Perspective Chapter: Mitigation of Power System Harmonics with the Incorporation of Active Filter for a Radial Distribution System

Abstract

Harmonics in power systems can cause various problems, including equipment damage, power quality degradation, and increased losses. Active filters have been proven to be an effective solution for mitigating harmonics in power systems. In this research work, the effectiveness of active filters in reducing harmonics is evaluated in MATLAB environment by implementing sparrow search optimization technique. To carry out the simulation results a standard IEEE 13 bus test system and unbalanced power system is considered to meet the IEEE 519 standards. The obtained simulation results demonstrate the significant reduction of harmonics with incorporation of active filters. The obtained simulation results show that hybrid active filter provides the best harmonic mitigation performance. The analysis shows that the use of active filters is economically feasible for reducing harmonics in power systems. Finally, this book chapter provides valuable insights into the application of active filters for power system harmonics mitigation and can help power system engineers and operators to improve the quality and reliability of their systems by implementing Sparrow search optimization technique.

1. Introduction

Electricity is provided via power systems, which are important infrastructures for a variety of industrial, commercial, and residential purposes. Power system harmonics, a major problem brought on by the growing usage of non-linear loads and power electronic devices, poses a serious obstacle. Harmonics are unwanted distortions in the voltage and current waveforms that can cause several problems, including higher losses, poorer power quality, and malfunctions in delicate equipment. As a result, power system engineers and researchers are now extremely concerned with the reduction of power system harmonics [1]. Newfound options for addressing harmonics-related issues have emerged with the emergence of sophisticated power electronic devices and control techniques. To reduce harmonics and boost the performance of the entire power system, researchers have been concentrating on creating creative solutions that integrate hardware and software techniques. In terms of harmonics mitigation, the addition of renewable energy sources like solar and wind to the power grid has created new difficulties. Therefore, there is an urgent need for current research and useful techniques to handle these harmonics-related problems and guarantee the dependable and effective operation of power systems. The power grid is subject to various disturbances, including power system harmonics. Harmonics are voltage or current waveforms with frequencies that are integer multiples of the fundamental frequency, typically 50 Hz or 60 Hz. The general schematic view of harmonics waveform with respect to reference waveform is shown in Figure 1 respectively.

Figure 1.

Harmonic distortion waveforms of power system.

These harmonics arise from non-linear loads, such as power electronic devices, and can cause a range of problems, including increased losses, reduced power factor, equipment overheating, and interference with communication systems [2]. In this book chapter the mitigation of power system harmonics for the IEEE 13 bus radial distributed test system with the incorporation of shunt active filter. The shunt active filters play a vital role in mitigating harmonic distortion, improving power quality, ensuring compliance with standards, compensating reactive power, and enhancing the performance and reliability of power systems. They are an essential tool in modern electrical networks where non-linear loads are prevalent.

