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Power is taken from transmission substationand fed to consumers through sub-transmission substations.

Distribution system will supply power to theconsumers depending on theirrequirements.

Distribution Substations will havetransformers, switch gear, metering andmeasuring equipment.

Distribution system study includes planningand design of feeders with optimal locationsof substations.

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Minimum length of line.Lowest line voltage drop.Lowest line losses.Location for easy maintenance.Minimum overall cost.Modeling and analysis.

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A distribution feeder provides service tounbalanced three-phase and single-phaseloads over un-transposed three-phase andsingle phase line segments.

This combination leads to three-phase linecurrents and line voltages being unbalanced.

In order to analyze these conditions asprecisely as possible, it will be necessary tomodel all three phases of the feederaccurately.

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When this is the case, some approximatemethods of modeling and analysis can beemployed.

All of the approximate methods of modelingand analysis will assume perfectly balancedthree-phase systems.

It will be assumed that all loads arebalanced three-phase, and all line segmentswill be three-phase and perfectlytransposed.

With these assumptions, a single line-to-neutral equivalent circuit for the feeder willbe used.

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The primary task is to determine the ratings of thefeeders and the substation.

The ideal location of a substation is at the centre ofthe network and all the feeders connected directly toit along radial lines as shown in Figure 9.1 below.

However, this arrangement is not possible inpractice.

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FIGURE 9.1:Ideal distribution of circular area.

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In most cases, the location of substation andfeeder arrangement is done such that

It satisfies the voltage regulation requirement atthe farthest load point.

Substation is as closer to the load center of the areato be served as possible.

Future expansion is possible when more load isadded.

Alternate feeder supply is possible in case offeeder failure.

Feeders are usually located along the road side foreasy maintenance and repair.

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A line-to-neutral equivalent circuit of a three-phase line segmentserving a balanced three-phase load is shown in Figure 9.2.

Kirchhoff’s voltage law applied to the circuit of Figure 9.2 gives:

IjXRVV LS (9.1)

FIGURE 9.2: Line-to-neutral equivalent circuit.

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The phasor diagram for Equation 9.1 is shown in Figure 9.3.

In Figure 9.3, the phasor for the voltage drop through the lineresistance (RI) is shown in phase with the current phasor, and thephasor for the voltage drop through the reactance is shown leading thecurrent phasor by 90 degrees.

The dashed lines represent the real and imaginary parts of theimpedance (ZI) drop. The voltage drop down the line is defined as thedifference between the magnitudes of the source and the load voltages.

Figure 9.3. Phasor diagram.

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The angle between the source voltage and theload voltage (δ) is very small.Because of that, the voltage drop between thesource and load voltage is approximately equalto the real part of the impedance drop.That is

(9.2) LL XRI sincos

IZVdrop .Re

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TP-9.1:Consider a line segment of a feeder line. Thesending end node is N1 and the receiving endnode is N2. The impedance of the line segment ofa feeder is Z12 = 0.2841 + j0.5682 Ω. The currentflowing through the line segment is I12 =43.0093/–25.8419 A. The voltage at node N1 is V1= 2400/0.0 V. Calculate the voltage drop betweenthe nodes.

The load connected to a feeder can be in any manner asshown in Figure: 9.4.

The load points can be at any distance L1, L2,L3, etc. from thesubstation feeding point with load current I1, I2 , I3 , etc.

The voltage drop calculations will be difficult in this case.

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Figure 9.4. Feeder line loading.

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To make the feeder load analysis simple,the feeder lines are analyzed withfollowing four ideal load models.

Load at end of the line. Load uniformly distributed.Uniformly increasing load.Uniformly decreasing load.

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Feeder with load at the end. Feeder with uniformly distributed load.

Feeder with uniformly increasing load Feeder with uniformly decreasing load

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A line-end load is one when a feeder supplies asingle load long distance away from thesubstation as illustrated by the following Figure9.5.

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Figure 9.5. Feeder with load at the end.

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Figure 9.5. Feeder with load at the end.

phz /Impedance per unit length

Total Impedance zLZ

Voltage Drop IzLVD

Power loss per phase RIrLIPr22

(9.3)

(9.4)

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Uniform loading is one when loads are connected atevery pole like street lights, residential houses etc.

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Figure 9.6. Feeder with uniformly distributed load.

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iLI

zdxixVL

D 0

If total current is ‘I’ and ‘i’is current per unit length

Consider a length ‘x’ from the beginning of the feeder.The current up to a point ‘x’ is ‘ix’Therefore the voltage drop in a length ‘dx’ at that pointis (ix)(zdx)The total voltage drop over the entire length ‘L’ is

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dxxizVL

D 0

2/IzLVD (9.5)

Comparing Equation (9.5) with Equation (9.3), we can see that the dropacross the feeder with uniformly distributed load is half of the drop iffeeder is loaded at the end point.

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2LizVD

But total current ‘I’ is ‘iL’

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L

r rdxixP0

2

Power Loss in the line

The power loss due to the current in any section ‘dx’ at adistance ‘x’ from the sending end is dPr=(ix)2rdx where ‘r’is resistance of the conductor per unit length.

Therefore the total power loss is

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Power Loss in the line

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22 RIrLIPr (9.6)

But total current ‘I’ is ‘iL’

L

r dxxriP0

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3

32rLiPr

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22 RIrLIPr (9.6)

The total voltage drop in uniformly distributed load is halfcompared to Load at the end of the feeder.

The total power loss is 1/3 in uniformly distributed load ishalf compared to Load at the end of the feeder.

In other words, the load were to be assumed to beconnected at 1/3 of the distance from sending end.

2/IzLVD (9.5)IzLVD (9.3)

RIrLIPr22 (9.4)

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Feeder with uniformly increasing load isshown in Figure 9.7 below

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Figure 9.7. Feeder with uniformly increasing load

Feeder with uniformly decreasing load is shownin Figure 9.8 below.

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Figure 9.8. Feeder with uniformly decreasing load

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