International Conference on Global Trends in Engineering, Technology and Management (ICGTETM-2016)
Power Flow Studies for Radial and Mesh Distribution System
Mr.Tanveer HusainShaikhFeroz Khatik#1, Mr.M. M. Khan#2, Mr. M.M. Ansari#3
#1
M.E (EPS) (Student),#2M.E (EPS),#3 Assistant Professor, #123 Electrical Department of SSBT’s COET
Bambhori
c/o Nisar Ahmad Abdul78/16 Aqsa Nagar, Master Colony, Mehrun, Jalgaon-425001(MH), India
Abstract— This paper presents a new and efficient
method for solving the load flow problem of
a distribution system. It is mainly based on network
topology, basic circuit laws and power summation
technique. The main contribution of this paper is: (i)
proposing a new and efficient load flow method
for radial and weakly meshed distribution systems, (ii)
evaluating the impact of load models, different
X/R ratios, load growth and tolerance levels, (iii)
analysis of impact of number of loops on weakly
meshed distribution systems, (iv) comparison of
radial and weakly meshed distribution system. The
results are obtained for voltage profile, total power
losses time of computation, and number of iterations.
Computer program coded to implement this power
flow solution scheme in MATLAB and successfully
applied to several practical distribution networks
with radial and weakly meshed structure. MATLAB
is viewed by many users not only as a highperformance language for technical computing but
also as a convenient environment for building
graphical user interfaces (GUI). Data visualization
and GUI design in MATLAB are based on the Handle
Graphics System in which the objects organized in a
Graphics Object Hierarchy can be manipulated by
various high and low level commands. If using
MATLAB7 the GUI design more flexible and versatile,
they also increase the complexity of the Handle
Graphics System and require some effort to adapt to.
Keywords —Power Flow, MATLAB, radial
distribution system, mesh distribution system, load
growth.
I. INTRODUCTION
Power flow analysis is the backbone of power
system analysis and design. They are necessary for
planning, operation, economic scheduling and
exchange of power between utilities. Power flow
analysis is required for many other analyses such as
transient stability, optimal power flow and
contingency studies. The principal information of
power flow analysis is to find the magnitude and
phase angle of voltage at each bus and the real and
reactive power flowing in each transmission lines.
Power flow analysis is an importance tool involving
numerical analysis applied to a power system. In this
analysis, iterative techniques are used due to there no
known analytical method to solve the problem. This
resulted nonlinear set of equations or called power
flow equations are generated. To finish this analysis
there are methods of mathematical calculations which
ISSN: 2231-5381
consist plenty of step depend on the size of system.
This process is difficult and takes much time to
perform by hand. By develop a toolbox for power
flow analysis surely will help the analysis become
easier. Power flow analysis software can help users to
calculate the power flow problem. Over the past
decade, a few versions of educational software
packages using 2 advanced programming languages,
such as C, C++, Pascal, or FORTRAN have been
developed for power engineering curriculums. These
choose an integrated study platform with support of
database and GUI functions. Power flow analysis
software develops by the author use MATLAB
software. MATLAB as a high-performance language
for technical computation integrates calculation,
visualization and programming in an easy-to-use
environment, thus becomes a standard instructional
tool for introductory and advanced courses in
mathematics, engineering and science in the university
environment. Most of the students are familiar with it.
Some efficient algorithms for solving the load flow
problem of a radial distribution networks have been
reported in the literature. However, these algorithms
are not suitable for a mesh network. Several load flow
algorithms specially designed for meshed distribution
systems have been reported in the literature.
Based on the previous work, a modified
compensation based method was developed in, which
uses active and reactive power as flow variables rather
than complex currents. The compensation based
method for weakly meshed networks presented in, was
modified from single-phase system to three-phase
system. The mesh network is converted into radial
network by breaking the loops and the load flow has
been carried out by calculating power injections at the
loop break points by using a reduced order bus
impedance matrix.
In this paper, a simple load flow method is
proposed based on network topology, basic circuit
theory concepts and power summation technique.
