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Day-ahead scheduling of isolated microgrid integrated demand side management

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Abstract

This paper suggests day-ahead scheduling of microgrid with and without demand side management considering hydrogen storage and plug-in electric vehicles. This is a highly constrained mixed integer nonlinear programming problem which is solved by using quasi-oppositional fast convergence evolutionary programming (QOFCEP) technique. The concept of the quasi-opposition-based learning is incorporated in fast convergence evolutionary programming (FCEP) to improve the efficiency and quality of the solution. QOFCEP employs quasi-oppositional based learning (QOBL) for population initialization and generation jumping. The studied microgrid comprises three diesel generators, one mini-hydro power plant, two wind turbine generators, two solar PV plants, one hydrogen storage system and plug-in electric vehicles. Simulation outcomes of the suggested QOFCEP technique have been compared with those obtained by FCEP and differential evolution (DE). It is seen from numerical results that the cost obtained with DSM is about 0.81% lower than the cost obtained without DSM. It is also seen that the cost obtained from QOFCEP is about 0.52% and 0.78% lower than the cost obtained from FCEP and DE, respectively. The suggested QOFCEP technique has the ability to bestow superior-quality solution.

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Data availability

Data will be made available on request.

Abbreviations

OBL:

Oppositional based learning

DG:

Diesel generator

DE:

Differential evolution

DSM:

Demand side management

FC:

Fuel cell

FCEP:

Fast convergence evolutionary programming

HSS:

Hydrogen storage system

MG:

Microgrid

MHPP:

Mini-hydro power plant

PEV:

Plug-in electric vehicles

QOBL:

Quasi-oppositional based learning

QOFCEP:

Quasi-oppositional fast convergence evolutionary programming

SPVP:

Solar PV plant

WTG:

Wind turbine generator

\(C_{T}\) :

Total cost

\(a_{di} ,b_{di} ,c_{di}\) :

Fuel cost coefficients of \(i\)th DG

\(P_{dt}\) :

Power output of \(i\)th DG at time \(t\)

\(P_{di}^{\min } ,P_{di}^{\max }\) :

Minimum and maximum generation limits for \(i\)th DG

\(UR_{di} ,DR_{di}\) :

Ramp-up and ramp-down rate limits of the \(i\)th DG

\(P_{hlt}\) :

Power output of \(l\)th MHPP at time \(t\)

\(Q_{lt}\) :

Inflow rate of \(l\)th MHPP at time \(t\)

\(H_{l}\) :

Height of the water fall of \(l\)th MHPP

\(\gamma\) :

Specific weight of water

\(\eta_{Gl}\) :

Efficiency of \(l\)th generator

\(\eta_{{{T}l}}\) :

Efficiency of \(l\)th turbine

\(P_{hl}^{\max }\) :

Installed capacity of \(l\)th MHPP

\(Pw_{jt}\) :

Available power output of \(j\)th WTG at time \(t\)

\(Pwr_{j}\) :

Rated power output of \(j\)th WTG

\(Kw_{j}\) :

Direct cost coefficient for the \(j\)th WTG

\(Ow_{jt} \left( {Pw_{jt} } \right)\) :

Reserve cost function due to overestimation of \(j\)th WTG at time \(t\)

\(Uw_{jt} \left( {Pw_{jt} } \right)\) :

Penalty cost function due to underestimation of \(j\)th WTG at time \(t\)

\(uw_{j} ,ow_{j}\) :

Penalty cost and reserve cost for the \(j\)th WTG

\(fw\left( y \right)\) :

Weibull probability distribution function of wind power \(y\)

\(Pw_{jt}^{\min } ,Pw_{jt}^{\max }\) :

Minimum and maximum power output of \(j\)th WTG at time \(t\)

\(V_{{{\text{in}}}}\) :

Cut in wind speed

\(V_{{{\text{out}}}}\) :

Cut out wind speed

\(Vr_{t}\) :

Rated wind speed at time \(t\)

\(Vw_{t}\) :

Forecasted wind speed at time \(t\)

\(Ppv_{kt}\) :

Power output from \(k\)th SPVP at time \(t\)

\(Ppv_{rk}\) :

Rated power output of \(k\)th SPVP

\(G_{t}\) :

Solar irradiation forecast at time \(t\)

\(Kpv_{k}\) :

Direct cost coefficient for the \(k\)th SPVP

\(Opv_{kt} \left( {Ppv_{kt} } \right)\) :

Reserve cost function due to overestimation of the \(k\)th SPVP at time \(t\)

\(Upv_{kt} \left( {Ppv_{kt} } \right)\) :

Penalty cost function due to underestimation of the \(k\)th SPVP at time \(t\)

\(upv_{k} ,opv_{k}\) :

Penalty cost and reserve cost for the \(k\)th SPVP

\(fpv\left( x \right)\) :

Lognormal probability distribution function of solar power \(x\)

\(Ppv_{kt}^{\min } ,Ppv_{kt}^{\max }\) :

Minimum maximum power output of \(k\)th SPVP at time \(t\)

\(T_{{{\text{ref}}}}\) :

Reference temperature

\(T_{{{\text{amb}}_{t} }}\) :

Ambient temperature at time \(t\)

\(\alpha\) :

Temperature coefficient.

\(HST_{t}\) :

The amount of hydrogen stored in the hydrogen tanks at time \(t\)

\(HST^{\min } ,HST^{\max }\) :

Lower and upper limits for amount of the stored hydrogen in the hydrogen tanks

\(P_{{{\text{FC}}_{t} }}\) :

FC power at time \(t\)

\(P_{EVmt}\) :

Charging load of \(m\) th PEV at time \(t\)

\(P_{EVm}^{\min } ,P_{EVm}^{\max }\) :

Minimum and maximum charging power of \(m\)th PEV

\(L_{{{\text{Base}},t}}\) :

Forecasted base load at time \(t\)

\(DR_{t}\) :

Percentage of forecasted based load participated in DRP at time \(t\)

\(Ls_{t}\) :

Shiftable load at time \(t\)

\(\eta_{{{\text{EL}}}}\) :

Efficiency of the electrolyzer

\(\eta_{{{\text{FC}}}}\) :

Efficiency of the FC

\(N_{d}\) :

Number of DGs

\(N_{{{\text{PV}}}}\) :

Number of SPVPs

\(N_{w}\) :

Number of WTGs

\(N_{hg}\) :

Number of MHPPs

\(N_{{{\text{EV}}}}\) :

Number of PEVs

\(t,T\) :

Time index and scheduling period

\(T_{{\text{equal - generation}}}\) :

Set that contains all time intervals when total generated power is equal to the demand

\(T_{{\text{excess - generation}}}\) :

Set that contains all time intervals when total generated power is more than the demand

\(T_{{\text{deficit - generation}}}\) :

Set that contains all time intervals when total generated power is less than the demand

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  1. Department of Power Engineering, Jadavpur University, Kolkata, 700098, India

    Mousumi Basu

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Appendix

Appendix

See Tables 2, 3 and 4, Figs. 10 and 11.

Table 2 Data of DGs
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Table 3 Hourly inflow of the MHPP
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Table 4 Hourly load demand and temperature
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Fig. 10
figure 10

The upper and lower forecast limits of solar irradiation

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Fig. 11
figure 11

The upper and lower forecast limits of wind speed

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Basu, M. Day-ahead scheduling of isolated microgrid integrated demand side management. Soft Comput 28, 5015–5027 (2024). https://doi.org/10.1007/s00500-023-09198-2

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