Hamed Mojallali

The integration of power electronic interface-based renewable energy systems, along with fast dynamic loads, has significantly changed the dynamics of microgrids. This shift has reduced rotational inertia while introducing virtual inertia and fast frequency regulation strategies, enabling faster responses to fluctuations and necessitating real-time operation. Real-time operation, supported by advanced information and communication technologies, forms the backbone of this framework. However, it also exposes microgrids to cyber threats, which can disrupt operations by introducing delays in transmitted measurements and reference signals. To maintain microgrid resilient operations, an innovative control strategy is proposed for robust frequency regulation in microgrids under uncertainty against time-varying delay attacks. The proposed method exploits the advantages of fractional-order calculus and model-following control to enhance system operation resilience. Furthermore, a finite-time robust tracking control mechanism is utilized to ensure rapid responses. Performance of the proposed method is ensured through MATLAB simulations of a typical microgrid. Experimental test results obtained from the Opal-RT testbed are also presented. Results demonstrate the method's effectiveness in real-time operation within renewable microgrids, showcasing a swift response and reduced fluctuations.

Selecting appropriate dynamics and developing accurate models for gas turbines is a complex yet essential task, as model accuracy directly affects the performance of model-based control strategies. To address this challenge, this article employs the Active Disturbance Rejection Control (ADRC) approach, a model-free control method, for the operation of gas turbines. In the proposed scheme, Linear ADRC (LADRC) is applied to regulate the fuel flow and exhaust temperature, while Nonlinear ADRC (NLADRC) is used for rotor speed control. Considering the inherent delays in gas turbine systems, a predictor observer is incorporated. Furthermore, the controller parameters are optimized using a type-2 fuzzy method, where a lookup table is implemented to accelerate the computation process compared to real-time fuzzy inferences significantly. Simulation results confirm the effectiveness of the proposed controller in handling uncertainties and external disturbances.

This paper investigates the application of reinforcement learning (RL) techniques for optimizing proportional–integral–derivative (PID) controller parameters in gas turbine speed control systems. The research employs the Rowen mathematical model as the foundational framework and introduces a novel approach utilizing twin‐delayed deep deterministic policy gradient (TD3) algorithms. The methodology integrates machine learning with classical control theory to address the persistent challenges of maintaining optimal turbine speed during both transient startup phases and steady‐state operations. Implementation was conducted using a simulation environment based on MATLAB/Simulink, with the General Electric 5001M heavy‐duty gas turbine serving as the reference system. The RL agent was designed to interact with the simulated environment, continuously refining controller parameters to minimize performance metrics including integral error values, rise time, and settling characteristics. Comparative analysis between the proposed TD3‐optimized PID controller and conventional tuning methods demonstrates significant performance enhancements across multiple control criteria. The optimized system achieved notable reductions in settling time, overshoot magnitude, and steady‐state error, while also demonstrating improved disturbance rejection capabilities under variable load conditions and sensor noise.

Nowadays, the participation of wind power plants in electricity markets has become a severe challenge due to their intermittent nature for decision makers of market. In the presence of uncertainties, some sellers and buyers experience a reduction in their satisfaction. This paper presents a new method for the participation of wind power plants and uncertain customers in a day-ahead electricity market based on the local marginal pricing mechanism to maximize the total profits of sellers and buyers considering their importance level through a two-level optimization problem. For this purpose, using the empirical cumulative distribution function and the Monte Carlo method, the uncertainties are modeled. Then, by defining some economic indices to evaluate participants' satisfaction and using the analytic hierarchy process, a new objective function is proposed to optimize the mentioned indices. Simulations are implemented on a realistic 8-bus sample system, and the results confirm the efficiency of the proposed method in significantly reducing the costs of producers and customers, and consequently their total profits. Based on the results obtained from the presented method, the expected ranges for total cost fall between 1,270.91$ and 1,719.50$, while the expected ranges for total payment range from 2,151.41$ to 2,192.58$.

