Abstract

The voltage quality (VQ) index has become a significant measure of recent power system stability. The integration of photovoltaic (PV) systems plus smart home loads (SHLs) at low voltage levels (LVLs) has resulted in various issues such as harmonics rise and voltage instabilities as a result of faults and systems nonlinearity. In this work, a dynamic voltage resistor (DVR) is implemented to enhance VQ, and its dynamic performance hinges on its control system ability. To enhance the DVR’s control system, for surpassing nonstandard voltage with a quick response and harmonics reduction at LVL under harsh operating events, an optimal controller design using the Harris Hawks algorithm (HHA) is proposed. To verify the value of the suggested solution, the hard operating events (voltage sag, voltage swell, fluctuating voltage, and imbalanced voltage) are examined and assessed. To show the effectiveness of the HHA technique, a comparison of the % total harmonic distortion (THD) reductions achieved by the suggested and conventional controllers of DVR is conducted for the scenarios under study. Moreover, the suggested controller stability is analyzed and assessed using Lyapunov’s function. The benefits of the optimized controller system are inferred from the results, including their robustness, simplicity, efficient harmonic rejection, minimal tracking error, quick response, and sinusoidal reference track. The results of the simulation show that the DVR’s optimized controller is efficient and effective in maintaining a voltage at the needed level with low THD, safeguarding the sensitive load as expected, and showing a noticeable improvement in voltage waveforms. The mathematical modeling of HHA, PV system, DVR, and SHLs are all verified using MATLAB\Simulink.

1. Introduction

Voltage quality (VQ) issues in the electricity sector have already been addressed in a number of ways [1], but specialized units like dynamic voltage restorers (DVRs) [2], STATCOM [3], and unified power quality conditioners [4] are particularly useful for enhancing VQ in power distributing networks (PDNs) [5]. Supplying voltage in series by DVR is a suitable tool for mitigating voltage sag (). is primarily brought on by system faults especially short circuits and overloads. Its degree and the employment of an appropriate DVR rely on the system’s nature, the fault location, type, and impedance, as well as the protection sort. Utilizing DVR is one of the best ways to augment VQ [2, 6]. Numerous types of specialized units were outlined in references [7, 8] together with their functions and merits. Previously and current control solutions mostly concentrate on the voltage compensation step to lower the DVR’s voltage and capacity rating needed. Additionally, phase jump (PJ) correction has drawn increased attention as well [9].

The interline DVR’s effectiveness in alleviating was described in reference [10]. In reference [11], DVR was modeled as an effective tool for protecting sensitive loads from extreme and voltage swells (), and also to control and adjust both and based on the injected power. In reference [12], the analysis of and harmonic suppression using DVR was studied, but renewable generators impacts were not considered. The examination of controlling the voltage of important loads under variable and fluctuating system frequency was made by applying DVR [13]. Despite DVR’s expensive cost, which prevented widespread deployment, particularly in PDNs, it was regarded as the superior unit in securing PDNs from disturbances [14]. In both DVR and STATCOM, a series of voltage and shunt currents were injected, respectively, into the power system to reduce VQ disturbances, and this work proved that the DVR was a more economical option than STATCOM [15]. In references [12, 16], the DVR system was tested and successfully mitigated the voltage instability, but renewable energy sources were not well thought-out where these sources inject harmonics into the power system. Literature [17] only studied DVR performance in surpassing , but our work gives a detailed analysis of DVR to solve the expected VQ problems in PDNs at the low voltage level (LVL).

Due to the flexibility, and low price of the PWM method [18], compared to alternative methods used for multilevel inverter (MI) topologies, the two-level converter (2LC) topology is adopted in this work. The switches in 2LC systems are unable to sustain medium voltage (MV); hence, they cannot be used in MV networks. Outcomes demonstrate great performance in this architecture, with program execution being simple and calculations occurring around 1.66 times faster than in previous topologies [19]. Several papers such as [20, 21] used MI in the DVR system to reduce the switching losses, but MI increases the system cost and complexity which reduce the system reliability. Splitting one DC source into many DC sources was a noticeable issue that appears when applying multilevel topologies [22].

