Uncertainties Of Load Demand Research Articles

Economical operation of modern power grids incorporating uncertainties of renewable energy sources and load demand using the adaptive fitness-distance balance-based stochastic fractal search algorithm

With the increase in the world population and the rapid developments in technology, the energy demands on modern electricity grids are also rising. In order to meet these demands, power systems are increasingly using renewable energy resources (RESs) in addition to traditional fossil fuel-powered generation units and thus, the structures being implemented in electricity grids are more complex. Consequently, the planning and operation of modern power systems presents important problems, one of which is that of the optimal power flow (OPF). With the integration of RESs, which are usually intermittent in nature, the OPF becomes a more difficult problem to solve. In this study, the OPF problem was designed under different operating cases, considering thermal, wind, solar, small-hydro, and tidal energy systems and load demand uncertainties. The adaptive fitness-distance balance selection-based stochastic fractal search (AFDB-SFS) algorithm was proposed to solve this designed OPF problem. The results for the proposed approach from the experimental studies were statistically evaluated and compared with the results obtained from competitive optimization algorithms in the literature. The comparison demonstrated that the proposed AFDB-SFS algorithm was able to outperform the other algorithms in finding the optimal solution, and convergence speed to the optimal solution. According to the experimental study results, the proposed AFDB-SFS algorithm was able to optimize cost by 5.7362%, 0.0954%, 7.6244%, 0.17871%, 2.4307%, 0.12585%, 2.01729%, 1.7408%, 1.95317%, 3.5486%, 2.2007%, and 1.5203% better than the AO, GBO, GPC, HGS, HHO, RUN, TSO, LSHADE, LSHADE-EPSIN, LSHADE-CNEPSIN, LSHADE-SPACMA, and MadDE optimization algorithms in the proposed OPF problem. The source codes of the AFDB-SFS algorithm (proposed method) can be accessed at this link: https://ch.mathworks.com/matlabcentral/fileexchange/118485-afdb-sfs.

A Novel Interval Programming Method and Its Application in Power System Optimization Considering Uncertainties in Load Demands and Renewable Power Generation

This paper expresses the output power of renewable generators and load demand as interval data and develops the interval economic dispatch (IED), as well as interval reactive power optimization (IRPO) models. The two models are generalized into a specific type of linear interval programming (LIP) and nonlinear interval programming (NLIP), respectively. A security limits method (SLM) is proposed to solve LIP and NLIP problems. As for the LIP, the maximum radii of the interval variables are first calculated by the optimizing-scenarios method (OSM) for defining security limits, and the LIP is transformed into deterministic linear programming (LP), for which its constraints are the security limits, which can be solved by the simplex method. As for the NLIP, Monte Carlo simulations were used to obtain the maximum radii of the interval variables, and the average interval ratio of the interval variables is defined to compute the security limits for transforming the NLIP to deterministic nonlinear programming (NLP), which can be solved by using the interior point method. Finally, the IED and IRPO are used to verify the effectiveness and engineering of the proposed SLM.

Sizing and Design of a PV-Wind-Fuel Cell Storage System Integrated into a Grid Considering the Uncertainty of Load Demand Using the Marine Predators Algorithm

In this paper, the utility grid is integrated with hybrid photovoltaic (PV)/wind/fuel cells to overcome the unavailability of the grid and the single implementation of renewable energy. The main purpose of this study is smart management of hydrogen storage tanks and power exchange between the hybrid renewable energy and the grid to minimize the total cost of the hybrid system and load uncertainties. PV and wind act as the main renewable energy sources, whereas fuel cells act as auxiliary sources designed to compensate for power variations and to ensure continuous power flow to the load. The grid is considered a backup system that works when hybrid renewable energy and fuel cells are unavailable. In this study, the optimal size of the components of the hybrid energy system is introduced using two methods: the marine predators’ algorithm (MPA) and the seagull optimization algorithm (SOA). The optimal sizing problem is also run accounting for the uncertainty in load demand. The results obtained from the proposed optimization are given with and without uncertainty in load demand. The simulation results of the hybrid system without uncertainty demonstrate the superiority of the MPA compared with SOA. However, in the case of load uncertainty, the simulation results (the uncertainty) are given using the MPA optimization technique with +5%, +10%, and +15% uncertainty in load, which showed that the net present cost and purchase energy are increased with uncertainty.

