solar interfacing is injected back into the grid. The inverter current was measured as I_inv = 15 A (Figure 6d). The dc-link capacitor is designed to produce a voltage of about V_dc = 300 V (Figure 6e).

The single phase obtained from the phase-neutral of the three-phase connection is modelled as the single-phase connection is connected to the non-linear SMPS loads and the rectifier units forming a set of non-linear loads connected to it. The phase voltage and the currents of the single-phase system are measured to have the phase peak values of I_ph = 30 A, V_ph = 300 V, respectively (Figure 7a,b).

Figure 8 shows the harmonics obtained through the FFT analysis in MATLAB/Simulink. At the fundamental frequency of 50Hz, the magnitude of the total harmonic distortions (THD) with respect to the fundamental value is noted. The voltage and the current harmonics are measured with and without the HCC. The voltage and current THD without the HCC are measured as 27.62% and 7.52%, respectively (Figure 8a,b). The voltage and the current THD with the HCC are measured as 17.62% and 2.56%, respectively (Figure 8c,d).

4. Experimental Validation

The experiment is validated using a single-phase line taken from the three-phase, 4 W distribution system. The experiment is tested for the single-phase line feeding the non-linear loads for convenience. The system considerations are tabulated in

Table 1. Experimental system parameters.

Three-phase supply (r.m.s):	Vl-l = 400 V, 50 Hz
Single-phase supply (r.m.s):	Vph = 230 V, 50 Hz
Single-phase linear load:	R = 36.66 Ω, L = 10 mH
Single-phase non-linear load:	R = 26.66 Ω, L = 10 mH
dc-link parameters:	C = 3000 µF, Vdc = 120 V

.

Using the three-phase voltage source inverter, the dc-link voltage has been inverted. Figure 9a shows the three-phase input voltage of 664 V. The three-phase input current of 40 A is shown in Figure 9b. The proposed system output current of 20 A is shown in Figure 9c, and the dc-link is measured as V_dc = 120 V and shown in Figure 9d.

The total harmonic distortions are measured for the proposed system. The THD measured for the voltage and current without and with the HCC is shown in Figure 10. The voltage and current THDs measured without the HCC are shown in Figure 10a,b. The voltage THD without the HCC is 30.80%, and the current THDs without the HCC are 14.10%. The HCC is designed, and the THDs of voltage and current are noted. Figure 10c,d show the voltage and the current THDs measured with the HCC. The voltage THD using the HCC is found to be 10.60%, and the current THD using the HCC is found to be 2.50%.

5. Comparative Analysis

To study the reliability of the proposed model, THD values are compared between the simulation and hardware experimentation with the HCC and without the HCC in Figure 11 and Figure 12.

The above figures compare the total harmonic distortion (THD) of the current and the voltage obtained with and without the HCC. This analysis indicates that the experimental and simulated results are relatively close for both voltage and current THD. Further, the HCC controlled using the artificial neural network is more efficient with a reduced THD scale, with simulated voltage and current THDs of 17.62% and 2.56%, respectively, and experimental voltage and current THDs of 10.60% and 2.50%, respectively.

6. Conclusions

The proposed system is mathematically modelled using an advanced converting technique along with an ANN, and the research was carried out to study the harmonic distortion in the non-linear loads. The special computers are considered to be the non-linear loads, and the proposed mathematical modelling is performed for a more extensive system of AC grid voltage of 1100 V. The current and the voltage THDs are calculated, and it is observed that the system without the hysteresis current controller (HCC) develops high THD values of voltage and current. The HCC is used for a similar system using an ANN and offers reduced voltage and current THDs. However, the ANN plays a vital role, the THD levels are well reduced, and the power quality is improved for the non-linear system. Compared with the conventional approach, the ANN-based hysteresis current controller has diminished both the voltage and the current THDs to 10.60% and 2.50%, respectively. Moreover, the ZETA converter control on the dc-link is more efficient for the HCC to control the non-linear loads in the three-phase grid system feeding various types of loads. This proposed system can be effectively used for the power quality improvement of the renewable-based distribution system.