Computer application to load – flow study of the
national 330kv transmission network
(using newton – raphson technique)
1 James agajo 2 Sylvester Ehijie Ezewele 3 Awolo C. I.
Dept. of Electrical and Electronics Engineering
Federal Polytechnic, Auchi,
Edo state Nigeria
Phone: +2348053312732
agajojul@yahoo.com
Abstract
Computer application to Load – flow or power – flow
studies involves the determination of the bus
voltages and their phase angles, actute and reactive
powers of a system. The Newton – Raphson method
as it is used in this project [Load flow studies of the
National 330Kv transmission Network] is based on
Taylor’s series and partial derivatives. And the
Jacobian matrix are formulated using this Newton –
Raphson technique. However, the application of
MATLAB program based on the Newton Raphson
method is used in the computation of the voltages
and the sinusoidal wave form of the three phase
voltages of the 330Kv transmission network is also
analyzed.
Keywords: Voltage ‘V’, phase angle ‘d’, active
power ‘P’, Reactive power ‘Q’.
1.0 INTRODUCTION
Because of large territorial extension of a typical power system, it’s interconnection with neighboring systems and its layered structure, a modern power system can be considered to be composed of several subsystems. Earlier standpoint on power system operation and control was based on underlying assumption of centrality. But a rigidly centralized monitoring and control of a large power system poses many problems load flow analysis or some variation of it has got an extensive use in the operation of modern power system. For an online load flow study, it is necessary to update some of its input data continuously and the output results are also to be used on a real time basis.
For a large power system it means a continuous collection of real time data form various points dispersed in a vast time data from various points dispersed in a vast geographical area, a continuous updating of a large data base and a continuous delivery of its output results to a large number of remote points. All these factors may seriously affect the reliability, speed and practicability of a monitoring and control scheme [1].
If computations for different subsystems of an integrated system are done concurrently using a number of processors, load–flow study can be done in a shorter time. If distributed processing is done in real time, data is to be collected from local points only and a comparatively smaller data base is to be updated locally at regular intervals. Transmission of data over long distance to the central processing computer is reduced when MATLAB is employed. The eastern part of the Nigeria 330Kv grid network consists of Onitsha – Newhaven (96 Km) 330kv transmission line, Onitsha – Alaoji (138km) 330kv transmission line and Alaoji – Afam (25km) 330kv transmission line [4]. The eastern part of the network takes its source from Benin, through the Benin – Onitsha (137km) 330 transmission line this location all in Nigeria. The performance of the transmission line depends on its four parameters; series inductance and resistance, shunt conductance and capacitance. These four parameters are uniform only distributed alone the line.
In a realistic power system, there are large numbers of buses, though; each bus is connected to only a small number of the remaining buses.
In a large power system, there is sparsity due to presents of zero elements. This sparsity help in reducing the bus admittances matrix, that the numbers of elements are minimized. Also, computer memory requirement is minimized, since only non – zero elements are to be stored. This resulted in high-speed computation.
1.1 ECONOMIC IMPORTANCE
Load–flow studies are the essential and vital part of power system studies. Load flow studies are extremely important and essential for power system planning, designing, expansion design and for providing guidelines to power system engineers.
1.3 Importance Of Load – Flow Study In Power System
Load–flow evaluations provides power flow and voltages for a specified capability of generators’ condensers and tap changing under load transformers as well as specified net interchange between individual operating systems.
1.4 Newton – Raphson Method as Applied to Load – Flow Studies
One of the methods applied to load – flow studies, which can easily be programmed and run in a digital computer is the Newton – Raphson techniques. The load – flow problem can be solved by using the Newton – Raphson technique. Among the numerous solution methods available for load flow studies, the Newton – Raphson technique is considered to be the most sophisticated and important. The Newton – Raphson technique is based on Taylor’s series and partial derivatives [3]. The method is recent, involves less number of iterations to reach convergence, takes less computer time, involves less computation cost and has convergence that is certain. The Newton – Raphson technique is very accurate, and it is independent of some factors like:
Swing bus selection
Transformer regulation and
Numbers of iterations.
The number of iterations needed in Newton – Raphson method is almost independent of the size of the power system.
Convergence can be achieved at a shorter time, if the first iteration is done through Gauss – Seidel technique and then use voltage value obtained for starting the Newton – Raphson iterations. These voltages obtained are used to evaluate active power (P) of every bus except the slack bus and also reactive power (Q) wherever reactive power is specified. The correction of bus voltage is determined by the difference between calculated and specified values. The process of iteration is continued till the difference in the specified and calculated values of the active power, reaction power and voltage magnitude are within the given permissible limit.
