A Linear Three-Phase Load Flows for Power Distribution System Muhammad Nur Ayman Bin Hussin Eng

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,
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.
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:
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:
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
Fig. 1. Schematic represent of the
proposed linearization. (a) Value of in the
complex planes. (b) Total errors in the
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
The formula as neglecting high
order terms and defining V=1-?V a
linear form is formed
c) Approximate Load Flows
A linear aspect for a nodal currents
(2) was given as follow:
By using the first formula and
arrange some term, a linear
formulation was extracted
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.
1 B. Stott, J. Jardim, and O. Alsac, “DC
power flow revisited,” IEEE Trans. Power
Syst., vol. 24, no. 3, pp. 1290, 1300, Aug.
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