The energy consumed by artificial lighting accounts for a significant part of the energy consumption in buildings. Thus, energy consumption can be significantly decreased using optimization techniques, such as the optimum placement of the lighting sensors. In this paper, an optimal placement method of the light sensors is presented to minimize the lighting system's equipment costs and energy consumption and also meet visual comfort under the requirements of the European standard EN12464–1 regarding illuminance-based criteria. In the beginning, based on the illumination measurement grid's mathematical model, the potential location of the sensors is determined. As an average of the dimming levels of the LED lights, the objective function has been introduced. Then, the illuminance and uniformity levels are defined as constraints for the optimization problem. The Battle Royale Optimization (BRO) algorithm is used to solve the optimization problem. Ultimately, based on the results of the BRO algorithm and the calculation of the illuminance deviation, the optimal location of the light sensors is determined. The proposed method is tested in an office room. A fuzzy logic controller is developed to regulate the lighting control system's dimming levels to evaluate the proposed method's performance with other approaches. The comparison results have shown that the proposed method is superior as regards the number of sensors and the optimal sensor position, significant savings in energy consumption of up to 30.8%, and satisfactory visual comfort per the requirements of the European standard EN12464–1.

Abstract This article studies the output feedback finite‐time boundary control for unstable heat systems with the spatially varying coefficient. First, a finite‐time observer with switched gains under a state‐dependent switching law is designed in order to estimate the states of the system in a finite‐time only exerting one displacement boundary measurement. Next, an observer‐based linear finite‐time control is planned. Namely, a linear switched control under a state‐dependent switching law is proposed to vanish every solution of an unstable heat partial differential equation with spatially varying coefficients in a finite time. We also present explicit forms for the proposed observer gains and output feedback finite‐time controller. Finally, some numerical simulations are provided to confirm the theoretical results.

Abstract In this study, a step‐up DC‐DC converter with a combination of a two‐phase interleaved structure and a quasi‐Z impedance network is proposed for fuel cell vehicle application. The operation of the converter in a small duty cycle (0 < D < 0.5) reduces the conductive losses of the switches and as a result increases the efficiency of this converter compared to conventional boost converters. Also, due to the common ground between the input and output, unlike the floating interleaved boost converter (FIBC) and the parallel input‐series output converter (PISO), it does not face the problem of imposing additional EMI on the converter circuit. This converter has a low input current ripple, suitable voltage gain for fuel cell vehicles system, as well as high reliability due to the ability to operate with one phase in case of failure in the other phase. It can be a suitable candidate for practical application in fuel cell vehicles. The principles of operation and the main characteristics of the converter such as voltage gain, input current ripple, and voltage and current stress of the elements are explained and also a 120‐W experimental prototype with 12‐V input voltage and 60‐V output voltage is made to validate the theoretical analysis results.

Recently, the participation of wind sources in electricity markets has become a severe challenge due to their intermittent nature. Reconfiguration of power systems can effectively reduce the negative effects of uncertainties. So, this article presents a new method for participating in wind power plants and uncertain customers in a day‐ahead electricity market considering the reconfiguration process. This method tries to maximize social welfare through a two‐level optimization problem. To this end, uncertainties are modeled using the empirical cumulative distribution function and the Monte–Carlo method, and a probabilistic analysis of the market is performed. Then, by defining some indices to evaluate the participants’ satisfaction and using the analytic hierarchy process method (AHP), a new objective function is proposed so that its minimization leads to planning the system configuration and market participants to optimize mentioned indices. The proposed methodology also assumes that the participation of uncertain participants in the spot market will eliminate the imbalances caused by uncertainties. The simulations are implemented using real data on an 8‐bus sample network. The results confirm the efficiency of the proposed method in significantly reducing power producers’ and customers’ costs along with increasing total income and profit from the sale of energy.

This paper represents a new generation of adaptive disturbance rejection control (ADRC) which is more robust against disturbances than conventional ADRC. The non-derivability of the fal function employed in the traditional ADRC has negative impacts on its operation, so alternate functions will be used which are derivable at all segments. In this regard, odd hyperbolic and trigonometric functions were employed. The performance of the proposed structure was investigated to control the doubly fed induction generator (DFIG) speed. To enhance the efficiency of the suggested ADRC, fractional-order calculations and fuzzy logic were utilized simultaneously. The results in MATLAB platform indicate that: 1) With constant wind speed and changing reference speed, using new fal functions in fuzzy fractional-order ADRC (FFOADRC) has improved the performance compared to the PI regulator and FFOADRC with default fal function. 2) During wind speed variations and using new fal functions, the DFIG speed reaches the final steady amount as over damping, while this condition is critical damping when using FFOADRC with default fal function. 3) During network voltage reduction, using new FFOADRCs leads to fewer oscillations in the stator flux, DC-bus voltage, and DFIG speed, which shows their better performance than PI regulator and traditional ADRC.

