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Abstract This paper proposes a new scheme for locating the faults of three‐terminal double‐circuit transmission line without transposer in the phase domain that is not affected by type of fault. Synchronous voltage and current were measured by phasor measurement units (PMUs) installed at three busbars. Considering the coupling effect of parallel lines, the distribution line model was used to obtain more accurate results and third‐order Taylor series expansion to decouple distributed line model. The phase and branch of all faults on the transmission lines were effectively identified, and various types of faults were accurately located including normal shunt fault, evolving fault and cross‐country fault. The proposed algorithm was tested under different fault locations, resistances, initial angles and types (including cross‐country faults and evolving faults). In addition, the effects of different sampling rates, measurement errors, earth resistivities and transmission line parameter errors were also considered. The simulation calculation was performed in MATLAB software and three‐terminal transmission lines were simulated in PSCAD/EMTP software. The results indicate that maximum estimated error was less than 1.8631%.

In this paper, an Improved Ant Colony Optimization (IACO) algorithm optimized fuzzy PID (FPID) controller is proposed for Load Frequency Control of multi area systems. The nonlinear incremental evaporation rate and improvement of pheromone increment updating are proposed in the IACO algorithm to improve the quality of solution. And, a modified objective function using integral time multiply absolute error (ITAE), overshoot, undershoot and settling time with appropriate weight coefficients is proposed to improve the performance of the controller. Initially, a two-area non-reheat thermal system is applied and the FPID controller parameters are optimized by the IACO algorithm with five different objective functions. The modified objective function has better performances than four conventional objective functions. To demonstrate the robustness of the proposed control method, sensitivity analysis is implemented under wide variation of operating conditions and system parameters. Further, the proposed approach is also extended to two-area four-sources hydro thermal power system with/without High Voltage Direct Current (HVDC) link. The superiority of the proposed approach is shown by comparing the results with ZN, GA and hPSO-PS algorithms. The robustness of the proposed method is verified under random load disturbances. Finally, the proposed approach is extended to a two-area power system with governor dead band nonlinearity and results show that the proposed approach can cope with nonlinearity well. The results obtained from all simulations show that the proposed algorithm and modified objective function achieves better performances, such as minimum objective values (ITAE = 0.0255, ITSE = 9.30e-5, ISE = 1.91e-4 and IAE = 0.0273) obtained for the two-area non-reheat thermal system.

To improve the accuracy of short term wind speed forecasting, a novel principle-subordinate prediction model based on Conv-LSTM network and BPNN is designed in this paper. The proposed model combines deep learning algorithms and improved neural network to deal with the problem of wind speed forecasting. In this model, the prediction sequence of each subseries is obtained by Conv-LSTM to form more smoother and characteristic series; the BPNN, optimized by MWOA (Modified Whale Optimization Algorithm), is trained with the reconstruction sequence, which processed for the prediction sequence by invert-EMD (inverse empirical model decomposition). Before prediction, singular spectrum analysis (SSA) and complete ensemble empirical model decomposition adaptive noise (CEEMDAN) are adopted to de-noise and decompose the original wind speed data into several subseries. This process is beneficial to improve the ratio of signal to noise and simply the features of wind speed data. In addition, the Conv-LSTM is tested on three datasets, the results proved that data process is advantaged to obtain higher quality wind speed datasets, and convolutional layer can deep extract the characteristics of each subseries, it can facilitate LSTM to make accurate prediction. The final prediction results, compared with other five different models, demonstrate that the proposed model can achieve higher precision. Such as the performance evaluation matrix (MAPE = 2.62%, RMSE = 0.151) are smallest obtained from experiments on three wind different wind speed datasets.

The short-term hydrothermal scheduling (STHS) is a complicated optimization problem, considering valve-point effect (VPE) and transmission losses, it exhibits the characteristics of nonlinearities and non-smoothness which increase the difficulty of solving the problem. Responding to these challenges, a hybrid algorithm that comprises chaotic local search technique, grey wolf optimizer, and dragonfly algorithm (CGWO-DA) is proposed to settle the STHS problem. The grey wolf optimizer (GWO) has strong local search ability with the slow convergence rate. The dragonfly algorithm (DA) owns superior global search capability and fast convergence rate, however, it exerts premature convergence and is easy to fall into local optimum. Using the chaotic local search as a supplement, the hybrid algorithm combined by two excellent algorithms can improve the shortcoming of each algorithm and enhance the exploration and exploitation of the algorithm simultaneously. In addition, two novel constraints handling strategies are presented to resolve the complicated equality constrains and guarantee the feasibility of solutions. Three systems have been tested by the proposed methodology. The solutions are compared with the ones from other available literatures, the feasibility and effectiveness of the proposed approach are well demonstrated, and the findings of case studies show that the proposed method has great competitive advantages to obtain better scheduling schemes.

