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Risk-Based Bi-Level Model for Simultaneous Profit Maximization of a Smart Distribution Company and Electric Vehicle Parking Lot Owner

S. Muhammad Bagher Sadati, Jamal Moshtagh, Miadreza Shafie-khah, João P. S. Catalão

2017
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Energies
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In this paper, the effect of renewable energy resources (RERs), demand response (DR) programs and electric vehicles (EVs) is evaluated on the optimal operation of a smart distribution company (SDISCO) in the form of a new bi-level model. According to the existence of private electric vehicle parking lots (PLs) in the network, the aim of both levels is to maximize the profits of SDISCO and the PL owners. Furthermore, due to the uncertainty of RERs and EVs, the conditional value-at-risk (CVaR)
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... hod is applied in order to limit the risk of expected profit. The model is transformed into a linear single-level model by the Karush-Kuhn-Tucker (KKT) conditions and tested on the IEEE 33-bus distribution system over a 24-h period. The results show that by using a proper charging/discharging schedule, as well as a time of use program, SDISCO gains more profit. Furthermore, by increasing the risk aversion parameter, this profit is reduced. According to the result of some studies such as [16, 17] , charging of EVs only with traditional power plants creates some inappropriate environmental impacts. Thus, it is inevitable to use RERs along with these types of power plants. The interactions of EVs with solar photovoltaic (PV) [18, 19] , wind turbine [20, 21] and both [22, 23] are investigated. The demand response (DR) program, which is divided into two groups, i.e., price-based demand response (PBDR) and incentive-based DR (IBDR) program, has become one of the most cost-effective and efficient solutions for reducing the load of SDISCO when the upstream network has a problem with respect to energy generation. For a more accurate assessment of the DR program on SDISCO, a proper model is needed. In [24], the economic model for the time of use (TOU) and emergency DR programs (EDRP) are explained. Moreover, in [25] , the modeling of the interruptible/curtailable (I/C) and capacity market programs (CAP) are proposed. In [26] , an economic model is obtained for the responsive load based on price elasticity of the demand, electricity price, as well as the incentive and penalty values. In the most cases, the SDISCO's purpose is to maximize profits or minimize costs while reducing the associated risk. This risk is because of the existence of uncertainty in the load, electricity price, etc. Usually, risk management is accomplished by means of the so-called risk measures. The profit variance, shortfall probability, expected shortfall, value-at-risk (VaR) and conditional value-at-risk (CVaR) are the examples of risk measures. Recently, for the linear formulation, CVaR has been used widely in the power system problems [27] . In [28] , due to market price and load forecast volatilities, for solving the CHP scheduling problem in the presence of DR programs, a CVaR-based stochastic model is presented with the aim of maximizing the profit of the combined heat and power (CHP) owner. In [29] , the CVaR-based scheduling model is proposed to maximize the operation revenue for a virtual power plant with the wind unit, PV unit, convention gas turbine, energy storage systems and the IBDR program. In [30], the CVaR-based stochastic scheduling model is suggested for a smart energy hub in the presence of DR programs and the wind unit, for the maximization of profit. In [31], due to the uncertainties in demand and the cost of energy, a CVaR-based model is presented for optimal feeder routing in which the cost of distribution system planning is optimized. In [32], for the siting and sizing of distribution transformers, a CVaR-based model in the low voltage distribution system is proposed. The market price, load growth and failure rate are the uncertainties in [32] . Furthermore, the aim of this model is to minimize the cost of distribution system planning. In [33], a CVaR-based reconfiguration of the active distribution network is presented for loss reduction and reliability improvement, as well as for considering the uncertainty associated with the load, generation and reliability parameter. If there are two decision makers in the optimization problem in the way that each decision affects the result, a bi-level model can be used. In [34, 35] , because of the distribution company and microgrid, a bi-level model is suggested. The aim of this model in the upper and lower level is maximizing the profit of the distribution company and minimizing the operation cost of the micro-grid, respectively. This model is converted to a single level by using the Karush-Kuhn-Tucker (KKT) conditions and dual theory. In [36] , for maximizing the profit of the active distribution network operator in the upper level and maximizing the social welfare independent system operator (ISO), a stochastic bi-level model is suggested. This model is converted to a mixed integer linear programming (MILP) model by KKT conditions. In [37] , according to the commercial virtual power plant and ISO, a three-stage stochastic bi-level model is proposed and converted into an MILP model using KKT conditions and strong duality theory. In the reviewed references, the operation of SDISCO in the presence of EVs' parking lots (PLs) and the energy transfer between them have not been addressed. Hence, in this paper, a new bi-level model is presented for the optimal operation of SDISCO due to the fact that PLs can have private owners and the SDISCO operator can own RERs and be responsible for implementing the PBDR and IBDR programs. In this model, at the upper level, the maximization of the profit of SDISCO and at the lower level the maximization of the profit of the PL owner are modeled. Due to the uncertainties in Energies 2017, 10, 1714 3 of 16 the system and the definition of CVaR, the bi-level model is converted to the risk-based bi-level model. Finally, the model is solved by using the KKT conditions, auxiliary binary variables, sufficiently large constants and stochastic programming. The main contributions of the paper are as follows:

doi:10.3390/en10111714
fatcat:u2qy74hpqneqjfy3dagoyjvqsu