A Linear Three-Phase Load Flows for Power

Distribution System

Muhammad Nur Ayman Bin Hussin

Eng. (Hons) Bachelor Degree of Electrical Engineering (Power System)

Faculty of Electrical and Electronics Engineering, Universiti Malaysia Pahang, 26600, Pekan, Pahang,

Malaysia.

EC16047

Abstract:

3-phase power distribution system that was

created for a linear load flow. The methodology

doesn’t required any possibilities that related to

R/X ratio. Unbalanced and balanced

operations that are consider as the ZIP models

of the load.

Introduction:

Dc power flows are the most study

methodology for researches and operations of

electrical power systems. But, linear

computation was not suited well for power

distribution system due to its high R/X ratio and

unbalance operation. This report state this issue

by using the linear approximate on the complex

plane. PV node does not included but

distribution generator can be include in the case

which the grid code have unity power factor

operation for these generators.

a) Basic Formula

Nodal voltage and current are

related with the admittance matrix

as follow:

(1)

Which is S correspond the slack

node and N are the set of remain

node. Every nodal currents was

related to the voltages with the

following ZIP model:

(2)

Where h = 1/Vnom (per unit

represent implies h=1). Take note

that the ZIP model was linear

except for the changeless power

load. This referent is approximately

in order to obtain the linear power

flows.

Fig. 1. Schematic represent of the

proposed linearization. (a) Value of in the

complex planes. (b) Total errors in the

percentage.

b) Linear Approximations

A linear approximations was

created on the complex number and

not on the real as in the conventional

loads flow formulation. The

function f(?V) = 1/(1-?V) was

analytic for all ||?V|| ; 1. The

Taylor series around zero is

(3)

The formula as neglecting high

order terms and defining V=1-?V a

linear form is formed

(4)

c) Approximate Load Flows

A linear aspect for a nodal currents

(2) was given as follow:

(5)

By using the first formula and

arrange some term, a linear

formulation was extracted

(6)

d) Extension to the Unbalanced Case

The propose methodologies was

expendable to 3-phase unbalance

power distribution system. A 3-phase

admittances matrix was required. VN

were phase-neutral voltages. Sub index

of S (1) represent in this case 3 nodes

fit in to each phases. The sizes of

problem was increase but (6) remain as

a precise computation. Note that angle

on the 3-phase systems were not

necessary close to 0, where (3) is valid.

Moreover, for delta connection

load, it was require to determine a

matrix that convert phase voltage into

line voltage VN(line) = M.VN . After

include this new term, the constant

matrices in (6) are stated by

linear load flows give comparatively low

error even in high load system.

Conclusion

Reference

1 B. Stott, J. Jardim, and O. Alsac, “DC

power flow revisited,” IEEE Trans. Power

Syst., vol. 24, no. 3, pp. 1290, 1300, Aug.

2009.

2 R. G. Cespedes, “New method for the

analysis of distribution networks,” IEEE

Trans. Power Del., vol. 5, no. 1, pp. 391,

396, Jan. 1990.

3 F. Flanigan, Complex Variables, Dover

Books on Mathematics , Ed. New York,

NY, USA: Dover, 2010.

4 A. Garces,A Linear Three-Phase Load

Flow for Power Distribution System, Ieee

Transactions On Power Systems, Vol. 31,

No. 1, January 2016

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