Arabian Journal for Science and Engineering

, Volume 44, Issue 3, pp 2003–2031

# Determination of Optimal Reserve Requirement for Fuel Cost Minimization of a Microgrid Under Load and Generation Uncertainties

Research Article - Electrical Engineering

## Abstract

In this paper, economic load dispatch (ELD) problem of a microgrid is formulated considering load and renewable generation uncertainties. Both load and generation uncertainties are modeled using triangular fuzzy numbers. The ELD problem minimizes the fuel cost of the dispatchable distributed generators (DGs) in the microgrid. The reserve requirement for generation and load uncertainties is formulated. Next, the reserve requirement for a stable transition of a grid-connected microgrid to islanded mode under load and generation uncertainties is also formulated. Moreover, the reserve requirement for a stable transition of an islanded microgrid to grid-connected mode under load and generation uncertainties is also formulated in this paper. The effects of these constraints on the daily fuel cost of dispatchable DGs are then investigated. A three-area microgrid test system is considered for the simulation. Each area in the microgrid comprises dispatchable DGs, loads, wind power DGs and solar power DGs. The economic dispatch problem is solved using four different techniques: (i) bisection method, (ii) regula falsi method, (iii) golden section method, and (iv) teaching–learning-based optimization (TLBO) technique. Simulation is carried out considering 24 h load, wind generation and solar generation profiles.

## Keywords

Microgrid Distributed generation Economic dispatch Uncertainty Fuzzy TLBO

## List of symbols

$$\tilde{f}_{{j}} \left( \cdot \right)$$

Fuel cost of jth dispatchable DG

$${\widetilde{\mathrm{Pg}}}_{{j}}$$

Power output of jth dispatchable DG

$$\widetilde{\hbox {Pg}}_{{j}}^{\mathrm{min}}$$

Fuzzy singleton representing minimum power limits of jth dispatchable DG

$$\widetilde{\hbox {Pg}}_{{j}}^{\mathrm{max}}$$

Fuzzy singleton representing maximum power limits of jth dispatchable DG

$$\widetilde{\hbox {Pg}}_{{pii}}$$

Power output of iith dispatchable DG in area p

$$\hbox {Pg}_{{pii}}^\mathrm{min}$$, $$\hbox {Pg}_{{pii}}^{\mathrm{max}}$$

Minimum and maximum power limits of iith dispatchable DG in area p

$$P_{0-1}$$

Power flow from main grid to microgrid

$$P_{{i-1{-}i}}$$

Inter-area power flow from area ‘$$i-1$$’ to area ‘i’ in microgrid

$${P}_{{{i}}-1{-}{{i}}}^{\mathrm{max}}$$

Maximum inter-area power flow limit between area ‘$$i-1$$’ to area ‘i’ in microgrid

$$\widetilde{\hbox {PL}}_{{jj}} =\big ( \hbox {PLL}_{{jj}},$$

Triangular fuzzy number

$$\hbox {PLM}_{{jj}}, \hbox {PLR}_{{jj}}\big )$$

representing the the jjth load power

$$\hbox {NG}$$

Total number of dispatchable DGs in microgrid

$$\hbox {NL}$$

Total number of loads in microgrid

$$\hbox {NS}$$

Total number of solar PV DGs in microgrid

$$\hbox {NW}$$

Total number of wind power DGs in microgrid

$$\tilde{{f}}$$

A triangular fuzzy number

$$\widetilde{\hbox {PS}}_{{mm}} = ( \hbox {PSL}_{{mm}}$$,

Triangular fuzzy number

$$\hbox {PSM}_{{mm}}$$, $$\hbox {PSR}_{{mm}} )$$

representing the power output of mmth solar PV DG

$$\widetilde{\hbox {PW}}_{{k}} =\big ( \hbox {PWL}_{{k}},$$

Triangular fuzzy number

$$\hbox {PWM}_{{k}},\hbox {PWR}_{{k}}\big )$$

representing the power output of kth wind power DG

$$\hbox {Rem}(\cdot )$$

Defuzzified value of a fuzzy number

n

Numbers of areas in microgrid

$$\hbox {Rg}_{{ii}}$$

Droop constant of dispatchable DG ‘ii

$$\Delta \hbox {Pa}_{{m}}$$

Total change in power generation of all dispatchable DGs in area ‘m’ after mode transition

$$\Delta \hbox {Pg}_{{ii}}$$

Change in power generation of iith dispatchable DG after mode transition

$$\widetilde{\hbox {PLa}}_{{m}}$$

Sum of all loads in area ‘m

$$\hbox {Pa}_{{m}}^\mathrm{min}$$, $$\hbox {Pa}_{{m}}^\mathrm{max}$$

Sum of minimum and maximum power limits of all generators in area ‘m

$$\widetilde{\hbox {PSa}}_{{m}}$$

Total power output from all solar PV DGs in area ‘m

$$\widetilde{\hbox {PWa}}_{{m}}$$

Total power output from all wind power DGs in area ‘m

$${A}_{p}$$

Control area p

$$\hbox {IT}$$

Iteration count

$$\lambda$$

Incremental fuel cost

$$\hbox {temp}1, \hbox {temp}2$$

Variables to store the incremental costs

$$\lambda ^\mathrm{min}$$, $$\lambda ^\mathrm{max}$$

Minimum and maximum incremental costs

$$\lambda _{1}$$, $$\lambda _{2}$$, $$\lambda _{3}$$, $$\lambda _{p}$$, $$\lambda _{q}$$

Estimates of incremental costs

t1, t2, t3, tptq

Variables to store the demand generation power mismatches

$$\hbox {Pg1}(i), \hbox {Pg2}(i), \hbox {Pg3}(i)$$

Estimates of power outputs of dispatchable DG ‘i’.

$$\hbox {Tol}$$

Absolute value of power mismatch

$$\hbox {Pd}$$

Effective system load (sum of total system load minus sum of generations from all renewable DGs)

$$\hbox {NPOP}$$

Population size

$$x(i, j)^{\mathrm{IT}}$$

Control variable representing the power output of the jth dispatchable DG of the ith member of the population at iteration step IT.

$$M(j)^{IT}$$

Mean value of the jth control variable (jth dispatchable DG power) in the population at iteration step IT

$${x}_{\mathrm{teacher}} \left( {j} \right) ^{\mathrm{IT}}$$

jth control variable (jth dispatchable DG power) of the teacher at iteration step IT

$$x(i, j)^{\mathrm{IT}}$$

Updated value of the control variable representing the power output of the jth dispatchable DG of the ith member of the population at iteration step IT.

cost(i)

Objective function representing the total fuel cost of the ith member of the population

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