One of the significant problems in demand response (DR) participation in the smart power system is calculating how much electrical power is required to extract from DR ( ) to keep the power system frequency in the allowable range. Calculating the precise amount of this value is impossible due to the random nature of load disturbance (LoD). In this paper, a new method is presented to control the DR participation in the load frequency control considering communication time delay. Extended State Observer is used to estimate the magnitude of the LoD, considering the structural uncertainty of the power system parameters. Then, the DR program is implemented in load frequency control to compensate the whole or part of LoD considering the available electrical power at the aggregators (PAV‐AGG) and communication time delay. Afterward, Active Disturbance Rejection Control is modified and adopted to control the uncompensated LoD. The salp swarm algorithm is employed to design the parameters of the proposed method, which is verified in comparison with the previous methods. The results demonstrate that the presented approach has potentially significant performance, assisting the power system frequency to be damped immediately with the small overshoot and undershoot.

Abstract In this paper, an overview of several strategies for fault ride-through (FRT) capability improvement of a doubly-fed induction generator (DFIG)-based wind turbine is presented. Uncertainties and parameter variations have adverse effects on the performance of these strategies. It is desirable to use a control method that is robust to such disturbances. Auto disturbance rejection control (ADRC) is one of the most common methods for eliminating the effects of disturbances. To improve the performance of the conventional ADRC, a modified ADRC is introduced that is more robust to disturbances and offers better responses. The non-derivability of the fal function used in the conventional ADRC degrades its efficiency, so the modified ADRC uses alternative functions that are derivable at all points, i.e., the odd trigonometric and hyperbolic functions (arcsinh, arctan, and tanh). To improve the efficiency of the proposed ADRC, fuzzy logic and fractional-order functions are used simultaneously. In fuzzy fractional-order ADRC (FFOADRC), all disturbances are evaluated using a nonlinear fractional-order extended state observer (NFESO). The performance of the suggested structure is investigated in MATLAB/Simulink. The simulation results show that during disturbances such as network voltage sag/swell, using the modified ADRCs leads to smaller fluctuations in stator flux amplitude and DC-link voltage, lower variations in DFIG velocity, and lower total harmonic distortion (THD) of the stator current. This demonstrates the superiority over conventional ADRC and a proportional-integral (PI) controller. Also, by changing the crowbar resistance and using the modified ADRCs, the peak values of the waveforms (torque and currents) can be controlled at the moment of fault occurrence with no significant distortion.

Simultaneous investigation of demand response programs and false data injection cyber-attack are critical issues for the smart power system frequency regulation. To this purpose, in this paper, the output of the studied system is simultaneously divided into two subsystems: one part including false data injection cyder-attack and another part without cyder-attack. Then, false data injection cyber-attack and load disturbance are estimated by a non-linear sliding mode observer, simultaneously and separately. After that, demand response is incorporated in the uncertain power system to compensate the whole or a part of the load disturbance based on the available electrical power in the aggregators considering communication time delay. Finally, active disturbance rejection control is modified and introduced to remove the false data injection cyber-attack and control the uncompensated load disturbance. The salp swarm algorithm is used to design the parameters. The results of several simulation scenarios indicate the efficient performance of the proposed method.

This paper represents a novel sensorless method for the vector control of doubly fed induction generator (DFIG) in a wind turbine system. The proposed method is based on the fuzzy fractional order adaptive disturbance rejection control (FFOADRC) estimating the rotor velocity. In this new method, there is no need to calculate the coupling terms and eliminate them by feed-forward compensation. In addition, all disturbances (internal and external) are estimated by a fractional order extended state observer (FESO). The effects of these disturbances are then neutralized by generating a suitable control command. The operation of the proposed system has been simulated in Matlab/Simulink environment. The comparisons were made between FFOADRC, adaptive disturbance rejection control (ADRC), fuzzy ADRC (FADRC), and proportional-integral (PI) controller under different operating conditions. The results show that: (1) After DFIG starts and under similar conditions, using FFOADRC, FADRC, and ADRC, the velocity reaches the steady state with the overshoot values of 0%, 3.64%, and 8.03%, respectively. (2) In the steady state after wind velocity variation, the %THD values of the stator current using FFOADRC, FADRC, and ADRC are, respectively, 1.47, 1.54, and 2.79. In this case, utilizing the PI controller, the control circuit has a slower performance than three other controllers. (3) The comparison between the aforementioned controllers during DFIG velocity control shows that using FFOADRC, the values of settling time, rise time, peak time, and delay time are smaller, and we have better performance that indicates the superiority of FFOADRC over ADRC, FADRC, and PI controller. Therefore, FFOADRC improves the wind turbine performance in different conditions

