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Licensed Unlicensed Requires Authentication Published by De Gruyter April 16, 2019

Determining Optimal Strategy of a Micro-Grid through Hybrid Method of Nash Equilibrium –Genetic Algorithm

  • Ehsan Jafari EMAIL logo


Increasing the fossil fuels consumption, pollution and rising prices of these fuels have led to the expansion of renewable resources and their replacement with conventional sources. In this paper, a robust algorithm for a micro-grid (MG) planning with the goal of maximizing profits is presented in day-ahead market. The energy resources in MG are wind farms (WFs), photovoltaic (PV), fuel cell (FC), combined heat and power(CHP) units, tidal steam turbine (TST) and energy storage devices (ESDs). This algorithm is divided into two main parts:

(1) Optimal planning of each energy resource;

(2) Using the Nash equilibrium –genetic algorithm (NE-GA) hybrid method to determine the optimal MG strategy.

In energy resources optimal planning, using a stochastic formulation, the generation bids of each energy resource is determined in such a way that the profit of each one is maximized. Also, the constraints of renewable and load demands and selection the best method of demand response (DR) program are investigated.

Then the Nash equilibrium point is determined using the primary population produced in the previous step using the NE-GA hybrid method to determine the optimal MG strategy. Thus, using the ability of the genetic algorithm method, the Nash equilibrium point of the generation units is obtained at an acceptable time, and This means that none of the units are willing to change their strategy and that the optimal strategy is extracted. Comparison of results with previous studies shows that the expected profit in the proposed method is more than other method.




Energy resources index

sp, sPV, sPL, sTSS/sW

Price, photovoltaic power generation, electrical load demand, tidal steam/wind speed index scenarios


wind farms, combined heat and power, photovoltaic, fuel cell, tidal steam turbine, electrical energy storage device index


Index of time intervals



Maximum shifting demand


Total time periods number


Shifting demand from other tims to t


Nominal power of W-th wind farm


The slope increases or decreases fuel cell generation capacity at time t


Startup/Shutdown state of i-th unit at hour t



Energy price for spth scenario of price


The cost of buying energy for battery charging


The charging power/maximum limit of k-th electrical energy storage device at hour t


Fuel cell maximum ramp up/down rate


Sufficient large number


Electrical energy storage device efficiency


Cost factors of wind farm, tidal steam turbine, photo-voltaic, combined heat and power, and fuel cell


Participation status of i-th energy resources


Fuel cell Minimum up/down time


nominal power of TST-th tidal steam turbine


Maximum demand that can be added at time t


The cost of i-th energy resource


The power purchased or sold on the market

PGW(sW,t), PGTST(sTSS,t), PG,CHP(t), PGFC(t)

Wind farm, tidal steam turbine, heat and power and fuel cell power generation


Fuel cell up/down duration till period t


Increase in demand at time t


Charge/Discharge mode of energy saving device t


The delivered /maximum limit of discharging power of k-th electrical energy storage device at time t


The study is made possible through financial assistance from Department of Electrical Engineering, Lenjan Branch, Islamic Azad University, Isfahan, Iran.

  1. Author Contributions: Dr. Jafari analyzed data and simulated numerical example.

  2. Conflicts of Interest: The authors declare that there are no financial or personal relationships which may have inappropriately influenced them in writing this article.


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Received: 2017-07-16
Revised: 2019-03-31
Accepted: 2019-04-01
Published Online: 2019-04-16

© 2019 Walter de Gruyter GmbH, Berlin/Boston

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