2. Significance of power quality in distributed power system

Poor power quality can lead to a range of issues, particularly in microelectronics environments. In the past, electrical problems on mechanical equipment may have gone unnoticed, but they can significantly impact the operations of high-tech equipment. Understanding and preventing power-related issues is crucial for equipment owners, managers, designers, and other meter users, as a substantial portion of power quality problems arise from the consumer’s end. Power quality pertains to the physical properties of the supplied power during regular conditions, ensuring that it does not cause any disruptions or problems in the customer’s processes [3]. Voltage, current, or frequency deviations resulting from power quality problems can cause equipment failures or malfunctions for customers [4]. The quality of power supply focuses primarily on voltage profile improvement and the reliability of electrical supply. Voltage disturbances occur when the phase voltage deviates from its normal characteristics, potentially leading to meter malfunctions. A reliable electrical supply, on the other hand, is adequate (in that it can meet the demand), secure (in that it can survive unexpected problems like system malfunctions), and available (in that it can prevent long-term outages) [5, 6]. Disruptions in power quality are widespread in commercial, industrial, and utility networks. Lightning events often bring on these disruptions. Disruptions in the electrical grid can also be caused by switching events and oscillatory transients. Current and voltage harmonic components are generated when non-linear loads are applied. Harmonics are voltage and current sinusoidal waves whose frequency is an integer multiple of the fundamental frequency. These periodic voltages are added on top of the system’s sinusoidal voltage. As a result, other devices plugged into the electrical system are subjected to increased strain due to these currents and voltages [7]. To overcome those concerns optimal placement of shunt active filters integrated with the radial distribution system is one of the key solutions. Shunt active filters play a significant role in reducing the total harmonic distortion (THD) in power systems. Shunt active filters are purpose-built to minimize the presence of harmonics within the power system. They achieve this by actively injecting harmonic currents that possess equal magnitudes but opposite phases to the existing harmonics. As a result, shunt active filters effectively cancel out these harmonics, leading to a reduction in total harmonic distortion (THD). This reduction in THD facilitates the generation of cleaner and more sinusoidal voltage and current waveforms. To maintain adherence to power quality standards and regulations like IEEE 519 and IEC 61000-3-4, power systems can employ shunt active filters to mitigate THD effectively.

3. Assessment of power quality indices under the harmonics

Power quality indices offer a quantitative assessment of the electrical power quality within a system. Harmonics, which refer to undesirable voltage or current distortions occurring at frequencies that are integer multiples of the fundamental frequency, can have a notable impact on power quality. The following are several commonly employed power quality indices utilized to evaluate the influence of harmonics [8].

Total Harmonic Distortion: The fundamental metric for measuring the degree to which distorted waveforms deviate from a pure sine wave is total harmonic distortion (THD). It provides a numerical representation of the power grid’s current and voltage waveform distortion. The total harmonic distortion (THD) is calculated by dividing the sum of all harmonic components by the power of the fundamental frequency. Eq. (1) gives a the generic mathematical formulation of the THD.

$$\mathit{THD}=\sqrt{{\mathit{ID}}_{\mathrm{1}}^{\mathrm{2}}}+{\mathit{ID}}_{\mathrm{2}}^{\mathrm{2}}+{\mathit{ID}}_{\mathrm{3}}^{\mathrm{2}}\dots \dots \dots \dots \dots {\mathit{ID}}_{\mathit{n}}^{\mathrm{2}}$$E1

Eq. (2) illustrates the mathematical representation of Total Harmonic Current (THC), which is caused by the summation of current orders from 2 to 40. The value of THC serves as the foundation for the installation of active filters. Mathematical representation of THC can be expressed as follows:

$$\mathit{THC}=\sqrt{{\sum }_{\mathit{n}=\mathrm{2}}^{\mathit{n}=\mathrm{40}}{\mathit{Ih}}^{\mathrm{2}}}$$E2

Eq. (3) represents the mathematical expression of Total Harmonic Distortion Current (THD_i), which quantifies the level of distortion in a waveform. THD_i is derived by dividing the THC by the fundamental current. This equation illustrates the relationship between THD_i, THC, and the fundamental current.

$${\mathit{THD}}_{\mathit{i}}\mathit{=}\sqrt{{\sum }_{\mathit{n}\mathit{=}\mathrm{2}}^{\mathit{n}\mathit{=}\mathrm{40}}\frac{{\mathit{Ih}}^{\mathrm{2}}}{{\mathit{I}}_{\mathrm{1}}}}=\frac{\mathit{THC}}{{\mathit{I}}_{\mathrm{1}}}$$E3

I₁ represents fundamental current component and I_h represents harmonic current of the n^th order. Eq. (4) represents the mathematical expression of Total Harmonic Distortion voltage (THD_v) respectively, which quantifies the level of distortion in a waveform. THD_V is derived by dividing the THC by the fundamental voltage. This equation illustrates the relationship between THD_v, THC, and the fundamental voltage.

