Uncertain Wind Power Research Articles

A Reserve Constrained Optimum Reactive Power Dispatch in Wind-Integrated Power Systems Using Coronavirus Herd Immunity Optimizer

The optimal reactive power dispatch (ORPD) plays a significant role in planning stable and secure power system operations. The challenges associated with the stable operation of power system networks increase with the rise in wind energy penetration into the system. To guarantee the secure operation of wind-integrated power system networks, a scenario-based reserve constrained optimal reactive power dispatch (RC-ORPD) approach is proposed in this work. For this, the effect of uncertain wind power penetration on the effective reactive reserve (ERR) and voltage stability indicator (L-index) is assessed. The threshold ERR required to retain in the system is evaluated, and is incorporated as an additional constraint to the conventional ORPD problems. The proposed problem is modeled as a scenario-based non-linear complex optimization problem and is solved using a newly developed meta-heuristic called “Coronavirus Herd Immunity Optimizer (CHIO)”. Programs are developed in MATLAB and tested on the wind-integrated IEEE 30, IEEE 118, and practical Indian 62 bus systems. The anticipated strategy is validated through several case studies and comparisons. The comparison reveals that the newly added constraint improves the voltage stability of the wind-integrated power systems without negotiating much on the numerical values of the objectives. Also, the efficacy of the CHIO is verified through statistical studies and comparisons with other contemporary algorithms.

Optimal Microgrid System Operating Strategy Considering Variable Wind Power Outputs and the Cooperative Game among Subsystem Operators

In recent years, the microgrid system (MGS) has become an important method for the consumption of renewable energy sources (RES). In the actual operation process, the uncertainties of RES add to the complexity of the MGS operation. Furthermore, the MGS is often operated by multiple subsystem operators. The benefit distribution among subsystem operators is an important factor affecting the overall stable operation of the MGS. In order to resist the interference of the above factors, a two-stage optimization method is proposed in this paper, which includes a bi-level robust optimization (BRO) model in the overall scheduling stage of the MGS and a nucleolus-based cooperative game (NCG) model in the internal cost allocation stage among the subsystem operators. The simulations demonstrated the following outcomes: (1) the P2G device can reduce the operating cost of the MGS by converting electricity into natural gas when the electricity price is low; (2) the two-stage optimization method can ensure the stable operation of the MGS by resisting the disturbance of uncertain wind power outputs in the overall scheduling stage and realizing a reasonable cost allocation among the subsystem operators in the internal cost allocation stage.

A two-stage distributionally robust optimization model for P2G-CCHP microgrid considering uncertainty and carbon emission

The utilization of energy efficient combined cooling heat and power (CCHP) microgrid systems provide an opportunity for us to considering both the increase of economic benefits and environmental costs, simultaneously. The goal of this paper is to propose a P2G-CCHP microgrid system integration framework, connect power to gas (P2G) devices to CCHP microgrid, and provide a two-stage distributionally robust optimization (DRO) model to solve the problem of economic dispatch. DRO model uses the Wasserstein metric to extract the ambiguity set of the probability distribution information of the wind power and photovoltaic output uncertainty. And environmental cost is also considered in the optimal operation of the system. In addition, based on the strong duality theory, the DRO model is transformed into an easy-to-solve MILP problem. The simulation results show that: 1) The introduction of a P2G device can effectively improve the electrical-gas coupling of the P2G-CCHP microgrid system, and improve the stability and economy of the system operation. 2) Considering environmental cost, the pollutant emission of the P2G-CCHP microgrid system is significantly reduced, which ensures the low-carbon operation of system. 3) The DRO model can resist the interference of uncertain wind power and PV output with relatively low conservatism and computational complexity and has the characteristics of data-driven.

