The document presents a new Lightning Attachment Procedure Optimization (LAPO) algorithm for solving the short-term hydrothermal scheduling (STHS) problem. The STHS problem aims to minimize total fuel costs of thermal power units over a period by determining optimal hourly generation of hydro and thermal units while satisfying constraints. LAPO is applied to three test systems of varying hydro and thermal unit combinations to evaluate its effectiveness in finding optimal solutions for the nonlinear, non-convex STHS optimization problem. Simulation results demonstrate LAPO's superiority over other techniques for this application.
PuShort Term Hydrothermal Scheduling using Evolutionary Programmingblished pa...Satyendra Singh
In this paper, Evolutionary Programming method
is used for short term hydrothermal scheduling which minimize
the total fuel cost while satisfying the constraints. This paper
developed and studies the performance of evolutionary programs
in solving hydrothermal scheduling problem. The effectiveness of
the developed program is tested for the system having one hydro
and one thermal unit for 24 hour load demand. Numerical results
show that highly near-optimal solutions can be obtained by
Evolutionary Programming.
Economic Load Dispatch Problem with Valve – Point Effect Using a Binary Bat A...IDES Editor
This paper proposes application of BAT algorithm
for solving economic load dispatch problem. BAT
algorithmic rule is predicated on the localization
characteristics of micro bats. The proposed approach has
been examined and tested with the numerical results of
economic load dispatch problems with three and five
generating units with valve - point loading without
considering prohibited operating zones and ramp rate limits.
The results of the projected BAT formula are compared with
that of other techniques such as lambda iteration, GA, PSO,
APSO, EP, ABC and basic principle. For each case, the
projected algorithmic program outperforms the answer
reported for the existing algorithms. Additionally, the
promising results show the hardness, quick convergence
and potency of the projected technique.
Antlion optimization algorithm for optimal non-smooth economic load dispatchIJECEIAES
This paper presents applications of Antlion optimization algorithm (ALO) for han- dling optimal economic load dispatch (OELD) problems. Electricity generation cost minimization by controlling power output of all available generating units is a major goal of the problem. ALO is a metaheuristic algorithm based on the hunting process of Antlions. The effect of ALO is investigated by solving a 10-unit system. Each studied case has different objective function and complex level of restraints. Three test cases are employed and arranged according to the complex level in which the first one only considers multi fuel sources while the second case is more complicated by taking valve point loading effects into account. And, the third case is the highest challenge to ALO since the valve effects together with ramp rate limits, prohibited operating zones and spinning reserve constraints are taken into consideration. The comparisons of the result obtained by ALO and other ones indicate the ALO algorithm is more potential than most methods on the solution, the stabilization, and the convergence velocity. Therefore, the ALO method is an effective and promising tool for systems with multi fuel sources and considering complicated constraints.
Optimal Power Flow with Reactive Power Compensation for Cost And Loss Minimiz...ijeei-iaes
One of the concerns of power system planners is the problem of optimum cost of generation as well as loss minimization on the grid system. This issue can be addressed in a number of ways; one of such ways is the use of reactive power support (shunt capacitor compensation). This paper used the method of shunt capacitor placement for cost and transmission loss minimization on Nigerian power grid system which is a 24-bus, 330kV network interconnecting four thermal generating stations (Sapele, Delta, Afam and Egbin) and three hydro stations to various load points. Simulation in MATLAB was performed on the Nigerian 330kV transmission grid system. The technique employed was based on the optimal power flow formulations using Newton-Raphson iterative method for the load flow analysis of the grid system. The results show that when shunt capacitor was employed as the inequality constraints on the power system, there is a reduction in the total cost of generation accompanied with reduction in the total system losses with a significant improvement in the system voltage profile
Comparative study of methods for optimal reactive power dispatchelelijjournal
Reactive power dispatch plays a main role in order to provide good facility secure and economic operation
in the power system. In a power system optimal reactive power dispatch is supported to improve the voltage
profile, to reduce losses, to improve voltage stability, to reduce cost etc. This paper presents a brief literature survey of reactive power dispatch and also discusses a comparative study of conventional and evolutionary computation techniques applied for reactive power dispatch. The paper is useful for researchers for further research and study so that it can apply in the various areas of power system
PuShort Term Hydrothermal Scheduling using Evolutionary Programmingblished pa...Satyendra Singh
In this paper, Evolutionary Programming method
is used for short term hydrothermal scheduling which minimize
the total fuel cost while satisfying the constraints. This paper
developed and studies the performance of evolutionary programs
in solving hydrothermal scheduling problem. The effectiveness of
the developed program is tested for the system having one hydro
and one thermal unit for 24 hour load demand. Numerical results
show that highly near-optimal solutions can be obtained by
Evolutionary Programming.
Economic Load Dispatch Problem with Valve – Point Effect Using a Binary Bat A...IDES Editor
This paper proposes application of BAT algorithm
for solving economic load dispatch problem. BAT
algorithmic rule is predicated on the localization
characteristics of micro bats. The proposed approach has
been examined and tested with the numerical results of
economic load dispatch problems with three and five
generating units with valve - point loading without
considering prohibited operating zones and ramp rate limits.
The results of the projected BAT formula are compared with
that of other techniques such as lambda iteration, GA, PSO,
APSO, EP, ABC and basic principle. For each case, the
projected algorithmic program outperforms the answer
reported for the existing algorithms. Additionally, the
promising results show the hardness, quick convergence
and potency of the projected technique.
Antlion optimization algorithm for optimal non-smooth economic load dispatchIJECEIAES
This paper presents applications of Antlion optimization algorithm (ALO) for han- dling optimal economic load dispatch (OELD) problems. Electricity generation cost minimization by controlling power output of all available generating units is a major goal of the problem. ALO is a metaheuristic algorithm based on the hunting process of Antlions. The effect of ALO is investigated by solving a 10-unit system. Each studied case has different objective function and complex level of restraints. Three test cases are employed and arranged according to the complex level in which the first one only considers multi fuel sources while the second case is more complicated by taking valve point loading effects into account. And, the third case is the highest challenge to ALO since the valve effects together with ramp rate limits, prohibited operating zones and spinning reserve constraints are taken into consideration. The comparisons of the result obtained by ALO and other ones indicate the ALO algorithm is more potential than most methods on the solution, the stabilization, and the convergence velocity. Therefore, the ALO method is an effective and promising tool for systems with multi fuel sources and considering complicated constraints.
Optimal Power Flow with Reactive Power Compensation for Cost And Loss Minimiz...ijeei-iaes
One of the concerns of power system planners is the problem of optimum cost of generation as well as loss minimization on the grid system. This issue can be addressed in a number of ways; one of such ways is the use of reactive power support (shunt capacitor compensation). This paper used the method of shunt capacitor placement for cost and transmission loss minimization on Nigerian power grid system which is a 24-bus, 330kV network interconnecting four thermal generating stations (Sapele, Delta, Afam and Egbin) and three hydro stations to various load points. Simulation in MATLAB was performed on the Nigerian 330kV transmission grid system. The technique employed was based on the optimal power flow formulations using Newton-Raphson iterative method for the load flow analysis of the grid system. The results show that when shunt capacitor was employed as the inequality constraints on the power system, there is a reduction in the total cost of generation accompanied with reduction in the total system losses with a significant improvement in the system voltage profile
Comparative study of methods for optimal reactive power dispatchelelijjournal
Reactive power dispatch plays a main role in order to provide good facility secure and economic operation
in the power system. In a power system optimal reactive power dispatch is supported to improve the voltage
profile, to reduce losses, to improve voltage stability, to reduce cost etc. This paper presents a brief literature survey of reactive power dispatch and also discusses a comparative study of conventional and evolutionary computation techniques applied for reactive power dispatch. The paper is useful for researchers for further research and study so that it can apply in the various areas of power system
Dynamic Economic Dispatch Assessment Using Particle Swarm Optimization TechniquejournalBEEI
This paper presents the application of particle swarm optimization (PSO) technique for solving the dynamic economic dispatch (DED) problem. The DED is one of the main functions in power system planning in order to obtain optimum power system operation and control. It determines the optimal operation of generating units at every predicted load demands over a certain period of time. The optimum operation of generating units is obtained by referring to the minimum total generation cost while the system is operating within its limits. The DED based PSO technique is tested on a 9-bus system containing of three generator bus, six load bus and twelve transmission lines.
Genetic Algorithm for Solving the Economic Load DispatchSatyendra Singh
In this paper, comparative study of two approaches, Genetic Algorithm
(GA) and Lambda Iteration method (LIM) have been used to provide
the solution of the economic load dispatch (ELD) problem. The ELD
problem is defined as to minimize the total operating cost of a power
system while meeting the total load plus transmission losses within
generation limits. GA and LIM have been used individually for solving
two cases, first is three generator test system and second is ten
generator test system. The results are compared which reveals that GA
can provide more accurate results with fast convergence characteristics
and is superior to LIM.
A Tactical Chaos based PWM Technique for Distortion Restraint and Power Spect...IJPEDS-IAES
The pulse width modulated voltage source inverters (PWM-VSI) dominate in the modern industrial environment. The conventional PWM methods are designed to have higher fundamental voltage, easy filtering and reduced total harmonic distortion (THD). There are number of clustered harmonics around the multiples of switching frequency in the output of conventional sinusoidal pulse width modulation (SPWM) and space vector pulse width modulation (SVPWM) inverters. This is due to their fixed switching frequency while the variable switching frequency makes the filtering very complex. Random carrier PWM (RCPWM) methods are the host of PWM methods, which use randomized carrier frequency and result in a harmonic profile with well distributed harmonic power (no harmonic possesses significant magnitude and hence no filtering is required). This paper proposes a chaos-based PWM (CPWM) strategy, which utilizes a chaotically changing switching frequency to spread the harmonics continuously to a wideband and to reduce the peak harmonics to a great extent. This can be an effective way to suppress the current harmonics and torque ripple in induction motor drives. The proposed CPWM scheme is simulated using MATLAB / SIMULINK software and implemented in three phase voltage source inverter (VSI) using field programmable gate array (FPGA).
A genetic algorithm for the optimal design of a multistage amplifier IJECEIAES
The optimal sizing of analog circuits is one of the most complicated processes, because of the number of variables taken into, to the number of required objectives to be optimized and to the constraint functions restrictions. The aim is to automate this activity in order to accelerate the circuits design and sizing. In this paper, we deal with the optimization of the three stage bipolar transistor amplifier performances namely the voltage gain (AV), the input impedance (ZIN), the output impedance (ZOUT), the power consumption (P) and the low and the high cutoff frequency (FL,FH), through the Genetic Algorithm (GA). The presented optimization problem is of multi-dimensional parameters, and the trade-off of all parameters. In fact, the passive components (Resistors and Capacitors) are selected from manufactured constant values (E12, E24, E48, E96, E192) for the purpose of reduce the cost of design; also, the intrinsic parameters of transistors (hybrid parameters and the junction capacitances) are considered variables in order not to be limited in design. SPICE simulation is used to validate the obtained result/performances.