An IGDT-based multi-criteria TSO-DSO coordination scheme for simultaneously clearing wholesale and retail electricity auctions

The electrical engineering world has encountered various issues due to integrating distributed energy resources in wholesale and retail electricity markets from various policy, modeling, and implementation perspectives. Hence, distribution system operators must be as more involved in operation of next-generation electricity markets as transmission system operators are. This paper proposes a new decentralized framework for clearing simultaneously both wholesale and retail electricity markets, focusing on various essential technical-economic analyses to explore major pros and cons in comparison with a centralized management strategy and two prevalent schemes. The proposed framework is based on optimality condition decomposition and is practically compatible with the liberalization rules of the EU’s Third Energy Package, so that achieves optimal solution of the theoretical models with a desirable solution precision in few clock time/iterations, without need for central coordinators or intermediary entities. Also, uncertainties of load demands and wind generation units are modeled by a new two-stage method based on information gap decision theory, in which the first stage obtains outcomes for next-hour market, and related deviations due to the mentioned uncertainties in real-time scenarios are explored in the second stage. The simulation results on 3-bus:15-node and IEEE 118-bus:33-node test systems confirm that the proposed method is the most applicable, mathematical feasible, successful in addressing severe uncertainties, and efficient in maximum utilization of distributed energy resources with thoroughly fair market prices; and in one sentence, this method is efficacious for implementation of short-term electricity markets and long-term strategic studies.

Multi-Objective Optimal Operation of Building Energy Management Systems with Thermal and Battery Energy Storage in the Presence of Load Uncertainty

This paper presents the optimal operation of a building energy management system (BEMS), with combined heat and power (CHP) generation, thermal energy storage (TES), and battery energy storage (BES), subject to load demand uncertainty. The main objective is to reduce the total operating cost (TOC) and total CO2 emission (TCOE). First, we develop two models of load demand forecasting, one for weekday and the other for weekend, using artificial neural networks, long short-term memory, and convolutional neural networks. Then, we incorporate the predicted load demand and load demand uncertainty for planning the energy dispatch of the BEMS. TES aims to store the thermal energy waste from the power generation of CHP and discharge the thermal energy to the absorption chiller to supply the cooling load. BES and spinning reserve (SR) play an important role in handling the uncertainty of the load demand. The operation of BEMS, subject to the load demand uncertainty, is formulated as a linear program. We can efficiently solve the linear program and provide an optimal solution that satisfies the dispatch constraints. Thereafter, we determine the optimal size of BES, based on economics and environmental optimal operation. The proposed BEMS is compared to the previous BEMS, without BES and SR. Furthermore, we propose the multi-objective optimal operation, where the normalization for TOC and TCOE is introduced, and the multi-objective function is defined as a linear combination of normalized TOC and TCOE. The numerical results reveal the trade-off relationship between TOC and TCOE. In particular, when TCOE is minimum, TOC becomes maximum. On the other hand, when TOC is minimum, TCOE becomes maximum. The relationship provides a method to select the operating point, as well as analyze the power flow for the multi-objective optimal operation.

Lightweight Online Scheduling for Home Energy Management Systems Under Uncertainty

The increasing use of renewable energy sources and electrical energy storage systems creates a new energy paradigm for residential houses and buildings. Such design reduces carbon footprint, but it also introduces a new challenge for minimizing the electricity bill while still meeting users’ needs. This challenge is often accompanied by deep uncertainty in user load demands, electricity tariffs, and renewable energy generations. To address this challenge, we propose an online algorithm, Virtual Algorithm-based Lightweight Online Scheduling (VALOS), to manage electricity purchasing and battery operations. Our solution does not use any prediction components in dealing with uncertainties. Instead, our algorithm employs a lightweight routine, Virtual Algorithm (VA), for making critical decisions to manage uncertainty. We prove that VA achieves an expected probability of 1/e for choosing the optimal purchasing timing online and incurs only a logarithmic computational cost. With VA, VALOS decides how the energy storage reacts to the load demands, which incurs only a linear-logarithmic online computational cost while achieving optimal performance under the specified conditions. Finally, we conduct extensive trace-driven simulations on real-world datasets to confirm the theoretical results and demonstrate the potential of VALOS.