The power summation method is an iterative
technique which includes two steps: (i) Calculation of
the effective power at each node in backward
propagation, (ii) then find the voltages at receiving
end node and losses of each branch in forward
propagation. First we’ll calculate the effective power
required by each node of the radial network. The
effective power will be modified from radial network
to mesh network by adding or subtracting the power
required at each node to flow the same loop current in
a loop and the loop current can be calculated by
applying KVL in the loop. With the help of effective
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power at each node (considering the loop effect also),
we’ll carry out the load flow. Due to the distinctive
solution techniques of the proposed method, the timeconsuming LU decomposition and forward/backward
substitution of the Jacobian matrix or admittance
matrix required in the traditional load flow methods
and formation BIBC and BCBV matrices , tree
labeling , breaking the loops and injecting power
injections are not required. The convergence ability
of the proposed load flow algorithm is tested on
different IEEE systems under different scenarios.
II. LITRATURE SURVEY
This chapter discuss about literature review that
been collected for this project. Author has refers
through journals and paper especially from IEEE. This
chapter consists of three parts. It is describe generally
on power flow analysis problems and the solutions,
Graphical User Interface in MATLAB and power
system toolbox in market.
A. Line Flow and Losses Calculation
The power loss in line i – j is the algebraic sum of
the power flows determined from
SLij = Sij + Sji
(05)
The distribution systems usually fall into the
category of ill-conditioned power systems for generic
Newton-Raphson like methods with its special
features
i. Radial or Weakly Meshed Topologies:
Most of the distribution systems are radial or
weakly meshed types. The increase in requirements
for reliability and outgoing distribution generation has
made the structure of distribution systems more
complex. Therefore, the power flow analysis in such
distribution systems has become more difficult.
ii. High R/X Ratio of the Distribution Lines:
Transmission networks are composed mainly of
overhead lines thus, the ratio is usually lower than 0.5.
In distribution networks where both overhead lines
and cables are used, the R/X ratio is high ranging from
0.5 to as high as 7, where high ratio values are
typically for low voltage networks.
iii. Unbalanced Operation:
Three-phase unbalanced orientation greatly
increases the complexity of the network model, since
phase quantities have to be considered including
mutual couplings.
Fig. 1 Transmission line model for calculating line flows
i → j = is given by
Iij = Il + Iio = yij (Vi - Vj) + yioVi
(01)
Similarly, the line current Iij measured at bus j and
defined positive in the direction j → i is given by
iv. Loading Conditions:
Most of the load flow methods were developed
assuming a static load model. But, a practical load
model is required for getting reliable results.
v. Dispersed Generation:
Distributed generation is being increasingly used to
meet the fast load increase in the deregulation era. The
utilities have to analyze the operating conditions of the
radial-type systems with distributed sources.
Iij = - Il + Iio = yij (Vj-Vi) + yjoVj
(02)
The complex power Sij from bus I to j and Sji from
bus j to i are
Sij= ViI*ij
(03)
Sji = Vj*Iji
(04)
ISSN: 2231-5381
vi. Non-linear Load Models:
Widespread use of non-linear loads such as,
rectifiers in distribution system distorts the current
drawn from the source.
Usually the commercial SCADA/DMS systems
treat these distribution systems as independent parts,
i.e., HVAC (high voltage a.c.) loop and MVAC
(medium voltage a.c.) or LVAC (low voltage a.c.)
radial systems. Such rough equivalence will cause
inaccuracies in the power flow solutions.
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III. SYSTEM DESIGN
Fig. 2 A typical bus of the power system
Referring to the above figure, power flow equations
are formulated in polar form for the n-bus system in
terms of bus admittance matrix Y as:
A. Proposed Load Flow Approach in Distribution
Systems:
An efficient and simple load flow method is
proposed for analysis of the radial and weakly meshed
network based on network topology and basic circuit
laws (KCL and KVL). Radial distribution systems
have poorest service reliability. In radial distribution
systems customers at far end of the substation suffers
from major voltage drops and distributor near to
substation gets heavily loaded. To improve reliability
and provide better voltage regulation meshed
distribution networks are used by closing the tie line
switches. Some distribution feeders serving high
density load areas contain loops created by closing tie
line switches.
