Corresponding author’s email address: muyik78@yahoo.com 1012 ARID ZONE JOURNAL OF ENGINEERING, TECHNOLOGY & ENVIRONMENT ORIGINAL RESEARCH ARTICLE AN ENHANCED AQUILA OPTIMIZER-BASED DISTRIBUTED GENERATION FRAMEWORK FOR HARMONIC MITIGATION I.M. Adeyinka1, I. Abubakar1, N.B. Kadandani1,2 and M.M. Sa’ad3 1Department of Electrical Engineering, Bayero University, PMB 3011, Kano, Nigeria. 2Department of Electrical and Electronics Engineering, Federal University of Transportation, PMB 1050, Daura, Katsina State, Nigeria. 3Department of Electrical and Electronics Engineering, Veritas University, Abuja, Nigeria. Corresponding author’s email: muyik78@yahoo.com ARTICLE INFORMATION ABSTRACT This research work presents an improved Aquila optimizer-based distributed generation system for solving power quality problems. This is particularly important for mitigating the harmonics presence in a radial distribution system (RDS). The radial distribution network (RDN) was modeled in the presence of the nonlinear load (NLLD) and nonlinear distributed generation (NLDG). RDN provides a simple, cost-effective structure with a single power source that can be analyzed with a simplified forward/backward sweep load flow algorithm, making it easier to determine the optimal size and location of active power filters to mitigate harmonics and improve voltage quality. An improved Aquila optimization algorithm was then used to optimally size and place active power filters (APFs) in the adaptive RDN to control the harmonics, ensuring that the harmonics present in the system do not exceed IEEE-519 of 1992 standard limits. The results obtained from the developed scheme were presented and compared with the results obtained when Adaptive Grey Wolf Optimizer (AGWO) and Aquila Algorithm (AO) were used. THD and fitness function were used as the performance metrics. All simulations were carried out in the MATLAB/Simulink environment R2022b. The THD values obtained during various periods of the day were presented and it was observed that high distortions were recorded between hours 11 to 13, with the highest distortion occurring at hour 12. To further analyze the efficacy of the developed approach after placement of the APF in the IEEE 69-bus network, the result of the THD obtained when the improved Aquila algorithm was used for the placement of the APFs were presented. It was observed that the THD values obtained for the entire 69-bus network were well within the IEEE standard limit. Further, the results obtained from the developed scheme were compared with those obtained when AGWO and AO were used for harmonic mitigation in the distribution system. It was observed that the THD values obtained by the developed scheme outperformed those obtained from the AGWO technique by 5.96%, 4.71%, 3.47%, 32.79%, 3.62%, 11.68%, and 30.25%, respectively, for the bus numbers that have higher distortion values, while it also outperformed the Aquila algorithm by 3.07%, 2.41%, 1.88%, 31.97%, 1.84%, 16.88%, and 25.98%, respectively. The developed approach provides a practical and computationally efficient solution for harmonic mitigation and can be extended to larger and more complex power systems for improved grid performance. Received: 16th October 2025 Revised: 12th November 2025 Accepted: 13th November 2025 Keywords: Improved aquila optimizer Aquila optimizer Adaptive grey wolf optimizer Total harmonic distortion Active power filter © 2025 Faculty of Engineering, University of Maiduguri, Nigeria. All rights reserved. 