$${\mathit{THD}}_{\mathit{v}}=\sqrt{{\sum }_{\mathit{n}=\mathrm{2}}^{\mathit{n}=\mathrm{40}}\frac{{{\mathit{V}}_{\mathit{n}}}^{\mathrm{2}}}{{\mathit{V}}_{\mathrm{1}}}}=\frac{\mathit{THC}}{{\mathit{V}}_{\mathrm{1}}}$$E4

Shunt active filters serve as electronic devices employed in power systems to mitigate harmonic distortion and enhance power quality. Their specific purpose is to compensate for reactive power and harmonic currents within the system, resulting in the reduction of voltage distortion and improvement of the overall power factor.${\mathit{V}}_{\mathbf{1}}$ indicates fundamental voltage component and ${\mathit{V}}_{\mathit{n}}$ represents voltage of nth harmonic order.

3.1 Integration of active filters in distribution systems

The integration of hybrid active filters into distributed systems involves incorporating these filters into power distribution networks. The primary objective is to address power quality concerns arising from harmonics, voltage fluctuations, and other disturbances. Hybrid active filters leverage the benefits of both active and passive filters to deliver efficient and reliable compensation for power quality issues.. The primary aim of active filtering is to address these issues dynamically, instead of relying on predetermined components with high ratings, which are typically bulky passive components [9]. This approach allows for a significant reduction in rating requirements. Based on the specific nature of the problem, active filters can be implemented in three primary topologies: shunt type, series type, or a combination of both known as shunt-series type active filters [10]. The schematic representation of active filter is integrated with distributed system is shown in Figure 2 respectively. By integrating hybrid active filters into distributed systems, several benefits can be achieved. Hybrid active filters exhibit effective harmonic suppression, reducing distortion levels and ensuring power supply quality remains within acceptable limits. They provide voltage regulation capabilities to compensate for sags, swells, and fluctuations, thereby ensuring a stable and reliable power supply. With fast response times and adaptability to changing system conditions, hybrid active filters are well-suited for distributed systems that experience diverse loads and disturbances. Moreover, the active filters integrated into the hybrid configuration enhance power factor, compensating for reactive power, minimizing energy losses, and improving overall system efficiency.

Figure 2.

Integration of active filter with distributed test system.

3.2 Active filter design

The Active Harmonic Filter, utilizing IGBT semiconductors and multiple control loops, injects a dynamic cancelation signal into the power line, effectively reducing harmonics and improving Power Factor. This advanced technology from Power Correction Systems enhances AC Motor Systems and AC Variable Frequency Drive (VFD) Systems’ performance and functionality, while seamlessly integrating with a wide range of electrical and electronic devices in their ability. Active filters provide harmonic compensation without concerns about reactive power at fundamental frequencies. Consequently, the rated power of an active filter can be lower compared to an equivalent passive filter serving the same non-linear load. Moreover, active filters avoid causing system resonances that might otherwise shift a harmonic problem from one frequency to another. Power electronics play a crucial role in the active filter concept by generating harmonic current components that counteract those from non-linear loads. The active filter achieves this by utilizing power electronic switching to nullify the harmonic currents produced by the non-linear load. The foundation of the active filter architecture under study in this lecture is a pulse-width modulated (PWM) voltage source inverter, which connects to the system through a system interface filter, as depicted in Figure 3 respectively. In this setup, the filter and the load being corrected are connected in parallel, commonly referred to as an active parallel or shunt filter.

Figure 3.

Active filter design and methodology.

