METHODOLOGY OF LOSS A~ALYSIS

Y mn /Ymm

5.2 LOSS ANALYSIS

5.2.2 METHODOLOGY OF LOSS A~ALYSIS

Load flow calculation on any system for various loads shows that losses are a function of load, system configuration and conductor impedences.

Therefore, the COlIHOOnapproximation of losses being proportional to load current squared is modified to incorporate all of the above mentioned variables.

Certain assumptions are considered ln the following analysis

i) All the power supplying the load 8, flows through the branches connecting the supply buses and level one buses. All the power supplying the load S, .flol-ls through the branches connecting level one and level two buses, and so on.

ii) Voltages of all buses at ¹¹ particular level are equal; therefore all branches connecting two particular levels can be assumed to be in parallel.

This assumption is obviously more correct when several links exist.

The parallel combination of branches connecting the supply buses and level one buses will be called Z,. The parallel combination connecting levels one and

two will be called

Z.,

and so on.

•

F'"OIll I'i,~.!).I,

ZI_.., 22-5 ZZ-6 23-6 Z, = ---

21-01 22-5 Z2-6 + 21.-4.22-5 Z:i-6 + 21-4 Z2-6,Z3-6

+ Z2-5 Z2-6 ZJ-6 ---

(5.1)

l1,e power loss belween any two bus level.. lhen is the real part of the combinedp"r'dllel impedence.. Limes the magnitude of the current - flowing in that imlK,dence••quared. 'Il,e nngnitude of current flowing in the impedence Zi is ini Hally approximated as

11; I ^{= ---}

Vi - ^I

wher'e, Vi^-1 is the voltage at bus level ]-1.

'Il,e voll,.ge at eill,h hus lcv"'. call Ix-, determ] ned by taking all average of the supply bus vol tages and usi ng thai, average as the voitage of all supply hUH""and as reference. ^'Ih,; supply bw; voll.age is llSSlDDed. to' remain nearly constant under varying load and can be determined from a single load flow or hou['ly metc,red data. 11,e volb,ges al. oU,er bus levels can be calculated from voltage droJls al,;ng ",,,ch impedence Z; . For example, from fig •. 5.I,

,

VbuSl + VbuS2 + VbUR3

= ---1-0.

V, = Vo

z,

(SI/VO)'/Io

=

Supply bus voltage.

--- (5.2) --- (5.3)

V2 = V, - Z2 (S2/V,)'" ---~--- (5.4)

and so on, where

*

means complex conj\J.l~ate'.

5.5

The power loss on any parallel branch combination between two levels i-I and i can nowbe calculated.

1';

=

Real(Z; )

I

^{Si /V.}

^_'1 ²

The total power loss at each load level can nowbe estimated as

PI.

=

^P, ⁺ ^P2 ⁺ ^P3 ⁺

----~---

2. 2.

2 =

Real(z.)]SI!V'oi 'I- Real(Z,) \S2/V1\ + Real(Z,)1~3/V21

+ ---

(5.5)

The total power loss is calculated as a function of system impedencesand configur-cltion, the -voltage at the supply bus, and the complexpower consUIlled at the various bus levels at each load level. With the possible exception of the complex power values, these quantities are readily accessible. If the metered data of complex powerat euch bus level is aV"dilable, then the method gi ves accurclte fib'Ure of power loss. But where metered data is not aV"ailable, it is assumed that each bus level load is the same percentage of the total subsystem load at various load levels and that the ratio of real(S; ) to imagi- nary (Si ) is constant at various load levels, then the values of Si can be determined.

Difficult case arises whenthere are loads distributed along the feeder.

Simplifying assumptions are madein this case. For instance, if the load can be considered as being uniformly distributed along the feeder, the losses are the same as if the total load were concentrated at a point one third of the wayout on the feeder. This mathematically correct for a very large numberof

9 9

2J ⁹ 6

[5r J_-,

L,-'

I !

loads (Appendix -F). TIds ,md other simplifications are shoWnin fig.5.2..'~-'-""•.'''.''"~__._ _

I

J l

- ~~: .--"tt

~....--r:;',~__,..J

Fj~.5.2 I\sstnnpt-jOTlH I"<>rdiHLr-j,but.ed 1uMleoncentret:.ed

loads.

.

^' ^"

!fowl.,ver", for a sn.dl numl.~rof distributed loads the error may be large and the loss in each section l.,tween loads should be calculated. Whenthe load call I., divided into a /lIllnlx".'of large concentrated loads distributed along the line",. the line is divided into the sections between loads, and the I2R 10SB or .. each section is calculab-~d eonsiderir~ each section as a se~rate bus lcvel.

" .:l SAMPLE CALCULATION OF r~)wJo:H---IDSS

Case -]; 3:J KV sYHLc~mund{.~r Ila..srulbad J32/33 KV grid suhstation.