Comparison of solving probabilistic optimal power flow methods in the presence of wind and solar sources

Power system control and operation studies have been experienced essential changes due to increasing the penetration of uncertain renewable energy resources. One of the most critical issues in this regard is the optimal power flow (OPF). As a result, the deterministic methods do not have the capability of different modeling uncertainties raised in new power systems, and there is a need to investigate the effective models in this regard. This paper focuses on probabilistic optimal power flow (POPF) methods applied to power systems with uncertain wind and Photovoltaic power generations. In this paper, the Monte Carlo simulation (MCS) and analytical methods such as the three-point estimation method (3PEM), unscented transformation (UT), and Interior-Point method (IPM) are applied to solve the probabilistic optimal power flow problem. MCS has been widely applied as a framework to assess the ability of analytical methods. The mentioned techniques are applied to a sample case study extracted from the IEEE 300-bus system. The main contribution of this work is the comparison of analytical methods concluding 3PEM, UT, and IPM, and with MCS as well. The obtained results on the studied networks by the suggested techniques show that in the 3PEM, due to the limited points, the optimal solution is achieved in less calculation time than the other methods. From another perspective, the voltage changes at the buses would be more stable in the IPM. Also, this method is much faster than the MCS method in terms of the convergence rate. To show the effectiveness of the mentioned methods, this paper presents probabilistic load flow method based on the statistical methods to deal with fluctuations because of large-scale renewable energy integration. The proposed methods are validated on the improved industrial 85–bus system of Kermanshah region (in the west of Iran) by adding solar and wind farms.

Flexibility-based generation maintenance scheduling in presence of uncertain wind power plants forecasted by deep learning considering demand response programs portfolio

The special characteristics of renewable energy resources, such as non-emission and low operating costs, have increased the penetration rate of renewable energy resources in the power system. However, the variability nature of renewable energy resources has led to some challenges in power system studies. Therefore, system flexibility has been taken into account, which plays a key role in dealing with renewable energy resources uncertainty. On the other hand, generation maintenance scheduling is one of the most important and effective programs for short-term studies of the power system. It seems necessary to implement a flexibility-based generation maintenance scheduling in order to achieve more flexible operation as a consequence of providing flexible resources. Here, a novel framework for flexibility-based multi-objective generation maintenance scheduling associated with a portfolio of demand response programs is introduced. Hence, a system flexibility index has been applied in this paper. Moreover, a portfolio of multifarious demand response programs as a negawatt resource has been applied as a provider of flexibility from demand-side point of view. In this paper, direct load control, real-time pricing, and emergency demand response programs are implemented as flexibility providers through comprehensive modelling of DRPs. Herein, proper modeling and forecasting of renewable energy resources production will increase the scheduling accuracy. Hence, the uncertainty of wind power plants is considered by deep learning methodology in Python. Reducing costs such as operation and maintenance costs, leveling the reserve margin and increasing flexibility index are regarded as multifarious objectives of flexibility-based generation maintenance scheduling. Due to the good handling of large-scale, non-convex and non-proportional objective functions, the augmented epsilon constraint method is utilized to evaluate flexibility-based multi-objective generation maintenance scheduling. According to the results, the system flexibility has been improved without increasing costs. Several analyses are carried out on a modified IEEE-RTS 24 bus to trace the capability of the proposed structure.

A holistic robust method for optimizing multi-timescale operations of a wind farm with energy storages

To ramp-up the utilization of wind energy, the uncertainty of wind power needs to be properly addressed in its integration into the power grid. The main challenge is to well tackle the risk induced by the uncertain wind power generation in different operation stages of a wind farm. This paper studies a novel bi-level multi-timescale scheduling approach for accommodating the wind power uncertainty via a robust optimization formulation. Wind farm day-ahead and intra-day operations consider different scheduling timescales. A two-stage robust optimization model is developed to plan the day-ahead power generation commitments to the power grid. A multi-stage robust optimization model is proposed to refine intra-day wind farm operation instructions. The overall decision-making process aims to minimize the wind farm operational cost. The proposed models are solved by using computationally tractable optimization methods, which offer a desired performance guarantee. A comprehensive case study based on real datasets to demonstrate the effectiveness and robustness of the proposed approach is carried out. Average cost reductions of 46.648% and 6.883% are achieved by comparing with the deterministic method and the static robust method, respectively. Results verify that the proposed method can provide optimal and robust wind farm operations schedules with a lower cost, higher flexibility, and less conservativeness. Results also demonstrate the feasibility of applying the proposed approach to the real-world wind farm and providing reliable operation guidelines.