1.0 Introduction Electricity is an indication of convenience life, and the demand for this energy source is increasing. Development in the power industry has led to a rise in both linear and nonlinear loads within power systems. Many solid-state switching converters consume reactive power and generate current harmonics from the AC AZOJETE December 2025. Vol.21(4):1012-1025 Published by the Faculty of Engineering, University of Maiduguri, Maiduguri, Nigeria. Print ISSN: 1596-2490, Electronic ISSN: 2545-5818 https://doi.org/10.63958/AZOJETE/2025/21/04/011 www.azojete.com.ng mailto:muyik78@yahoo.com mailto:muyik78@yahoo.com http://www.azojete.com.ng/ Arid Zone Journal of Engineering, Technology and Environment, December 2025; Vol. 21(4): 1012-1025. ISSN 1596-2490; e-ISSN2545-5818; www.azojete.com.ng Corresponding author’s email address: muyik78@yahoo.com 1013 grid, contributing to total harmonic distortion in voltage (THDv) and current (THDi) under nonlinear load conditions (Abbas et al., 2021). In modern power systems, the increasing penetration of distributed generation (DG) units particularly those interfaced through power electronics has introduced complex power quality challenges such as voltage instability, harmonic distortion, elevated thermal losses due to heat loss (I²R), and reactive power imbalance. These issues degrade the efficiency and reliability of radial distribution networks, especially under dynamic and nonlinear operating conditions. The growing integration of distributed generation (DG) units, especially those using power electronic interfaces, has therefore introduced significant power quality issues in radial distribution networks. These include harmonic distortion, voltage instability, increased thermal losses, and reactive power imbalance all of which compromise system efficiency and reliability under nonlinear and dynamic conditions. While Aquila Optimizer-based DG placement has been shown to effectively reduce real power losses and enhance voltage profiles, it lacks mechanisms for harmonic suppression and reactive power management. Moreover, the unpredictable output of DGs and the nonlinear behavior of inverter-based sources further intensify these challenges. To address these limitations, this research proposes the incorporation of an Active Power Filter (APF) into the Aquila-optimized DG framework. The APF actively mitigates harmonics and compensates reactive power, forming a hybrid solution that improves voltage stability, reduces distortion, and enhances overall energy efficiency ultimately boosting the resilience and sustainability of distributed radial networks. These nonlinear loads generate harmonics that cause disturbances and can lead to system malfunction. Today, almost every modern equipment, power system, and service such as furnaces, computer power supplies, communication systems, renewable energy systems, electrical power generation, and high-voltage systems— requires a continuous and high-quality power supply. Consequently, researchers and utility companies continue to explore solutions to power quality problems (Sakar et al., 2017), including harmonics, voltage fluctuation, voltage sag, unbalance, frequency variation, and transient spikes. The increasing proliferation of nonlinear loads worsens harmonic distortion in the power system, resulting in degraded power quality. Flexible AC Transmission System (FACTS) devices such as Static Compensators (STATCOMs) and Active Power Filters (APFs) have emerged as dominant technologies for mitigating these issues in industrial and commercial systems. In radial distribution networks (RDN), nonlinear loads (NLLDs) and nonlinear distributed generations (NLDGs) are the primary sources of harmonics, which elevate both the individual and total harmonic distortion in voltage (THDv). The degradation of electrical power quality due to multiple nonlinear loads—such as rectifiers, uninterruptible power supplies (UPS), and various electronic circuits leads to low power factor, poor energy efficiency, and voltage distortion (Sakar et al., 2017; Battu et al., 2015; Uniyal & Kumar, 2018). The inclusion of a shunt active power filter (SAPF) and photovoltaic (PV) system represents an effective