To overcome the premature-convergence of standard bat algorithm in solving the multi-objective optimal power flow (MOOPF) problems, a novel hybrid bat algorithm (NHBA) is proposed in this paper. The suggested NHBA algorithm modifies the local search manner by a monotone random filling model based on extreme (MRFME) and improves the population-diversity by mutation and crossover mechanisms. To obtain the uniformly distributed Pareto optimal set (POS) with zero constraint-violation, an innovative non-dominated sorting method combined with the constrained Pareto fuzzy dominant (CPFD) strategy is put forward in this paper. To verify the superiority of the proposed NHBA-CPFD algorithm, which is federated by the NHBA algorithm and the CPFD strategy, ten MOOPF simulation cases considering the basic fuel cost, the fuel cost with value-point loadings, the total emission, and the active power loss are studied on the IEEE 30-node, IEEE 57-node, and IEEE 118-node systems. In contrast to the NHBA, MOPSO, and NSGA-III algorithms which adopt the constrain-prior Pareto-dominance method (CPM), numerous results validate the NHBA-CPFD algorithm that can achieve more superior compromise solutions and preferable Pareto fronts (PFs) even in the large-scale systems. Furthermore, two performance metrics of generational distance (GD) and hyper-volume (HV) also demonstrate that the NHBA-CPFD algorithm has great advantages to obtain the feasible POS with evenly distribution and favorable-diversity.

In this paper, a novel hybrid firefly-bat algorithm with constraints-prior object-fuzzy sorting strategy (HFBA-COFS) is put forward to solve the strictly-constrained multi-objective optimal power flow (MOOPF) problems. The hybrid firefly-bat algorithm (HFBA) integrates the dimension-based firefly algorithm and the modified bat algorithm to improve the population-diversity and global-exploration ability of original algorithm. To handle the unqualified state variables and overcome the deficiency of traditional penalty function approach (PFA), the constraints-prior Pareto-dominant rule (CPR) which takes constraints-violation and objectives-value into consideration is proposed in this paper. Furthermore, an effective constraints-prior object-fuzzy sorting (COFS) strategy based on CPR rule is presented to seek the well-distributed Pareto optimal set (POS) in solving the MOOPF problems. To validate the great advantages of HFBA-COFS algorithm, ten MOOPF cases optimizing active power loss, total emission and fuel cost are simulated on the IEEE 30-bus, IEEE 57-bus and IEEE 118-bus systems. In addition, the generational distance and SPREAD evaluation indexes powerfully demonstrate that the proposed HFBA-COFS algorithm can achieve high-quality POS, which has great significance to realize the safe and economic operation of large-scale power systems.

Economic dispatch (ED) is of cardinal significance for the power system operation. It is mathematically a typical complex nonlinear multivariable strongly coupled optimization problem with equality and inequality constraints, especially considering the valve-point effects. In order to effectively solve the problem, a simple yet very young and efficient population-based algorithm named across neighborhood search (ANS) is implemented in this paper. In ANS, a group of individuals collaboratively navigate through the search space for obtaining the optimal solution by simultaneously searching the neighborhoods of multiple superior solutions. Four benchmark test cases with diverse complexities and characteristics are firstly employed to comprehensively verify the feasibility and effectiveness of ANS. The experimental and comparison results fully demonstrate the superiority of ANS in terms of the final solution quality, convergence speed, robustness, and statistics. In addition, the sensitivities of ANS to variations of population size and across-search degree are studied. Furthermore, ANS is applied to a practical provincial power grid of China. All the comparison results consistently indicate that ANS is highly competitive and can be used as a promising alternative for ED problems.