Available transfer capability evaluation in electricity-dominated integrated hybrid energy systems with uncertain wind power: An interval optimization solution

Available transfer capability (ATC) is widely used in the deregulated electricity market to ensure secure and reliable power trading among market participants. However, most conventional ATC calculation methods do not fully consider the impacts of renewable energy integration and the close interdependency among electricity, natural gas, and district heating networks. To overcome these challenges, this work evaluates the ATC in an electricity-gas-heating integrated hybrid energy system (IHES) in a more practical manner by considering renewable energy uncertainties. In the proposed approach, the detailed models of electricity, natural gas, and district heating infrastructures are provided and their operational constraints are fully respected. To reduce input data requirements, the wind power uncertainty is modeled as interval bounds instead of detailed probability distribution functions (PDFs). Consequently, this interval optimization-based ATC model is converted to two sub-problems to solve the lower and upper boundaries of the objective function value. The proposed approach provides a quantitative approach to numerically calculate the impact on ATC from various components in an IHES. Simulation results on the IHES 5–7-6 and the IHES 118–96-6 + 32 systems validate its effectiveness.

Robustly Coordinated Generation Dispatch and Load Shedding for Power Systems Against Transient Instability Under Uncertain Wind Power

Transient stability of a power system can be significantly affected by wind power generators due to their stochastic power output and complex dynamic characteristics. This paper proposes a robust optimization approach for coordinating generation dispatch and emergency load shedding against transient instability under uncertain wind power output. The problem is modelled as a two-stage robust optimization (TSRO) model considering transient stability constraints, where the first-stage is to optimize the generation dispatch (preventive control) before a contingency and the second-stage decision is the emergency load shedding (emergency control) after the contingency occurrence under the worst case of wind power variation. To solve this TSRO problem, this paper also proposes a solution algorithm which integrates transient stability assessment and transient stability constraint construction in a column and constraint generation framework. The proposed method is validated on the New-England 39-bus system and the Nordic32 system, which shows high computational efficiency and stability robustness against uncertain wind power.

Robust LFC of Power Systems With Wind Power Under Packet Losses and Communication Delays

Network-induced packet losses and communication delays, as well as load fluctuations and uncertain wind power have a negative effect on the frequency regulation of power system. This paper is concerned with designing a robust load frequency control (LFC) scheme for a multi-area power system penetrated by wind power via sampled-data control. Firstly, considering the effects of the inertia reduction, packet losses, communication delays and measurement noise, a decentralized aperiodic sampled-data LFC model with time delay is constructed, where the maximum sampling interval is characterized by limiting the maximum count of successive packet losses (MCSPL). Secondly, by applying Lyapunov theory and linear matrix inequality technique, a new exponential stability condition for the modeled LFC system with given controller is proposed based on a combination method of Lyapunov-Krasovskii functional and loop function, which is dependent on delay and MCSPL. It can be used to find the delay margin and allowable MCSPL of the LFC system. Thirdly, based on the <inline-formula> <tex-math notation="LaTeX">$\mathcal {L}_{2}$ </tex-math></inline-formula>-gain performance condition developed by the stability condition above, a design method of robust PI-type controller is proposed by maximizing an exponential decay rate (EDR). The larger EDR, the faster frequency response speed to cope with the effect of inertia reduction, but the worse robustness to load fluctuations, packet losses and delays, and vice versa. Finally, case studies are carried out by a one-area power system and a three-area power system with wind power. By comparing with the existing LFC schemes, simulation results show that the proposed LFC scheme for the tested system is more effective and has better robustness.

Distributionally Robust Joint Chance-Constrained Dispatch for Electricity–Gas–Heat Integrated Energy System Considering Wind Uncertainty

With the increasing penetration of wind power, the uncertainty associated with it brings more challenges to the operation of the integrated energy system (IES), especially the power subsystem. However, the typical strategies to deal with wind power uncertainty have poor performance in balancing economy and robustness. Therefore, this paper proposes a distributionally robust joint chance-constrained dispatch (DR-JCCD) model to coordinate the economy and robustness of the IES with uncertain wind power. The optimization dispatch model is formulated as a two-stage problem to minimize both the day-ahead and the real-time operation costs. Moreover, the ambiguity set is generated using Wasserstein distance, and the joint chance constraints are used to ensure that the safety constraints (e.g., ramping limit and transmission limit) can be satisfied jointly under the worst-case probability distribution of wind power. The model is remodeled as a mixed-integer tractable programming issue, which can be solved efficiently by ready-made solvers using linear decision rules and linearization methods. Case studies on an electricity–gas–heat regional integrated system, which includes a modified IEEE 24-bus system, 20 natural gas-nodes, and 6 heat-node system, are investigated for verification. Numerical simulation results demonstrate that the proposed DR-JCCD approach effectively coordinates the economy and robustness of IES and can offer operators a reasonable energy management scheme with an acceptable risk level.