The effects of photovoltaic (PV) systems’ radiation and temperature fluctuations were taken into account when designing various sorts of PV cells [23] and [24]. By developing the proper links and controls, PV models can be utilized as renewable generators with wind generators. In reference [25], mitigation in the PDN using a simultaneous injection of reactive current\power was reported. In reference [26], the performance of a PI controller (PIC)-based DVR for alleviating was studied. Electricity price, reliability, and enhancing VQ are of essential significance to customers in smart systems. To fulfill customers and provide clean energy, utilities with smart PDNs spend a lot of money. The smart grid’s main elements include the smart home (SH). Any SH includes expensive, and electronic devices, where these devices are sensitive to harmonics and instability voltages. In addition SH operation and concepts were fully described in references [2729].

Conventional PIC gains can be adjusted using a variety of methods such as fuzzy logic, genetic algorithms (GAs), quadratic linear regulators (QLRs), neural networks (NNs), and others. The primary limitations of employing a QLR are that overshoot and steady-state errors cannot be completely eliminated, while the major drawbacks of using a GA are that it needs basic data and difficult computations [3032]. The use of NNs produces precise responses, a decrease in deviation, and errors, but it has the drawback that it takes training, and the precision of the outcome is dependent on the quantity of training when used to adjust the coefficient of controllers [33]. The system dynamic response fluctuations and overshoot are reduced when the PID controller is used in place of the PIC, but employing it slows down the system response and also introduces noise when the error is changing quickly [34]. The aforementioned techniques can also be used to adjust the PID controller gains. In this study, Harris Hawks algorithm (HHA) is applied because it achieves success in engineering design problems, satellite image segmentation, air pollution forecasting, prediction of slope stability, two-layer foundation soils, and color image multilevel thresholding segmentation [35]. Finally, to clarify the current work’s importance and superiority a comparison with previously published papers interested in the VQ research area using DVR is performed in Table 1.

This study examines the effectiveness of DVR with its upgraded control system and its effects on enhancing VQ at LVL in PDNs. The total harmonic distortion (THD) produced at the low voltage bus (LVB) is decreased with DVR based on the HHA-PIC compared to without DVR in normal and abnormal conditions, which is a fast transient response for alleviating VQ issues. This research also applies the suggested technique to a PDN and investigates how well it compensates for and and presents the simulation software’s outcomes. Investigating the effectiveness of an HHA-PIC-based DVR in PDN for VQ enhancement under various fault scenarios is the main contribution of this paper. To further demonstrate the advantages of the HHA technique, comparisons between HHA-PIC and Ziegler–Nichols (ZN)-PIC performance in lowering THD at the LVB are made. The outcomes are highly energizing and useful for SH applications.

The rest of this work is structured as follows: The general structure and system elements under study, including DVR, are covered in Section 2, and the PV system is presented at the end of this part. The construction of the proposed DVR control scheme based on the HHA is then presented in Section 3. In addition, the HHA method is introduced in this part. Following that, Section 4 presents the software simulations and outcomes. Section 5 presents the conclusions from the discussions of simulated scenarios.

2. System Description and Modeling

The current work involves connecting the PV for the SH system to an LVB and connecting it to the power grid via a transformer (11 kV/380 V). Figure 1 shows the proposed configuration, which consists of a PV system, SH, power grid, and a DVR with an upgraded control system. Table 2 lists the investigated system parameters.

2.1. DVR System Analysis

To protect sensitive loads, DVR is typically installed on the LVB to which they are linked. Figure 2 depicts the DVR’s structural layout. The storage device, DC capacitor, 2LC, low pass filter (LPF), IT, and bypass switch are the DVR parts. In references [43, 44], details of the DVR unit are described. Literature [45] also offered its equivalent circuit, as well as the voltage and power that it injects under different operating conditions.

The DVR’s injected voltage () is described as follows [46]:where , , , and are the desired load voltage, load impedance, load current, and system voltage under fault conditions, respectively.

is clarified in equation (2):

Equation (1) can be rewritten to be equation (3):where θ, (α, β, and δ) are load power factor angles, phase-angles of , , and .