Simultaneous Planning of the Medium and Low Voltage Distribution Networks under Uncertainty: A Bi-Level Optimization Approach

Distribution network expansion planning (DNEP) is one of the important matters in the field of planning and operation of electrical power systems. Since many costs and losses have occurred in the distribution networks, it has increased attention towards this network. The electrical energy distribution network is divided into two parts: the medium voltage (MV) network and the low voltage (LV) network. The main problem in this field is that planning is done either only on the MV network or only on the LV network. While planning in each of these networks has a significant effect on the other networks, this important case has not been considered in most research studies. Therefore, this study has tried to do integrated planning in the form of a bi-level model in the presence of different types of distributed generations (DGs) and consider the uncertainties of renewable sources and load demand in both MV and LV networks so that the planning and operation costs are minimized. In the proposed bi-level model, the upper-level section aims to minimize the investment and the operation cost of the MV network, and the lower-level problem minimizes the investment and the operation cost of the LV network considering the DGs and pollution emission. The obtained results show the effectiveness of the proposed model.

Exploring multiple investment strategies for non-utility-owned DGs: A decentralized risked-based approach

The development of distributed generator (DG) and energy market has facilitated the investment in non-utility-owned DGs, leading to the necessity of decentralized optimization and finical risk management due to multiple uncertainties. To cope with these problems, this paper addresses the planning framework of non-utility-owned DGs considering multiple investment strategies, from the perspective of risk and profit. Initially, the autonomous planning and operation strategy (APOS), and leasing planning and operation strategy (LPOS) are proposed, considering the different ownership of DG investment/operation rights and pricing mechanism. Then the DG planning problem is modeled as the independent decision-making stage of multiple DG investors and the global coordination stage of distribution system operator (DSO). Furthermore, in the DSO coordination problem, to accurately model the real-time uncertainties in DGs, load demand and main grid price, the conditional value at risk (CVaR) is adopted to manage the risk in profit (RIP). The effect of multiple investment strategies on the tradeoff between RIP and expected profit is analyzed. The planning problem is solved by a decentralized optimization approach that ensures the privacy protection and autonomous optimization of investors. Finally, results from the case study of the IEEE 33-bus system and IEEE 123-bus system demonstrate the superiority and effectiveness of the proposed method in dealing with the planning problem for multiple DG investors.

A novel forward operator-based Bayesian recurrent neural network-based short-term net load demand forecasting considering demand-side renewable energy

Currently, traditional electricity consumers are now shifting to a new role of prosumers since more integration of renewable energy to demand side. Accurate short-term load demand forecasting is significant to safe, stable, and reliable operation of a renewable energy-dominated power system. In this paper, a short-term load forecasting model based on a bidirectional long short-term memory network (Bi-LSTM) using kernel transfer operator is proposed to achieve short-term load demand forecasting. To consider the influence of seasonality, holiday effects and weather on load demand forecasting, and simultaneously to improve the accuracy and performance of the forecasting model, this paper implements the dimensionality reduction of the input data by introducing an improved kernel transfer operator based on the Perron-Frobenius method. On this basis, a Bayesian Bi-LSTM for short-term load demand forecasting is formulated to obtain the probability prediction interval of load demand. To verify the validity of the proposed method, the actual historical load demand in a certain region in China was used for model training and verification. The forecasting results are compared with several conventional load demand methods using probability prediction technics. Simulation analysis shows that the proposed method can effectively reflect the short-term uncertainty of load demand, and is superior to the conventional methods in terms of forecasting accuracy and computational performance.

A hierarchical scheduling framework for resilience enhancement of decentralized renewable-based microgrids considering proactive actions and mobile units

Nowadays, decentralized microgrids (DC-MGs) have become a popular topic due to the effectiveness and the less complexity. In fact, DC-MGs resist to share their internal information with the distribution system operator (DSO) to protect their privacy and compete in the electricity market. Further, lack of information sharing among MGs in normal operation conditions leads to form a competitive market. However, in emergency operation conditions, it results numerous challenges in managing network outages. Therefore, this paper presents a hierarchical model consisting of three stages to enhance the resilience of DC-MGs. In all stages, the network outage management is performed considering the reported data of MGs. In the first stage, proactive actions are performed with the aim of increasing the network readiness against the upcoming windstorm. In the second stage, generation scheduling, allocation of mobile units and distribution feeder reconfiguration (DFR) are operated by DSO to minimize operating costs. In the final stage, the repair crew is allocated to minimize the energy not served (ENS). Uncertainties of load demand, wind speed and solar radiation are considered, and the effectiveness of the proposed model is investigated by integrating to the 118-bus distribution network. Finally, the results of the simulation indicate that DFR and proactive actions decrease the ENS by 19,124 kWh and 4101 kWh, respectively. Further, the sharing of information among MGs leads to a 48.16% growth in the supply service level to critical loads, and consequently a 3.47% increase in the resilience index.