Projection method for blockchain-enabled non-iterative decentralized management in integrated natural gas-electric systems and its application in digital twin modelling

Integrating natural gas and electricity systems increases system flexibility for the accommodation of the large penetration level of renewable energy and thus achieves decarbonization in the energy system. This paper aims at providing non-iterative and scalable decentralized energy management for multi-integrated natural gas-electricity systems with uncertain wind power. An operation space projection transformation method is proposed to reformulate the electricity and natural gas system operation problems for constructing equivalent feasible operation space with the optimality information contained. Accordingly, the proposed decentralized management is privacy-preserving, low-complex, and globally optimal. Moreover, the mathematical proof of the optimality of the reformulated problem is provided. In addition to privacy protection, trust issues are taken into account. Blockchain is applied to safeguard the proposed decentralized management against potential malicious behaviours. We introduce how the proposed decentralized management is embedded in the consensus process of the blockchain. The potential of the projection transformation method in the digital twin application is analyzed. Numerical results are presented to validate the effectiveness of the proposed decentralized energy management method. The synergistic effect and robustness of the proposed operation model are embodied, while the computational accuracy and performance of the non-iterative solution technique are validated.

Long-Term Voltage Stability-Constrained Coordinated Scheduling for Gas and Power Grids With Uncertain Wind Power

Considering the increased trend that power systems are closer to the operating bounds because of the increased demand and new challenges in consideration of gas systems and wind power, this paper investigates long-term voltage stability-constrained integrated electric and gas system optimal scheduling in consideration of wind energy integration. A sufficient condition, which is represented as an explicit function of voltage and injected power, is used to constrain power system long-term voltage stability. Due to bilinear terms in this condition, tightening piecewise McCormick envelope relaxation is used to convert it into convex constraints. The second-order cone programming (SOCP) formulation is employed to represent the operational constraints of the integrated electric and gas system. The loss of wind power probability, representing wind power uncertainties, is established by a chance-constrained programming model, which is transformed into a deterministic optimization model by means of the star-inequality-based extended formulation of sample average approximation. Two test systems, the 9-bus electric system with the 6-node gas system and the IEEE 118-bus electric system with the 40-node gas system, are used to validate the proposed model.

Deep Learning to Optimize: Security-Constrained Unit Commitment With Uncertain Wind Power Generation and BESSs

This paper proposes a new model of scenario-based security-constrained unit commitment (SCUC) with BESSs. By formulating such a model as a mixed-integer programming (MIP) problem, we can obtain the optimal control strategy of units and BESSs to reduce the operating cost. To solve this MIP with the proposed model, we propose a new learning-based approach to tackle the SCUC problem. The proposed convolutional neural network (CNN)-based SCUC algorithm (CNN-SCUC) has two main stages. First, CNN-SCUC trains a CNN to obtain solutions to the binary variables corresponding to unit commitment decisions. Then, the continuous variables corresponding to unit power outputs are solved by a small-scale convex optimization problem. In contrast to existing work, CNN-SCUC eliminates the need of explicitly considering the scenario-based security constraints in the optimization problem, and thus greatly reduces the computational complexity. The average gap to the optimal solution is as small as 0.0267%. The algorithm is also scalable in the sense that the computational time is reduced from about 1236.32 seconds to 0.8379 seconds in a 10-unit and 200-scenario system. Besides, the computation time remains almost constant when the number of scenarios increases. Case studies show that compared with the traditional scenario-based SCUC model, more than 4.70% operating cost reduction is achieved by incorporating BESSs in the system.

Distributed Demand Side Management With Stochastic Wind Power Forecasting

In this article, we propose a distributed demand-side management (DSM) approach for smart grids taking into account uncertainty in wind power forecasting. The smart grid model comprehends traditional users as well as active users (prosumers). Through a rolling-horizon approach, prosumers participate in a DSM program, aiming at minimizing their cost in the presence of uncertain wind power generation by a game theory approach. We assume that each user selfishly formulates its grid optimization problem as a noncooperative game. The core challenge in this article is defining an approach to cope with the uncertainty in wind power availability. We tackle this issue from two different sides: by employing the expected value to define a deterministic counterpart for the problem and by adopting a stochastic approximated framework. In the latter case, we employ the sample average approximation (SAA) technique, whose results are based on a probability density function (PDF) for the wind speed forecasts. We improve the PDF by using historical wind speed data, and by employing a control index that takes into account the weather condition stability. Numerical simulations on a real data set show that the proposed stochastic strategy generates lower individual costs compared to the standard expected value approach.