The DVR’s power output can be written as follows:

The inverter is a vital part of the DVR system, notably in terms of cost. The DC-link capacitor, IGBT switches, and LC filter have the most impact on its cost, with the rest of the electronics having just minor effects. Additionally, a clamped diode that is not required in a 2LC design is included in the price of a 3LC. As listed in Table 3, we will investigate the costs and contrast the 2LC and 3LC systems with the expected world average market pricing in 2021. This analysis clearly shows that the 2LC of DVR system is 46% less expensive than a 3LC of DVR system. The approximate cost of manufacturing the 2L-DVR system under investigation is 70 $/KVAR, or, on average, $700. To preserve VQ and stability in SHs while achieving high efficiency, this price is appropriate [35].

A fault must be detected by the applied control system, which must also compute and determine the voltage\current needed for balancing, produce trigger pulses for the used 2LC, and inject the necessary voltage\current. The 2LC must make up for voltage distortions brought on by PDNs. The system’s inverter injects standard voltages, which are calculated by the 2LC controller. A sinusoidal voltage control method is suggested for controlling the DVR-2LC. To mitigate entire distortions and maintain a steady voltage in this situation, the DVR should be managed. DVR is managed such that its losses are kept to a minimum while the voltage value is normal. To add voltage to the system as soon as is discovered, DVR must respond quickly. The synchronous reference frame method, which also is built on instantaneous supply data, is used to accomplish this [35]. The control system’s overall layout is depicted in Figure 3, along with the system parameters.

2.2. PV System

In general, the PV arrangement under consideration uses DC/DC and DC/AC converters to link the PV array to the LVB [47]. As seen in Figure 4, a PV cell is typically represented electrically by a single diode, series resistance (), and parallel resistance (). Figure 4 symbols are as follows: is the diode current, I is the output current, V is the output voltage, is the produced current, is the irradiance from the sunshine, and is the cell temperature.

The PV’s concept and model are fully defined in references [20, 48]. To model the solar cell, the subsequent equations between (6)–(9) are used:where k is the Boltzmann constant (1.381 × 10−23 J/K), q is the elementary electron charge (1.602 × 10−19 C), is the diode voltage, is the reverse saturation current of the diode a is the diode quality factor, t is the temperature, and V is the cell voltage.

The PV terminal voltage can be written as follows:

The can be given by the following expression:

The PV output power is given by the following expression:where are the number of PV cells, PV voltage, and PV current, respectively.

3. Proposed Control Technique

3.1. Design of PIC Using the ZN Method

Because of PIC’s straightforward design, inexpensive price, and high stability margin merits, it is frequently utilized in engineering applications. However, PIC tuning is challenging, particularly in nonlinear dynamic systems (power system elements). The considered DVR includes a PWM with a PIC and it is described in equation (10) [49].where X and ε are functional to the PWM producer and error signal, respectively.

ε is the difference between a desired and injected voltage. Both and values are dependent on system parameters to determine the wanted stability and response. The ZN technique is fully described and discussed for tuning the PIC in references [50, 51].

3.2. HHA Technique

Heuristic optimization algorithms have already been employed to optimize PIC gains. The HHA is a metaheuristic method that imitates the cooperative behavior of the HH’s successful pursuit technique. It includes the phases of exploration and exploitation similar to other algorithms. Two exploration phases and four exploitation steps are part of the HHA as described in the below equations. Additionally, a novel stochastic strategy to solve several optimization methods is suggested by the mathematical depiction of this cooperative action. The following stages, which are imitated and simulated by the HHA mathematical model, are used by HHs to hunt their rabbits. It is used in this study because, when tested against 29 unrestricted benchmark issues and 6 limited design engineering tasks, it performed better than the other 11 approaches [52]. The following equations are employed to represent the HH’s behavior while around rabbits, and the idea of the HHA is completely defined in [5254]. The implementation of the suggested HHA on the DVR control system is shown in a flowchart in Figure 5.(1)Exploration phase:(2)The transition from exploration to exploitation:(3)Exploitation phase:(a)Soft besiege, where(b)hard besiege (c)soft besiege with progressive rapid dives where,(d)hard besiege with progressive rapid dives

To choose the optimum PIC parameters, HHA and the ZN technique are contrasted in this study. The objective function provided by equation (19) to minimize the integral time absolute error (ITAE) serves as the foundation for the problem formulation for the DVR control system. The chosen PIC gains for the investigated options are presented in Table 4.