Participation of Grid-Connected Energy Hubs and Energy Distribution Companies in the Day-Ahead Energy Wholesale and Retail Markets Constrained to Network Operation Indices

In this paper, the optimal scheduling of energy grids and networked energy hubs based on their participation in the day-ahead energy wholesale and retail markets is presented. The problem is formulated as a bilevel model. Its upper level minimizes the expected energy cost of electricity, gas, and heating grids, especially in the form of private distribution companies in the mentioned markets, in the first objective function, and it minimizes the expected energy loss of these networks in the second objective function. This problem is constrained by linearized optimal power flow equations. The lower-level formulation minimizes the expected energy cost of hubs (equal to the difference between sell and purchase of energy) as an objective function in the retail market. Constraints of this model are the operation formulation of sources and active loads and the flexibility limit of hubs. The unscented transformation approach models the uncertainties of load, renewable power, energy price, and energy demand of mobile storage. Then, the Karush–Kuhn–Tucker approach and Pareto optimization technique based on ε-constraint are adopted to extract the single-level single-objective formulation. Finally, obtained results verify the capability of the present method in improving the economic status of hubs and the economic and operation situation of the mentioned networks simultaneously so that the proposed scheme by managing the power of energy hubs compared with power flow studies has been able to reduce operating costs by 8%, reduce energy losses by 10%, and improve voltage profile and temperature by 36% and 30%.

A risk‐averse multiyear framework for resilience improvement planning of active distribution networks against hurricanes

This paper proposes a risk-averse strategy for resilience improvement multiyear planning for distribution networks against hurricanes, considering the uncertainty of load demand and wind power generation. For resilience enhancement, DG placement and line hardening are regarded as planning measures, and DG rescheduling, topology reconfiguration, microgrid forming, and priority-based load curtailment are considered as operational measures. The most conservative scenario is considered for modelling the high-impact/low-probability (HILP) event's impacts. Besides, the information-gap decision theory (IGDT) is utilized to acquire a robust solution protected against the different realization of uncertain variables. As the uncertain loads and wind power generation competitively tend to maximize their robust regions for a particular value of the budget of uncertainty, the ε-constraint method is applied to solve the proposed multi-objective IGDT-based resilience-oriented distribution network planning (RODNP) model. Afterwards, fuzzy decision-making is exploited to find the best solution among Pareto optimal solutions. The proposed risk-averse strategy is implemented on IEEE 33-bus test system, and various case studies are analyzed to demonstrate the proficiency of the approach. The results indicate that the proposed risk-averse strategy can optimally find the hardening schemes to achieve a resilient distribution network in a medium-term planning horizon with a yearly limited monetary budget.

A two-stage scheduling method for integrated community energy system based on a hybrid mechanism and data-driven model

The integrated community energy system (ICES) is an effective means to promote the synergies among multiple energy carriers. However, the off-design performance of equipment challenges the accurate and economical scheduling of the ICES. To solve this problem, a two-stage scheduling method for the ICES based on a hybrid mechanism and data-driven model is proposed in this paper. Combing the mechanism energy hub (EH) model with a data-driven efficiency correction model, a hybrid-driven dynamic energy hub (DEH) with variable equipment efficiency is built first. The EH describes the multi-energy coupling relationship; the embedded efficiency correction model adopts data-driven approaches of polynomial regression (PR) and backpropagation neural networks (BPNNs) to accurately extract nonlinear characteristics of equipment efficiency. On this basis, a two-stage scheduling model for the ICES is developed. In the day-ahead stage, the PR method is applied to calculate equipment efficiency which varies with load rate. The day-ahead scheduling model is established with the aim of minimizing the operating cost. In the intraday stage, considering the effects of load rate, temperature, and atmospheric pressure, the BPNNs method is employed to further correct equipment efficiency using the latest data. Furthermore, a rolling optimization (RO) strategy is used to address the uncertainties of equipment efficiency and load demand to improve the accuracy and economy of the scheduling scheme. Case studies demonstrate that the proposed method can improve the solution speed and accuracy of the scheduling model, and enhance the operating economy of the ICES.