solution for harmonic reduction and reactive power compensation, ensuring an improved power factor correction (PFC) at the point of common coupling (PCC). Metaheuristic optimization techniques such as Genetic Algorithm (GA), Ant Colony Optimization (ACO), Bee Colony Optimization, and Particle Swarm Optimization (PSO) have gained popularity due to their simplicity, flexibility, derivation-free mechanisms, and avoidance of local optima (Mirjalili & Lewis, 2016). Among recent advances, the Aquila Optimizer (AO) a nature-inspired algorithm based on the hunting behavior of the Aquila bird (Dhal et al., 2024) has demonstrated remarkable performance in solving complex nonlinear optimization problems. Similarly, the Grey Wolf Optimizer (GWO), inspired by the leadership hierarchy and hunting mechanism of grey wolves, has shown competitive performance when benchmarked against well-known metaheuristic algorithms such as PSO, Gravitational Search Algorithm (GSA), Differential Evolution (DE), and Evolutionary Programming (EP) (Mirjalili & Lewis, 2016). Previous works have explored various approaches for harmonic mitigation and optimal placement of filters or DG units. For instance, (Sakar et al., 2017) determined hosting capacity for distorted systems with PV-based DGs under harmonic constraints, while (Fahmi et al., 2018) utilized a single-tuned passive filter to reduce harmonics in industrial systems. However, passive filters are inadequate for complex, nonlinear environments. (Lakum & Mahajan, 2019) examined the impact of DG penetration on APF placement using the GWO algorithm, revealing that DG integration significantly affects APF sizing. Moreover, (Abbas et al., 2021) used a Water Cycle Algorithm (WCA) to plan single-tuned filters for inverter-based DGs, reducing THD effectively but without addressing adaptive compensation under nonlinear dynamics. From these reviewed studies, it is evident that determining the optimal placement and sizing of APFs remains crucial for minimizing cost while maintaining high power quality in RDNs. The introduction of DG converters brings additional harmonic challenges that necessitate more adaptive mitigation strategies. Hence, this work presents an improved Aquila Optimizer-based approach for optimal APF placement and sizing, aiming to reduce power losses, enhance http://www.azojete.com.ng/ mailto:muyik78@yahoo.com Arid Zone Journal of Engineering, Technology and Environment, December 2025; Vol. 21(4): 1012-1025. ISSN 1596-2490; e-ISSN2545-5818; www.azojete.com.ng Corresponding author’s email address: muyik78@yahoo.com 1014 voltage profiles, and effectively suppress harmonics thereby improving the overall stability and efficiency of radial distribution networks. 2. Materials and Method This section presents the comprehensive methodology employed in this paper. It provides detail of the mathematical model of the system, the formulation of the objective function used to evaluate performance of the algorithm. 2.1 Modeling of the Radial Distribution Network The radial distribution network employed is represented as a branch impedance (Zab) which is expressed in equation 1 (Lakum & Mahajan, 2021). 𝐙𝐚,𝐛 = 𝐑𝐚,𝐛 + 𝐣𝐗𝐋,𝐚,𝐛 1 Where Zab is the impedance between line a to b, Rab is the resistance between line a to b, XLab is the reactance between line a to b. The graphical modeling of the RDS with the NLDGs, harmonic filters and nonlinear loads developed in MATLAB Simulink is as shown in Figure 1. Figure 1: IEEE 69- Bus System with Nonlinear Loads and NLDGs (Lakum & Mahajan, 2021) As the RDN contains NLDGs and nonlinear loads, the branch impedance equation must be modified to include harmonics. As such the expression for the branch impedance can now be expressed as in equations 2 to 4: Za,b (h) = Ra,b + jXL,a,b (h) 2 XL,a,b (h) = ωhLa,b 3 ωh = 2πfh 4 where 𝑍 is the equivalent impedance of the system a and b, represent the bus numbers, h represents the order of harmonics, 𝑅𝑎,𝑏 depicts the resistances of branch ab, fh represents the harmonic frequency of the current, 𝐿𝑎,𝑏 denotes the inductance of branch ab and 𝜔ℎ represents the angular frequency of the harmonic current. 