CONTROL SYSTEM ENGINEERING Module III

MODULE III

LOAD FLOW STUDIES

Load flow studies are important in planning and designing future expansion of power systems.
The load flow gives us the sinusoidal steady state of the entire system  voltages, real and
reactive power generated and absorbed and line losses. Generally, load flow studies are limited
to the transmission system, which involves bulk power transmission.

Through the load flow studies we can obtain the voltage magnitudes and angles at each bus in
the steady state. This is rather important as the magnitudes of the bus voltages are required to be
held within a specified limit. Once the bus voltage magnitudes and their angles are computed
using the load flow, the real and reactive power flow through each line can be computed. Also
based on the difference between power flow in the sending and receiving ends, the losses in a
particular line can also be computed. Furthermore, from the line flow we can also determine the
over and under load conditions. Load flow studies throw light on some of the important aspects
of the system operation, such as: violation of voltage magnitudes at the buses, overloading of
lines, overloading of generators, stability margin reduction, indicated by power angle differences
between buses linked by a line, effect of contingencies like line voltages, emergency shutdown
of generators, etc. Load flow studies are required for deciding the economic operation of the
power system. They are also required in transient stability studies. Hence, load flow studies play
a vital role in power system studies.

CLASSIFICATION OF BUSES

For load flow studies it is assumed that the loads are constant and they are defined by their real
and reactive power consumption. It is further assumed that the generator terminal voltages are
tightly regulated and therefore are constant. The main objective of the load flow is to find the
voltage magnitude of each bus and its angle when the powers generated and loads are pre-
specified. To facilitate this we classify the different buses of the power system as listed below.

1. Load Buses: In these buses no generators are connected and hence the generated real power
PGi and reactive power QGi are taken as zero. The load drawn by these buses are defined by
real power  PLi and reactive power  QLi in which the negative sign accommodates for the

, power flowing out of the bus. This is why these buses are sometimes referred to as P-Q bus.
The objective of the load flow is to find the bus voltage magnitude Vi and its angle i.



2. Voltage Controlled Buses: These are the buses where generators are connected. Therefore
the power generation in such buses is controlled through a prime mover while the terminal
voltage is controlled through the generator excitation. Keeping the input power constant
through turbine-governor control and keeping the bus voltage constant using automatic
voltage regulator, we can specify constant PGi and Vi for these buses. This is why such
buses are also referred to as P-V buses.
3. Slack or Swing Bus: Usually this bus is numbered 1 for the load flow studies. This bus sets
the angular reference for all the other buses. Since it is the angle difference between two
voltage sources that dictates the real and reactive power flow between them, the particular
angle of the slack bus is not important. However it sets the reference against which angles
of all the other bus voltages are measured. For this reason the angle of this bus is usually
chosen as 0. Furthermore it is assumed that the magnitude of the voltage of this bus is
known.



Now consider a typical load flow problem in which all the load demands are known. Even if the
generation matches the sum total of these demands exactly, the mismatch between generation
and load will persist because of the line I2R losses. Since the I2R loss of a line depends on the
line current which, in turn, depends on the magnitudes and angles of voltages of the two buses
connected to the line, it is rather difficult to estimate the loss without calculating the voltages and
angles. For this reason a generator bus is usually chosen as the slack bus without specifying its
real power. It is assumed that the generator connected to this bus will supply the balance of the
real power required and the line losses.

REAL AND REACTIVE POWER INJECTED IN A BUS

For the formulation of the real and reactive power entering a bus, we need to define the
following quantities. Let the voltage at the ith bus be denoted by

, Vi  Vi  i  Vi cos  i  j sin  i 

(3.1)

Also let us define the self admittance at bus-i as

Yii  Yii  ii  Yii cos ii  j sin  ii   Gii  jBii (3.2)

Similarly the mutual admittance between the buses i and j can be written as

Yij  Yij  ij  Yij cos ij  j sin  ij   Gij  jBij (3.3)

Let the power system contains a total number of n buses. The current injected at bus-i is given as

I i  Yi1V1  Yi 2V2    YinVn
n (3.4)
  YikVk
k 1



It is to be noted we shall assume the current entering a bus to be positive and that leaving the bus
to be negative. As a consequence the power and reactive power entering a bus will also be
assumed to be positive. The complex power at bus-i is then given by

n
Pi  jQi  Vi  I i  Vi   YikVk
k 1
n
 Vi cos  i  j sin  i  YikVk cos ik  j sin  ik cos  k  j sin  k  (3.5)
k 1
n
  YikViVk cos i  j sin  i cos ik  j sin  ik cos k  j sin  k 
k 1



Note that

cos i  j sin  i cos ik  j sin ik cos  k  j sin  k 
 cos i  j sin  i cos ik   k   j sin  ik   k 
 cos ik   k   i   j sin  ik   k   i 

Therefore substituting in (3.5) we get the real and reactive power as