Electric distribution network reconfiguration for power loss reduction based ...IJECEIAES
This paper proposes a method for solving the distribution network reconfiguration (NR) problem based on runner root algorithm (RRA) for reducing active power loss. The RRA is a recent developed metaheuristic algorithm inspired from runners and roots of plants to search water and minerals. RRA is equipped with four tools for searching the optimal solution. In which, the random jumps and the restart of population are used for exploring and the elite selection and random jumps around the current best solution are used for exploiting. The effectiveness of the RRA is evaluated on the 16 and 69-node system. The obtained results are compared with particle swarm optimization and other methods. The numerical results show that the RRA is the potential method for the NR problem.
This paper discusses the possible applications of particle swarm optimization (PSO) in the Power system. One of the problems in Power System is Economic Load dispatch (ED). The discussion is carried out in view of the saving money, computational speed – up and expandability that can be achieved by using PSO method. The general approach of the method of this paper is that of Dynamic Programming Method coupled with PSO method. The feasibility of the proposed method is demonstrated, and it is compared with the lambda iterative method in terms of the solution quality and computation efficiency. The experimental results show that the proposed PSO method was indeed capable of obtaining higher quality solutions efficiently in ED problems.
In this study, optimal economic load dispatch problem (OELD) is resolved by
a novel improved algorithm. The proposed modified moth swarm algorithm
(MMSA), is developed by proposing two modifications on the classical moth
swarm algorithm (MSA). The first modification applies an effective formula
to replace an ineffective formula of the mutation technique. The second
modification is to cancel the crossover technique. For proving the efficient
improvements of the proposed method, different systems with discontinuous
objective functions as well as complicated constraints are used. Experiment
results on the investigated cases show that the proposed method can get less
cost and achieve stable search ability than MSA. As compared to other
previous methods, MMSA can archive equal or better results. From this view,
it can give a conclusion that MMSA method can be valued as a useful method
for OELD problem.
Parallel-in-Time Object-Oriented Electromagnetic Transient Simulation of Powe...Power System Operation
Parallel-in-time methods are emerging to accelerate the solution of time-consuming problems
in different research elds. However, the complexity of power system component models brings challenges to
realize the parallel-in-time power system electromagnetic transient (EMT) simulation, including the traveling
wave transmission lines. This paper proposes a system-level parallel-in-time EMT simulation method based
on traditional nodal analysis and the Parareal algorithm. A new interpretation scheme is proposed to solve the
transmission line convergence problem. To integrate different kinds of traditional EMT models, a componentbased
EMT system solver architecture is proposed to address the increasing model complexity. An objectoriented
C++ implementation is proposed to realize the parallel-in-time Parareal algorithm based on the
proposed architecture. The results on the IEEE-118 test system show 2.30x speed-up compared to the
sequential algorithm under the same accuracy with 6 CPU threads, and a high parallel efciency around 40%.
The performance comparison of various IEEE test cases shows that the system's time-domain characteristics
determine the speed-up of Parareal algorithm, and the delays in transmission lines signicantly affect the
performance of parallel-in-time power system EMT simulations.
Finding optimal reactive power dispatch solutions by using a novel improved s...TELKOMNIKA JOURNAL
In this paper, a novel improved Stochastic Fractal Search optimization algorithm (ISFSOA) is
proposed for finding effective solutions of a complex optimal reactive power dispatch (ORPD) problem with
consideration of all constraints in transmission power network. Three different objectives consisting of total
power loss (TPL), total voltage deviation (TVD) and voltage stabilization enhancement index are
independently optimized by running the proposed ISFSOA and standard Stochastic Fractal Search
optimization algorithm (SFSOA). The potential search of the proposed ISFSOA can be highly improved
since diffusion process of SFSOA is modified. Compared to SFSOA, the proposed method can explore
large search zones and exploit local search zones effectively based on the comparison of solution quality.
One standard IEEE 30-bus system with three study cases is employed for testing the proposed method
and compared to other so far applied methods. For each study case, the proposed method together with
SFSOA are run fifty run and three main results consisting of the best, mean and standard deviation fitness
function are compared. The indication is that the proposed method can find more promising solutions for
the three cases and its search ability is always more stable than those of SFSOA. The comparison with
other methods also give the same evaluation that the proposed method can be superior to almost all
compared methods. As a result, it can conclude that the proposed modification is really appropriate for
SFSOA in dealing with ORPD problem and the method can be used for other engineering
optimization problems.
Decomposition coordinating method for the solution of a multi-area power syst...Litha123
The use of renewable energy sources such as wind can reduce the emission of atmospheric gases and fuel consumption (Wang & Singh, 2008). The integration of wind turbines to the existing thermal generating units can also introduce challenges in balancing of the power system generation.
Wind energy can reduce tremendously the life span of thermal generators while these units play a vital role by functioning as reserves in compensation of the wind uncertainties.Power system generations areas interconnect because interconnected areas are more reliable and they can be operated at minimum cost than isolated areas.
Optimal Reactive Power Scheduling Using Cuckoo Search AlgorithmIJECEIAES
The article describes multidisciplinary design process of high-performance electric generator for advanced aircrafts by analytical methods and computer modeling techniques (electromagnetic, thermal and mechanical calculations). New technical solutions used in its development are described. The main ideas are revealed of the method of EG voltage stabilization we used. To improve the heat dissipation efficiency, we have developed a new cooling system, and provide its study and description in this paper. The advantages of this cooling system include the fact that EG is made with dry, uncooled rotor. This allowed eliminating additional pumps, and significantly reducing tThis paper solves an optimal reactive power scheduling problem in the deregulated power system using the evolutionary based Cuckoo Search Algorithm (CSA). Reactive power scheduling is a very important problem in the power system operation, which is a nonlinear and mixed integer programming problem. It optimizes a specific objective function while satisfying all the equality and inequality constraints. In this paper, CSA is used to determine the optimal settings of control variables such as generator voltages, transformer tap positions and the amount of reactive compensation required to optimize the certain objective functions. The CSA algorithm has been developed from the inspiration that the obligate brood parasitism of some Cuckoo species lay their eggs in nests of other host birds which are of other species. The performance of CSA for solving the proposed optimal reactive power scheduling problem is examined on standard Ward Hale 6 bus, IEEE 30 bus, 57 bus, 118 bus and 300 bus test systems. The simulation results show that the proposed approach is more suitable, effective and efficient compared to other optimization techniques presented in the literature.he size of CSD. According to the results of our study, we created an experimental full capacity layout, and its studies are also provided in this paper.
Multi-objective Pareto front and particle swarm optimization algorithms for p...IJECEIAES
The progress of microelectronics making possible higher integration densities, and a considerable development of on-board systems are currently undergoing, this growth comes up against a limiting factor of power dissipation. Higher power dissipation will cause an immediate spread of generated heat which causes thermal problems. Consequently, the system's total consumed energy will increase as the system temperature increase. High temperatures in microprocessors and large thermal energy of computer systems produce huge problems of system confidence, performance, and cooling expenses. Power consumed by processors are mainly due to the increase in number of cores and the clock frequency, which is dissipated in the form of heat and causes thermal challenges for chip designers. As the microprocessor’s performance has increased remarkably in Nano-meter technology, power dissipation is becoming non-negligible. To solve this problem, this article addresses power dissipation reduction issues for high performance processors using multi-objective Pareto front (PF), and particle swarm optimization (PSO) algorithms to achieve power dissipation as a prior computation that reduces the real delay of a target microprocessor unit. Simulation is verified the conceptual fundamentals and optimization of joint body and supply voltages (V thV DD ) which showing satisfactory findings.
Identification study of solar cell/module using recent optimization techniquesIJECEIAES
This paper proposes the application of a novel metaphor-free population optimization based on the mathematics of the Runge Kutta method (RUN) for parameter extraction of a double-diode model of the unknown solar cell and photovoltaic (PV) module parameters. The RUN optimizer is employed to determine the seven unknown parameters of the two-diode model. Fitting the experimental data is the main objective of the extracted unknown parameters to develop a generic PV model. Consequently, the root means squared error (RMSE) between the measured and estimated data is considered as the primary objective function. The suggested objective function achieves the closeness degree between the estimated and experimental data. For getting the generic model, applications of the proposed RUN are carried out on two different commercial PV cells. To assess the proposed algorithm, a comprehensive comparison study is employed and compared with several well-matured optimization algorithms reported in the literature. Numerical simulations prove the high precision and fast response of the proposed RUN algorithm for solving multiple PV models. Added to that, the RUN can be considered as a good alternative optimization method for solving power systems optimization problems.
A Novel Approach to GSA, GA and Wavelet Transform to Design Fuzzy Logic Contr...IAES-IJPEDS
This paper proposes a novel approach for obtaining a closed loop control
scheme based on Fuzzy Logic Controller to regulate the output voltage
waveform of multilevel inverter. Fuzzy Logic Controller is used to guide and
control the inverter to synthesize a stepped output voltage waveform with
reduced harmonics. In this paper, three different intelligent soft-computing
methods are used to design a fuzzy system to be used as a closed loop control
system for regulating the inverter output. Gravitational Search Algorithm
and Genetic Algorithm are used as optimization methods to evaluate
switching angles for different combination of input voltages applied to MLI.
Wavelet Transform is used as synthesizing technique to shape stepped output
waveform of inverter using orthogonal wavelet sets. The proposed FLC
controlled method is carried out for a wider range of input dc voltages by
considering ±10% variations in nominal voltage value. A 7-level inverter is
used to validate the results of proposed control methods. The three proposed
methods are then compared in terms of various parameters like
computational time, switching angles and THD to justify the performance
and system flexibility. Finally, hardware based results are also obtained to
verify the viability of the proposed method.
HYDROTHERMAL COORDINATION FOR SHORT RANGE FIXED HEAD STATIONS USING FAST GENE...ecij
This paper presents a Fast genetic algorithm for solving Hydrothermal coordination (HTC) problem. Genetic Algorithms (GAs) perform powerful global searches, but their long computation times, put a limitation when solving large scale optimization problems. The present paper describes a Fast GA (FGA) to overcome this limitation, by starting with random solutions within the search space and narrowing down the search space by considering the minimum and maximum errors of the population members. Since the search space is restricted to a small region within the available search space the algorithm
works very fast. This algorithm reduces the computational burden and number of generations to converge. The proposed algorithm has been demonstrated for HTC of various combinations of Hydro thermal systems. In all the cases Fast GA shows reliable convergence. The final results obtained using
Fast GA are compared with simple (conventional) GA and found to be encouraging.
Optimal power flow with distributed energy sources using whale optimization a...IJECEIAES
Renewable energy generation is increasingly attractive since it is non-polluting and viable. Recently, the technical and economic performance of power system networks has been enhanced by integrating renewable energy sources (RES). This work focuses on the size of solar and wind production by replacing the thermal generation to decrease cost and losses on a big electrical power system. The Weibull and Lognormal probability density functions are used to calculate the deliverable power of wind and solar energy, to be integrated into the power system. Due to the uncertain and intermittent conditions of these sources, their integration complicates the optimal power flow problem. This paper proposes an optimal power flow (OPF) using the whale optimization algorithm (WOA), to solve for the stochastic wind and solar power integrated power system. In this paper, the ideal capacity of RES along with thermal generators has been determined by considering total generation cost as an objective function. The proposed methodology is tested on the IEEE-30 system to ensure its usefulness. Obtained results show the effectiveness of WOA when compared with other algorithms like non-dominated sorting genetic algorithm (NSGA-II), grey wolf optimization (GWO) and particle swarm optimization-GWO (PSOGWO).