Known as a multi-objective, large-scale, and complicated optimization problem, the multi-objective optimal power flow (MOOPF) problem tends to be introduced with many constraints. In this paper, compared with the frequently-used penalty function-based method (PFA), a novel constraint processing approach named the constraints-prior Pareto-domination approach (CPA) is proposed for ensuring non-violation of various inequality constraints on dependent variables by introducing the Pareto-domination principle based on the sum of constraint violations. Moreover, for solving the constrained MOOPF problem, the multi-objective firefly algorithm with CPA (MOFA-CPA) is proposed and some optimization strategies, such as the crowding distance calculation and non-dominated sorting based on the presented CPA, are utilized to sustain well-distributed Pareto front (PF). Finally, in order to demonstrate the feasible and effective improvement of MOFA-CPA, a comparison study between MOFA-CPA and MOFA-PFA is performed on two test systems, including three bi-objective optimization cases and three tri-objective optimization cases. The simulation results demonstrate the capability of the MOFA-CPA for obtaining PF with good distribution and superiority of the proposed CPA for dealing with inequality constraints on dependent variables. In addition, some quality indicators are used to evaluate the convergence, distribution, and uniformity of the PFs found by the MOFA-CPA and MOFA-PFA.

Clean energy has taken center stage in discussions about how to ensure that humanity has a sustainable future when fossil resources are depleted. Wind energy is also playing a bigger and bigger part in the energy supply as a clean, renewable energy source. Hence, the use of wind energy is significantly impacted by an accurate and appropriate wind speed prediction system. The non-linear wind speed prediction in this research is handled by a master-slave prediction model based on a convolutional neural network and long-short memory (CNN-LSTM) network and an improved Pelican Optimization Algorithm BP neural network (IPOABP). In this model, CNN-LSTM is used to obtain a prediction sequence for each subsequence, producing a smoother feature sequence. A BPNN BP (Back-Propagion Neural Network) is then trained using the reconstructed sequence, and the reconstructed sequence is processed by inverse empirical modal decomposition (EMD) for the prediction sequence. Hence, the use of wind energy is significantly impacted by an accurate and appropriate wind speed prediction system. The non-linear wind speed prediction in this research is handled by a master-slave prediction model based on a convolutional neural network and long-short memory (CNN-LSTM) network and an improved Pelican Optimization Algorithm BP neural network (IPOABP). In this model, CNN-LSTM is used to obtain a prediction sequence for each subsequence, producing a smoother feature sequence. A BPNN BP (Back-Propagion Neural Network) is then trained using the reconstructed sequence, and the reconstructed sequence is processed by inverse empirical modal decomposition (EMD) for the prediction sequence. (RMSE=0.0596, MAPE=0.8923, MAE=0.0481) were obtained as minimum values from experiments on 3 different datasets. [ABSTRACT FROM AUTHOR]

This paper proposes a distributed generator (DG) optimization framework based on an improved northern goshawk optimization (INGO) algorithm to install multiple DGs into the distributed system (DS) simultaneously. Various case studies are conducted in constant or varying load and generation models. The framework considers the power system's critical constraints while optimizing each DG's location, capacity, and power factor to minimize energy losses and voltage deviations and improve DG penetration levels and system voltage distribution. The effectiveness and stability of the INGO algorithm were first verified in two constant test systems, and the effect of the optimal power factor of the DG on the system was considered. The results of all case studies show that the INGO algorithm performs better than other existing methods in reducing active power losses and voltage deviations. When the three parameters of generator location, capacity, and power factor were optimized simultaneously, the active power losses of the two test systems were reduced by 93.96% and 98.11%, respectively. On this basis, photovoltaics (PVs) and wind turbines (WTs) as renewable energy DGs (REDGs) were also introduced in two changing test systems. The performance gap between two REDGs and conventional generators (CGs) is compared. The all-day active energy losses in the two tested systems were reduced by 88.27% and 94.74% after WTs installation. Much higher than 51.23% and 53.64% after installing PVs, almost as good as installing CGs. Therefore, WTs can replace CGs to reduce carbon emissions because the difference in energy loss and voltage deviation between the two is tiny. [ABSTRACT FROM AUTHOR]