Two-Stage Robust and Economic Scheduling for Electricity-Heat Integrated Energy System under Wind Power Uncertainty

As renewable energy increasingly penetrates into electricity-heat integrated energy system (IES), the severe challenges arise for system reliability under uncertain generations. A two-stage approach consisting of pre-scheduling and re-dispatching coordination is introduced for IES under wind power uncertainty. In pre-scheduling coordination framework, with the forecasted wind power, the robust and economic generations and reserves are optimized. In re-dispatching, the coordination of electric generators and combined heat and power (CHP) unit, constrained by the pre-scheduled results, are implemented to absorb the uncertain wind power prediction error. The dynamics of building and heat network is modeled to characterize their inherent thermal storage capability, being utilized in enhancing the flexibility and improving the economics of IES operation; accordingly, the multi-timescale of heating and electric networks is considered in pre-scheduling and re-dispatching coordination. In simulations, it is shown that the approach could improve the economics and robustness of IES under wind power uncertainty by taking advantage of thermal storage properties of building and heat network, and the reserves of electricity and heat are discussed when generators have different inertia constants and ramping rates.

Scheduling coordination of back pressure CHP coupled electricity-heat energy system with adaptive constraint strategy to accommodate uncertain wind power

A scheduling coordination approach with adaptive constraint strategy is proposed for electricity-heat integrated energy system (IES). The approach takes full advantage of heat network flexibility to smooth uncertain wind power and its natural storage capability to improve operational economics. Transmission dynamics of heating network is modeled by describing the heat dissipation in radial direction toward the insulation layer and the heat propagation in axial direction through water flow. Dynamical heating flow and steady power flow with different timescales are integrated to constitute the coordinated scheduling optimization by energy coupling component, i.e. CHP (combined heat and power) unit. In order to mitigate the discrepancy between the predicted and real values of wind power by utilizing the allowed upper limit of water temperature constraint violation, a PID idea based closed-loop adaptive adjustment strategy is implemented on the water temperature constraint at the beginning of supply pipeline. Simulations are conducted to show that in the proposed coordinated scheduling approach, heat network can serve as a natural energy storage to achieve the economic operation of IES, and simultaneously wind power uncertainties can be smoothed by the flexible temperature constraint of water flowing in heat network, with no any probability distribution information of uncertainties needed.

Optimal electric vehicles charging scheduling for energy and reserve markets considering wind uncertainty and generator contingency

Decarburization of electrical systems encourage high wind power into electric power systems and the electrification of transport sectors through electric vehicles (EVs). The increasing penetration of uncertain wind power generation and transportation networks via EV charging stations has introduced challenges for system operators to manage power systems and market operations. In this context, this paper presents a stochastic AC security-constrained unit commitment (SCUC) model to clear day-ahead energy and reserve markets considering transportation–electricity networks through EV charging stations in the presence of uncertain wind power and generator contingency. Pre-contingency ranking is a common strategy for reducing the time of the SCUC problem, but it provides high-impact outages. To address this issue, generator outages ranked first are identified using the post-contingency generator response ranking approach. The main contribution of this paper is the development of a structure with the most effective outages in the presence of uncertain wind power and transportation networks. The stochastic optimization approach is modeled through scenarios with corresponding probabilities to manage the wind uncertainty. The computationally complex proposed model is solved by a prominent bender decomposition approach. Case studies are shown on a modified IEEE 118-bus system with 26 nodes and 74 connected links of the electricity transportation network. The results show that optimal EV travel scheduling can optimize the transportation network and a sufficient energy reserve, confirming the security of the power system with minimum operating cost.

