LOAD FLOW STUDIES - Aliah University

Load flow studies 1

LOAD FLOW STUDIES (LFS)

INTRODUCTION

Load flow studies 2

Load flow studies are one of the most important

aspects of power system planning and operation.

The load flow gives us the sinusoidal steady state of

the entire system voltages, real and reactive power

generated and absorbed and line losses.

Load flow studies 3

Since the load is a static quantity and it is the

power that flows through transmission lines, the

purists prefer to call this Power Flow studies rather

than load flow studies. We shall however stick to the

original nomenclature of load flow.

Load flow studies 4

Introduction

Load flow studies or Power flow studies is the

analysis of a power system in normal steady state

condition

Load flow studies basically comprises of the

determination of

• Voltage

• Current

• Active Power

• Reactive Power

Load flow studies 5

Importance

• Generation supplies demand(Load) plus

losses.

• Bus voltage magnitude remain close to rated

value.

• Generation operates within specified real

and reactive power limits.

• Transmission line and transformer are not

overloaded.

Load flow studies 6

Need of Load flow study

• Designing a power system.

• Planning a power system.

• Expansion of power system.

• Providing guide lines for optimum operation of

power system.

• Providing guide lines for various power system

studies.

Load flow studies 7

Bus Classification

• Bus is a node at which many Transmission lines, Loads Generators are

connected.

• It is not necessary that all of them be connected to every bus.

• Bus is indicated by vertical line at which no. of components are

connected.

• In load flow study two out of four quantities specified and other two

quantities are to be determined by load flow equation.

• Depending upon that bus are classified.

Load flow studies 8

Load bus or PQ Bus

• A buss at which the Active power and reactive power are

specified.

• Magnitude(V) and phase angle(δ) of the voltage will be

calculated.

• This type of busses are most common, comprising

almost 80% of all the busses in given power system.

Load flow studies 9

Generator bus or P-V bus

• A bus at which the magnitude(V) of the voltage and

active power(P) is defined.

• Reactive power(Q) and Phase angle(δ) are to be

determined through load flow equation.

• It is also known as P-V bus.

• This bus is always connected to generator.

• This type of bus is comprises about 10% of all the

buses in power system.

Load flow studies 10

Slack Bus

• Voltage magnitude(V) and voltage phase angle(δ) are

specified and real(P) and reactive(Q) power are to be

obtained.

• Normally there is only one bus of this type is given in

power system.

• One generator bus is selected as the reference bus.

• In slack bus voltage angle and magnitude is normally

considered 1+j0 p.u.


Static method

The following variables are associated with each

bus:

• Magnitude of voltage(V)

• Phase angle of voltage(δ)

• Active power(P)

• Reactive power(Q)

The load flow problem can solved with the help of

load flow equation(Static load flow equation).


Classical methods

Gauss-Seidal method

Newton Raphson method

Fast Decoupled method

Load/Power Flow studies • Load-flow studies are performed to determine the steady-state

operation of an electric power system. It calculates the voltage drop on each feeder, the voltage at each bus, and the power flow in all branch and feeder circuits.

• Determine if system voltages remain within specified limits under various contingency conditions, and whether equipment such as transformers and conductors are overloaded.

• Load-flow studies are often used to identify the need for additional generation, capacitive, or inductive VAR support, or the placement of capacitors and/or reactors to maintain system voltages within specified limits.

• Losses in each branch and total system power losses are also calculated.

• Necessary for planning, economic scheduling, and control of an existing system as well as planning its future expansion

• Pulse of the system

Power Flow Equation

Note: Transmission lines are represented by their equivalent pi models (impedance in p.u.)

Applying KCL to this bus results in

(1)

Fig. 1. A typical bus of the power system.

(2)

The real and reactive power at bus i is

Substituting for Ii in (2) yields

Equation (5) is an algebraic non linear equation which must be solved by iterative techniques

Gauss-Seidel method

• Equation (5) is solved for Vi solved iteratively

Where yij is the actual admittance in p.u. Pi

sch and Qisch are the net real and reactive powers in p.u.

In writing the KCL, current entering bus I was assumed positive. Thus for: Generator buses (where real and reactive powers are injected), Pi

sch and Qisch

have positive values. Load buses (real and reactive powers flow away from the bus), Pi

sch and Qisch

have negative values.