In this paper, a multi-objective modified seagull optimization algorithm (MOMSOA) is proposed to handle multi-objective environmental economic power dispatch (EED) problems. The algorithm utilizes logistic map to randomize the parameter u, which increases the diversity of the algorithm and speeds up the convergence rate. Besides, the mutation operator is combined to enlarge the range of the search and to avoid falling into the local optimum. The exploration as well as exploitation capabilities for MOSOA are balanced by non-linearizing the original linear parameter A through a cosine dynamic variation strategy. Furthermore, with the assistance of a unique constraint handling approach and non-inferior sorting, MOMSOA can obtain a set of uniform Pareto optimal solution (POS). In order to verify the effectiveness of MOMSOA, experiments were conducted on diverse test systems including IEEE30-Bus, IEEE57-Bus and IEEE118-Bus test systems. During the experimental process, MOSOA and MOPSO/MODE are compared with MOMSOA. Eight trials were conducted, and optimized objective functions include fuel cost, fuel cost with valve point effect, power loss and pollution emission. The results of experiments demonstrate that the proposed MOMSOA can obtain more uniform Pareto fronts (PFs) and optimal best compromise solution (BCS). Finally, two metrics that measure the performance of multi-objective algorithms, SP and HV, are employed to evaluate the results of each algorithm, and the results reveal that solutions obtained by MOMSOA are the most uniform, with the broadest diversity and the best convergence. [ABSTRACT FROM AUTHOR]

The intermittency of renewable energy generation and the randomness of power load variations lead to voltage and frequency fluctuations among the interconnected power system. In this study, a control strategy based on sliding mode control theory and disturbance observer is proposed for the multi-area power system with parameter uncertainties to handle load frequency control. By choosing an appropriate integral-type sliding-mode surface and reaching law, a slidingmode load frequency controller is constructed. In order to reduce the influence of uncertainties, a disturbance observer is designed to estimate lumped disturbances. On this basis, the sliding mode controller is reconstructed to provide better control effect. And the improved honey badger algorithm is used to tune out the optimal parameters of the designed controller. Simulation studies are carried out on a two-region reference system and an unequal capacity three-area power system with nonlinearity connected wind turbine generators to illustrate the favorable performance of the power system under the proposed control strategy. The comparison results show that the proposed control method possesses excellent frequency control ability under the uncertainty of load disturbance, wind power fluctuations and parameter uncertainties. And it also achieves efficient frequency control under a certain range of communication delay. [ABSTRACT FROM AUTHOR]

Power system is the primary basis for national development, and electricity load prediction is an essential part of the power system. Accurate short-term load forecasting can ensure the stable operation of the power system. To improve the accuracy of short-term load forecasting, a hybrid prediction model with an improved Carnivorous Plant Algorithm (ICPA) to Optimize the Group Method of Data Handling (GMDH) and Long Short-term Memory (LSTM) is proposed. This prediction model includes Improved Complete Ensemble Empirical Mode Decomposition Adaptive Noise (ICEEMDAN), Information Entropy (IE), LSTM, GMDH, and ICPA. Firstly, ICEEMDAN is applied to the original load data to obtain the Intrinsic Mode Functions (IMF) with different characteristic information. The obtained IMFs are reconstructed according to the IE. Then, the reconstructed IMFs are predicted using LSTM and GMDH forecasting models, respectively. Finally, the final forecasting results are weighted by the optimal weights obtained using ICAP. To verify the performance of the model, two power load datasets are selected as test datasets. And Mean Absolute Percentage Error (MAPE), Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and inequality coefficient (TIC) are selected as indicators. The prediction model proposed in this paper outperforms other prediction models in all indicators. [ABSTRACT FROM AUTHOR]

An improved hybrid crow search algorithm (IHCSA), whose purpose is to find the best measured solution (BMS), is proposed to solve the multi-objective optimal power flow (MOOPF) problem. The proposed IHCSA, which creatively combines the advanced ideas and strategies of sinusoidal nonlinear dynamic transformation awareness probability (SNDTAP) and tent map switching fly length (TMSFL), introducing the mutation and crossover processes of differential evolution (DE), obtains a better BMS. Three innovative optimization strategies are integrated into this paper. The proposed screening approach of Pareto-priority mechanism (SAPM) ensures that the state variables meet the inequality constraints of power systems. The Pareto optimal set (POS) is obtained by elite non-dominant sorting method (ENSM). Besides, the BMS, obtained by fuzzy membership theory, is filtered from POS. For practical purposes, five objective functions are considered. Three various scale test systems are applied to validate the performance of the IHCSA. Simulation results reveal that the proposed method has a greater competitive advantage in addressing non-convex MOOPF problems of different scales. In addition, Hypervolume (HV) and Spacing (SP) are used to quantitatively evaluate the diversity and consistency of POS gained by IHCSA. The evaluation results prove that the proposed approach has excellent performance and great application prospects. [ABSTRACT FROM AUTHOR]

