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The interval sensitivity analysis and optimization of the distribution

network parameters considering the load uncertainty

Zhigang Lu

⇑

, Jia Liu

a,b

, Yane Liu

a,c

, Rongrong Ding

, Fang Yang

Key Lab of Power Electronics for Energy Conservation and Motor Drive, Yanshan University, Hebei Province 066004, PR China

Qinhuangdao Power Corporation Limited, Qinhuangdao 066004, Hebei Province, PR China

State Grid Jibei Changli Power Supply Co. Ltd., Changli Hebei 066600, PR China

article info

Article history:

Received 6 September 2012

Received in revised form 27 July 2014

Accepted 19 August 2014

Available online 18 September 2014

Keywords:

Loss sensitivity

Network loss

Interval analysis

Bacterial colony chemotaxis

Distribution system

abstract

This paper proposes an advanced approach to optimize the line and transformer parameters for the

distribution system. The approach ﬁrst adopts a novel set of interval sensitivity models, based on which

an interval forward–backward power ﬂow algorithm and an interval analysis method are further

developed. In order to improve computational speed, this approach uses a simpliﬁed set models to cal-

culate power system loss interval sensitivity with respect to the admittance of lines and transformers.

An interval objective function is formulated and the optimization problem is solved with a discrete

bacterial colony chemotaxis algorithm. The applicability and effectiveness of the proposed approach is

demonstrated on two real distribution systems.

Introduction

In recent years, with the considerable increase of the load

demand, some distribution lines and transformers can no longer

meet the actual power delivery requirements, which leads to the

loss increase and distribution system operation. Hence, the identi-

ﬁcation of lines and transformers that are responsible for the sys-

tem loss increase becomes necessary in order to establish the

reconstruction strategies.

The subject of power system loss sensitivity is widely addressed

in various areas such as transaction evaluation, voltage stability,

sensitivity analysis and loss minimization [1–6]. Refs. [7–9] present

a set of models to calculate power system loss sensitivities with

respect to power system parameters. These models are derived

from the Tellegen’s theorem and the adjoint network concept.

Ref. [10] adopts the least-square ﬁtting technique to ﬁt the rela-

tionship curves between the line cross-sectional area and invest-

ment, proposes a sensitivity analysis method to optimize line

parameters based on Particle Swarm Algorithm, and formulates

the objective function to minimize the comprehensive investment

cost and system power loss. Ref. [11] uses the economic current

density and load rate to reconstruct lines and transformers and

analyze their economic operation range. Based on the deﬁnition

of the conjugate branch current sensitivity with respect to the line

or transformer parameters, the power system loss sensitivity with

respect to the line or transformer parameters is calculated. Accord-

ing to the loss sensitivities, it is possible to determine every com-

ponent’s inﬂuence degree to the power system loss, and provide an

easy way for estimating the network loss when the parameters are

changed. Besides, Ref. [12] selects optimization interval using the

lines and transformers economic operation range. In addition, a

particle location library is establish to update particle location.

Ref. [13] improves the adequacy of constructed sensitivity models

and allows to consider a power system reaction on the basis of con-

structing so-called functionally oriented equivalents.

Taking load uncertainties [14] into consideration, the loss sensi-

tivity with respect to certain parameters varies along with time

changes. Therefore, this paper focuses on computing the loss inter-

val sensitivities over a period of time. The meaning of the loss

interval sensitivity is that the value of the sensitivity is an interval

number consisting of all the numbers between a pair of given num-

bers. The two given numbers are referred to as upper and lower

limits. Using the loss interval sensitivities makes it more reason-

able to identify weakness in the distribution system and establish

reconstruction measures in time.

This paper applies the three-phase system modeling technique

[15] including nine transformer connection types (both grounded

and ungrounded connections), lines, switches, and ZIP loads. In

http://dx.doi.org/10.1016/j.ijepes.2014.08.022

⇑

Corresponding author. Address: School of Electrical Engineering, Yanshan

University, Qinhuangdao, Hebei 066004, PR China.

E-mail addresses: zhglu@ysu.edu.cn (Z. Lu), ljia1987@sina.com (J. Liu),

lyeysu@163.com (Y. Liu), 1250094720@qq.com (R. Ding), faayaa2013@hotmail.

com (F. Yang).

Electrical Power and Energy Systems 64 (2015) 931–936

Contents lists available at ScienceDirect

Electrical Power and Energy Systems

journal homepage: www.elsevier.com/locate/ijepes

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