Operational Planning and Design of Market-Based Virtual Power Plant with High Penetration of Renewable Energy Sources

Renewable energy sources (RESs) are becoming more prevalent as a source of clean energy, and their integration into the power market is speeding up. The fundamental reason for this is the growing global concern about climate change. However, their weather-dependent and uncertain nature raise questions about grid reliability particularly, when photovoltaics (PVs) and wind turbines (WTs) technologies are used. As a result, rationally managing Energy Storage Systems (ESSs) under the virtual power plant (VPP) setting is being encouraged as a way of minimizing the impact of the uncertain nature of renewable energies. A VPP is comparatively a new concept that aggregates the capacities of dispatchable and non-dispatchable energy sources, electrical loads, and energy storage systems for the purpose of improving energy supply and demand imbalance. It enables individual consumers and producers to participate in the power markets. In this study, a new market-based (MB)-VPP operational planning model is designed and developed with the aim to evaluate the optimal active power dispatched by (WT, PV, and ESS) operating in the day-ahead power market to maximize the social welfare (SW) of the market. SW can be described as the maximization of the consumer’s benefit function minus the cost of energy generation. The optimization process was carried out by using a scenario-based approach to model the uncertainties of renewable energy sources (i.e, WTs & PVs) and load demand. The proposed model and method performance is validated by simulation studies on a 16-bus UK generic distribution system (UKGDS). The simulation results reveal that the proposed approach maximizes overall system social welfare. The capacity of total active power dispatched by (WT, PV, and ESS) has a positive impact on the VPP profit maximization. This empirical study could be used as a reference baseline model for other energy services providers interested in conducting similar research in the future.

Optimal Allocation of BESS in Distribution Network Based on Improved Equilibrium Optimizer

The battery energy storage system (BESS) can accommodate the uncertainties of renewable energy sources (RESs) and load demand. Proper allocation of the BESS in the distribution network (DN) can bring cost-effectiveness and enhance system stability. To realize the reliable and economic operation of BESS in the DN, a multi-objective optimization model for optimal BESS allocation is established, which aims at minimizing the annual overall cost of the whole system, including life cycle cost (LCC), power loss cost, peak-shaving cost, tie-line fluctuation penalty, and voltage deviation penalty. Then, a novel implementation of the improved equilibrium optimizer (IEO) algorithm is proposed to solve the optimal BESS allocation scheme. In order to verify the effectiveness of the proposed method, the simulation experiment based on the IEEE 33-bus test system is performed. Simulation results prove that the IEO algorithm is capable of rapid stable convergence and efficient searching for optimum in the multidimensional space. By the end of the iteration, the annual overall cost of the whole system records a minimum value of $1.8692e+06 every year. A meticulous techno-economic analysis demonstrates that the obtained BESS allocation scheme not only effectively ensures cost-effectiveness of BESS but also significantly reduces power loss, load peak-valley difference, tie-line power fluctuation, and voltage deviation.

Probabilistic optimal siting and sizing of distributed generation and shunt capacitors considering feeder flow control units using a novel distribution power flow

A modern energy system should be reliable, economically viable, and environment-friendly. This paper addresses the above issue by proposing a probabilistic approach of optimally placing and sizing distributed generation and shunt capacitors in a distribution network. Objectives are to simultaneously reduce the cost, emission, network loss, improve the system voltage profile, and avoid line overloads. A feeder flow control generator is considered so that the distribution network draws a constant amount of active and reactive power from the substation. The operation is modeled using a Zero-PQVδ bus pair in the power flow. A novel distribution system power flow is proposed to embody the operation philosophy. Uncertainties of renewable power sources and load demand are modeled using ‘Hong's 2m point estimate method’. A fuzzy multi-objective satisfaction criterion is used to realize multiple objectives. Simulation studies on a thirty-three node distribution network reveal the efficacy of the proposed method.