Eqn.5 can be solved for Pi and Qi

The power flow equation is usually expressed in terms of the elements of the bus admittance matrix, Ybus , shown by upper case letters, are Yij = -yij, and the diagonal elements are Yii = ∑ yij. Hence eqn. 6 can be written as

Iterative steps: •Slack bus: both components of the voltage are specified. 2(n-1) equations to be solved iteratively. • Flat voltage start: initial voltage of 1.0+j0 for unknown voltages. • PQ buses: Pi

sch and Qisch are known. with flat voltage start, Eqn. 9 is solved for

real and imaginary components of Voltage. •PV buses: Pi

sch and [Vi] are known. Eqn. 11 is solved for Qik+1 which is then

substituted in Eqn. 9 to solve for Vik+1

However, since [Vi] is specified, only the imaginary part of Vik+1 is retained, and

its real part is selected in order to satisfy

• acceleration factor: the rate of convergence is increased by applying an acceleration factor to the approx. solution obtained from each iteration.

•Iteration is continued until

Once a solution is converged, the net real and reactive powers at the slack bus are computed from Eqns.10 & 11.

Line flows and Line losses

Considering Iij positive in the given direction,

Similarly, considering the line current Iji in the given direction,

The complex power Sij from bus i to j and Sji from bus j to i are


EXAMPLE: For the load flow studies we shall

consider the system of Fig. 4.1, which has 2 generator and

3 load buses. We define bus-1 as the slack bus while

taking bus-5 as the P-V bus. Buses 2, 3 and 4 are P-Q

buses. The line impedances and the line charging

admittances are given in Table 4.1. Based on this data the

Ybus matrix is given in Table 4.2. This matrix is formed

using the same procedure as given in Section 3.1.3. It is to

be noted here that the sources and their internal

impedances are not considered while forming the Ybus

matrix for load flow studies which deal only with the bus

voltages.


Fig. The simple power system used for load flow studies.


Table: Line impedance and line charging data of the system

Line (bus to bus) Impedance Line charging (Y/2)

1-2 0.02 + j0.10 j0.030

1-5 0.05 + j0.25 j0.020

2-3 0.04 + j0.20 j0.025

2-5 0.05 + j0.25 j0.020

3-4 0.05 + j0.25 j0.020

3-5 0.08 + j0.40 j0.010

4-5 0.10 + j0.50 j0.075


Table: Ybus matrix of the system

1 2 3 4 5

1 2.6923 j13.4115

1.9231 + j9.6154

0 0 0.7692 + j3.8462

2 1.9231 + j9.6154

3.6538 j18.1942

0.9615 + j4.8077

0 0.7692 + j3.8462

3 0 0.9615 + j4.8077

2.2115 j11.0027

0.7692 + j3.8462

0.4808 + j2.4038

4 0 0 0.7692 + j3.8462

1.1538 j5.6742

0.3846 + j1.9231

5 0.7692 + j3.8462

0.7692 + j3.8462

0.4808 + j2.4038

0.3846 + j1.9231

2.4038 j11.8942


The bus voltage magnitudes, their angles, the power generated and

consumed at each bus are given in Table. In this table some of the

voltages and their angles are given in boldface letters. This indicates

that these are initial data used for starting the load flow program. The

power and reactive power generated at the slack bus and the reactive

power generated at the P-V bus are unknown. Therefore each of these

quantities are indicated by a dash (). Since we do not need these

quantities for our load flow calculations, their initial estimates are not

required. Also note from Fig. that the slack bus does not contain any

load while the P-V bus 5 has a local load and this is indicated in the

load column.


Table: Bus voltages, power generated and load – initial data.

Bus no. Bus voltage Power generated

Load

Magnitude (pu)

Angle (deg)

P (MW)

Q (MVAr)

P (MW)

P (MVAr)

1 1.05 0 0 0

2 1 0 0 0 96 62

3 1 0 0 0 35 14

4 1 0 0 0 16 8

5 1.02 0 48 24 11


Table: Gauss-Seidel method: bus voltages after 1st

iteration and number of iterations required for

convergence for different values of .

Bus voltages (per unit) after 1st iteration No of iterations for convergence V2 V3 V4 V5

1 0.9927 2.6 0.9883 2.83 0.9968 3.48 1.02 0.89 28

2 0.9874 5.22 0.9766 8.04 0.9918 14.02

1.02 4.39 860

1.8 0.9883 4.7 0.9785 6.8 0.9903 11.12

1.02 3.52 54

1.6 0.9893 4.17 0.9807 5.67 0.9909 8.65 1.02 2.74 24

1.4 0.9903 3.64 0.9831 4.62 0.9926 6.57 1.02 2.05 14

1.2 0.9915 3.11 0.9857 3.68 0.9947 4.87 1.02 1.43 19

LOAD FLOW STUDIES - Aliah University

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