B. Simple Radial Distribution System:
Ii = ∑ YijVj
(06)
where, i,j are to denote ith and jth bus
Expressing in polar form:
Ii = ∑ │Yij││ Vj │ ∟ θij+ δj
(07)
The current can be expressed in terms of the active
and the reactive power at bus i as:
Fig. 3Simple radial Distribution System
Ii =
(08)
Substituting for Ii from eqn.(08) in eqn.(07)
Pi – j Qi = │ Vi │ ∟– δi ∑ │Yij││ Vj │ ∟ θij + δj
(09)
Separating the real and imaginary parts
Pi = ∑ │ Vi │ │ Vj │ │ Vij │
(10)
Qi = – ∑ │ Vi │ │ Vj │ │ Vij │
(11)
–
–
The simple radial distribution system is shown in
Fig. 3. The voltages can be calculated by knowing
effective powers at each node as obtained. For
example, the loads of six bus radial network are
shown in Fig. 3.
The effective powers at each node
P(2)+jQ(2), P(3)+jQ(3), P(4)+jQ(4),
P(6)+jQ(6).
P(1)+jQ(1),
P(5)+jQ(5),
P(1)+jQ(1) = PL2 + jQL2 + PL3 + jQL3 + PL4
+ jQL4 + PL5 + jQL5 + PL6 + jQL6 +
ploss(B1) + jqloss(B1) + ploss(B2) + jqloss(B2) +
ploss(B3) + jqloss(B3)+ ploss(B4) + jqloss(B4) +
ploss(B5) + jqloss(B5) (12)
P(2)+jQ(2) = PL2 + jQL2 + PL3 + jQL3 + PL4
+ jQL4 + PL5 + jQL5 + PL6 + jQL6 +
ploss(B2) + jqloss(B2) + ploss(B3) + jqloss(B3) +
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International Conference on Global Trends in Engineering, Technology and Management (ICGTETM-2016)
ploss(B4) + jqloss(B4) + ploss(B5) + jqloss(B5)
(13)
P (3)+jQ(3) = PL3 + jQL3 + PL4 + jQL4 +
PL5 + jQL5 + PL6 + jQL6 + ploss(B3) +
jqloss(B3) + ploss(B4) + jqloss(B4) + ploss(B5) +
jqloss(B5)
(14)
P (4)+jQ(4) = PL4 + jQL4 + PL5 + jQL5 +
ploss(B4) + jqloss(B4)
Fig. 4Simple radial Distribution System
(15)
P(5)+jQ(5) = PL5 + jQL5
(16)
P(6)+jQ(6) = PL6 + jQL6
(17)
In this seminar, a simple load flow method is
proposed based on network topology, basic circuit
theory concepts and power summation technique. The
power summation method is an iterative technique
which includes two steps: (i) Calculation of the
effective power at each node in backward propagation,
(ii) then find the voltages at receiving end node and
losses of each branch in forward propagation. First
we’ll calculate the effective power required by each
node of the radial network. The effective power will
be modified from radial network to mesh network by
adding or subtracting the power required at each node
to flow the same loop current in a loop and the loop
current can be calculated by applying KVL in the loop.
With the help of effective power at each node
(considering the loop effect also), we’ll carry out the
load flow. Due to the distinctive solution techniques of
the proposed method, the time consuming LU
decomposition and forward/backward substitution of
the Jacobian matrix or admittance matrix required in
the traditional load flow methods and formation BIBC
and BCBV matrices tree labeling breaking the loops
and injecting power injections are not required. The
convergence ability of the proposed load flow
algorithm is tested on different IEEE systems under
different scenarios.
C. Simple Meshed Distribution System with Three
Loops:
The simple distribution system with three loops
addition to make the network as a mesh network is
shown in Fig. 4. The mathematical modeling for load
flow analysis of weakly meshed distribution network
is explained in detail as below. In the presence of tie
lines, the current in the each branch from radial
network to mesh network will be changed because of
the tie line currents. From Fig. 4, let the current
flowing in branch 2 in radial network is IB2. In Fig. 4
because of the loop-3, the modified current in branch
2 is IB2 – Iloop-3. That means the effective power at
receiving end node of each branch in the loops will be
changed from radial network to mesh network. The
modified effective power at all nodes in each loop will
be decided by the receiving end node voltage of the
branches in that loop. So modified effective power can
be calculated by adding or subtracting the effective
power (in radial) with power at the node which is
multiplication of the loop current with the receiving
end node voltage of each branch in the loop.