2.2 Mathematical model of RDS with NLLD The nonlinear loads are modeled as harmonic current injection source and their rms value is given in equations 5 and 6. The harmonic current 𝐼𝑛𝑙,𝑎 (ℎ) at harmonic h is represented as a complex number, with real and imaginary parts: http://www.azojete.com.ng/ mailto:muyik78@yahoo.com Arid Zone Journal of Engineering, Technology and Environment, December 2025; Vol. 21(4): 1012-1025. ISSN 1596-2490; e-ISSN2545-5818; www.azojete.com.ng Corresponding author’s email address: muyik78@yahoo.com 1015 Inl,a (h) = Inl,a,r (h) + jInl,a,im (h) 5 Inl,a (h) = √∑(Inl,a,r 2(h) + Inl,a,im 2(h) ) H h=2 6 where 𝐼𝑛𝑙,𝑟 (ℎ) and 𝐼𝑛𝑙,𝑖𝑚 (ℎ) represent the real and imaginary parts of the load current repectively. 𝐼𝑛𝑙,𝑎 (ℎ) depicts the rms value for the nonlinear load current at bus “a”, while H represents the highest order of harmonics. 2.3 Mathematical Model of RDS with NLDG Since the NLDG is in charge of introducing nonlinear current into the system, it is modeled as a current source in this work. The fundamental current is determined by the DG's power rating, and the DG's nonlinear harmonic current value can be obtained by using the expression in equation 7 in accordance with the harmonic spectrum. Inldg,a (h) = KdgIdg,a 7 where 𝐼𝑛𝑙𝑑𝑔,𝑎 (ℎ) is the harmonic current of the DG, while 𝐾𝑑𝑔 depicts the percentage of harmonic current as per the harmonic spectrum of DG, lastly 𝐼𝑑𝑔,𝑎 is the fundamental current of DG. 2.4 APF Modeling The APF is modeled as a current source. The calculation of the APF current is done on the basis of net nonlinear which is a vector addition of nonlinear currents of loads and NLDGs. When the phase angle is zero, the distortion is worst as the net nonlinear current is a function of phase angle. So it causes maximum distortion while harmonic currents are in phase; Inldg (h) = Ihdg (h) + Inl (h) 8 Iapf = k(Inldg) 9 where k is proportionate to net nonlinear current. Since APF is represented as a set of current sources. It injects harmonics order at a point of common coupling (PCC) as per the value of k. the APF can be expressed as: Iapf (h) = Iapf,r (h) + jIapf,im (h) 10 Iapf = √∑ {I apf,r 2(h) + I apf,im 2(h) } H h=2 11 where 𝐼𝑎𝑝𝑓,𝑟 2(ℎ) represents the real part of the APF, while 𝐼𝑎𝑝𝑓,𝑖𝑚 2(ℎ) and 𝐼𝑎𝑝𝑓 depicts the imaginary part and rms value of current of the APF respectively. 2.5 Modeling of Solar Power Generation It is evident that the power output from solar PV is proportional to the irradiance. The solar PV output power can be calculated as shown in equation 12. Ppv(si) = ηpv × Spv × si 12 where, 𝑃𝑝𝑣 represents the output power in kW, 𝑆𝑝𝑣 denotes the total area of PV in meter square and ŋpv represents the efficiency. Normal probability density function is used in this work to generate the samples of the output power of the solar power plant. A k-means scenario reduction algorithm is employed to reduce the number of samples (output power of the solar PV) to 100. The reduced samples were then used to calculate the harmonic currents injected by the NLDG. http://www.azojete.com.ng/ mailto:muyik78@yahoo.com Arid Zone Journal of Engineering, Technology and Environment, December 2025; Vol. 21(4): 1012-1025. ISSN 1596-2490; e-ISSN2545-5818; www.azojete.com.ng Corresponding author’s email address: muyik78@yahoo.com 1016 2.6 Harmonic Load Flow In this study, a harmonic load flow based on network topology is used. Two matrices are created in this approach: bus injection to branch current (BIBC), and branch current to the bus voltage (BCBV). With harmonic load flow, the THDv is computed at each bus. It is necessary