Dynamic Economic Dispatch Assessment Using Particle Swarm Optimization TechniquejournalBEEI
This paper presents the application of particle swarm optimization (PSO) technique for solving the dynamic economic dispatch (DED) problem. The DED is one of the main functions in power system planning in order to obtain optimum power system operation and control. It determines the optimal operation of generating units at every predicted load demands over a certain period of time. The optimum operation of generating units is obtained by referring to the minimum total generation cost while the system is operating within its limits. The DED based PSO technique is tested on a 9-bus system containing of three generator bus, six load bus and twelve transmission lines.
Genetic Algorithm for Solving the Economic Load DispatchSatyendra Singh
In this paper, comparative study of two approaches, Genetic Algorithm
(GA) and Lambda Iteration method (LIM) have been used to provide
the solution of the economic load dispatch (ELD) problem. The ELD
problem is defined as to minimize the total operating cost of a power
system while meeting the total load plus transmission losses within
generation limits. GA and LIM have been used individually for solving
two cases, first is three generator test system and second is ten
generator test system. The results are compared which reveals that GA
can provide more accurate results with fast convergence characteristics
and is superior to LIM.
A Tactical Chaos based PWM Technique for Distortion Restraint and Power Spect...IJPEDS-IAES
The pulse width modulated voltage source inverters (PWM-VSI) dominate in the modern industrial environment. The conventional PWM methods are designed to have higher fundamental voltage, easy filtering and reduced total harmonic distortion (THD). There are number of clustered harmonics around the multiples of switching frequency in the output of conventional sinusoidal pulse width modulation (SPWM) and space vector pulse width modulation (SVPWM) inverters. This is due to their fixed switching frequency while the variable switching frequency makes the filtering very complex. Random carrier PWM (RCPWM) methods are the host of PWM methods, which use randomized carrier frequency and result in a harmonic profile with well distributed harmonic power (no harmonic possesses significant magnitude and hence no filtering is required). This paper proposes a chaos-based PWM (CPWM) strategy, which utilizes a chaotically changing switching frequency to spread the harmonics continuously to a wideband and to reduce the peak harmonics to a great extent. This can be an effective way to suppress the current harmonics and torque ripple in induction motor drives. The proposed CPWM scheme is simulated using MATLAB / SIMULINK software and implemented in three phase voltage source inverter (VSI) using field programmable gate array (FPGA).
A genetic algorithm for the optimal design of a multistage amplifier IJECEIAES
The optimal sizing of analog circuits is one of the most complicated processes, because of the number of variables taken into, to the number of required objectives to be optimized and to the constraint functions restrictions. The aim is to automate this activity in order to accelerate the circuits design and sizing. In this paper, we deal with the optimization of the three stage bipolar transistor amplifier performances namely the voltage gain (AV), the input impedance (ZIN), the output impedance (ZOUT), the power consumption (P) and the low and the high cutoff frequency (FL,FH), through the Genetic Algorithm (GA). The presented optimization problem is of multi-dimensional parameters, and the trade-off of all parameters. In fact, the passive components (Resistors and Capacitors) are selected from manufactured constant values (E12, E24, E48, E96, E192) for the purpose of reduce the cost of design; also, the intrinsic parameters of transistors (hybrid parameters and the junction capacitances) are considered variables in order not to be limited in design. SPICE simulation is used to validate the obtained result/performances.
Electric distribution network reconfiguration for power loss reduction based ...IJECEIAES
This paper proposes a method for solving the distribution network reconfiguration (NR) problem based on runner root algorithm (RRA) for reducing active power loss. The RRA is a recent developed metaheuristic algorithm inspired from runners and roots of plants to search water and minerals. RRA is equipped with four tools for searching the optimal solution. In which, the random jumps and the restart of population are used for exploring and the elite selection and random jumps around the current best solution are used for exploiting. The effectiveness of the RRA is evaluated on the 16 and 69-node system. The obtained results are compared with particle swarm optimization and other methods. The numerical results show that the RRA is the potential method for the NR problem.
This paper discusses the possible applications of particle swarm optimization (PSO) in the Power system. One of the problems in Power System is Economic Load dispatch (ED). The discussion is carried out in view of the saving money, computational speed – up and expandability that can be achieved by using PSO method. The general approach of the method of this paper is that of Dynamic Programming Method coupled with PSO method. The feasibility of the proposed method is demonstrated, and it is compared with the lambda iterative method in terms of the solution quality and computation efficiency. The experimental results show that the proposed PSO method was indeed capable of obtaining higher quality solutions efficiently in ED problems.
In this study, optimal economic load dispatch problem (OELD) is resolved by
a novel improved algorithm. The proposed modified moth swarm algorithm
(MMSA), is developed by proposing two modifications on the classical moth
swarm algorithm (MSA). The first modification applies an effective formula
to replace an ineffective formula of the mutation technique. The second
modification is to cancel the crossover technique. For proving the efficient
improvements of the proposed method, different systems with discontinuous
objective functions as well as complicated constraints are used. Experiment
results on the investigated cases show that the proposed method can get less
cost and achieve stable search ability than MSA. As compared to other
previous methods, MMSA can archive equal or better results. From this view,
it can give a conclusion that MMSA method can be valued as a useful method
for OELD problem.
Parallel-in-Time Object-Oriented Electromagnetic Transient Simulation of Powe...Power System Operation
Parallel-in-time methods are emerging to accelerate the solution of time-consuming problems
in different research elds. However, the complexity of power system component models brings challenges to
realize the parallel-in-time power system electromagnetic transient (EMT) simulation, including the traveling
wave transmission lines. This paper proposes a system-level parallel-in-time EMT simulation method based
on traditional nodal analysis and the Parareal algorithm. A new interpretation scheme is proposed to solve the
transmission line convergence problem. To integrate different kinds of traditional EMT models, a componentbased
EMT system solver architecture is proposed to address the increasing model complexity. An objectoriented
C++ implementation is proposed to realize the parallel-in-time Parareal algorithm based on the
proposed architecture. The results on the IEEE-118 test system show 2.30x speed-up compared to the
sequential algorithm under the same accuracy with 6 CPU threads, and a high parallel efciency around 40%.
The performance comparison of various IEEE test cases shows that the system's time-domain characteristics
determine the speed-up of Parareal algorithm, and the delays in transmission lines signicantly affect the
performance of parallel-in-time power system EMT simulations.
Finding optimal reactive power dispatch solutions by using a novel improved s...TELKOMNIKA JOURNAL
In this paper, a novel improved Stochastic Fractal Search optimization algorithm (ISFSOA) is
proposed for finding effective solutions of a complex optimal reactive power dispatch (ORPD) problem with
consideration of all constraints in transmission power network. Three different objectives consisting of total
power loss (TPL), total voltage deviation (TVD) and voltage stabilization enhancement index are
independently optimized by running the proposed ISFSOA and standard Stochastic Fractal Search
optimization algorithm (SFSOA). The potential search of the proposed ISFSOA can be highly improved
since diffusion process of SFSOA is modified. Compared to SFSOA, the proposed method can explore
large search zones and exploit local search zones effectively based on the comparison of solution quality.
One standard IEEE 30-bus system with three study cases is employed for testing the proposed method
and compared to other so far applied methods. For each study case, the proposed method together with
SFSOA are run fifty run and three main results consisting of the best, mean and standard deviation fitness
function are compared. The indication is that the proposed method can find more promising solutions for
the three cases and its search ability is always more stable than those of SFSOA. The comparison with
other methods also give the same evaluation that the proposed method can be superior to almost all
compared methods. As a result, it can conclude that the proposed modification is really appropriate for
SFSOA in dealing with ORPD problem and the method can be used for other engineering
optimization problems.
Decomposition coordinating method for the solution of a multi-area power syst...Litha123
The use of renewable energy sources such as wind can reduce the emission of atmospheric gases and fuel consumption (Wang & Singh, 2008). The integration of wind turbines to the existing thermal generating units can also introduce challenges in balancing of the power system generation.
Wind energy can reduce tremendously the life span of thermal generators while these units play a vital role by functioning as reserves in compensation of the wind uncertainties.Power system generations areas interconnect because interconnected areas are more reliable and they can be operated at minimum cost than isolated areas.
Optimal Reactive Power Scheduling Using Cuckoo Search AlgorithmIJECEIAES
The article describes multidisciplinary design process of high-performance electric generator for advanced aircrafts by analytical methods and computer modeling techniques (electromagnetic, thermal and mechanical calculations). New technical solutions used in its development are described. The main ideas are revealed of the method of EG voltage stabilization we used. To improve the heat dissipation efficiency, we have developed a new cooling system, and provide its study and description in this paper. The advantages of this cooling system include the fact that EG is made with dry, uncooled rotor. This allowed eliminating additional pumps, and significantly reducing tThis paper solves an optimal reactive power scheduling problem in the deregulated power system using the evolutionary based Cuckoo Search Algorithm (CSA). Reactive power scheduling is a very important problem in the power system operation, which is a nonlinear and mixed integer programming problem. It optimizes a specific objective function while satisfying all the equality and inequality constraints. In this paper, CSA is used to determine the optimal settings of control variables such as generator voltages, transformer tap positions and the amount of reactive compensation required to optimize the certain objective functions. The CSA algorithm has been developed from the inspiration that the obligate brood parasitism of some Cuckoo species lay their eggs in nests of other host birds which are of other species. The performance of CSA for solving the proposed optimal reactive power scheduling problem is examined on standard Ward Hale 6 bus, IEEE 30 bus, 57 bus, 118 bus and 300 bus test systems. The simulation results show that the proposed approach is more suitable, effective and efficient compared to other optimization techniques presented in the literature.he size of CSD. According to the results of our study, we created an experimental full capacity layout, and its studies are also provided in this paper.
Multi-objective Pareto front and particle swarm optimization algorithms for p...IJECEIAES
The progress of microelectronics making possible higher integration densities, and a considerable development of on-board systems are currently undergoing, this growth comes up against a limiting factor of power dissipation. Higher power dissipation will cause an immediate spread of generated heat which causes thermal problems. Consequently, the system's total consumed energy will increase as the system temperature increase. High temperatures in microprocessors and large thermal energy of computer systems produce huge problems of system confidence, performance, and cooling expenses. Power consumed by processors are mainly due to the increase in number of cores and the clock frequency, which is dissipated in the form of heat and causes thermal challenges for chip designers. As the microprocessor’s performance has increased remarkably in Nano-meter technology, power dissipation is becoming non-negligible. To solve this problem, this article addresses power dissipation reduction issues for high performance processors using multi-objective Pareto front (PF), and particle swarm optimization (PSO) algorithms to achieve power dissipation as a prior computation that reduces the real delay of a target microprocessor unit. Simulation is verified the conceptual fundamentals and optimization of joint body and supply voltages (V thV DD ) which showing satisfactory findings.