3.3. Proposed HHA-PIC

The proposed DVR control system operation is depicted in Figure 6. at the PCC are transformed to the and then to the using Clark’s transformation. is compared with its reference value to produce the error () and then is passed through a rate limiter to regulate its impact on the reaction of the control scheme reaction to eliminate load voltage () overshoot. At the same time, the direct () is compared with its reference value to produce the error () and then is conditioned using the PIC1 to produce . The is summed up with to produce . Meanwhile, the quadrature () is compared with its reference value to produce the error (); then, is conditioned via the PIC2 to generate . Both and are transformed back to employed to generate the appropriate space vector PWM signal. This signal is used to control the converter switches. The converter output voltage is stepped down with the series IT to the electric grid voltage level to get the . is summed up with to produce the regulated . During the compensation process, the feedforward term and the closed-loop feedback control signal are combined to improve the transient responsiveness and get rid of unwanted transient oscillation as seen in Figure 6.

3.4. Analysis of the System’s Robustness and Stability

Many theories, including the Bode diagram, zero pole mapping, and Lyapunov function (LF), can be used to evaluate SA [55, 56]. LF is taken into consideration because it has demonstrated its efficacy in several engineering issues [57]. Equation (1) illustrates the fundamental idea of the DVR, in which the suggested controller will calculate and adjust for all upsets and uncertainties instantaneously while detecting the system’s standard voltage, or LPF. An LPF is in this research to facilitate the suggested controller layout. As a first-order filter, has indeed been chosen, where, .

Also, in (1) can be expressed as follows:where the symbols , , are the time constant, inverse Laplace transformation, and convolution operator, respectively.

Equation (20) is a representation of the dynamics:where , and the symbol represents the lumped uncertain term.

Figure 7 shows the organizational layout of the suggested DVR control system. The standard that the controller uses is produced with normal amplitude, and the frequency and phase are synchronized with the using 3-PLLs [58].

The suggested controller has two inputs ( and ) and one output ( reference). The voltage control loop includes the inputs. The output is utilized to drive the PWM, which creates the converter’s switching signals. A reliable linear reference model should be used in conjunction with the investigated control method to ensure that the closed-loop system responds as needed [59]. The following can be expressed as the control signal:

Using the process outlined in reference [60] supports assessing the LF bounds for . The controlled system’s SA has been implemented using the LF below.

With derivation of (23) and given dynamics (21) and (22), the SA is executed as follows:

When , the equation is formulated as follows:where Q is the nonpositive semi-fixed with the Hurwitz matrix is the supreme eigenvalue of Q. is a limited signal with the upper limit of P, where p is a positive number.

When Young’s inequality is applied, where and is a tuning coefficient to calculate size.

Using yields the correct design for the error signal feedback gain . Therefore, equation (28) is expressed as follows:

When , tends to 0 makings in (28) upper limited by . As a result, for all , has no upper and lower bounds. According to the study above, the closed-loop system is stable with respect to LF bounds.

4. Simulated Results and Discussion

Numerous delicate electrical and electronic parts of SHs, such as nonlinear loads fed by renewable energy sources like PV systems, can rise harmonics and VQ disturbances at the LVB where these systems are connected. Figure 1 shows the single-line schematic of the studied configuration. In this part, to verify the effectiveness of the DVR control system optimized by the HHA in mitigating VQ disturbances, a set of simulation scenarios have been carried out using MATLAB/Simulink environment within a changeable voltage profile in the grid. For more details, the system characteristics (PV, SH, DVR, and other elements) used in the simulation process are listed in Table 2. The studied simulation scenarios are: , , voltage fluctuations (), and transient double line to ground fault (DLGF) as well as measuring generated harmonics at the LVB are performed to assess the DVR efficacy. The HHA is designed and implemented in the DVR two-control loop system to obtain the optimal PIC gains, which improves the functionality of the DVR. Additionally, as shown in Table 5, %THD at LVB is assessed in the investigated scenarios to further elucidate the efficacy of the HHA. To properly validate the DVR impact on VQ improvement, the security mechanisms are turned off in the current article during fault situations.