A new buck–boost converter with coupled inductors is presented in this article. The converter benefits from low ripple input current, simple control (both power switches operate synchronously), common ground sharing between input and output ports, low-voltage stress across the power switches, positive output voltage, and quadratic voltage gain. Since the proposed converter has continuous input current, it is a proper choice for fuel cell (FC) and photovoltaic applications. Operating principles, mathematical calculation for steady-state operation, and small-signal modeling analysis are described in detail. Finally, an experimental 25-20-200 V prototype has been implemented to confirm all the mathematical derivation and aforementioned features of the proposed buck–boost converter.

Abstract The aim of this paper is to present a new topology of single‐phase transformerless inverters, which can be tied to the local grid as a low‐scaled ac module system. The proposed topology offers a common ground between the neutral point of the ac grid and the negative terminal of the dc supply, and can properly alleviate the concern of variable common mode voltage and leakage current problems. This promising feature is acquired by the aim of both the switched‐capacitor and charge pumped circuit cells. In order to inject a tightly controlled ac current to the grid, an adaptive hysteresis current controller scheme is also presented, which can guarantee almost fixed switching frequency operation of the involved power switches. A complete theoretical analysis, comparative study, and the relevant experimental results are also given to confirm the superior performance of the proposed topology.

A buck–boost dc–dc converter with semi-quadratic voltage gain is introduced in this article. The proposed converter benefits from continuous input current and common ground characteristic between input–output voltage ports. Due to low ripple input current, the proposed converter is a proper choice for carbon-free power sources such as photovoltaic (PV). Unlike the traditional buck–boost converter, the presented converter offers positive output voltage and large voltage gain without using an extreme duty cycle. In addition, the voltage stresses across the power switches of the proposed converter are very low compared with the output voltage. Hence, power switches with low on-resistance are used in practical implementation, which leads to power loss reduction and efficiency improvement. The performance principles, dc analysis, modeling process, and power loss analysis of the proposed converter are fully described. Finally, a laboratory prototype is implemented so as to evaluate the previously mentioned features of the proposed converter.

The simultaneous investigation of false data injection cyber-attack (FDICA) and demand response (DR) participation in smart power systems are dealt with in this paper. For this purpose, simultaneous and separate detection of FDICA and determination of the changes in the power consumption for participation in DR (PDR) are necessary. To balance between generation and consumption, PDR must be equal to the load disturbances (LDs). Active-disturbance rejection control (ADRC) with the extended state observer (ESO) is implemented to detect FDICA and LDs. But, ESO only detects the sum of FDICA and LDs without the ability to separate them. Therefore, a nonlinear sliding mode observer (NSMO) is implemented to detach FDICA from LDs. In order to improve the NSMO estimation accuracy, the modified salp swarm algorithm (SSA) is implemented to design NSMO parameters. Moreover, to achieve better performance of ADRC, a fuzzy tuner is applied to the online tuning of controller parameters. The proposed optimized fuzzy sliding-based modified active-disturbance rejection control (FSADRC) is tested for load frequency control of the IEEE 9 bus standard test system and the 10 machines New England test power system considering communications time delay. The results of several simulation scenarios indicate the efficient performance of the proposed method.

The paper is devoted to the study of boundary finite-time control for a reaction-diffusion (RD) system with switching time-delayed input. The RD system with switching time-delay input is converted to a switching system of RD equation cascaded with a transport equation with non-delay boundary input. Next, a novel switching controller is designed for the cascaded RD-transport system based on the backstepping technique, and this causes the closed-loop system to be convergence in a finite-time. Simulation results are provided to exhibit the effectiveness of the proposed method.