Identification study of solar cell/module using recent optimization techniquesIJECEIAES
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HYDROTHERMAL COORDINATION FOR SHORT RANGE FIXED HEAD STATIONS USING FAST GENE...ecij
This paper presents a Fast genetic algorithm for solving Hydrothermal coordination (HTC) problem. Genetic Algorithms (GAs) perform powerful global searches, but their long computation times, put a limitation when solving large scale optimization problems. The present paper describes a Fast GA (FGA) to overcome this limitation, by starting with random solutions within the search space and narrowing down the search space by considering the minimum and maximum errors of the population members. Since the search space is restricted to a small region within the available search space the algorithm
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Renewable energy generation is increasingly attractive since it is non-polluting and viable. Recently, the technical and economic performance of power system networks has been enhanced by integrating renewable energy sources (RES). This work focuses on the size of solar and wind production by replacing the thermal generation to decrease cost and losses on a big electrical power system. The Weibull and Lognormal probability density functions are used to calculate the deliverable power of wind and solar energy, to be integrated into the power system. Due to the uncertain and intermittent conditions of these sources, their integration complicates the optimal power flow problem. This paper proposes an optimal power flow (OPF) using the whale optimization algorithm (WOA), to solve for the stochastic wind and solar power integrated power system. In this paper, the ideal capacity of RES along with thermal generators has been determined by considering total generation cost as an objective function. The proposed methodology is tested on the IEEE-30 system to ensure its usefulness. Obtained results show the effectiveness of WOA when compared with other algorithms like non-dominated sorting genetic algorithm (NSGA-II), grey wolf optimization (GWO) and particle swarm optimization-GWO (PSOGWO).
Final project report on grocery store management system..pdfKamal Acharya
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Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
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Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
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1. METHODOLOGIES AND APPLICATION
Lightning attachment procedure optimization algorithm for nonlinear
non-convex short-term hydrothermal generation scheduling
Maha Mohamed1 • Abdel-Raheem Youssef1 • Salah Kamel2,4 • Mohamed Ebeed3
Published online: 17 April 2020
Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract
Short-term hydrothermal scheduling (STHS) is considered an important problem in the field of power system economics.
The solution of this problem gives the hourly output of power generation schedule of the available hydro and thermal
power units, which leads to minimization of the total fuel cost of thermal units for a given period of a time. The optimal
generation of STHS is considered as a complicated and nonlinear optimization problem with a set of equality and
inequality constraints such as the valve point loading effect of thermal units, the power transmission loss and the load
balance. This paper proposes lightning attachment procedure Optimization (LAPO) algorithm for solving the nonlinear
non-convex STHS optimization problem in order to minimize the operating fuel cost of thermal units with satisfying the
operating constraints of the system. The performance of LAPO algorithm is validated using three different test systems
considering the valve point loading effects of thermal units and the power transmission losses. The obtained results prove
the effectiveness and superiority of LAPO algorithm for solving the STHS problem compared with other well-known
optimization techniques.
Keywords Short-term hydrothermal scheduling Non-convex optimization problem Lightning attachment procedure
optimization Valve point loading effect
List of symbols
F Total fuel cost from all thermal plants
Ns Total number of thermal plants
T Total time of whole scheduling period
ai; bi; ci Power generation coefficients of thermal
plant
Pt
si Output power generation from thermal plant
di; ei Coefficients of the valve point effects of the
thermal plant
Pmin
si
Lower power generation limit of thermal
plant
Vt
hj Reservoir storage volume of hydropower
plant jth at a period of time t
It
hj External inflow to reservoir jth at a period of
time t
Qt
hj Water discharge amount of hydropower plant
j at a period of time t
S Spillage discharge rate of reservoir jth at
time interval t
Ruj Number of upstream hydropower plant
Nh Number of hydropower plant
Pt
D Power demand at a period of time t
Communicated by V. Loia.
Salah Kamel
skamel@aswu.edu.eg
Maha Mohamed
mahamohamed21@yahoo.com
Abdel-Raheem Youssef
abou_radwan@hotmail.com
Mohamed Ebeed
mohamedebeed11@gmail.com
1
Department of Electrical Engineering, Faculty of
Engineering, South Valley University, Qena, Egypt
2
Department of Electrical Engineering, Faculty of
Engineering, Aswan University, Aswân 81542, Egypt
3
Department of Electrical Engineering, Faculty of
Engineering, Sohag University, Sohâg, Egypt
4
State Key Laboratory of Power Transmission Equipment and
System Security and New Technology, Chongqing
University, Chongqing, China
123
Soft Computing (2020) 24:16225–16248
https://doi.org/10.1007/s00500-020-04936-2(0123456789().,-volV)
(0123456789().
,- volV)
2. Pt
hj Power generation of hydropower plant j at a
period of time t
Pt
L Power transmission loss of the system at a
period of time t
Vmin
hj
Minimum storage volume of hydro plant j
Vmax
hj Maximum storage volume of hydro plant j
Qmin
hj
Minimum water discharge of hydro plant j
QMax
hj Maximum water discharge of hydro plant j
Pmin
hj ; Pmax
hj
Minimum and maximum power generation
of hydro plant j
Pmin
si ; Pmax
si
Minimum and maximum power generation
of thermal plant i
Vbegin
hj ; Vend
hj
Initial and final reservoir storage volumes of
hydropower plant j
VT
hj Reservoir storage of hydro plant j at a period
of time from (0 to 24)
Abbreviations
STHS Short-term hydrothermal scheduling
LAPO Lightning attachment procedure
optimization
VPL Valve point loading
LP Linear programming
NLP Nonlinear programming
DP Dynamic programming
GS Gradient search
GA Genetic algorithm
EP Evolutionary programming
DE Differential evolution
PSO Particle swarm optimization
IPSO Improved particle swarm optimization
MAPSO Modified adaptive PSO
SSPSO Small population-based particle swarm
optimization
ABC Artificial bee colony
LR Lagrange relaxation
IDE Improved differential evolution
FAPSO Fuzzy adaptive particle swarm
optimization
RCGA Real-coded genetic algorithm
HIS Improved harmony search
RCGA-IMM Real-coded genetic algorithm based on
improved Mühlenbein mutation
CPSO Couple-based particle swarm optimization
TLBO Teaching learning-based optimization
ACABC Adaptive chaotic artificial bee colony
MDNLPSO Modified dynamic neighborhood learning-
based particle swarm optimization
RCGA–
AFSA
Hybrid of real-coded genetic algorithm and
artificial fish swarm algorithm
ORCCRO Oppositional real-coded chemical reaction
based optimization
DRQEA Differential real-coded quantum-inspired
evolutionary algorithm
MHDE Modified hybrid differential evolution
ACDE Adaptive chaotic differential evolution
ALO Ant lion optimization
1 Introduction
The optimal power generation of short-term hydrothermal
scheduling (STHS) has a great importance in the electric grid
systems. The main objective of STHS problem is to minimize
the total operation fuel cost of the thermal units through
determining the optimal power generation of hydro and
thermal units in each scheduling interval, while satisfying the
various equality and inequality constraints on the hydraulic
power plants and the power system network. The STHS is
considering a complicated problem, which includes the dif-
ferent equality and inequality constraints. The equality con-
straints include power balance, water storage balance, and
initial and terminal reservoir storage volumes. Also, the
inequality constraints are limitations of hydrothermal power
generation, limitations of water storage volumes and limita-
tions of water discharge rate. These constraints with the valve
point loading effect (VPLE) make the STHS problem a
nonlinear, non-convex and complicated constrained opti-
mization problem. Several optimization techniques have been
presented for solving the STHS problem. Firstly, analytical
optimization techniques have been implemented for obtaining
the optimal solution of hydrothermal scheduling problem
such as linear programming (LP) (Chang et al. 2001; Wu
et al. 2009), nonlinear programming (NLP) (Catalão et al.
2011), dynamic programming (DP) (Homem-de-Mello et al.
2011), gradient search (GS) (Wood and Wollenberg 2003),
Newton’s method (Zaghlool and Trutt 1988) and Lagrange
relaxation (LR) (Dieu and Ongsakul 2009). Linear program-
ming (LP) is applied to the problems which has linear
objective function and constraints, but the STHS problem is a
difficult and nonlinear optimization problem; therefore, this
will lead to errors in the result of the scheduling problem. The
NLP method requires large memory to reach the ideal solu-
tion of the nonlinear optimization problem and has slow
convergence. The DP is a popular method for overcoming the
difficulty of nonlinearity and non-convexity of the STHS
problem. However, the DP method suffers from the curse of
dimensionality when the size of the system increases and this
will lead to large memory storage and long computational
time. To overcome the handling constraints, the LR is more
accurate. However, the main drawback in LR is the
16226 M. Mohamed et al.
123
3. oscillation of solutions. The main shortage of these methods is
that they may stuck in local optima and suffer from
stagnation.
In order to overcome the drawbacks of analytical opti-
mization techniques, heuristic algorithms have been
implemented to solve the non-convex nonlinear STHS
problem such as genetic algorithm (GA) (Nazari-Heris
et al. 2017a; Haghrah et al. 2014), evolutionary program-
ming (EP) (Hota et al. 1999; Türkay et al. 2011), differ-
ential evolution (DE) (Malik et al. 2016), particle swarm
optimization (PSO) (Ramesh 2016; Mahor and Rangnekar
2012), improved particle swarm optimization (IPSO) (Hota
et al. 2009), modified adaptive PSO (MAPSO) and small
population-based particle swarm optimization (SSPSO)
(Amjady and Soleymanpour 2010), artificial bee colony
(ABC) (Liao et al. 2013; Zhou et al. 2014).
In Nazari-Heris et al. (2017a), the authors improved the GA
for finding the ideal solution of the STHS optimizationproblem
with considering the valve point loading effect of the thermal
power units and the power transmission losses. The real-coded
genetic algorithm with random transfer vectors-based mutation
(RCGA-RTVM) has been presented in Haghrah et al. (2014),
and the authorsrepresented with an innovatedmutation method
utilizing genetic algorithm (GA) to solve the nonlinear non-
convexSTHSproblem.InHotaetal.(1999;Türkayetal.2011),
the authors proposed the EP optimization algorithm to find the
optimal power generation scheduling for thermal and hydro
plants.InMaliketal.(2016),theauthorspresentedanimproved
hybrid approach based on the chaos theory in the differential
evolution (DE) algorithm for solving the STHS problem to
minimize the emission of the thermal units. The improved PSO
technique for solving the STHS problem has been presented in
Ramesh (2016), Mahor and Rangnekar (2012) and Hota et al.
(2009). The modified adaptive particle swarm optimization
(MAPSO) for determining the optimal thermal and hydro
power generation is presented in Hota et al. (x2010). To solve
the STHS problem, an adaptive chaotic artificial bee colony
(ACABC) algorithm has been considered in Liao et al. (2013).
In Zhou et al. (2014), the authors have been studied a multi-
objective artificial bee colony (MOABC) algorithm for solving
the nonlinear STHS optimization algorithm. Predator–prey-
based optimization (PPO) technique to obtain optimal genera-
tion scheduling of short-term hydrothermal system has been
offered in Narang et al. (2014). Table 1 shows the different
definitions of test systems uses for solving the STHS problems.
Moreover, literature reviews articles related to solve the STHS
optimization algorithm are summarized by Table 2.