In Newton – Raphson technique, partial derivatives of second and higher order are neglected, this assumption requires the initial solution to be close to the final solution [2].
1.5 BUS CLASSIFICATION IN LOAD FLOW STUDIES
In load – flow studies, four quantities are associated with each bus, the four quantities are; active power (P), reactive power (Q), voltage magnitude /V/, and phase angle (d). In a load–flow problem, two of the four quantities are specified and the bus classification depends on the type of quantities specified at each bus. Base on the type of quantities specified, three types of buses are classified. They are;
1.5.1 Generation Bus
1.5.2 Slack or Swing Bus
The summary of the above discussion is given in the table below;
Table 1.1: Bus classification
TYPE OF BUS
SPECIFIED QUANTITIES
UNKNOWN
Generation Bus
P, /V/
Q, d
Load Bus
P, Q
/V/, d
Slack Bus
/V/, d
P, Q
2.0 LOAD–FLOW EQUATIONS BASED ON NEWTON – RAPHSON
TECHNIQUE
Newton – Raphson method can be applied to load – flow problems in a number of ways. The most common is those that uses polar co – ordinates and rectangular coordinates. In practice, Newton – Raphson method using polar coordinates is used. This is because the use of polar form results in a smaller number of equations than the total numbers of equations involves in rectangular form [6]. In this project, only the polar coordinate form will be discussed.
2.1 NEWTON – RAPHSON TECHNIQUE USING POLAR
COORDINATES
When the bus voltages are expressed in polar form, Newton – Raphson technique can be applied to the load flow problem.
For any ith bus,
Vi = Vi ejdi – - – - – - – - (2.1)
Taking the complex conjugate of equation 3.1, gives
Vi* = Vie-jdi – - – - – - - (2.2)
Vk = Vk ejdk – - – - – - (2.3)
yik = yik e-jqik – - – - - (2.4)
Where d is the phase angle of the bus voltage and θik is admittance angle.
The complex conjugate of the power injected by the generating source is given as;
Si = Pi – j Qi = Vi S yik Vk – - – - - (2.5)
Substituting the values of equations 3.2, 3.3, and 3.4 into equation 3.5 gives
Pi – j Qi = S Vi Vk yik e-j(θik + dI – dk) – - – - – (2.6)
Thus,
Pi = S Vi Vk yik Cos (θik + di + dk ) – - – - – (2.7)
And,
Q = S Vi Vk yik Sin (θik + di – dk) – - – - (2.8)
For n = 2, 3, 4 – - – - n and slack bus is bus 1
The off – diagonal elements are
pi = Vi Vk yik Sin (θik + di – dk) for J1 – - – - – - (2.9
dk
pi = Vi yik Cos (θik + di – dk) for J2 – - - – - (2.10)
Qi = Vi Vk yik Cos (θik + di – dk) for J3 – - - – - (2.11)
Qi = Vi yik Sin (θik + di – dk) for J4 – - - – - (2.12)
The diagonal element are:
pi = S Vi Vk yik Sin (θik + di – dk) for J1 – - – - (2.13)di
pi = 2Vi yii Cos θii + S Vk yik Cos (θik + di – dk) for J2
Vi – - – - (2.14)Qi = S Vi Vk yik Cos (θik + di – dk) for J3 – - - - (2.15)
pi = 2Vi yii Sin θii + S Vk yik Sin (θik + di – dk) for J4,
Vi - – - – - - - (2.16)
2.2 APPLICATION OF NEWTON – RAPHSON METHOD TO LOAD FLOW STUDIES OF THE EASTERN PART OF THE NATIONAL 330KV TRANSMISSION NETWORK
The eastern part of the national 330kv transmission network consists of Onitsha, Newhaven, Alaoji and Afam. For the purpose of this study, Afam (22) is taken as slack bus and given code as Bus 1, Alaoji (18) is taken as Bus 2, Onitsha (17) as Bus 3 and Newhaven (14) as Bus 4. The bus data for the system is given as
Bus Code
Pa
Qa
/V/
d
PL
QL
Bus Type
1
4.51
0.00
1.03
0.00
0.44
0.21
Swing
2
0.00
0.00
1.00
0.00
2.76
1.34
Load
3
0.00
0.00
1.00
0.00
1.52
0.73
Load
4
0.00
0.00
1.00
0.00
1.32
0.64
Load
Table 2.0 Bus DataThe line admittance is given in the table below:
Bus Number
X(PU)
R(PU)
Z = R + jx
y = 1/z
1 – 2
0.0035
0.0005
0.0005 + j0.0035
40 – j280
2 – 3
0.419
0.0049
0.0049 + j0.0419
2.8 – j24
3 – 4
0.0296
0.0034
0.0034 + j0.0419
1.9 – j25
Table 2.1 Line Data The Mutual – Admittances are computed as follows
y12 = y21 = -40 + j280
y23 = y32 = -28 + j24
y34 = y43 = -1.9 + j25
The Self – Admittances are computed as follows