The SAPF structure comprises two main components: power circuits, consisting of power semiconductor switches, capacitors, inductors, and possibly power diodes in certain SAPF topologies, and the control system, designed to regulate the switching function of the switches. Using Figure 3 and the PCC, one can apply Kirchhoff’s current law (KCL) to calculate the current flow in a harmonic-polluted power system before integrating a Active Power Filter (APF). This makes understanding the fundamental concept of APF relatively straightforward through observation of current flow in the power system.

$${\mathit{i}}_{\mathit{s}}\mathrm{=}{\mathit{i}}_{\mathit{L}}\mathrm{=}{\mathit{i}}_{\mathrm{1}\mathit{L}}\mathrm{+}{\mathit{i}}_{\mathit{H}}$$E5

In the context of i_S representing the source current and i_L representing the load current, the latter may consist of i_1L (fundamental current) and i_H (harmonic current caused by the presence of harmonic-producing loads). It is crucial to recognize that i_S is currently distorted and not in phase with the source voltage V_s, primarily due to the influence of i_H. Therefore, the main objective of implementing a shunt active power filter is to eliminate i_H.

Figure 3 illustrates the addition of two more current flows to the power system following the installation of SAPF at PCC. Firstly, the SAPF injects a mitigation current into the power system through PCC to cancel out i_H (referred to as the injection current in this study). The injected mitigation current matches the size and phase of the i_H current. Secondly, the SAPF utilizes a small amount of current (known as the dc-link charging current i_dc) to maintain a constant voltage V_dc across its dc-link capacitor C_dc. This ensures effective control of switching losses and ensures the SAPF operates consistently and reliably. Eq. (5) can be expressed mathematically using KCL as follows;

$${\mathit{i}}_{\mathit{s}}\mathrm{=}\left[{\mathit{i}}_{\mathit{L}}\mathrm{+}{\mathit{i}}_{\mathit{H}}\right]\mathrm{-}{\mathit{i}}_{\mathit{inj}}\mathrm{+}{\mathit{i}}_{\mathit{dc}}$$E6

The voltage level across the dc-link capacitor has a direct impact on the size of the produced${\mathrm{i}}_{\mathrm{inj}}$. The produced${\mathrm{i}}_{\mathrm{inj}}$ will perfectly match the${\mathrm{i}}_{\mathrm{H}}$ current, causing their total cancelation, after the voltage across the dc-link capacitor has reached the correct level and is constantly maintained. As a result, Eq. (6) can be further simplified and represented in Eq. (7) respectively.

$${\mathit{i}}_{\mathit{s}}\mathrm{=}{\mathit{i}}_{\mathrm{1}\mathit{L}}\mathrm{+}{\mathit{i}}_{\mathit{dc}}$$E7

With this regard the harmonic distortion of the implemented test system has mitigated effectively by incorporating shunt active power filters and improves the system stability.

4. Optimization techniques taxonomy in reduction of THD

Optimization is a fundamental mathematical discipline extensively utilized across various engineering fields. It provides essential tools in the pursuit of increasingly optimal solutions. Typically, an optimization problem encompasses a defined objective function and constraints. In many scenarios, multiple objectives exist simultaneously, necessitating the use of several goal functions. To attain the best possible outcome, a multicriteria analysis becomes imperative. Multi-objective optimization is notably complex since objectives often conflict with each other, requiring a trade-off to be established. As a result, solutions obtained through multi-objective optimization represent Evolution-based algorithms, inspired by natural evolution, and are utilized to generate populations for algorithmic solutions [11, 12]. These algorithms involve creating individuals through processes such as mutation, crossover, or selection of the best solutions from a mathematical model [13]. The Genetic Algorithm (GA) is a well-known example of this type of algorithm because it is inspired by Darwin’s theories of evolution. Differential Evolution (DE), Backtracking Search Algorithm (BSA), and the Evolution Strategy are only some of the numerous methods that have been created.