Lightning attachment procedure optimization (LAPO) is
a new physical-based algorithm presented by Nematollahi
et al. (2017, 2019). LAPO is conceptualized from Light-
ning occurrence steps. The simulated steps of the LAPO
include trail spots, leader upward motion, section fading,
downward leader motion and the final strike point of
lightning which mimics the optimal solution.
In this paper, the authors present a new application of
lightning attachment procedure Optimization (LAPO)
technique to find the hourly optimal power generation of
thermal units and hydro power units for minimizing the
total fuel cost. The effect of valve point loading and the
power transmission loss are taken into consideration for
finding the optimal solution of the STHS optimization
problem. To evaluate the performance of proposed algo-
rithm, it is applied on three test systems including four
hydro power plants with single equivalent thermal units
and four hydro plants with three thermal units and four
hydro plants with ten thermal units.
The rest of paper is organized as follows. The formu-
lation of STHS problem is presented in Sect. 2. Section 3
presents the overview of proposed algorithm. The simula-
tion results in different studied cases are presented in
Sect. 4. Finally, the conclusion is presented in Sect. 5.
2 Problem formulation of hydrothermal
system
The STHS problem aims to minimize the total fuel cost of
thermal plants by use the hydropower as much as possible
and with negligible cost of the hydro power generation
units. The scheduling generation of hydro and thermal units
is provided during STHS process for a given period of time
for meeting the load demand and satisfying the all equality
and inequality constraints. The objective function and the
different constraints of the STHS problem are formulated
as follows.
2.1 Objective function
The objective function of total fuel cost of thermal units,
which is expressed as quadratic and a sinusoidal function
(Nazari-Heris et al. 2017b), can be represented as follows:
Table 1 Definition of test
systems studied for the solution
of STHS problem
Test system Number of hydrothermal generation units
Test system 1 One equivalent thermal unit and four cascaded hydro units
Test system 2 Four cascaded hydro power plants and three thermal plants
Test system 3 Four cascaded hydro power plants and ten thermal plants
Lightning attachment procedure optimization algorithm for nonlinear non-convex short-term… 16227
123
4. F ¼ min
X
T
t¼1
X
Ns
i¼1
ai þ biPt
si þ ci Pt
si
2
ð1Þ
where F is the total power generation fuel cost from all
thermal units at a time t, Ns is the total number of thermal
units, T is the total time of whole scheduling period, ai,bi,ci
are the power generation coefficients of thermal unit,Pt
si is
the output power generation from thermal unit of the ith
thermal plant at period t, respectively. The fuel cost
function of the ith thermal plant, and it is usually
Table 2 Objective functions and main contribution of researches in the area of STHS problem solution
Reference Method Year Test system Main consideration
Nazari-Heris et al. (2018) IHS 2018 Test system 1,
Test system
2
The cost of thermal units is commonly studied as a quadratic function,
valve point loading effect, transmission losses
Chang (2010) FAPSO 2010 Test system 1 The cost of thermal units is commonly studied as a quadratic function
Basu (2014b) Improved DE 2014 Test system 1,
Test system
2
Prohibited discharge zones (PDZs) of water reservoir of the hydro
units and valve point loading effect, ramp rate limits of thermal
generators, transmission losses
Mandal and Chakraborty
(2011)
SOHPSO_TVAC 2011 Test system 1 Economic emission, the cost of thermal units is commonly studied as
a quadratic function
Wu et al. (2019) CPSO 2019 Test system 1,
Test system
2
The cost of thermal units is commonly studied as a quadratic function,
valve point loading effect, prohibited discharge zones (PDZs) of
hydro units
Rasoulzadeh-Akhijahani
and Mohammadi-Ivatloo
(2015)
MDNLPSO 2015 Test system 1,
Test system
2
Prohibited discharge zones (PDZs) of water reservoir of the hydro
units and Valve point loading effect, transmission losses
Zhang et al. (2012) SPPSO 2012 Test system 1,
Test system
2
Valve point loading effect, transmission losses
Fang et al. (2014) RCGA–AFSA 2014 Test system 1,
Test system
2
Valve point loading effect, transmission losses, prohibited discharge
zones (PDZs) and ramp rate limits
Roy (2013) TLBO 2013 Test system 1,
Test system
2
Prohibited discharge zones (PDZs) of water reservoir of the hydro
units and Valve point loading effect
Roy (2014) HCRO-DE 2014 Test system 1 Valve point loading effect, emission of thermal units
Lu et al. (2010) MHDE 2010 Test system 1 Valve point loading effect, transmission losses
Kang et al. (2017) TLPSOS 2017 Test system 2 Valve point loading effect
Dubey et al. (2016) ALO 2016 Test system 2 Valve point loading effect, transmission losses
Bhattacharjee et al. (2014a) ORCCRO 2014 Test system 1,
Test system
2
Valve point loading effect
Zhang et al. (2015) MCDE 2015 Test system 2 Valve point loading effect, transmission losses
Bhattacharjee et al. (2014b) RCCRO 2014 Test system 2 Valve point loading effect, prohibited discharge zones (PDZs) of
hydro units and ramp rate limit
Gouthamkumar et al.
(2015)
DGSA 2015 Test system 2 Valve point loading effect
Swain et al. (2011) CSA 2011 Test system 2 Valve point loading effect
Lakshminarasimman and
Subramanian (2006)
MDE 2006 Test system 2 Valve point loading effect, prohibited discharge zones (PDZs) of
hydro units, emission of thermal units
Mandal et al. (2008) PSO 2008 Test system 2 Valve point loading effect
Roy et al. (2013) QTLBO 2013 Test system 2 Prohibited discharge zones (PDZs) of hydro units and valve point
loading effect
Mandal and Chakraborty
(2009)
DE 2009 Test system 2 Valve point loading effect, economic emission
Basu (2004a) EP 2004 Test system 2 Valve point loading effect
16228 M. Mohamed et al.
123
5. represented as follows with consideration of valve loading
point effect (Liao et al. 2013).
F ¼ min
X
T
t¼1
X
Ns
i¼1
ai þ biPt
si þ ci Pt
si
2
þ di sin ei Pmin
si Pt
si
n o
ð2Þ
where di and ei are the coefficients of the valve point
effects of the thermal unit i, Pmin
si is the lower power gen-
eration limit of thermal unit i.
2.2 Constraints
The objective function of STHS optimization problem is
subjected to the following equality and inequality con-
straints. The equality constraints include power balance,
water storage balance, and initial and terminal reservoir
storage volumes. Also, the inequality constraints are limi-
tations of hydrothermal power generation, limitations of
water storage volumes and limitations of water discharge
rate.
2.2.1 Water storage balance constraint
The reservoir storage of hydro plant is determined by
inflow and spillage, reservoir storage at previous period
and discharges from upstream reservoir. They must meet
the hydraulic continuity equations as follows (Wang et al.
2012).
Vt
hj ¼ Vt1
hj þ It
hj Qt
hj St
hj þ
X
Ruj
l¼1
Q
tdlj
hl þ S
tdlj
hl
jNh
tT:
ð3Þ
where Vt
hj is storage volume of hydropower plant jth at a
time t, It
hj is the external inflow rate to reservoir jth at time
t,Q
tdlj
hl is the water discharge rate from lth to jth reservoir
during the time delay dlj, dlj is the water transport delay
from lth to jth reservoir ; St
hj is the spillage discharge rate of
reservoir jth at time t, Ruj is the number of upstream
hydropower plants of jth reservoir.
2.2.2 Load demand balance constraint
Power generations of hydro and thermal power units must
meet the load demands of the hydrothermal including the
power transmission losses. Hence, load balance constraint
is expressed as follows:
X
Ns
i¼1
Pt
si þ
X
Nh
j¼1
Pt
hj Pt
L ¼ Pt
D tT ð4Þ
where Nh is the number of hydropower units, Pt
D represents
the power load demand at a period of time t,Pt
hj is the
power generation of hydropower unit j at a period of time t,
Pt
L is the transmission loss of the system at a period of time
t; Pt
hj is formulated as the following equation:
Pt
hj ¼ C1j Vt
hj
2
þC2j Qt
hj
2
þC3jVt
hjQt
hj þ C4jVt
hj þ C5jQt
hj
þ C6j jNh tT
ð5Þ
where Vt
hj,Qt
hj represent the storage volume and water
discharge amount of hydropower unit j at a period of time t,
C1j, C2j, C3j, C4j, C5j and C6j are the power generation
coefficients of hydropower unit j, respectively. The power
transmission loss Pt
L is expressed by the following
equation:
Pt
L ¼
X
NhþNs
i¼0
X
NhþNs
j¼0
Pt
iBijPt
j þ
X
NhþNs
i¼0
BoiPj
i þ Boo ð6Þ
where Bij; Boi and Boo are the power transmission loss
coefficients.
2.2.3 Reservoir storage volumes constraint
0Vmin
hj Vt
hj Vmax
hj ; jNh; tT: ð7Þ
where Vmin
hj ; Vmax
hj represent the minimum and maximum
storage volume limits of the jth hydro plant.
2.2.4 Water discharge constraint
0Qmin
hj Qt
hj Qmax
hj jNh; tT: ð8Þ
where Qmin
hj ; Qmax
hj represent the minimum and maximum
water discharge limits of the jth hydro plant.
2.2.5 Power generation constraint
Pmin
hj Pt
hj Pmax
hj jNh tT: ð9Þ
Pmin
si Pt
si Pmax
si jNs tT: ð10Þ
where Pmin
hj ; Pmax
hj are the minimum and maximum power
generation of the jth hydro plant, respectively and Pmin
si ;
Pmax
si are the minimum and maximum power generation of
the ith thermal plant, respectively.
The initial and terminal reservoir storage volumes:
Vend
hj ¼ VT
hj ð11Þ
VT
hj ¼ Vbegin
hj ð12Þ
Lightning attachment procedure optimization algorithm for nonlinear non-convex short-term… 16229
123
6. where Vbegin
hj ,Vend
hj are the initial and final reservoir storage
volumes of the jth hydro plant and VT
hj is the reservoir
storage of the jth hydro plant at a period of time from (0 to
24).
2.2.6 Handling constraints
It should be highlighted here that Michalewicz and Schoe-
nauer have presented a review survey for constraints handling
methods in optimization algorithms including preserving
feasibility method, penalty functions method, feasible and
infeasible solutions method and a hybrid method. In the pre-
sent, work the dependent systems have been considered using
the penalty functions method as follows:
Fg ¼ F þ KV
X
Nh
j¼1
DVhj
2
þKP
X
Nh
i¼1
DPhj
2
ð13Þ
where KV and KP represent the penalty factors for the water
discharge limits of the hydro plant and the power genera-
tion of the hydro plant, respectively. Fg is the augmented
objective function. DVhj and DQGi are given as follows:
DVhj ¼
Vt
hj Vmax
hj
Vt
hj [ Vmax
hj
Vmin
hj Vt
hj
Vt
hjVmin
hj
0 Vmin
hj Vt
hjVmax
hj
8
:
ð14Þ
DPhj ¼
Pt
hj Pmax
hj
Pt
hj [ Pmax
hj
Pmin
hj Pt
hj
Pt
hjPmin
hj
0 Pmin
hj Pt
hjPmax
hj
8
:
ð15Þ
3 Lighting attachment procedure
optimization (LAPO)
Lightning attachment procedure optimization (LAPO) is a
novel optimization technique conceptualized from Light-
ning phenomena where huge amounts of electric charges
are cumulated in the cloud. The distribution of these
charges in the cloud is depicted in Fig. 1. Lightning is
created with increasing the amount of charges in the cloud
which lead to increase the electrical strength consequently.