Plug‐in electric vehicles (PEVs) can contribute to eliminating undesirable harmonics generated by nonlinear loads. In this study, a novel stochastic optimization approach for harmonic compensation is proposed which is capable of optimizing contrary objectives, including total harmonic distortion and harmonic inject current, simultaneously, while meeting the relevant constraints. This problem can be influenced by the uncertainty of PEVs which is reflected in the force outage rate concept. The Monte–Carlo simulation technique is implemented to consider the uncertainty associated with PEVs by generating plausible scenarios with the aim of converting the mentioned framework to the respective deterministic equivalents. Afterward, adaptive particularly tunable fuzzy chaotic particle swarm optimization (APTFCPSO) is utilized, based on the weighted sum method, and the acquired results are compared with those obtained by other implemented swarm intelligence‐based algorithms. Accordingly, at first, several benchmark optimization functions are considered to verify the performance of the APTFCPSO. Afterward, active power line conditioners (APLCs) and PEVs are separately employed for harmonics cancellation in the deterministic form. After adopting the scenario reduction technique, the optimization framework is solved for each remaining scenario by the mentioned procedure. The statistical analysis reveals that PEVs outperform APLCs to cancel harmonic orders defined in a 14‐node micro‐grid.

In this paper, a predictor-based fractional disturbance rejection control (PFDRC) scheme is proposed for processes subject to input delay. The proposed scheme can be generally applied to open-loop stable, integrative, and unstable integer-order processes, but it can be particularly utilized for open-loop stable fractional-order systems. A closed-loop reference model is formulated based on Bode’s ideal transfer function. The primary control design objective is to enable the output of input-delay process to follow the closed-loop reference model. Towards this end, the closed-loop transfer function of the PFDRC must take the same structure as that of the reference model. Meanwhile, the adverse effects of the input delay must be mitigated. To meet the latter, a filtered Smith predictor (FSP) is employed to provide a prediction of delay-less output response. To address the former, process dynamics are treated as a common disturbance; then, a fractional-order extended state observer (FESO) is introduced to estimate the delay-less output response and also the total disturbance (i.e. external disturbance and system uncertainties). The PFDRC feedback controller is easily derived by the gain crossover frequency of Bode’s ideal transfer function which facilitates the tuning process. The convergence analysis of the FESO is carried out in terms of BIBO stability. The effectiveness of the proposed control scheme is verified through three illustrative examples from the literature.

A new coupled-inductor buck-boost converter (CIBuBoC) is proposed in this article. In the proposed CIBuBoC, an ultra-high step-up/step-down voltage conversion ratio and step-up/step-down boundary adjustment are achieved compared to the other related buck-boost converters using two power switches with simultaneous operation along with a coupled inductor. This circuit has a simple structure with two cascade semistage and some features including ultra-extended output voltage, continuous input current with low ripple, positive polarity of the output voltage, and common ground. These features make the CIBuBoC more suitable for many applications such as photovoltaic systems. Moreover, the voltage stress across each power switch is much lower than the other buck-boost converters, which led to power mosfets selection with lower drain-source on-resistance (Rds). Therefore, the proposed converter has also enough high efficiency. All steady-state and stress analysis, and also, comparisons with other related converters in continuous conduction mode are provided in detail. Also, using the state-space averaging technique, the low-frequency behavior of the proposed CIBuBoC is studied completely. Experimental results of a 100-W step-up 30-200 V and a 35-W step-down 30-22 V confirm the theoretical advantages of the proposed circuit.

Summary This paper presents a novel transformerless semi‐quadratic buck‐boost converter (SQBuBoC). In the proposed SQBuBoC, two power switches with simultaneous operation are used and a higher step‐up/step‐down voltage conversion ratio is achieved compared with the traditional buck‐boost, Cuk, single‐ended primary‐inductor converter, and Zeta converters. The positive polarity of the output voltage, along with low ripple continuous input current and common ground between the source and the output voltages, are some features that make the suggested topology more suitable for many applications with wide range of output voltage such as photovoltaic systems. Moreover, the total voltage stress across the power switches in this converter is lower than the cascade boost, and the traditional buck‐boost converters led to power MOSFETs selection with lower drain‐source ON resistance (Rds) and efficiency improvement. All the steady‐state analysis and comparisons in continuous conduction mode (CCM) are discussed in details. In addition, to study the low frequency behavior of the SQBuBoC by means of the state‐space averaging technique, the small and large signal models of this converter in CCM are presented. Finally, the SQBuBoC analysis is justified using experimental results of a 50 W step‐up 25 V to 120 V and a 28 W step‐down 25 V to 14 V laboratory prototypes.