Algorithms based on Swarm Intelligence mimic the cooperative efforts of insects, fish, and birds as they forage for food or pursue prey. These collective actions serve as the basis for mathematical models [14, 15]. Particle swarm optimization (PSO), created by Kennedy and Eberhart, is a well-known example of such an algorithm. Cat swarm optimization (CSO) is another computational paradigm like those used by ants and honeybees. Algorithmic techniques like Simulated Annealing (SA) and the Gravitational Search Algorithm (GSA) are based on the principles of physics that govern the cosmos [16]. Modeling human behavior mathematically allows for the development of relational algorithms. The success of these models has a one-to-one correlation with how people act [17, 18]. These trade-off solutions, which enhance one criterion while sacrificing another, constitute a Pareto set. The selection of a solution from the Pareto set ultimately depends on individual preferences. So far many of the research problems have been solved by implementing PSO, GA, and other mathematical algorithms. The possibility of implementing Sparrow search algorithm in harmonic mitigation of IEEE- 13 bus test system is identified in this book chapter. One of the applications of sparrow search algorithm is implemented to solve optimal energy management of grid-connected microgrid problem in [19]. The optimization taxonomy which includes heuristic, meta-heuristic and other mathematical optimization approaches is represented in Figure 4 respectively.

Figure 4.

Optimization taxonomy.

4.1 Methodology for minimizing THD of IEEE: 13 bus test system

The use of optimization algorithms influenced by nature has been increasingly common in recent decades [20] due to the tendency of deterministic algorithms to get stuck in local optima. Swarm intelligence-based optimization algorithms are at the forefront of the field because of their ability to efficiently solve global optimization problems. The Sparrow Search Algorithm, developed by Jiankai Xue and Bo Shen [21] is a notable addition to this class. The biological traits of sparrows inspired this program’s robustness and stability. The system took cues from the birds’ foraging behavior, collective knowledge, and anti-predator strategies. Sparrows, intelligent omnivores that primarily feed on grains and weeds, are used as a basis for the mathematical modeling of SSA. Both producers and scavengers, these sparrows use a wide variety of foraging strategies to ensure the survival of their flocks. Scroungers rely on producers to get their food, while producers actively search for it. Seventy-five percent of the sparrow hosts act as producers, while the other 25% act as scavengers. Foraging refers to the practice of gathering food in a social group. When one or a few sparrows sneak away with food while evading predators, they sound an alarm chirp to warn their fellow birds. Figure 5 depicts how sparrows forage for food. The mathematical formulation of the sparrow optimization approach and its applications in solving complex engineering problems is briefly discussed in [22] respectively. In [23] optimal placement of DG unit problem is solved by implementing intelligent optimization approach. The harmonic mitigation problem is tackled in [24] by implementing ETAP software. So far discussed in the existing literature review the optimization approaches are implemented for different research problems like energy management, optimal scheduling, overall reduction of operating costs respectively. But in case of mitigation of harmonic distortion of the IEEE-13 bus test system by using sparrow search algorithm is not implemented. The application of sparrow search optimization approaches has been discussed in [25] with real time engineering problems. The proposed algorithm is to evaluate the performance of IEEE-13 bus radial distributed test system followed by minimizing harmonic distortion content. The decision variables are voltage and current harmonics followed by Eq. [3] and Eq. [4] respectively. The proposed problem is deal with the harmonic mitigation of the IEEE-13 bus standard test system. The proposed SSA algorithm is implemented to find the distribution network load flow parameters such as voltage profile at each node and other network parameters subjected to load flow analysis with and without incorporation of active filters. Further the incorporation of shunt active filter in the test system is evaluated all the network flow parameters by using SSA algorithm. The obtained simulation results are represented by using FFT window in MATLAB to analyze the harmonic distortion for the IEEE 13 bus test system respectively.

Figure 5.

Conceptual illustration of foraging behavior of sparrows [22].

5. Numerical evaluation and discussion

In this book chapter mitigation of power system harmonics with the integration of active filters by implementing sparrow search optimization technique is evaluated. The considered standard radial distributed test system IEEE 13 bus with the integration of active filter is optimally placed to enhance the voltage profile indexes and mitigate the harmonic distortion content in the considered test system. The single line diagram of IEEE 13 bus radial distributed test system is shown in Figure 6 respectively. The proposed optimizer sparrow search effectively mitigates the harmonic content distortion of voltage and current of the considered test system. The incorporation of active filters with the unbalanced test system mitigates the harmonic content distortion and enhances the voltage profile indices effectively are represented in Figures 7 and 8 respectively.