Lightning strike will occur, and it may emanate at several
points.
The procedure of lightning attachment includes four
steps which are: (1) breakdown of air at surface of cloud,
(2) lightning channel downward motion, (3) upward leader
extension and (4) final strike point.
As mentioned before, huge amounts of positive and
negative charges exist in the cloud where the highest
amount of the negative charges exist in the upper portion of
the cloud and the huge positive charges will be in the lower
portion of the cloud including also small amount of posi-
tive charges as depicted in Fig. 1. With increasing the
amount of the charges, the electrical potential will also
increase. Consequently, the breakdown between the char-
ges occurs. Moreover, the negative charges at the bottom of
the cloud increase more and potential gradient between the
cloud edge and the ground rises, leading to formation of the
lightning. The lightning starts from one or more points
from the cloud. The downward leaders of the lightning
move to the earth in a gradual motion due to the collapse
caused by air contact with the cloud surface and the leaders
do not continue in one direction as depicted in Fig. 1.
3.1 Mathematical presentation of LAPO
algorithm
Step 1 Trail spots.
The trial spots represent the initial points of the down-
ward leaders which can be found as follows:
Xi
ts ¼ Xi
min þ Xi
max Xi
min
rand ð16Þ
where Xi
ts denotes the initial trial spots. Xmin is the mini-
mum value of the control variable, while Xmax is its max-
imum value. rand is a random value in the range [0,1]. The
fitness function for the initial spots is calculated as:
Fi
ts ¼ obj Xi
ts
ð17Þ
Step 2 Determination of the next jump
All initial points are averaged, and fitness values are
calculated as follows:
Xavr ¼ mean Xts
ð Þ ð18Þ
Favr ¼ obj Xavr
ð Þ ð19Þ
Downward Leader
Upward Leader
+
+
+
+
+
+
+
+ +
+
+
+ +
+ + + +
+
+
+
+ +
+
+
+
- -
+
- -
- -
- -
-
-
- -
-
- +
-
- - - -
- -
- -
- -
-
- -
-
-
-
-
-
- - -
-
- - -
-
- -
-
-- -
-
-
-
-
-
-
-
-
+
+
+ +
+
+ +
+
-
Fig. 1 Charges form in the cloud
16230 M. Mohamed et al.
123
7. Fig. 2 Solution process of
STHS problem using proposed
algorithm
Lightning attachment procedure optimization algorithm for nonlinear non-convex short-term… 16231
123
8. Xavr is the averaged point, while Favr is the objective
function of the averaged point. As mentioned before, the
lightning has several tracks where the lightning is jumped
to the next high optional point. For updating the point i, a
random solution j is selected (potential point), so i = j.
Then the obtained solution is compared with the potential
solution. Hence, the next jump can be calculated as
follows:
Xi
ts new ¼ Xi
ts þ rand Xavr þ X j
PS
IF FjFavr ð20Þ
Xi
ts new ¼ Xi
ts rand Xavr þ X j
PS
IF Fj [ Favr ð21Þ
Step 3 Section fading
The branch will remain continuous if the critical value is
less than the electric field of the new test point; otherwise,
it will fade, which can be expressed as follows:
Xi
ts ¼ Xi
ts new IF Fi
ts newFi
ts ð22Þ
Xi
ts new ¼ Xi
ts otherwise ð23Þ
Test points are executed in this process, and all the
remaining points in the first stage are moving down.
Step 4 Leader upward motion
In this procedure, the points move up mimics the motion
of upward leader which is distributed exponentially along
the channel. Hence, an exponent operator can be repre-
sented as follows:
S ¼ 1
t
tmax
exp
t
tmax
ð24Þ
where t denotes the iteration number, while tmax is the
maximum number of iterations, and next jump depends on
the charge of the channel and the next point is given as
follows:
Xi
ts new ¼ Xi
ts new þ rand S Xi
best Xi
worst
ð25Þ
where Xi
best and Xi
worst are the best and the worse solutions
among the populations.
Step 5 Final strike point
The lightning operation pauses when the down leader
and the up leader gather each other and the striking point is
assigned.
The flowchart of the LAPO algorithm for obtaining the
optimal solution is shown in Fig. 2.
4 Simulation results and discussion
The effectiveness of the proposed LAPO algorithm is
validated using two hydrothermal test systems. The first
test system focuses on a multi-chain cascade of four hydro
units and one thermal power generating unit. There are two
case studies in this system. In case 1, the objective function
is smooth quadratic operation cost of thermal power gen-
eration as presented in Eq. (1). The valve point loading
effect of the thermal unit is considering in case (2) as given
1
I 2
I
3
I
4
I
1
Q 2
Q
3
Q
4
Q
Reservior 1 Reservior 2
Reservior 3
Reservior 4
Fig. 3 Scheme of the hydraulic network of the hydrothermal test
system
Table 3 Reservoir inflows of
hydropower plants for test
systems 1 and 2
Hour Reservoir Hour Reservoir Hour Reservoir
1 2 3 4 1 2 3 4 1 2 3 4
1 10 8 8.1 2.8 9 10 8 1 0 17 9 7 2 0
2 9 8 8.2 2.4 10 11 9 1 0 18 8 6 2 0
3 8 9 4 1.6 11 12 9 1 0 19 7 7 1 0
4 7 9 2 0 12 10 8 2 0 20 6 8 1 0
5 6 8 3 0 13 11 8 4 0 21 7 9 2 0
6 7 7 4 0 14 12 9 3 0 22 8 9 2 0
7 8 6 3 0 15 11 9 3 0 23 9 8 1 0
8 9 7 2 0 16 10 8 2 0 24 10 8 0 0
16232 M. Mohamed et al.
123
9. in Eq. (2). The second test system consists of four cascaded
hydro and three thermal generating units. In the second
system, two different case studies are considered. In the
first case study, the STHS problem is solved considering
the valve point loading effect without considering the
power transmission losses. In the second case study, the
STHS problem is solved considering the valve point
loading effect and the power transmission losses of the
system. The hydraulic network of these test systems is
shown in Fig. 3. The total period is 1 day that is divided
into 24 intervals. The coefficients of hydropower generat-
ing units, reservoir inflows, water discharge limits, initial
and terminal reservoir storage limits and hourly load
demands of power systems are given in Tables 3, 4, 5, 6, 7,
8 and 9. The cost coefficient of thermal and hydro gener-
ating units is adopted from Nazari-Heris et al. (2017a).
4.1 Test system 1
The first test system consists of four cascaded hydro units
and an equivalent thermal unit. In this system, the power
transmission losses are neglected for simplicity. To eval-
uate the performance of the LAPO, two different case
studies have been taken into account as follows;
Table 4 The coefficients of hydropower generation for test systems 1
and 2
Plant C1j C2j C3j C4j C5j C6j
1 - 0.0042 - 0.42 0.030 0.90 10.0 - 50
2 - 0.0040 - 0.30 0.015 1.14 9.5 - 70
3 - 0.0016 - 0.30 0.014 0.55 5.5 - 40
4 - 0.0030 - 0.31 0.027 1.44 14.0 - 90
Table 5 Hydro power generation unit characteristics
Plant Vmin
hj
Vmax
hj Vbegin
hj
Vend
hj Qmin
hj
Qmax
hj pmin
hi
pmax
hi
1 80 150 100 120 5 15 0 500
2 60 120 80 70 6 15 0 500
3 100 240 170 170 10 30 0 500
4 70 160 120 140 6 25 0 500
Table 6 The coefficients of thermal units power generation for test
system 1
Plant ai bi ci di ei pmin
si
pmax
si
1 0.002 19.2 5000 700 0.085 500 2500
Table 7 Load demands of hydrothermal system for test system 1
Hour Load Hour Load Hour Load Hour Load
1 1370 7 1650 13 2230 19 2240
2 1390 8 2000 14 2200 20 2280
3 1360 9 2240 15 2130 21 2240
4 1290 10 2320 16 2070 22 2120
5 1200 11 2230 17 2130 23 1850
6 1410 12 2310 18 2140 24 1590
Table 8 The coefficients of thermal units power generation for test
system 2
Plant ai bi ci di ei pmin
si
pmax
si
1 0.0012 2.45 0.0012 160 0.038 20 175
2 0.0010 2.32 0.0010 180 0.037 40 300
3 0.0015 2.10 0.0015 200 0.035 50 500
Table 9 Load demands of hydrothermal system for test system 2
Hour Load Hour Load Hour Load Hour Load
1 750 7 950 13 1110 19 1070
2 780 8 1010 14 1030 20 1050
3 700 9 1090 15 1010 21 910
4 650 10 1080 16 1060 22 860
5 670 11 1100 17 1050 23 850
6 800 12 1150 18 1120 24 800
Lightning attachment procedure optimization algorithm for nonlinear non-convex short-term… 16233
123
10. 4.1.1 Test system 1 case 1
The first case study is solved without considering the valve
point loading effect of the thermal units. The fuel cost
function of thermal unit is a quadratic function of the STHS
problem as shown in Eq. (1). The optimal hourly water
discharge and hydrothermal power generation obtained by
LAPO method for solving the STHS problem during 24 h
scheduling are reported in Table 10. It is obvious from
Table 10 that the optimal solution satisfies all the con-
straints on hydro discharges and thermal power generation.
The best results of the STHS problem proposed by LAPO
method are compared with different optimization tech-
niques in Table 11. The minimum fuel cost obtained by the
LAPO method is 871,910.67 $ which shows the capability
of the proposed method for obtaining the optimal solution
of the STHS problem with respect to other optimization
methods. The minimum cost is obtained by the proposed
method better than the recent optimization algorithm with
3483.56 $/day. The optimal hourly hydro and thermal
power generation for each hour for the first case study is
shown in Fig. 4. It is obvious that the load demand is equal
to the sum of the power generation for each hour. Figure 5
shows the convergence characteristic of the LAPO method
for this case study.