P(1)’ + jQ(1)’ = P(1)+jQ(1)
(18)
P(2)’ + jQ(2)’ = P(2)+jQ(2)
(19)
P(3)’ + jQ(3)’ = P(3)+jQ(3) – { Iloop(3) * [V(3)]*}*
(20)
P(4)’ + jQ(4)’ = P(4)+jQ(4) + { Iloop(1) * [V(4)]*}*
– { Iloop(2) * [V(4)]*}*
(21)
P(5)’ + jQ(5)’ = P(5)+jQ(5) + { Iloop(1) * [V(5)]*}*
– { Iloop(2) * [V(5)]*}*
(22)
P(6)’ + jQ(6)’ = P(6)+jQ(6) – { Iloop(1) * [V(6)]*}*
– { Iloop(3) * [V(6)]*}*
(23)
ISSN: 2231-5381
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International Conference on Global Trends in Engineering, Technology and Management (ICGTETM-2016)
D. Model of Load Growth:
For future expansion and planning of the
distribution systems, it is desirable that a system
engineer must know the future estimate of the system
solutions for planning and expansion or the efficient
operation of distribution systems. The load growth
(LG) pattern is essential to know for future planning
and expansion of the distribution systems. In this
paperwork, load growth is modelled as
relationship as a polynomial equation of voltage
magnitude. It is usually referred to as the ZIP model,
as it is made up of three different load models:
constant impedance (CZ), constant current (CI) and
constant power (CP). The real and reactive power
characteristics of ZIP load model are given as:
P = P0 [ ap (
)2 + bp (
) + cp ]
)2 + bq (
)+ cq ]
(27)
Loadi = Load * (1 + r)m
(24)
Q = Q0 [ aq (
Where,
r = annual growth rate
m = plan period up to which feeder can take
the load
In this paper work r=0.07 and m=5. The load
growth is incorporated for all the systems to consider
the impact of load growth on voltage profile, total real
and reactive power losses, number of iterations and
convergence time.
(28)
Where, the sum of the ZIP load coefficients for
both P, and Q loads is equal to 1.
ap +bp + cp = 1,
aq +bq + cq = 1
i.
Static Load Model:
In conventional load flow studies, it is presumed
that active and reactive power demands are specified
constant values, regardless of the amplitude of
voltages in the same bus. In actual power systems
operation, different categories and types of loads such
as residential, industrial, and commercial loads are
present. The nature of these types of loads is such that
their active and reactive powers are dependent on the
voltage and frequency of the system. Moreover, load
characteristics have significant effects on load flow
solutions and convergence ability. Common static load
models for active and reactive power are expressed in
a polynomial or an exponential form. The
characteristic of the exponential load models can be
given as:
P = P0 (
)np
(25)
Q = Q0 (
)nq
(26)
Where np and nq stand for load exponents, P0 and
Q0 stand for the values of the active and reactive
powers at the nominal voltages. V and V0 stand for
load bus voltage and load nominal voltage,
respectively.
ii.
Polynomial Load Model :
In this paper, a realistic static load model is
considered that represents the power-voltage
ISSN: 2231-5381
In this seminar work ap = aq = 0.3 , bp =
bq = 0.2 , cp = cq = 0.5. P0 and Q0 are the real and
reactive power consumed at a reference voltage Vo.
IV. CONCLUSION
Conclusion:
In this paper, a new and efficient method for
solving the load flow problem of a distribution system
is proposed. The proposed method is compared with
existing methods and it has been shown to be superior
in the number of iterations, computationally efficient,
and the robustness of convergence while the solution
accuracy is well maintained. The proposed load flow
approach is in close agreement with the existing
methods. The proposed load flow method has been
tested on two IEEE benchmark distribution systems
under different loading conditions, different R/X ratio,
different static load models, and considering load
growth also. Load flow problem under different load
conditions and for various ratios R/X has been
determined with the proposed to check its
convergence. It can be observed that the proposed
method converges with varying load conditions and
R/X ratios. It has been found from the cases that the
method has good and fast convergence characteristics.
Because of distinctive solution techniques of the
proposed method, the time intensiveness due to LU
decomposition and forward/backward substitution of
the Jacobian matrix or admittance matrix required in
the traditional load flow methods and formation BIBC
and BCBV matrices, tree labeling, breaking the loops
and injecting power injections are not necessary. Test
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International Conference on Global Trends in Engineering, Technology and Management (ICGTETM-2016)
results show that the proposed method is faster and
converges with load variations and different R/X
ratios and is suitable for large-scale distribution
systems.
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