International Journal of Scientific & Engineering Research, Volume 5, Issue 4, April-2014 1130

ISSN 2229-5518

Solving the Problem of Mismatched Loads in High Voltage Networks Applying Power Circle Diagram Technique

Assistant Professor Mohammed Sabri A. Raheem *

ABSTRACT: This paper deals mainly with the problem of mismatched loads with the power networks and to discuss the solution for this problem by the insertion of reactive power at the receiving end terminal. The process is basically calculated applying the Receiving End Power Diagram Analysis method , which gives an easier & faster calculating process ,also a computer program is constructed to perform the calculation and selection process. The network condition ,taken as a case study example load, can be changed and the calculation process is performed ,hence the results will be discussed for each system parameters

KEY W ORDS: Power Factor Improvement, Reactive Power Injection , Power Circle Diagram , T.L. General Parameters .

Delivering electric energy to loads, especially at peak loads periods, forms a challenge task to the electric utility control [1]

. The problem arises when there is a mismatching in the

parameters between sending, receiving end network terminals, for which a T.L. forms the electric media for the power transmission [2] .

The power circle diagram technique gives simple solution

methodology that relates send. ,T.L. & receiving end parts of the network, hence presenting a locus diagram that assists the utility engineer in correcting the problems arises during The network operating conditions , especially on different load fluctuations [3] .

The task here seems to be similar to the criteria of power factor correction, by adding reactive power to the network, but here the aim is to locate the receiving end load point on the locus of the power circle diagram & solve the mismatching problem rather than adding reactive power to improve the p.f. [4,5].

* Assist. Prof. Mohammed Sabri is working at the College of Electrical & Electronic Techniques , Foundation Of Technical Education β Baghdad β Iraq .

E Mail. mohsab2008@gmail.com

Moreover for the network shown in figure (1A) ,& of the voltage phasor of figure (1B), the electric power system voltage equations are :[6]

π½π = π¨ π½π + π© π°π ------ ( 1 )

Converting the system of eq. (1) above to a power equation

yields to the form of equation (2),below

π·ππππ = (π½πβπ½π) πππ(π· β Π±) β οΏ½π¨ π½ππ /π©οΏ½ πππ(π· β πΆ) ----------

π©

- ( 2 )

From this equation it is possible to draw the power circle diagram for the case of network conditions of equations (1) & (2) and as shown in figure (2) below .

From what is shown in figure (2) & equation (2) above , it can

be noted that the operating torque angle (Ξ΄) is calculated from equation (3) below & to be compared with that found from figure (2) above :

πππβποΏ½π·ππππ + π¨π½ππ πππ(π·βπΆ)οΏ½

πΉ = π· β -------- ( 3 )

π½ππ½π/π©

The power circle diagram technique is initialized taking the case of the network shown in fig. (1A) ,and for a load condition of a lagging p.f. load.

The T.L. is to be represented by its general matrix

(A,B,C,D) parameters for which the voltage phasor diagram is shown in fig(1B).

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Figure (1) Power Network System

It is noted also from above that if the load point does not locate on the power circle diagram locus , there will be a need to insert a reactive power at the receiving end (inductive or capacitive) to force the load point to be moved vertically, hence located on the locus , as in Fig.(3) , with an additional reactive power ( Qadd. )

as in equation (4) below :

πΈππ π . = πΈπΉππ. β πΈπ³ππππ ------------- ( 4 )

Where :

Qadd | , | the additional reactive power . |

QRec. | , | = Received = = . |

QLocus | , | the locus point reactive power . |

Where :

For a case study to be considered as a power system

respectively

condition , the power network parameters are as below :

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ISSN 2229-5518

& for a constant **lagging p.f. load of 0.866 **.