y11 = 40 – j280
y22 = y12 + y23 = 40 – j280 + 2.8 – j24 = 42.8 – j304
y33 = y23 + y34
y44 = 1.9 – j25
From equation 4.8
Q02 = -V V1 V21 Sin (q21 + d - d ) – V V23 Sin
(θ23 + d - d ) – (V ) y22 Sin q22
= -1.0 x 1.03 x 283 Sin 98 – 1.0 x 1.0 x 37 Sin 139
-12 x 307 sin (-82)= -288.7 – 2.4.3 + 304 = -9
D Q = 2.76 – (-9) = 11.76
Q = -V V2 y32 sin (q32 + d – d ) – V V4 y34 Sin
(q34 + d – d ) – (V )2 y33 Sin q33
= -1 x 1 x 37 Sin 139 – 1 x 1 x 25 Sin 95 – 12 x 49 Sin (-85)
= -24.3 – 25 + 48.8 = 0.5 Q = 0.73 – (-0.5) = 1.23
Q = -V V3 y43 Sin (q43 + d – d ) – (V )2 y44 Sin q44
= -1 x 1 x 25 Sin 95 – 12 x 25 Sin (-85)= -24.9 + 24.9 = 0
D Q = 0.64 + 0 = 0.64
Therefore,
D V = 0.00368 x 11.76 – 0.00373 x 1.23 + 0.00373 x 0.64 = 0.04
D V = -0.00373 x 11.76 + 0.0458 x 123 – 0.0458 x 0.64= 0.017
D V = 000373 x 11.76 – 0.0458 x 1.23 + 0.0859 x 0.64
= 0.04
Hence,V = V + D V = 1.00 + 0.04 = 1.04 Pu
V = V + D V = 1.00 – 0.017 = 0.983 pu
V = V + D V = 1.00 + 0.04 = 1.04 pu
3.0 SYSTEM IMPLEMENTATION
Since we are determining the magnitude of voltages, partial derivatives of the reactive power with respect to voltage magnitude is considered when formulating the Jacobian’s – Matrix. This is so because the flow of reactive power (Q) is not much affected by the changes in the phase angle (d), but affected by the variation in magnitude of bus voltage (DV).
The elements of Jocobian’s matrix are formulated with latest voltages given and computed power (reactive). However, manual computation of load – flow done using Newton – Raphson method is very complex and it very easy and simple. This is shown in Appendix one, which is the MATLAB code that generates computed voltages. The MATLAB program for Newton – Raphson is simpler and contains few lines when compared with MATLAB program for Gauss – Seidel method.
The sinusoidal wave form of the three phase voltage of the 330Kv transmission network is analyzed in appendix two, using MATLAB subplot command.
The beauty of the work – done is the fast convergences of computed values.
Finally, the values obtained when MATLAB is used are in accordance with the once obtained using numerical analysis (Newton – Raphson Technique in polar coordinates to show the bus voltage angles). These values converge with the specified values from PHCN data book, see appendix.
4.0 CONCLUSION AND
Load – flow studies is extremely important and essential in power system analysis. It provides (1) guide line to power system engineers and acts as operating instructor to generating station and substation for relay settings, switching sequence, loading, tap – setting etc.
Informations obtained from load flow studies are used in analyzing the effect of temporary loss of generating station or transmission path on the power flow. Also it help in preparing software for on line operation, control and monitoring of power system.
When digital computers are employed in load – flow studies, it is important to use the Newton – Raphson method.
RECOMMENDATIONS
i. Accurate and effective load – flow studies should be done to provide required information for power system operation.
ii. The initial solution for the values obtained should not be very for from the actual solution.
iii. The Newton – Raphson method should be analyze by using computer program such as MATLAB.
REFERENCE
[1] Gupta, J.B. A Course in Power Systems, Tenth Edition, S.K. Kataria & Sons, 2006.
[2] Gupta, B.R. Power System Analysis and Design, Second Edition, Whereler Puplishing 1997.
[3] Stevenso, William D, Elemement of Power System Analysis, Second Edition, Mchraw Hill Book Company, New York, 1962.
[4] Anazia, E. Lecture Note on Power System analysis.
[5] www. Weley. Com
[6] Suml S. Rao, Switchgear Protection and Power Systems, Eleventh Edition, Khanna Publishers, 2004.
[7] www. Synergetix. Com/tech/source book/material.
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