A single‐input double‐output dc–dc isolated high step‐up dc–dc converter with soft‐switching feature is presented in this study. The concept is to utilise quadrupler technique to reach high voltage gain without large duty cycle. Additionally, soft‐switching operation for all power switches and diodes is realised to reduce overall power losses and increase power conversion efficiency over a broad range. Furthermore, the leakage inductance energy of transformer is recycled to output with an active clamp circuit. Thus, the voltage stress on main switch is reduced and a low‐voltage‐rated metal–oxide–semiconductor field‐effect transistors (with low ) can be used. Moreover, low input current ripple feature is helpful to lengthen life time of renewable energy power sources. Finally, the analysis is described in detail and performance of the proposed converter has been verified through experimental results.

Generally, the modelling of high step‐up converters with a large number of passive components consisting of inductors, coupled‐inductors (CL) and capacitors is very complex. Recently, to further increase the voltage gain in high step‐up converters in a simple and low‐cost manner, voltage multiplier (VM) circuits have been increasingly used. Also, to reduce the switch voltage spike, clamp circuits are applied. This leads to an increase in the order of systems and operational modes as well. Thus, for simpler modelling and reducing the state variables, the use of reduced‐order techniques are required. A general structure for small signal modelling of such converters including passive clamp, CL and VM circuits is presented. For this purpose, an example of these types of converters is selected. At first, a full‐order model of this high‐order converter is derived using the state‐space averaging method. Then, two reduced‐order models of the converter are derived and then compared with the full‐order model. Also, the small signal and low frequency behaviour is evaluated. In addition, the impact of the parameter variations on the frequency response and stability margin is investigated. Finally, experimental results based on laboratory prototype are presented to verify the validity of the theoretical analysis.

In this paper, a new modified single-switch single-ended primary inductor converter (MS2-SEPIC)-based high step-up dc-dc converter is presented. The proposed topology uses the coupled-inductor (CL) technique and a voltage tripler rectifier, which results in a high voltage gain for the converter. Here, the switching loss has been reduced significantly owing to the quasi-resonance operation of the circuit created by the leakage inductance of the CL along with circuit capacitors. The operational principles and steady-state analysis are discussed. Experimental results based on a 100 W laboratory prototype verify the validity of theoretical analysis.

This paper presents a new multiple‐input–single‐output nonlinear system identification method based on Hammerstein model, which includes a fractional transfer function and a Modified Radial Basis Function Neural Network (MRBFNN) as linear dynamic part and static nonlinear subsystem, respectively. The size of Radial Basis Function Neural Network (RBFNN) grows with the number of inputs exponentially. As a novel idea, the MRBFNN is proposed, whose adjustable parameters are far fewer than other RBFNNs presented yet. A Modified Genetic Algorithm is used to identify the fractional orders and the centers and widths of MRBFNN and obtain an initial estimation of other unknown parameters. The Recursive Least Square (RLS) method is used to improve the estimation by updating the weighting parameters of MRBFNN and the transfer function coefficients. The convergence analysis of the proposed RLS is provided. Simulation results show the effectiveness and accuracy of the proposed method.

Due to the fact that the error surface of adaptive infinite impulse response (IIR) systems is generally nonlinear and multimodal, conventional derivative-based techniques fail when used in adaptive Filter design. In this sense, global optimization techniques are required in order to avoid local minima. Harmony search (HS), a musical inspired metaheuristic, is a recently introduced population-based algorithm that has been successfully applied to global optimization problems. In the present paper, adaptive IIR filtering is formulated as a nonlinear optimization problem and then an improved version of HS incorporating chaotic search (CIHS) is introduced to solve the identification problem of three benchmark IIR systems. Furthermore, the performance of the proposed methodology is compared with HS and two well-known metaheuristic algorithms, genetic algorithm (GA) and particle swarm optimization (PSO) and a modified version of PSO called PSOW (Particle Swarm Optimization with weight Factor). The results demonstrate that the proposed method has superior performance over the other above-mentioned algorithms in terms of convergence speed and accuracy.

Imperialist competitive algorithm is an evolutionary algorithm introduced for optimization problems. In this paper, multi-objective modified imperialist competitive algorithm is proposed for brushless DC motor optimization problem. In the proposed algorithm, the movement of countries toward the best imperialist is concentrated and some techniques are used to extend the single-objective algorithm to the multi-objective version. Then, the algorithm is used to optimize the design variables of brushless DC motor to maximize efficiency, minimize total mass, and satisfy six inequality constraints simultaneously. Simulation results show the superiority of the proposed algorithm over multi-objective versions of standard imperialist competitive algorithm, particle swarm optimization, improved strength Pareto evolutionary algorithm and non-dominated sorting genetic algorithm III.