One-parameter battery degradation model for optimization of islanded microgrid system

ABSTRACT

Methods for optimization of islanded microgrid systems are usually based on hourly models where each subcomponent is described by a simple algebraic model. There are many studies on this topic, which are usually based on the minimization of total lifetime cost by determining the number of required batteries, wind turbines, PV panels, the positioning of PV panels, etc. In this paper, we further improve the modeling of the microgrid system optimization process by developing a simplified algebraic model that uses one parameter to simulate accelerated battery degradation with respect to depth of discharge. The model consists of simply linearly increasing the degradation of the battery when the state of charge (SOC) becomes lower than a fixed value, and the only model constant is the factor of degradation f. The objective of the paper is to examine the effect of the degree of degradation on the obtained optimal microgrid system parameters. The analysis was performed for several different systems, and the results show that optimal parameters of the system and the overall system cost strongly depend on battery degradation characteristics. The overall system cost can be reduced by 1–6% for lower battery degradation rates and up to 20% for high degradation factor cases. Increasing the degradation factor also has an influence on the ratio of wind turbines to PV panels, and the optimal size of the battery system.

KEYWORDS:

• Islanded microgrid
• microgrid optimization
• battery degradation
• PV panel positioning
• sizing

Nomenclature

CBES	=	total battery energy storage system cost
Cb	=	the unit cost of a battery per 1kWh (500$/kWh)
$C_{\mathrm{D}\mathrm{e}\mathrm{g}\mathrm{r}\mathrm{a}\mathrm{d}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}}$	=	the cost of accelerated battery degradation
$c_p$	=	wind turbine power coefficient
$E_{\mathrm{a}\mathrm{w}\mathrm{t}}$	=	wind turbine electrical energy production
$E_{Load}\left(t_i\right)$	=	electrical energy requirement at time interval $t_i$, J
$E_{BES}\left(t_i\right)$	=	electrical energy input/output from battery energy storage at time interval $t_i$, J
$E_{PV}\left(t_i\right)$	=	electrical energy produced by photovoltaics at time interval $t_i$, J
$e_{\mathrm{a}\mathrm{w}\mathrm{t}}$	=	available specific wind energy, kWh m−2
$f\left(v\right)$	=	probability density of wind speeds
Itilt	=	solar irradiance on a tilted plane
Ibeam	=	direct solar irradiance
Idiff	=	sky diffuse radiation
Irefl	=	ground-reflected radiation
$n_{\mathrm{B}}$	=	number of batteries
$P_{wt}$	=	wind turbine power, W
$t_i$	=	time interval used for simulation (6 min)
v	=	wind speed, ms−1
$v_{ci}$	=	cut-in wind speed, ms−1
$v_{co}$	=	cutout wind speed, ms−1
$v_n$	=	nominal wind speed, ms−1
Greek symbols	=
α	=	the angle of incidence (°)
β	=	solar zenith angle (°
${\eta }_{g}wt$	=	wind turbine electric generator efficiency
${\eta }_{B}ES$	=	battery charge/discharge efficiency
$\rho$	=	density of air, kgm−3
φ	=	PV panel tilt angle (°)
Abbreviations	=
BES	=	battery energy storage
DOD	=	depth of discharge
$DO{D}_{m}ax$	=	maximal depth of discharge
DES	=	dispatchable energy source
HAWT	=	horizontal axis wind turbines
MG	=	microgrid
PEM	=	proton exchange membrane
PV	=	photovoltaics
RES	=	renewable energy sources
SOC	=	state of charge
VAWT	=	vertical axis wind turbines
WT	=	wind turbine

Acknowledgements

This research was partially supported under the project STIM – REI (KK.01.1.1.01.0003), a project funded by the European Union through the European Regional Development Fund – the Operational Programme Competitiveness and Cohesion 2014-2020 (KK.01.1.1.01). Andrej Z. Tomić acknowledges the support from the Croatian Science Foundation (DOK-2018-01-7027).

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work was supported by the Croatian Science Foundation (DOK-2018-01-7027) project STIM – REI (KK.01.1.1.01.0003) .