To achieve the optimal operation of power system, an improved multi-goal particle swarm optimization (IMPSO) algorithm is proposed in this paper. Based on the multi-goal optimal power flow (MOOPF) calculation, IMPSO algorithm can determine high-quality scheduling schemes which effectively reduce fuel cost, power loss and exhaust emission. Compared with the basic multi-goal PSO (BMPSO) algorithm, IMPSO algorithm realizes better solution diversity and searching ability by integrating an innovative dominant strategy and the mutation-crossover operation of inferior solutions. Four experiments prove that the proposed IMPSO algorithm achieves more superior Pareto optimal set (POS) and best compromise scheme (BCS) than BMPSO algorithm. Furthermore, the multi-output BP power flow prediction model is put forward in this paper to seek the winning elite schemes (WES) around the BCS of IMPSO algorithm. The presented BP prediction model can find multiple WES schemes of bi-objective and tri-objective MOOPF problems, which realize zero constraint violation and smaller goals. In general, the superior WES schemes determined by proposed IMPSO and BP power flow prediction model are of great help to realize the optimal operation of power system with improved economy and safety. [ABSTRACT FROM AUTHOR]

The short-term hydrothermal scheduling (STHS) is a complex non-linear, non-convex and high-dimensional mathematical optimization problem. Due to the fact that the original chimp optimization algorithm (ChOA) is likely to fall into local optimum and has the disadvantage of low population diversity, an improved chimp optimization algorithm (IChOA) is proposed to solve the STHS problem. Firstly, Logistic-Tent chaotic mapping is employed to initialize the population and increase the population diversity. Then a new nonlinear convergence factor is introduced to make the optimization search process more applicable to STHS problems. Next, particle swarm algorithm (PSO) and gravitational search algorithm (GSA) are combined to enhance the shortcoming and balance the global search ability and local exploration ability of ChOA. Moreover, Cauchy mutation and opposition-based learning strategy are supplemented as perturbation interference when the optimal position is not updated to improve the ability to leap out of the local optimum. Finally, a graded optimization strategy is adopted for the constraint handing of dynamic reservoir balance and thermal power balance. Three standard hydrothermal power systems are utilized to verify the practicability and validity of the proposed method. Results of simulations reveal that IChOA has significant competitive advantages in addressing the STHS problem. [ABSTRACT FROM AUTHOR]

This paper proposes an improved novel bionic intelligent Moth-Flame Optimization (MFO) algorithm optimized linear active disturbance rejection control (LADRC) strategy for automatic generation control (AGC) problems. LADRC is a control strategy that combines linear extended state observer (LESO) and traditional proportional-derivative (PD) control, with the advantages of its resistance to disturbance and simplicity. The three-order LADRC controller is designed in load frequency control (LFC) system. The Improved MFO (IMFO) algorithm is proposed by Cauchy mutation strategy and self-adaptive weight to overcome the weaknesses in easily falling into local optima and poor optimization search accuracy, and the IMFO algorithm is employed for tuning the parameters of LADRC. Besides, an objective function takes account of the performance index integral-time-multiplied-AE (ITAE) with dynamic indicators, which is used to improve the effectiveness of LADRC. The proposed control strategy is tested for robustness in a two-area non-reheat thermal system and compared with recent control methods published in the literature. As a result, its superiority is demonstrated for the lowest cost function values of ITAE = 0.0036, ITSE = 1.24E-05, ISE = 6.81E-05 and IAE= 0.0086. To further explore the potential of the LADRC controller based on the IMFO algorithm, it is also extended to a two-area nonlinear system and an unequal three-area reheat system. The performance indicator functions and dynamic performance indicators are analyzed qualitatively in the meantime. [ABSTRACT FROM AUTHOR]

The optimal configuration problem of distributed generators (DGs) and shunt capacitors (SCs) in a radial distributed network (RDN) is to find the best installation locations and optimal capacities of DGs and SCs for optimizing a certain performance indicator. The discontinuity characteristic and huge computation of optimizing DGs and SCs in RDN make it no longer applicable by traditional methods. In this paper, a new bus processing method and an improved butterfly algorithm are proposed to solve the optimal configuration of DGs and SCs. The method of processing nodes considers not only the power loss index (PLI) but also the voltage amplitude of the original system, forming a sequence of candidate nodes to guide algorithm to optimizing, which can simplify the algorithm search space and improve search efficiency. Meanwhile, the butterfly algorithm with constriction factor (BF-CF) combines the inertia coefficient to introduce a constriction factor, improves the speed update model and the local search pattern, and overcomes the disadvantages of the original butterfly algorithm which is easy to fall into the local optimum and the precision of result is not high. To verify the performance of the proposed method, minimizing the active power loss and voltage deviation are selected as the objective function and reactive power loss and the worst voltage are taken as reference targets, which are performed in three standard test systems of 33-bus, 69-bus and 119-bus, respectively. The simulation results illustrate that, compared with the original butterfly algorithm and other intelligent algorithms, the method proposed in this paper has more obvious advantages and performance in solving the configuration problem of DGs and SCs in systems of various scales. [ABSTRACT FROM AUTHOR]

