# Participation of responsive electrical consumers in load smoothing and reserve providing to optimize the schedule of a typical microgrid

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## Abstract

The task of energy management in electrical microgrids (MGs) is facing more difficulties with the integration of different schedulable components, e.g. responsive loads, energy storage systems (ESSs) and variety of generating units. In this paper the formulation of generation scheduling for a typical MG is done by the unit commitment problem (UCP) to minimize costs and emissions. Demand response program (DRP) is utilized to achieve two goals, i.e. to reshape and smooth the load profile, and also for providing reserve capacity along with dispatchable units. The aforementioned tasks are carried out by differential evolution (DE) algorithm which is a simple and powerful optimizer. In order to deal with multiple criteria decision making in the energy management problem, an algorithm called fuzzified modified (FM) *ε*-constraint is proposed as a non-Pareto based multi-objective solver. The optimal scheduling plan tends to benefit from different electricity prices in day-ahead market and also from the ESS to achieve optimal scheduling results. It is shown that in single objective cases, committing less generating units simultaneously is favorable, as opposed to multi-objective one in which more available units are tuned on at a lower generating power. Meanwhile in all cases, the responsive loads are mostly aggregated in off-peak periods to help peak load shaving. Finally it is verified that the proposed multi-objective approach is able to find an intermediate solution between the two conflicting functions so that as a trade-off each objective is optimized to some extent.

## Keywords

Microgrid energy management Demand response program Reserve scheduling Unit commitment problem## List of symbols

## Indices

*i*DG index

*j*Shiftable load index

- \( t \)
Hourly interval index (\( h \))

- \( m \)
Objective function index

## Parameters

- \( N_{DG} \)
Number of dispatchable units

- \( N_{SL} \)
Number of shiftable loads

- \( T \)
Number of scheduling intervals (\( h \))

- \( N_{dim} \)
Number of decision variables

- \( M \)
Number of objective functions

- \( N_{Pop} \)
Number of individuals in the population

- \( iter_{Max} \)
Number of maximum allowed iterations

- \( r_{i} \)
Cost of reserve provision for

*i*th dispatchable unit ($/kW)- \( scc_{i} \)
Startup cost of

*i*th dispatchable unit ($)- \( a_{i} ,b_{i} ,c_{i} \)
Generation cost coefficients of

*i*th dispatchable unit- \( \alpha_{i} ,\beta_{i} ,\gamma_{i} \)
Generation emission coefficients of

*i*th dispatchable unit- \( sec_{i} \)
Startup emission production of

*i*th dispatchable unit (kg)- \( Gr_{t} \)
Day-ahead market price at

*t*th interval ($/kW)- \( gec \)
Up-stream grid emission coefficient (kg/kW)

- \( bes \)
BESS emission coefficient (kg/kW)

- \( \eta_{dis} \)
BESS discharge efficiency

- \( \eta_{ch} \)
BESS charge efficiency

- \( REE \)
Renewable energy forecasting error

- \( moc \)
Reserve coefficient for maximum online unit

- \( ldc \)
Reserve coefficient for load demand

- \( P_{10,i} \)
Reserve capacity of

*i*th offline unit (kW)- \( P_{sh,j} \)
Rated power of

*j*th shiftable load (kW)- \( C_{ini} \)
BESS initial stored energy (kWh)

- \( P_{min,i} /P_{max,i} \)
Generation limits of

*i*th dispatchable unit (kW)- \( P_{Bat,min} /P_{Bat,max} \)
Power ratings for BESS charge/discharge (kW)

- \( C_{rem,min} /C_{rem,max} \)
Stored energy limits of BESS (kWh)

- \( P_{Grid,max} \)
Power exchange limit of up-stream grid (kW)

- \( TR_{j} \)
Daily total runtime of

*j*th shiftable load (\( h \))- \( CT_{j} \)
Consumer’s discomfort threshold of

*j*th shiftable load (\( h \))

## Variables

- \( X \)
Vector of all decision variables

- \( U_{i,t} \)
Binary state of

*i*th dispatchable unit at*t*th interval- \( P_{i,t} \)
Power generation of

*i*th dispatchable unit at*t*th interval (kW)- \( P_{Bat,t} \)
Power exchange with the BESS at

*t*th interval (kW)- \( P_{Grid,t} \)
Power exchange with the up-stream grid at

*t*th interval (kW)- \( A_{j,t} \)
Binary state of

*j*th shiftable load at*t*th interval- \( TUCC \)
Total unit commitment cost ($)

- \( TE \)
Total amount of produced emissions (kg)

- \( R_{i,t} \)
Reserve provision of

*i*th dispatchable unit at*t*th interval (kW)- \( P_{PV,t} \)
Power generation of the PV system at

*t*th interval (kW)- \( P_{Wind,t} \)
Power generation of the wind turbine at

*t*th interval (kW)- \( P_{Load,t} \)
Load demand at

*t*th interval including fixed and shiftable loads (kW)- \( ASR_{t} \)
Available spinning reserve at

*t*th interval (kW)- \( RSR_{t} \)
Required spinning reserve at

*t*th interval (kW)- \( C_{rem,t} \)
Remaining energy of BESS at

*t*th interval (kWh)- \( P_{max,online,t} \)
Maximum generated power between online units at

*t*th interval (kW)- \( ANSR_{r} \)
Available non-spinning reserve at

*t*th interval (kW)- \( RNSR_{r} \)
Required non-spinning reserve at

*t*th interval (kW)- \( g\left( X \right) \)
Equations of equality constraints

- \( h\left( X \right) \)
Equations of inequality constraints

- \( f\left( m \right)_{best} \)
Best possible value for

*m*th objective function- \( f\left( m \right)_{worst} \)
Worst possible value for

*m*th objective function- \( \mu \left( {f_{m} } \right) \)
Membership function obtained for

*m*th objective function- \( TMF\left( f \right) \)
Total membership function obtained for all objectives

## Notes

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