Figure 6.

Single line diagram of IEEE-13bus radial distributed test system [23].

Figure 7.

Voltage THD of bus number 10 (a) with active filter (b) without filter.

Figure 8.

Total harmonic distortion (%) of the corresponding bus number (a) with active filter (b) without filter.

The primary objective of this book chapter is implementing sparrow search algorithm on IEEE 13-bus radial distributed unbalanced test system equipped with active filters is evaluated within the MATLAB computing environment. The implementation was conducted on an HP Laptop equipped with an Intel Core i7 processor running at 2.4 GHz and with a RAM capacity of 12 GB. The effectiveness of the developed algorithm was evaluated using an unbalanced-13-bus radial distribution system (unbalanced-13-bus-RDS).A harmonics analysis is performed on an IEEE 13-bus distribution system that supplies various types of industrial and commercial loads, as shown in Figure 5. The system comprises a main supply at 69 kV connected to bus 4 and a local generator operating at bus 1 with a voltage of 13.8 kV. A 6000 kVAr capacitor, rated for improving power factor, is connected at bus 3. The customers on bus 7 and bus 10 are served by non-linear loads, which are known to produce harmonics. The integration of active filters to the IEEE-13bus distributed test system with and without presence the voltage profiles and total harmonic distortion is shown in Figures 7 and 8 respectively.

To conduct further testing on the proposed sparrow search algorithm, the active filter incorporation in the power system for reducing total harmonic distortion content which includes voltage and current harmonics. Instead of placement of DG units or harmonic filters the shunt active hybrid filters play a significant role for reducing power system harmonics. To determine the optimal settings of the proposed algorithm parameters, 20 independent runs were performed, with a maximum of 100 iterations allocated for adjusting each parameter. A swarm population size of 50 particles, which includes number of Producers are 0.8, and number of Scroungers are 0.2 respectively. By utilizing the developed sparrow search algorithm, the optimal location of active filters in the considered test system were successfully identified, resulting in minimized overall total harmonic distortion of the IEEE-13 bus radial distributed unbalanced test system. In addition to the evaluation of total harmonic distortion of IEEE- 13 bus distributed test system with the proposed algorithm the voltage profiles of the corresponding busses are evaluated and represented in Figure 9 respectively. The voltage profile at bus 10 has been enhanced by 7% after the incorporation of active power filter. The incorporation of active power filters in the considered test system enhances the voltage profiles of the corresponding busses and improves the system stability. Figures 7 and 8 illustrate that the incorporation of active filters in the 13-Bus-RDS results in an improvement in the voltage profile. The current harmonics of the considered unbalanced test system with and without incorporation of active filter is shown in Figure 10 respectively. Conversely, by considering harmonics, the harmonic distortion levels at load busses are kept within permissible limits according to the IEEE 519 standards respectively.

Figure 9.

Voltage profile with and without incorporation of active filters.

Figure 10.

Current harmonics with and without incorporation of filter.

6. Conclusion

In this book chapter mitigation of total harmonic distortion of IEEE- 13 bus radial distributed standard test system with the incorporation of active filters by implementing sparrow search optimization technique respectively. The main objective of this book chapter is to mitigate the harmonic distortion content of the considered test system associated with non-linear loads. The voltage profiles have been enhanced by incorporating active filters that brings the system into a stabilizer manner. The voltage profiles at the corresponding busses are enhanced effectively by incorporating active filters. The findings of the study show that ignoring the existence of harmonics and incorporating hybrid active filters in the system can result in unwanted levels of harmonic distortion, resulting in greater damage to electrical equipment for both the electric utility and consumers.