4.1. Scenario A: Alleviation

A serious fault that happens at the grid leads to 54% at the LVB for (0.04–0.06) seconds, as depicted in Figure 8(a). Figure 8(a) and 8(b) depicts the waveforms of the 3-phase voltage at the LVB without and with improved DVR control loops, respectively. Injection of the proper voltage value by DVR maintains the voltage at LVB at its rated value of 1 pu, which reflects the DVR role. The installation of the DVR system quickly restored the value of in 0.5 ms as depicted in Figure 8(b).

The injection voltage from the DVR is not completely sinusoidal because it is dependent on PWM and higher frequency switches, and this issue makes harmonics arise\ appearance. To boost the DVR’s dynamic performance, it is therefore required to upgrade the control system. Equation (29) yields the value of %THD of the voltage () [61].where and are voltage fundamental and voltage harmonic components, respectively.

The obtained %THD of voltages in the studied operating conditions: without DVR\base case (), ZN-PIC-based DVR (), and HHA-PIC-based DVR () are 17.19%, 3.9%, and 1.74%, respectively at the LVB as listed in Table 5. THD reduction in was 89.877%, compared to 77.31% in , showing a significant improvement in these waveforms and the significance of the HHA.

4.2. Scenario B: Alleviation

A severe fault that takes place at the grid results in 160% during the range, t = 0.04 seconds and t = 0.06 seconds, as shown in Figure 9(a). Figure 9(a) and 9(b) displays the waveforms of the 3-phase instantaneous voltage at the LVB either without or with an upgraded DVR control system, respectively. The voltage at LVB is kept constant at 1 pu by infusing the desired voltage value by the DVR unit fast (0.5 ms), as shown in Figure 9(b). Additionally, maintaining the voltage at 1 pu ensures that the devolved DVR equipment properly does its necessary work (mitigation of ).

The measured %THD of voltages in , , and are 14.97%, 2.04%, and 1.28%, respectively, at the LVB during as listed in Table 5. In , THD percentage reduction was 86.37%, while THD percentage reduction in was 91.38% showing a significant improvement in these waveforms and the value of the HHA. As a result, in both these instances () and the one before it (), using an HHA-PIC in the DVR control loops is preferable to using a ZN-PIC.

4.3. Scenario C: Alleviation

In this scenario, the dynamic performance assessment of devolved DVR to surpasses is investigated here. The system voltage fluctuated between 0.04 and 0.08 seconds, reaches 1.5 pu from (0.06–0.08 seconds) and reaches 0.65 pu from (0.04–0.06 seconds) as displayed in Figure 10(a). Figure 10(a) and 10(b) depicts the waveforms of the 3-phase voltages at the LVB either without or with an upgraded DVR control system, respectively. Figure 10(b) illustrates that the proposed DVR successfully surpasses the harsh fluctuated voltage and kept it at its reference value (1 pu).

The generated %THD of voltages in , , and are 29.83%, 5.96%, and 2.76%, respectively, at the LVB during as listed in Table 5. In , THD percentage reduction was 80.02%, while THD percentage reduction in was 90.74% showing an important perfection in voltage waveforms and the HHA effect. From this table, the HHA-PIC performs better than the ZN-PIC for the DVR.

4.4. Scenario D: Mitigation of Transient DLGF

A transient DLGF is applied between (0.03–0.08) seconds at the grid as seen in Figure 11, which causes system instability. Waveforms of 3-phase instantaneous voltage on the LVB with and without the proposed DVR are shown in Figure 11(a) and 11(b), respectively. When this fault takes place in the investigated system, the LVB magnitude is decreased from 100% to approximately 40% and that causes voltage instability as seen in Figure 11(a). Figure 11(b) indicates that the DVR overcomes this fault, keeping LVB voltage value at 1 pu, and maintains network stability speedily within 0.5 ms.

The obtained %THD of voltages in , , and are 20.79%, 1.84%, and 1.29%, respectively, at the LVB under DLGF as listed in Table 5. In , THD percentage reduction was 91.14%, while THD percentage reduction in was 93.79% which indicates a great enhancement in these waveforms and the HHA importance. Consequently, in this scenario, the same as in previous scenarios, the use of an HHA-PIC in the DVR control loops is superior to the ZN-PIC. Table 6 sums up voltage values under all studied fault scenarios for clarifying the benefit and impact of the developed DVR.