Integrated Planning of Cyber-Physical Active Distribution System Considering Multidimensional Uncertainties

The integration of cyber technologies is transforming the power distribution network into a cyber-physical active distribution system (CPADS), and brings more flexibility to its operation. However, various uncertainties from the cyber space and physical space are emerging and coupled with each other, which results in significant challenges for the distribution network planning and operation. Thus, a bilevel integrated planning model accounting for multidimensional uncertainties from both the cyber space and physical space is proposed for the CPADS in this paper. With the goal of minimizing the annual investment and operation costs, the model comprehensively considers the location and selection of active-management elements (e.g., electrical storage systems, capacitor banks, and switches), investment constraints, power flow constraints, and operation constraints for all the active-management elements, etc. Moreover, based on the typical cyber system failure scenario represented by information link failure (ILF), a novel <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N-k</i> uncertainty set considering the failure probability distribution is proposed, while the uncertainties of renewable energy and load demand are characterized by box-like uncertainty sets. Finally, the proposed planning model is recast into a multi-stage robust optimization model which can be divided into a master problem and two-step subproblems (SP-1 and SP-2) to be solved by the column and constraint generation (CCG) algorithm. Case studies and comparative analysis on the PG 69 distribution system are performed to verify the effectiveness of the proposed method.

The roles of carbon capture, utilization and storage in the transition to a low-carbon energy system using a stochastic optimal scheduling approach

Decarbonizing energy sector through deploying the technology of carbon capture, utilization and storage (CCUS) is required to keep global temperature rise below 1.5 °C by 2060. The true roles of CCUS have to be validated from the perspective of integrated energy system with features of high penetration of uncertain renewable power and strong interactions among multiple energy generation, conversion and storage technologies. To this end, this paper proposes a stochastic power-heat-gas-carbon scheduling approach for the wind-solar-thermal-battery energy mix integrated with CCUS (WSTB-CCUS) to manage the operation of energy conversion devices and CCUS in a coordinated manner. Coal/biomass co-fired and natural gas fired cogeneration units integrated with carbon capture system are built to reflect complex relationship between fuel, power, heat and carbon. A stochastic optimization model based on chance-constrained programming is presented to fully consider the uncertainties of renewable power and load demands. Case study shows that the stochastic scheduling can reduce 7.25% of average total operating costs compared with the deterministic scheduling by providing a more robust solution for the WSTB-CCUS. Discussions are then carried out to explore the roles of CCUS in carbon reduction, flexibility enhancement, negative emission and robustness improvement from the perspective of energy system operation through stochastic scheduling. The influences of other low carbon technologies on the operation of carbon capture are further discussed to provide more insight on the low carbon transformation of energy system.

Energy management of renewable energy sources incorporating with energy storage device

The best solution to exploit renewable energy sources (RES) together is by using the application of microgrid (MG). This indeterminate of resources such as solar panels, wind farm, diesel generator, and battery storage system paired with load profile result in random changes within the generation and the load phases, which create it is challenging to properly manage an MG. Due to this problem energy management technique for real-time scheduling of an MG takes into consideration the uncertainty of load demand, renewable energy, and electricity price are proposed. In this paper, linear programming with two methods (optimized problem and solver based) of dual-simplex are suggested to tackle the energy management issue of the renewable microgrid. The simulation is done in each method using four cases fast wind speed with clear solar irradiance, fast wind speed with cloudy solar irradiance, slow wind speed with clear solar radiation, and slow wind speed with clear solar irradiance. The result showed that the first and second cases in the first method are higher cost than the two corresponding cases in the second method. In addition, the third and fourth cases in the first method are lower cost than the two corresponding cases in the second method.

Joint expansion planning of distribution network with uncertainty of demand load and renewable energy

Rational planning plays a key role in developing and improving operation security and stability of distribution networks (DNs). This paper proposes a novel method to solve the expansion of transmission lines (TLs) and the allocation of distributed generators (DGs) considering the uncertainty of load demand and renewable energy. The spanning-tree is a theoretical method specifically tailored to guarantee the radiality operation of distribution networks. Also, to guarantee the stability and reliability of the network, the probability function is used to describe the stochastic nature of load behavior and renewable sources fluctuation. Thus, the most proper installation location and time for TL and DG assets can be identified by modeling the joint expansion planning. The objective of the proposed model is minimizing the present value of the total social costs, including the cost of investment, purchasing energy, and environmental benefits. This mixed-integer nonlinear problem (MINLP) optimization model is solved based on GAMS environment. The effectiveness and scalability of this model is validated and illustrated based on the IEEE RTS-24 system.