For the network data above two solution methods had

a) For a comparative purposes the same torque angles (Π±) is taken as an input data, more over & for the network data given (Π±) can be calculated applying equation (5) ,

βπ

been carried out & the solutions are compared, the **TWO**

solution procedures are :

πΉ = ππ β πππ

(π·ππππ + ππ.π πππ ππ)

ππ.π

------- ( 5 )

3-1 : POWER CIRCLE DIAGRAM DRAWING METHDOLOGY

According to figure (2) , a load active power of ( 1 GW β 10

GW ) at a constant lagging p.f. of (0.866) , ,leads to the data obtained in Table (1) , and the condition of the operating point shows the need for adding reactive power according to the power locus

& the power factor line alignments :

b) From equation (2) above , the locus active power is calculated (PR ) , then the reactive power is calculated for a

0.866 lagging p.f. load.

c) The calculated reactive power is compared with that of power locus diagram ( QLocus ).

d) If the TWO reactive powers does not coincide , there will be

a need for reactive power injection , of values of ( QLocus β Q

R ) .

The above algorithm results are listed in Table (2) below & the differences between the TWO solution methodologies can be noticed. The majority of the differences of results comes from the choice of the

drawing scale & of course the accuracy in the eq.

calculations methodology.

3-3 : THE COMPUTER PROGRAM FLOW CHART

The flow chart of the computer program is shown in figure (4) below. Assuming the followings ,just for calculations & case study comparative purposes :

a) The power factor , load condition & the active power values .

b) The torque angles (Π±) is as found in the power circle diagram drawing method & hence taken to be the values of the system operating torque angles .

What is noted from this flow chart , the followings :

1 ) The main statement deciding the type of additional reactive power is as in equation ( 6 ):

3-2 : COMPUTER PROGRAM SOLUTION METHDOLOGY

As an alternative & more accurate solution method is carried out , a computer program is constructed to

calculate the necessary network parameters as given in the

algorithm below :

πΈ π¨π π πππππππ = πΈ πΉππ.π¬ππ β πΈ π³ππππ ------- ( 6 )

Where the conditions are :

a- Adding Inductive Reactive Power for the case of

QAdditional Negative .

b- Adding Capacitive Reactive Power For the case of QAdditional Positive .

c- The Rec. End Load point Coincide with the Power

Locus Point ( QAdditional =Zero ) .

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2) The construction of the computer program presents

a more accurate methodology for choosing the proper additional reactive power to match the load & the T.L.

system.

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Two comparable methods had been presented to solve the problem of mismatching of the electric load with the network parameters .

The solution method based on the construction of the power circle diagram .

The two solution approaches are mainly :

1 ) The drawing of the power circle diagram & find the necessary data from the drawing where the effect of the drawing scale & angles measurement affects directly the accuracy of the data obtained , but gives a fast & easy solution method ( data of Table ( 1 ) ).

2 ) The equations ( that are necessary to construct

the circle diagram ) are used , with necessary assumptions , to construct the computer program calculation method giving a more accurate way to find the solution results , data of Table ( 2 ) , .

What forms the dominant factor for both methods is the

operating torque angle , that is found from the drawing method & forms the basic operating torque angles for the computer program method. This is set just to show a basic comparison & solution calculation methodology.

The solution approach presented in the paper had been

performed for two-port network ,namely, sending & receiving end terminals . For other networks the approach should be little modified to fit the other networks

formulations.

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, Third Edition, 2002 .

2 β B.R.Gupta ,βPower System Analysis & Design

β,S.Chand & Company Ltd ., Fifth Revised Edition ,2008 .

3- Chard F. de la C., "Transmission-line estimations by combined power circle diagrams", Proceedings of the IEE

- Part IV : Institution Monographs , vol.101, no.7,

pp.204,208, August 1954 .

4 β M.S. A.Raheem , βOptimal Reactive Power Insertion

& Allocation To The Iraqi Super Grid 400 Kv Network Applying Genetic Algorithm Technology β , International Journal of & Scientific Engineering Research, IJSER , Vol. 4 , Issue 12, December-2013 .

5 - A. M. Sharaf and S. T. Ibrahim, βOptimal Capacitor Placement in Distribution networks", Electric Power System Research, no. 37, pp. 181β187

, 1996.

6 β M. S .A .Raheem , β Transmission & Distribution Lecture Notes β , Electric Power Techniques Dept . , College Of Electric & Electronic Techniques , Baghdad β Iraq , 2013 .

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