Distributionally robust chance-constrained flexibility planning for integrated energy system

Inflexible combined heat and power (CHP) plants and uncertain wind power production result in excess power in distribution networks, which leads to inverse power flow challenging grid operations. Power-to-X facilities such as electrolysers and electric boilers can offer extra flexibility to the integrated energy system. In this regard, we aim to jointly determine the optimal Power-to-X facility sizing and integrated energy system operations in this study. To account for wind power uncertainties, a distributionally robust chance-constrained model is developed to characterize wind power uncertainties using ambiguity sets. Linear decision rules are applied to analytically express real-time recourse actions when uncertainties are exposed, which allows the propagation of wind power uncertainties to gas and heat systems. Accordingly, the developed three-stage distributionally robust chance-constrained model is converted into a computationally tractable single-stage mixed-integer conic model. A case study validates the effectiveness of introducing the electrolyser and electric boiler into the integrated energy system, with respect to the decreased system cost, expanded CHP plant flexibility and reduced inverse power flow. The developed distributionally robust optimization model exhibits better effectiveness and robustness compared to a chance-constrained optimization model assuming wind forecast errors follow Gaussian distribution. Detailed profit analysis reveals that although the overall system cost is minimized, the profit is distributed unevenly across various stakeholders in the system. The profit mainly falls with the wind power plants, which therefore are most motivated to make investments in the flexibility resources. Other parties rely on additional policies such as bilateral contracts with the wind power plants to gain incentives to invest. The findings from this study can be used to motivate policy-makers to make proper regulations to incentivize investments in flexibility resources and establish a more reliable power grid.

Multi‐objective optimization of integrated gas–electricity energy system based on improved multi‐object cuckoo algorithm

AbstractWith the depletion of sources of primary energy across the world, the prospect of a global energy crisis in the near future has raised considerable concern. Among the many sources of clean energy, wind energy is considered to be the most effective means of sustainable and environmentally friendly energy. Traditional systems of energy based on oil and natural gas still operate in a discrete manner, and the promise offered by the mutual coordination between energy systems to draw complementary benefits has not yet been fully exploited. This has prompted all energy sectors to examine the optimal integration of interconnected gas–electricity energy systems. In this context, this study proposes a multi‐objective collaborative operational optimization model of P2G for an interconnected, integrated gas–electricity energy system in case of uncertain wind power. Based on the effect of carbon capture by using P2G, the effect of coupling gas and electricity, and the cost of low‐capacity reserves, the authors use conditional risk values to design four targets of optimization—the operating cost of the system, rate of consumption of the natural gas system, total carbon emissions and capacity stand‐by cost—according to the power system, natural gas system, thermal energy system, and their elements of coupling from multiple perspectives to clarify the constraints on the model. Moreover, to reduce the likelihood of the optimal solution falling into the local optimum, the improved cuckoo algorithm is used to optimize the multi‐objective scheduling model. The authors used a 10‐node power system and a six‐node natural gas system as examples for simulation to verify the proposed model. The results of empirical analysis show the following: (a) Once the P2G equipment had been connected, it reduced the total operating cost and improved the consumption of wind power of the natural gas system regardless of whether backup services were provided. (b) The P2G equipment could be combined with gas‐fired CHP units to “cut peaks and fill valleys” in the electrical load of the power system. These results verify the effectiveness of the proposed multi‐objective optimal dispatch model of an interconnected gas–electricity energy system.

Stochastic day-ahead scheduling of irrigation system integrated agricultural microgrid with pumped storage and uncertain wind power

Agricultural microgrid provides a promising solution for energy supply of rural areas in a cost-effective way. In this paper, the principle of wind-pumped storage integrated agricultural microgrid to fulfill both the electric and water load demand is explored. From the perspective of risk aversion, the indexes of expected power not served (EPNS) and expected power curtailment (EPC) are derived to evaluate the uncertain wind power. Then, a stochastic day-ahead scheduling model of wind-pumped storage power system and irrigation system is proposed to minimize the total operation cost whilst achieve the peak load shaving by taking the advantage of wind-pumped storage compensation. The proposed model is a complex optimization problem that takes into account distributed generations, electrical and water demand, turbine flow rate, and irrigation time and volume. We propose a intraspecific competition (IC) based evolutionary predator and prey strategy (EPPS) to solve the model. Finally, simulation results conducted on an agricultural microgrid have verified that, compared to previous works in the literature, the proposed model can effectively improve the utilization of wind power, reduce the operation cost of microgrid as well as smooth load curve. Additionally, the proposed algorithm can get a more competitive solution than other recently developed algorithms.