4.1.2 Test system 1 case 2
The effect of valve point loading has been taken into
account in this case to illustrate the performance of the
LAPO method. Table 12 presents the optimal variables of
water discharges and the optimal power generation of
hydro and thermal generating units obtained by LAPO
method. The best results obtained by LAPO method are
compared with recent meta-heuristic method like a real-
coded genetic algorithm based on improved Mühlenbein
mutation (RCGA-IMM) (Nazari-Heris et al. 2017a) as
illustrated in Table 13. The minimum cost found by LAPO
Hydro Power Units
Thermal
Power Unit
Electric Power
System
Load
16234 M. Mohamed et al.
123
11. Table 10 Optimal water discharge of hydro and thermal power generation for case 1 of test system 1
Hours Water discharge rates (104
m3
/s) Hydro plant power generation (MW) Thermal plant
generation (MW)
Total power
generation (MW)
Plant 1 Plant 2 Plant 3 Plant 4 Plant 1 Plant 2 Plant 3 Plant 4
1 13.248 13.377 13.574 22.250 94.981 81.167 37.384 242.897 913.567 1370
2 13.553 14.806 11.524 23.506 93.146 78.868 38.674 213.683 965.630 1390
3 14.988 14.997 11.479 24.971 90.038 74.092 38.674 199.588 957.607 1360
4 14.995 14.999 11.510 24.883 86.620 72.499 38.674 199.550 892.642 1290
5 14.852 14.999 10.544 24.990 86.640 72.499 41.245 288.581 801.027 1290
6 14.940 14.985 11.924 24.997 86.630 72.478 44.823 327.843 878.223 1410
7 14.853 15 29.934 24.998 86.640 72.500 0 327.845 1162.995 1650
8 14.925 14.998 13.595 24.999 86.632 72.498 37.357 327.849 1475.660 2000
9 14.892 14.989 11.691 24.989 86.636 72.485 38.664 327.819 1714.390 2240
10 14.724 14.994 10.663 24.999 86.643 72.491 38.465 327.848 1794.545 2320
11 14.797 14.993 29.669 24.999 86.643 72.491 0 327.848 1743.013 2230
12 14.994 14.999 29.965 24.994 86.621 72.499 0 314.280 1836.598 2310
13 14.990 14.999 11.522 24.999 86.621 72.499 38.674 327.849 1704.354 2230
14 14.988 14.998 11.474 24.978 86.622 72.497 41.700 327.789 1671.386 2200
15 14.999 14.999 12.298 24.989 86.620 72.499 44.511 327.819 1598.550 2130
16 14.953 14.999 12.307 24.991 86.628 72.499 46.881 327.825 1536.171 2070
17 14.992 14.992 12.048 24.999 86.621 72.490 49.108 327.847 1593.925 2130
18 14.990 14.976 13.147 24.981 86.621 72.466 51.001 327.795 1602.111 2140
19 14.910 14.980 12.553 24.993 86.634 72.472 52.829 327.828 1700.235 2240
20 14.954 14.999 12.194 24.996 86.628 72.499 57.180 327.839 1735.846 2280
21 14.788 14.997 12.805 24.975 86.643 72.496 60.775 327.779 1692.306 2240
22 14.489 14.887 13.477 24.961 86.612 72.339 63.265 327.703 1570.078 2120
23 14.960 14.982 13.761 24.998 86.627 72.475 64.612 327.845 1298.445 1850
24 14.999 14.846 12.812 24.972 107.01 80.704 58.974 303.488 1039.811 1590
Table 11 Comparison of the best results of the STHS problem for case 1 of test system 1
Algorithm Minimum cost
($)
Average cost
($)
Maximum cost
($)
Computation time
(s)
LAPO 871,910.67 873,820.11 878,850.11 4.08
IHS (Nazari-Heris et al. 2018) 875,394.2288 875,687.1443 876,371.0758 NA
RCGA-IMM (Nazari-Heris et al. 2017a) 875,856.41 NA NA NA
RCGA-RTVM (Haghrah et al. 2014) 877,735.9 878,597.2406 880,948.518 NA
FAPSO (Chang 2010) 914,660.00 NA NA 4.73
Improved DE (Basu 2014b) 917,250.1 NA NA NA
PSO (Chang 2010) 921,920 NA NA 10.67
SOHPSO_TVAC (Mandal and Chakraborty 2011) 922,018.24 NA NA NA
CPSO (Wu et al. 2019) 922,328.64 922,367.85 922,564.52 12.9
MDNLPSO (Rasoulzadeh-Akhijahani and Mohammadi-Ivatloo
2015)
922,336.3 922,676.2 923,404.5 35
SPPSO (Zhang et al. 2012) 922,336.31 922,668.45 927,203.63 16.3
RCGA–AFSA (Fang et al. 2014) 922,339.625 922,346.323 922,362.532 NA
TLBO (Roy 2013) 922,373.39 922,462.24 922,873.81 NA
HCRO-DE (Roy 2014) 922,444.79 922,513.62 922,936.17 NA
IPSO (Hota et al. 2009) 922,553.49 NA NA 38.46
MDE (Zhang et al. 2012) 922,556.38 923,201.13 923,813.99 53
RCGA (Fang et al. 2014) 923,966.285 924,108.731 924,232.072 NA
Lightning attachment procedure optimization algorithm for nonlinear non-convex short-term… 16235
123
12. method is 881,184.5 $ which is found to be superior to all
other reported methods in Table 13. The total fuel cost can
be saved when compared to recent optimization techniques
which is 10,595.35 $/day. In addition, the proposed method
successful to maintain the load demand is equal to the total
power generation. The optimal power generation for hydro
and thermal generating units is depicted in Fig. 6. The
optimal cost convergence characteristic for this test system
is shown in Fig. 7. It is clear from these tables and fig-
ures that the best solution obtained by the LAPO method
satisfies all the constraints of the STHS problem for this
case study.
4.2 Test system 2
To evaluate the performance of the proposed LAPO
method, it is applied to another system. This system
includes four hydro and three thermal power generating
units, but this test system is more complex than the first test
system because this system includes the effect of valve
point loading and the power transmission losses.
0
500
1000
1500
2000
2500
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Generation
(MW)
Time ( hour)
hydro 4
hydro 3
hydro 2
hydro 1
Thermal
Fig. 4 Hourly optimal power
generation of hydro and thermal
units for test system 1 case 1
Hydro Power Units
Thermal
Power Units
Electric Power
System
Load
16236 M. Mohamed et al.
123
13. 4.2.1 Test system 2 case 1
In this case, the valve point loading effect of thermal units
is considered and the power transmission losses are
neglected. The optimal solution of the STHS problem is
given in Table 14. The water discharge and hydro power
generation of four hydro units are reported in this table. In
addition, thermal power generation of three thermal units is
provided in this table. It is obvious that the scheduling
results obtained by LAPO method satisfy all hydraulic and
electric system constraints. The minimum fuel cost of test
system 2 case 1 with recent optimization method is
40,204.32 $ which is reduced to 38,800.75 $ with the
proposed LAPO method as shown in Table 15. In the other
words, the total daily saving is 1403.57 $ compared to the
recent optimization method in Fang et al. (2014). Figure 8
shows the hourly hydro and thermal power generation of
0 500 1000 1500 2000 2500 3000
0.85
0.9
0.95
1
1.05
1.1
1.15
x 10
6
Iteration
Total
cost
($)
Fig. 5 Optimal cost of STHS problem for case 2 of test system 1
Table 12 Optimal water discharge of hydro and thermal power generation for case 2 of test system 1
Hours Water discharge rates (104
m3
/s) Hydro plant power generation (MW) Thermal plant
generation (MW)
Total power
generation (MW)
Plant 1 Plant 2 Plant 3 Plant 4 Plant 1 Plant 2 Plant 3 Plant 4
1 7.4753 12.880 10.321 19.324 72.400 80.171 38.258 235.651 943.518 1370
2 12.798 8.0651 29.437 23.685 95.012 59.213 0 218.334 1017.434 1390
3 14.061 14.997 11.571 24.990 93.993 80.183 38.673 199.596 947.517 1360
4 8.2914 13.378 13.259 23.542 73.938 73.379 37.746 198.373 906.561 1290
5 7.0003 14.732 13.828 23.904 65.434 72.103 37.049 282.771 832.640 1290
6 7.3898 14.177 28.302 24.860 67.888 71.146 0 327.449 943.513 1410
7 11.230 14.831 11.075 24.316 85.029 72.255 38.620 325.779 1128.313 1650
8 9.4620 13.681 17.170 24.089 77.900 70.132 29.029 325.025 1497.917 2000
9 12.576 12.977 10.490 24.603 86.827 68.441 38.369 326.684 1719.677 2240
10 13.639 14.938 11.775 25 86.794 72.412 39.335 327.850 1793.595 2320
11 13.167 10.335 10.600 24.668 85.575 59.442 38.432 326.881 1719.668 2230
12 11.135 14.872 10.333 24.835 81.120 72.316 44.582 318.382 1793.597 2310
13 10.405 14.676 11.610 22.920 78.992 72.016 38.671 320.643 1719.676 2230
14 10.593 14.905 11.294 24.799 80.422 72.365 38.662 325.832 1682.718 2200
15 14.804 14.145 13.874 24.543 86.643 71.085 36.983 326.496 1608.792 2130
16 14.861 14.991 27.340 24.999 86.639 72.487 0 327.849 1583.036 2070
17 12.518 14.925 11.706 24.267 84.530 72.394 38.662 325.617 1608.798 2130
18 14.844 15 11.447 24.999 86.640 72.500 38.674 327.849 1614.295 2140
19 13.142 14.834 12.917 23.920 85.541 72.260 38.072 324.445 1719.679 2240
20 14.533 13.074 16.371 18.966 86.621 68.691 31.554 299.549 1793.581 2280
21 14.473 11.346 10.251 24.597 86.608 63.381 43.667 326.666 1719.673 2240
22 14.668 8.2687 10.463 24.080 86.640 50.054 49.516 324.995 1608.796 2120
23 14.288 7.6359 11.623 24.595 86.549 46.764 39.951 326.658 1350.071 1850
24 14.184 14.706 10.063 21.786 105.92 80.468 56.178 293.020 1054.406 1590
Lightning attachment procedure optimization algorithm for nonlinear non-convex short-term… 16237
123
14. the optimal solution for test system 2 case 1. The conver-
gence characteristics of STHS problem by employing the
LAPO method are shown in Fig. 9.
4.2.2 Test system 2 case 2
The valve point loading effect and the power transmission
lossesofthehydrothermalsystemareconsideredinthiscasefor
obtaining the optimal generation scheduling. The optimal
generation scheduling for four hydro and three thermal units,
Table 13 Comparison of the best results of the STHS problem for case 2 of test system 1
Algorithm Minimum cost
($)
Average cost
($)
Maximum cost
($)
Computation
time(s)
LAPO 881,184.5 885,721.3 889,151.6 5.06
RCGA-IMM (Nazari-Heris et al. 2017a) 891,779.85 NA NA NA
RCGA-RTVM (Haghrah et al. 2014) 917,222.73 NA NA NA
IDE (Basu 2014b) 923,016.29 923,036.28 923,152.06 547.07
MDNLPSO (Rasoulzadeh-Akhijahani and Mohammadi-Ivatloo
2015)
923,961 925,258 926,230 119
CPSO (Wu et al. 2019) 924,042.14 925,086.38 926,213.26 18.6
MAPSO (Amjady and Soleymanpour 2010) 924,636.88 926,496 927,431 NA
DRQEA (Wang et al. 2012) 925,485.21 NA NA 7.5
MHDE (Lu et al. 2010) 925,547.31 NA NA 9
IPSO (Hota et al. 2009) 925,978.84 NA NA 31
RQEA (Wang et al. 2012) 926,068.33 NA NA 7.6
RCGA–AFSA (Fang et al. 2014) 927,899.872 927,693.764 928,025.343 NA
DE (Wang et al. 2012) 928,662.84 NA NA 8.7
RCGA (Fang et al. 2014) 930,565.242 930,966.356 931,427.212 NA
0
500
1000
1500
2000
2500
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Generation
(MW)
Time (hour)
Hydro 4
Hydro 3
Hydro 2
Hydro 1
Thermal
Fig. 6 Hourly optimal power
generation of hydro and thermal
units for test system 1 case 2
0 500 1000 1500 2000 2500 3000
0.9
1
1.1
1.2
1.3
x 10
6
Iteration
Total
cost
($)
Fig. 7 Optimal cost of STHS problem for case 2 of test system 1
16238 M. Mohamed et al.
123
16. hourly water discharge and the power transmission losses are
shown in Table 16. The LAPO algorithm is the best for solving
the STHS problem by obtaining the minimal total fuel cost with
efficiency as shown in Table 17. The minimum cost obtained
by LAPO is 39,691.86 $ which helps in daily saving the cost by
234.87 $ as compared the RCGA-IMM (Nazari-Heris et al.