to identify the crucial busses that go beyond the accepted bounds. The THDv equation is represented as: THDv = √∑ (IHDv)2H h=2 Vf 1 13 where the fundamental frequency voltage is denoted with 𝑉𝑓 1. From the value of THDv at all buses, the vital buses where the IEEE standard limits are not satisfied are found. It helps to decide the policy to alleviate the harmonics which in this research is the placement and sizing of APF. 2.7 Objective Function The objective function formulated is subject to satisfying the following constraints: 𝑇𝐻𝐷𝑣 ≤ 5% 14 𝐼𝐻𝐷𝑣 ≤ 3% 15 𝐼𝑎𝑝𝑓 ≤ 𝐼𝑎𝑝𝑓,𝑚𝑎𝑥 16 Where 𝐼𝑎𝑝𝑓,𝑚𝑎𝑥 represents the maximum current of APF and DP represents the dynamic penalty. The value set in the constraints for the 𝑇𝐻𝐷𝑣 𝑎𝑛𝑑 𝐼𝐻𝐷𝐼 are selected to ensure that the requirement of IEEE standard 519 are met. 2.8 Extended Nonlinear Load Position Base APF Current Injection Formulation Formulation of the extended NLPCI is done in this sub-section. The extended NLPCI is used to find the optimal buses for placement of APF in the RDS. The proposed technique consists of three cases: a) only one feasible state with a minimum number of APF, b) more than one state with same number of APFs with different THDv, and c) more than one state with same number of APF and same THDv. NLPCI technique has been introduced to decide the feasible buses for the entire 33-bus RDS. Create the nonlinear load position based APF placement matrix: The total number of nonlinear load is denoted by NL and its buses is denoted by B NL. Then nonlinear loads are represented as, matrix of [1 0 0 0,…,…NL] The nonlinear load buses are represented as, matrix of [1 0 0 0,…,... 𝐵NL ]. The nonlinear load position based matrix is formed and possible combinations of APFs placement are calculated. Each combination comprises of a set of nonlinear load buses and it is denoted by state St. Number of total state ST is determined from nonlinear load buses as: ST = 2 NL -1 17 The nonlinear load position based APF placement combination matrix of zeros and 1 here, ‘1’ represents the placement of APF and ‘0 represents no APF. Form the set of feasible states SF: APF with an equal rating of the nonlinear load is connected at possible combination i.e., each state. Then THDv is calculated at all the buses using harmonic load flow for all the states. According to their maximum THDv the states are denoted as, St1THDV max; ……, ….. ,ST THDV max. Separation of feasible and infeasible state is done by fulfilling the standard limit of THDv as, http://www.azojete.com.ng/ mailto:muyik78@yahoo.com Arid Zone Journal of Engineering, Technology and Environment, December 2025; Vol. 21(4): 1012-1025. ISSN 1596-2490; e-ISSN2545-5818; www.azojete.com.ng Corresponding author’s email address: muyik78@yahoo.com 1017 State S ={ SF, StTHDvmax ≤ 5% infeasible, StTHDvmax > 5% } 18 Form the group according to the number of APFs: All the states are arranged as per their number of filters. Here, the total nonlinear load buses are NL. Therefore, the maximum possible combination according to the number of APFs is decided by NLC Nft . 𝐺𝑁𝑓𝑡 {𝑆𝐹𝑁𝑓𝑡} (𝐺𝑟𝑜𝑢𝑝 𝑤𝑖𝑡ℎ 𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝑓𝑖𝑙𝑡𝑒𝑟). The group with the maximum number of APFs has only one state. This technique is extended here and formulated as follows: The steps employed in ensuring efficient operation of the extended NLPCI is as shown in the flowchart below: START Read RDS data, Non linear load and NLDG data and its location Create NLPCI matrix Using (17 - 18) Hour hr = 1 Initialize St=1, h=2, calculate Inl, Set Iapf=Iapf max Run harmonic load flow Calculate IHDv at buses Is h>H? Calculate THDv using (13) Is St1? Sort the SFnf.min according to their THDV (23) Select the state with lowest with lowest THDv Is SFnf.min,thdv,min >1? Mapped the state with priority rank of buses Select the SF with highest priority rank buses Is hr