'11",) Si Ilgl" .Ii",; diagram of :J:J KVsystem under IImmabud 132/33 KVBubsta- Lion is shown in fig.5.:l. '11", system consist of 5 buses,'! branches and 1 link.

'11", I."" Ullit ,impeden"e of each Une is gi ven in table 5.1 on a 100 MVAbase.

5.7

. I

!

SIDOHIRGONJ MIRPUR

HASNABAO

35/50/55 MVA

132 KV

35/50/55 MVA

6 KM

2 KM

10/.141/6.

MVA 7.1 KM

10/14/16.5 MVA 11 KV

10/14' MVA h1 KV

5.5 KM

2 x 10/14 MVA 11 KV

"---v---'"'

Dog. Co

9.1 KM

MIRKAOIM

@

2 x 10/14 MVA 11 kv

Fig. 5.3 33 KV System Under Hasnabad 132/33 KV Grid Substation.

5.8

'I'l,,, load nn p.ach lnm at ti,e L.1I11Cof local Ix"l!< (metp.red data ) for the finan- ci.al Y""U' l!lB5-1l6 aml I!JBG,'B7 ^'H'C given. in table 5.2 and table 5.3 reslx~,l.iv,,1.y. The voltage on th" supply lnlS. which is represented as one ^bus, at t.h(~time of l,x;al l>ell!<is 0.!H8 per unit for the year 1985-86 and 0.94 per unit. for the year 1986-87. The power factor for both the cases are 0.85 and 0.!l1 reslx,cLi ve.1.y.

Table 5.1 1,ine'imp,,,,knce (p.u.)

---

z

1-2 O.Wi(;!;:l+ jO.0!l55li 1-:\ O.O:J7GIl+ jO. ()!i701 1-1 O. 1:J:171l+ jO.20250

:1-1 O. 10:1(i:1+ ^{jO. 15(;HG} ^'_~^.

11-5 0.2!i195 + jO.30551

Table 5.2 Bus loading at peak load (p.u.) .lulyB5-.Junc86; 1Dca1 peak 3.8.85 20:00 !lours.

/\ ().1900 + jO.]1775

n

O. 1:lfiO+ jO.OB12!l

C 0.1112 + jO.01l937

]) 0,.0971 + jO.0602

E O.OG95+ jO.01307

'5.9

'.I,

Table 5.3 Bus loading at peak load (p.li.)

July86-June87 ; local peak 29.10.86 19:00 Hours.

Magnitude

A 0.2262 + jO.14611

B 0.1738 + jO.11226

C 0.1174 + jO.07583

D 0.0977 + jO.06311

E 0.0766 + jO.04948

Calculation for FY 1985-86 Using,equation (5.1),

(0.05f;5:l+jO.0855fi)(0.037fi8fi+jO.(5704) (0. 13:1785+jO. 2025)

z,

= --- _

(O.05653+jO.OB556)+(0.037686+jO.05704)+(O.133785+jO.2025)

=

0.0350134 56.312

=

O.01942+jO.029134

=

O.25495+jO.305506 8,

=

0.5673+jO.3516 using equation (5.2),

=

^0.848

5 •.10

in

.\:

, '\'

.1 ,'.

Using equation (5.3),

v,

⁼ Vo - 2, (8, IVo )

=

0.848+jO.0-(0.0350134 56.312)(0.5673-jO.3561)/0.848

=

^0.823 ^-0.796

Now,using equation (5.5),

Total Loss

=

^p, ⁺ ^p,

=

(0.01942) (0.5673+jO.3616)/0.848 0

+ (0.25495) (0.0971+jO.06021/0.82432 -0.753

=

0.1,203 + 0.004913

=

0.016943 P.U.

::: .L.694:3 HW(2.~)% of power despatch into 33 h.v system)

In a similar wuy,power loss for the FY 1986-87 ^1S 2.52% of power at 33 KV bus.

i'

Case-II 33 KV system under NewMirpur 132/33 KVgrid substation.

The single line diagram of 33 Kv system under NewMirpur 132/33 KV sub- ststion is shown in fig. 5.4. The system consists of 6 buses and 5 branches.

METHODOLOGY OF LOSS A~ALYSIS

Y mn /Ymm

5.2 LOSS ANALYSIS

5.2.2 METHODOLOGY OF LOSS A~ALYSIS

Z.,

(5.1)

11; I = ---

,

= ---1-0.

z,

=

--- (5.2) --- (5.3)

*

5.5

=

I

_'1 2

=

----~---

2

=

(5.5)

9 9

2J 9 6

[5r J_-,

L,-'

I !

I

J l

- ~~: .--"tt

.

5.7

!

"---v---'"'

@

5.8

z

n

'5.9

Magnitude

z,

=

=

=

=

=

in

v,

=

=

=

=

=

=

i'

--..- ~----

POSTAGOLA TQNGI

NEW>MIRPUR . 132 KV,

50 MVA 50 MVA

3.8 KM 7 KM

11; I ^{= ---}

^_'1 ²

2J ⁹ 6