4.5. Harmonics Mitigation Analysis

The main reasons for generated harmonics are power converters and nonlinear loads, discharge lighting, and electrical machinery. THD thus appears as one of the key factors to consider when examining the output waveforms of an electric system. The voltage harmonics have reached high hazardous levels at the LVB under regular conditions, exceeding the allowable limits, and exposing the LVB elements to severe damage. The obtained %THD of voltages in , , and are 13.42%, 0.1%, and 0.04%, respectively, at the LVB during normal operating condition (NOC) as listed in Table 6. In , THD percentage reduction was 99.25%, while THD percentage reduction in was 99.71% which indicates a great enhancement in these waveforms and the HHA method impact.

The %THD results are clarified in Table 6, which involve normal and abnormal operating conditions. Table 5 indicates the superiority of the HHA-PIC over the conventional ZN-PIC in mitigating harmonics. In addition, more instability in the system voltage injects more harmonics. The bar chart in Figure 12 is used to display the performance comparison of all , , and in terms of percentage figures for %THD of LVB to highlight the superiority of the HHA-PIC for the DVR. In particular, it is useful for showing the relationship between , , and and % THD under the studied scenarios.

5. Conclusion

This manuscript proposed an optimized and efficient DVR control system to effectively protect LVB from voltage abnormalities with low THD. The PICs of DVR are designed and implemented using the proposed HHA and ZN methods to mitigate the studied harsh operating events that may take place in the power system. To emphasize the distinctive contribution of this work, a review of other pertinent previous publications on the subject has also been summarized and presented. The analysis and validation of the suggested controller’s stability using LF stability show that the control has been bounded stable. The outcomes prove that HHA is efficiently finding the optimal PIC gains with no complexity and simple calculations. Furthermore, the obtained gains from HHA compared to ZN showed that the DVR was more efficient, especially in reducing harmonics. The efficiency of the proposed approach is assessed under , , , and DLGF scenarios and it improves the VQ as well as harmonics reduction compared with and . Tables 5 and 6 show the voltage values and %THD of voltage, respectively, at LVB under all the studied scenarios to declare the effectiveness of HHA. Performance-wise, HHA-PIC outperforms ZN-PIC, and THD generated by DVRs based on HHA-PIC is lower than THD produced by DVRs based on ZN-PIC. The THD study revealed that was the worst scenario, and with ZN-PIC %THD damped by 80.02%, this percentage was insufficient to keep the LVB within acceptable bounds (per IEEE standards), whereas HHA-PIC %THD damped by 90.74%, was sufficient to do so. Finally, it can be mentioned that with , simple control method, faster response, balanced voltages, and effective harmonic cancelation are the deduced key points that assist SH to operate without VQ problems.

5.1. Future Research Directions

The future research directions of the current study are as follows:(1)Adaption of the optimized DVR controller with HHA for microgrids applications(2)Integration of fuel cell at the DC side of DVR and comparing it with battery and PV systems(3)Implementing newly hybrid optimization algorithms(4)The proposed option can be applied to achieve fault ride-through capability for renewable generators

Abbreviations

DVR:Dynamic voltage resistor
THD:Total harmonic distortion
VQ:Voltage quality
PWM:Pulse-width modulation
:Voltage swell
:Voltage sag
PDNs:Power distributing networks
2LC:Two-level converter
MV:Medium voltage
PCC:Point of common coupling
LVB:Low voltage bus
LVL:Low voltage level
PIC:PI controller
GA:Genetic algorithm
QLR:Quadratic linear regulator
NNs:Neural networks
ZN:Ziegler–Nichol’s
HHA:Harris Hawks algorithm
DLGF:Double line to ground fault
SH:Smart home
IEEE:Institute of Electrical and Electronics Engineers
:Voltage fluctuations
MI:Multilevel inverter
IT:Injection transformer
PV:Photovoltaic
NOC:Normal operating condition
CS:Cuckoo Search
HIL:Hardware-in-the-loop
PSCAD:Power system computer-aided design
EMTDC:Electromagnetic transient design and control
OC1:Without DVR\base case
OC2:ZN-PIC-based DVR
OC3:HHA-PIC-based DVR
pu:per unit.

Data Availability

The data used to support the findings of the study are available on request from the corresponding author.

Conflicts of Interest

The authors declare that they have no conflicts of interest regarding the publication of this article.