2017a). The optimal results obtained by LAPO method satisfy
all constraints of STHS problem considering valve point
loading effect and the power transmission losses. The optimal
power generation for hydrothermal units is shown in Fig. 10. It
is clearly seen from Fig. 10 that the total power generation
satisfies the power load demand. Figure 11 shows convergence
characteristicsofSTHSproblemforcase 2oftestsystem2.The
power transmission loss coefficients are as follows:
Bij ¼
0:34 0:13 0:09 0:01 0:08 0:01 0:02
0:13 0:14 0:10 0:01 0:05 0:02 0:01
0:09 0:10 0:31 0:00 0:01 0:07 0:05
0:01 0:01 0:00 0:24 0:08 0:04 0:07
0:08 0:05 0:01 0:08 1:92 0:27 0:02
0:01 0:02 0:07 0:04 0:27 0:32 0:00
0:02 0:01 0:05 0:07 0:02 0:00 1:35
2
6
6
6
6
6
6
6
6
6
6
6
4
3
7
7
7
7
7
7
7
7
7
7
7
5
104
MW1
ð20Þ
Boj ¼ 0:75 0:06 0:7 0:03 0:27 0:77 0:01
½
106
ð21Þ
B00 ¼ 0:55 MW ð22Þ
4.3 Test system 3
Test system 3 consists of four hydro and ten thermal power
generating units. Here valve point loading effect of thermal
plants is considered, but the power transmission loss is not
considered. The data of this system have been taken from
Ref. (Mandal and Chakraborty 2008). The optimal cost
obtained by LAPO method for this system is 165,675.084
$. The hourly water discharge of hydro units and the
optimal power generation scheduling of hydro and thermal
0
200
400
600
800
1000
1200
1400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Generation
(MW)
Time (hour)
Hydro 4
Hydro 3
Hydro 2
Hydro 1
Thermal 3
Thermal 2
Thermal 1
Fig. 8 Hourly optimal power
generation of hydro and thermal
units for test system 2 case 1
0 500 1000 1500 2000 2500 3000
3.5
4
4.5
5
5.5
6
6.5
7
x 10
4
Iteration
Total
cost
($)
Fig. 9 Optimal cost of STHS problem for case 1of test system 2
16240 M. Mohamed et al.
123
18. units are shown in Table 18 and 19. It can be observed
from Tables 18 and 19 that the power load demand during
24-h scheduling time is satisfied by total power generation
of four hydro units and ten thermal unit. Table 20 shows
the results obtained by different methods for test system 3.
The convergence characteristics of the proposed method
for this system are presented in Fig. 12. The optimal hourly
hydro and thermal power generation for each hour for test
system 3 is shown in Fig. 13.
Table 17 Comparison of the best results of the STHS problem for case 2 of test system 2
Algorithm Minimum cost
($)
Average cost
($)
Maximum cost
($)
Computation
time(s)
LAPO 39,691.86 40,150.23 40,563.5 7.5328
RCGA-IMM (Nazari-Heris et al. 2017a) 40,483.26196 NA NA NA
RCGA-RTVM (Haghrah et al. 2014) 40,486.6676 NA NA NA
Improved DE (Basu 2014b) 40,627.92 40,708.53 40,860.70 627.06
RCGA–AFSA (Fang et al. 2014) 40,913.828 41,235.72 41,362.575 NA
ACABC (Liao et al. 2013) 41,074.42 NA NA 16
MDNLPSO (Rasoulzadeh-Akhijahani and Mohammadi-Ivatloo
2015)
41,183 41595 41994 192
CPSO (Wu et al. 2019) 41,215.47 41682.92 41843.55 45.5
DRQEA (Wang et al. 2012) 41,435.76 NA NA 18
MCDE (Zhang et al. 2015) 41,586.18 42,022.67 42,365.84 100.05
ACDE (Lu et al. 2010) 41,593.48 NA NA 29
MHDE (Lakshminarasimman and Subramanian 2006) 41,856.50 NA NA 31
QTLBO (Roy et al. 2013) 42,187.49 42,193.46 42,202.75 NA
DE (Wang et al. 2012) 42,801.04 NA NA 21
ALO (Dubey et al. 2016) 42,833.908 NA NA 55.63
RCGA (Fang et al. 2014) 42,886.352 43,261.912 43,032.334 NA
CABC (Liao et al. 2013) 43,362.68 NA NA 21
DE (Mandal and Chakraborty 2009) 43,500.00 NA NA 72.9570
IPSO (Swain et al. 2011) 44,321.236 NA NA NA
DE (Lakshminarasimman and Subramanian 2006) 44,526.10 NA NA NA
EP (Basu 2004a) 45,063.04 NA NA NA
Fig. 10 Hourly optimal power
generation of hydro and thermal
units for test system 2 case 2
16242 M. Mohamed et al.
123
19. 4.4 Spillage effect
The spillage effect appears in the third hydropower only
(Kang et al. 2017), an quantity suitable of spillage from the
third hydropower plant will lead to more hydropower
production. The problem formulation of the STHS involves
the spillage effect in Eq. (3), so the spillage rate for the
hydraulic system is taken into account in short-term
hydrothermal. The STHS problem involving the spillage
effect has been solved with the proposed algorithm LAPO.
The spillage effect is taken on two test systems. Table 21
shows the effect of the spillage at different test system.
Moreover, the minimum fuel cost reduces with the pres-
ence of spillage effect compared to the spillage effect not
taking into account in short-term hydrothermal. The min-
imum cost value with considering the spillage effects
illustrates in Table 21. Table 22 illustrates the spillage
0 500 1000 1500 2000 2500 3000
3.5
4
4.5
5
5.5
6
6.5
7
x 10
4
Iteration
Total
cost
($)
Fig. 11 Optimal cost of STHS problem for case 2 of test system 2
Table 18 Optimal water
discharge and power generation
of hydro units for test system 3
Hours (h) Water discharge rates (104
m3
/s) Hydro plant power generation (MW)
Plant 1 Plant 2 Plant 3 Plant 4 Plant 1 Plant 2 Plant 3 Plant 4
1 11.660 12.757 29.986 9.538 91.787 79.899 0.000 169.112
2 9.634 14.997 29.970 7.152 83.435 79.521 0.000 136.154
3 6.237 14.973 29.987 7.661 62.614 74.452 0.000 136.285
4 8.207 14.908 17.102 7.967 75.858 72.369 37.725 131.459
5 5.402 14.973 29.959 15.492 55.715 72.462 0.000 219.372
6 12.716 9.468 14.811 16.966 92.170 55.575 45.658 245.181
7 7.543 14.925 10.112 10.320 70.159 72.393 50.191 204.712
8 12.436 14.931 29.965 11.903 90.047 72.402 0.000 226.682
9 12.394 14.881 18.114 20.282 88.697 72.330 41.897 304.037
10 11.741 9.678 20.047 17.257 86.681 56.551 37.258 281.721
11 10.496 14.974 14.595 21.218 83.329 72.464 56.297 293.952
12 11.588 14.935 17.550 12.999 86.208 72.408 53.622 249.307
13 12.686 14.990 29.998 22.011 87.918 72.486 0.000 312.352
14 12.561 11.202 14.130 21.883 87.359 62.854 60.839 309.742
15 10.622 9.711 17.746 15.658 82.112 56.704 57.874 268.119
16 13.021 13.738 18.970 21.129 86.624 70.256 56.324 300.998
17 14.866 14.983 18.466 20.720 86.639 72.476 58.537 308.891
18 12.503 14.953 29.974 17.282 84.501 72.434 0.000 283.482
19 14.208 10.966 21.739 19.979 86.515 61.972 47.161 299.075
20 8.983 14.975 17.290 19.772 72.618 72.465 62.561 297.025
21 14.713 11.351 12.981 22.524 86.643 63.395 64.299 306.165
22 11.263 12.472 20.979 24.904 81.501 67.044 53.678 320.156
23 14.989 14.986 15.978 24.957 86.622 72.480 64.816 316.434
24 9.920 14.827 19.095 12.504 91.104 80.674 48.342 226.653
Lightning attachment procedure optimization algorithm for nonlinear non-convex short-term… 16243
123
21. effect on the optimal hydro and thermal power generation
for case 1 of test system 1.
5 Conclusion
In this paper, the optimal solution of the nonlinear non-
convex STHS problem has been solved LAPO as a recent
optimization technique. To examine the effectiveness of
the proposed LAPO algorithm, three different test systems
consisting of multi-chain cascaded of hydro power plants
and different thermal units have been used. The effect of
the valve point loading effect and power system trans-
mission losses has been considered. Moreover, the per-
formance of proposed algorithm has been compared with
various well-known optimization techniques: IHS and
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
1.6
1.7
1.8
1.9
2
2.1
2.2
2.3
2.4
2.5
2.6
x 10
5
Iteration
Total
Cost
($)
Fig. 12 Optimal cost of STHS problem for test system 3
0
500
1000
1500
2000
2500
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Power
Generation
(MW)
Time (Hour)
Hydro4
Hydro3
Hydro2
Hydro1
Thermal 10
Thermal 9
Thermal 8
Thermal 7
Thermal 6
Thermal 5
Thermal 4
Thermal 3
Thermal 2
Thermal 1
Fig. 13 Hourly optimal power
generation of hydro and thermal
units for test system 3
Table 21 Spillage reduces fuel
cost
No allowed spillage allowed spillage
Test system 1 Case 1 871,910.67 867,946.554
Test system 1 Case 2 881,184.5 877,858.408
Test system 2 case 1 38,800.75 38,615.12
Test system 2 case 2 39,691.86 39,512.974
Lightning attachment procedure optimization algorithm for nonlinear non-convex short-term… 16245
123
22. RCGA-IMM. However, the numerical results and simula-
tions prove the efficacy and superiority of the proposed
algorithm compared with these techniques. Using the
proposed algorithm, the minimum cost value for test sys-
tem 1 without considering the valve point loading effects is
3483.56 $/day compared to the best technique, while the
total daily saving is 234.87 $ for test system 2 with con-
sidering the valve point loading effect and transmission
power losses. Moreover, the proposed algorithm succeeded
to minimize the fuel cost with the presence of the spillage
effect compared to the spillage effect not taking into
account in short-term hydrothermal.
Compliance with ethical standards
Conflict of interest Authors declare that they have no conflict of
interest.
Ethical approval This article does not contain any studies with human
participants or animals performed by any of the authors.
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