Maximizing technical and economical benefits of distribution systems by optimal allocation and hourly scheduling of capacitors and distributed energy resources

ABSTRACT

Technical and economic benefits of installing distributed energy resources (DERs) and capacitor banks (C-Bs) can be maximized by optimal allocation of them. The aim of this paper is to enrich technical benefits such as voltage profile, system losses and reliability and also to increase economic benefits by maximizing the savings of energy losses and decreasing the cost of energy not supplied. The work in this paper is divided into three stages; (i) optimal placement of DERs, (ii) optimal placement of C-Bs and (iii) optimal placement of C-Bs with the existence of installed optimal DERs. The daily load variations have been considered to optimally schedule fixed and switched C-Bs. Aim of this work is formulated as a maximum objective function and is solved by a modern optimization algorithm called sine cosine algorithm (SCA). The proposed SCA method is tested on standard IEEE 33 and 69-bus radial distribution systems. Results show that the developed SCA is able to maximize the annual savings and hybrid integration of DGs and C-Bs to distribution networks is preferable than integrating one of them alone. Also, superiority of the proposed algorithm is verified by comparing its results with other optimization methods and by using a non-parametric Wilcoxon statistical test.

KEYWORDS:

• Capacitor banks allocation
• sine cosine algorithm
• energy saving
• distribution system
• optimization
• reliability

Nomenclature

${\beta }_i$	=	compensation coefficient of the ith branch
Bij	=	branch current
BijMax	=	branch maximum current
c1	=	sinusoidal control parameter that balance the exploration and exploitation phases of SCA algorithm
$c_{DER}$	=	cost of energy generated by DERs
$c_e$	=	cost of average energy
$c_{ENS}$	=	cost of ENS
Fcc	=	compensation cost
Fls	=	system energy loss reduction saving
Fpder	=	DERs purchased energy
Frs	=	system reliability improvement saving
Fus	=	energy demand from the utility reduction saving
$I_A$	=	active components of branch current
$I_R$	=	reactive components of branch current
$I_R{ }_{new}^i$	=	reactive components of the ith branch current after compensation
$I_R{ }_{old}^i$	=	reactive components of the ith branch current before compensation
${L_a}_i$	=	average load connected to load point i in kW.
${\lambda }_i$	=	average failure rate of the ith component in failure/yr
${\lambda }_s$	=	average failure rate
${\mu }_a$	=	mean value of bus voltages after connecting DERs and C-Bs
${\mu }_o$	=	mean value of bus voltages in the base case
$P_D$	=	total real power demand
$P_{DERs}$	=	power generated by DERs
PV	=	photovoltaic
${P_{PV}}_r$	=	rated power of PV at $W_r$ and temperature of 25${ }^{\circ }$C
PWr	=	rated output power of wind turbine at the rated wind velocity
${Q_c}_{m\mathrm{a}\mathrm{x}}$	=	total C-Bs size allowed
$Q_{tot\mathrm{a}\mathrm{l}}$	=	total reactive load.
$r_i$	=	average outage time of the ith component.
$r_s$	=	average outage time
τ	=	depreciation factor
t	=	current number of iteration
$U_s$	=	annual outage time
v	=	wind velocity at the candidate location
vci	=	cut-in wind velocity
vco	=	cut-out wind velocity
$V_{m\mathrm{a}\mathrm{x}}$	=	upper limit of bus voltage
$V_{min}$	=	lower limit of bus voltage.
vr	=	rated wind velocity
W	=	solar irradiance of the connection site
Wr	=	rated solar irradiance of the earth’s surface
x	=	penetration limit of DERs as a percentage of maximum demand

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Notes on contributors

Abdelazeem A. Abdelsalam

Abdelazeem A. Abdelsalam is an Associate Professor at Suez Canal University, Egypt. He was a post-doctorate fellow at University of Ontario Institute of Technology (UOIT), Canada. He received his B.Sc., M.Sc. and Ph.D. degrees in Electrical Engineering from Suez Canal University, Egypt in 2001, 2005 and 2011, respectively. He is a Member of the IEEE. His research areas include power quality, D-FACTS technology, switched filter compensators, microgrid interface and control and application of artificial intelligence techniques on power systems.