With the rapid consumption of fossil fuels, traditional power generation methods not only cannot issue future energy needs, but also bring serious environmental problems. As a clean and renewable energy, wind energy plays an increasingly important role in energy supply structure. However, the wind speed itself is intermittent, unstable and random, which brings severe challenges to wind power generation. Aimed at improving the accuracy and reliability of short-term wind speed forecasting, this paper proposes a new hybrid model. The model includes time-varying filter, modal decomposition, permutation entropy, adaptive noise modal decomposition, adaptive neuro-fuzzy inference system (ANFIS), packet data processing method neural network (GMDH), and improved monarch butterfly optimization algorithm (IMBO). First, the original wind speed sequence is significantly decomposed twice to obtain the sub-sequence to be predicted. Then, the reconstructed data uses ANFIS and GMDH neural network models to predict sequences in different frequency domains to get prediction results. To further improve the performance of the model, the improved monarch butterfly optimization algorithm is used to modify the model parameters. Finally, the final prediction result is obtained by summing the prediction results of each component. In addition, for verifying the performance of the model, this paper designs six sets of comparative experiments from two dimensions to verify the model on three data sets. The results show that the model proposed in this paper has high prediction accuracy and good stability. [ABSTRACT FROM AUTHOR]

In this paper, an objective function considering performance index and an improved gravitational search algorithm (IGSA) are proposed to optimize the parameters of fuzzy PID (FPID) controller. IGSA is obtained by combining elite strategies and the mining capability of PSO algorithm. The IGSA FPID method which integrates IGSA and FPID controller is tested in a typical two-area non-reheat system, and system responses reflect the advantages of proposed objective function and IGSA. Additionally, the proposed IGSA FPID method still has excellent effects even on the two-area multi-source system with thermal power, hydropower and gas turbines. Meanwhile, the effect of high voltage direct current (HVDC) links in suppressing fluctuations is verified. Due to the popularity of wind power, a novel three-area interconnected power system with nonlinearity connected wind turbine (WT) is designed. Under the control of IGSA FPID, the good stability and dynamic performance of mentioned three-area system are verified. Therefore, FPID controller optimized by IGSA has excellent control effects, stability and universal applicability on the different power systems with multiple area and sources. [ABSTRACT FROM AUTHOR]

In this paper, a modified and hybrid flower pollination algorithms (MHFPA) is proposed for dealing with the multi-objective optimal power flow (MOOPF) problem with conflictive objectives. The algorithm combines the mutation and crossover process in the differential evolution (DE) algorithm, introduces the sinusoidal nonlinear dynamic switching probability (SNDSP) and the elite strategy of elder generation (ESEG), which can improve the shortcomings of the original pollen algorithm that it is easy to fall into the local optimum and the diversity is insufficient. A screening approach with Pareto-dominant rule (SAPR) is proposed to ensure that the state variable can satisfy the inequality constraints of the power system. A uniformly distributed Pareto optimal set (POS) is obtained by the non-dominant sorting with elite strategy (NSES) based on Rank and Density estimation, and the best trade-off solution (BTS) is determined from the POS obtained by the fuzzy affiliation theory. For practicality, the total fuel cost, active power loss, emissions and voltage deviation are selected as objective functions. Due to the limitations of the actual power system, the valve point effect is also considered. The IEEE30-, 57- and IEEE118-bus test systems are used to verify the performance of the proposed MHFPA. In addition, two performance indicators, Hypervolume (HV) and Spacing (SP), quantitatively evaluate the diversity and uniformity of the POS obtained by MHFPA. The simulation results show that, compared with the classic MOPSO and NSGA-II algorithms, the method proposed in this paper shows a greater competitive advantage in dealing with different scales and non-convex optimization problems. [ABSTRACT FROM AUTHOR]