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Optimal Sizing of Renewable Sources and Energy Storage in Low-Carbon Microgrid Nodes


Despite the fact that microgrids are growing in popularity, their integration in distribution networks is problematic because of the omnipresent variability of renewable energy sources. New research focuses on viewing microgrids as having an active role in the system and providing additional services, such as the concept of low-carbon microgrid nodes. The paper presents a mixed integer linear programming optimization algorithm for determining the optimal size of the distributed generation unit and battery storage system based on operational savings and investment costs, as well as estimation of environmental benefits. The flexibility of the analyzed power node comes not only from its capability to store electricity in the battery banks but to optimally schedule flexible loads such as electric vehicles (EVs). Stochasticity of EV arrival and their state of charge are modeled daily and seasonally. The results show that active market signal-driven integration of such nodes is still not feasible without incentives. But as additional services start creating profits, the gap to feasibility will become smaller.

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i :

One DGU from DG set

j :

One BES from BES set

k :

One EV

n :

One flexible load

\(C_\mathrm{dg,INV}^i\) :

DGU i investment costs in €/kW

\( C_{\mathrm{dg},O \& M}^i\) :

DGU i operation and maintenance costs in €/kW

\(C_\mathrm{BES,PINV}^j\) :

BESj investment costs in €/kW

\(C_\mathrm{BES,CINV}^j \) :

BESj investment costs in €/kWh

\(C_\mathrm{net}\) :

Price of electricity taken from the grid in each time interval Y

\(C_\mathrm{ems} \) :

Price of \(\hbox {CO}_{2}\) per kWh of electricity taken from the distribution network

\(C_{\mathrm{feed}\text {-}\mathrm{in}}^1 \) :

Feed-in tariff for electricity produced from distributed units and consumed in the microgrid

\(C_{\mathrm{feed}\text {-}\mathrm{in}}^2 \) :

Feed-in tariff for electricity produced from DGU and exported into the distribution network

\(P_\mathrm{imp,MAX} \) :

Maximal power that can be taken from the distribution network

\(P_\mathrm{dg,INS}^i\) :

Installed power of DGU i

\(P_\mathrm{BES,INS}^j \) :

Installed power of BES j

\(E_\mathrm{BES,INS}^j \) :

Installed capacity of BES j

\(P_\mathrm{BESdch,MAX}^j \) :

Maximal charging power of BES j

\(P_\mathrm{BESdch,MAX}^j \) :

Maximal discharge power of BES j

\(P_\mathrm{flMIN}^n \) :

Minimal power of flexible load n

\(P_\mathrm{flMAX}^n \) :

Maximal power of flexible load n

\(p_\mathrm{dg}\) :

Production factor which determines the output power of DGU in each time interval

\(E_\mathrm{BES,MAX}^j\) :

Maximal amount of energy that can be stored in BES j

\(E_\mathrm{BES,MIN}^j\) :

Amount of energy after which no further discharging of BES j is allowed

\(E_\mathrm{EV,BATT}^j\) :

Battery capacity of EV k

\(SOC_\mathrm{ac}^k\) :

Expected SOC after charging of EV k

\(\eta _\mathrm{ch}\) :

BES charging efficiency

\(\eta _\mathrm{dch}\) :

BES discharge efficiency

\(\eta _\mathrm{chEV}\) :

EV charging efficiency

m :

Number of DGUs

l :

Number of BESs

\(\mathrm {T}_{\mathrm{int}}\) :

Duration of one time il in hours

\(\hbox {NINT}\) :

Number of time intervals

\(\hbox {NoFL}\) :

Number of flexible loads

\(\hbox {NYEAR}\) :

Defined duration of the investment in years

d :

Discount rate


Set of m DGUs which are being considered


Set of l BESs which are being considered

\(C_\mathrm{opr} \) :

Annual operating costs of a microgrid system

\(C_\mathrm{INV} \) :

Total investment costs

\(C_\mathrm{opr,net}\) :

Annual operating cost of a microgrid when all electricity is imported from the distribution network

\(P_\mathrm{imp}\) :

Power taken from the distribution network in each time interval

\(P_\mathrm{exp}\) :

Exported power into the distribution network in each time interval

\(P_\mathrm{nfl}\) :

Non-flexible microgrid load in each time interval

\(P_\mathrm{fl}\) :

Total flexible load in each time interval

\(P_\mathrm{BESch}^j \) :

Charging power of BES j in each time interval

\(P_\mathrm{BESdch}^j \) :

Discharge power of BES j in each time interval

\(P_\mathrm{fl}^n\) :

Load of a single flexible load n in each time interval

\(E_\mathrm{BES}^j\) :

Amount of energy stored in BES j in each time interval

\(E_\mathrm{EV}^k\) :

Energy demand of EV k

\(SOC_\mathrm{bc}^k\) :

SOC before charging of EV k


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Correspondence to Rene Prenc.

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Strnad, I., Prenc, R. Optimal Sizing of Renewable Sources and Energy Storage in Low-Carbon Microgrid Nodes. Electr Eng 100, 1661–1674 (2018).

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  • Distributed generation
  • Battery storage
  • Optimal sizing
  • Flexible load
  • Electric vehicles