Indi an Journ al of Enginee ring & Materi als Sciences Vol. 9, August 2002, pp. 260-264

Determination of bus security governed by sensitivity indicator in a reactive power constraint longitudinal power supply (LPS) system

C K Chandaa, Sun ita Del, A Chakrabarti'· & A K Mukhopadhyay'

"Department of Electrica l Eng ineering, Bengal Eng ineering College (Deemed University), Botanic Garden, Howrah 711 103, India

bDepartment of Electrical Engi neering, Jadavpur University, Ko lkata 700032, Indi a CDepartment of Applied Physics, Uni ver ity College of Techno logy, Ca lcutta Uni vers ity. Kolkata 700 009, Indi a

Received 19 February 2001; accepted 15 April 2002

Degree of weakness o f a bus in a longitudinal power supply (LPS) system, governed by the react ive power sensiti vity of the concerned bus being investigated, simulati ons have been performed in order to exhibit the va ri ation of real and reacti ve power sensiti vity with respect to bus vo ltages fo r vari ations in load levels of that bus. The effects of S tatic Var Compensator (SVC) application in capaci ti ve as well as in induct ive modes of operation on the bus power sensitivities, the variation in corresponding margins of bus power sensiti vities, as well as on bus voltage magnitudes are reported here.

The voltage collapse In EHV system power transmiss ion system is the upshoot of complex phenomena and depends on a vast number of parameters. This collapse is often assoc iated with cascade of unforeseen events leading to steady state voltage instabilit/ 3

. Literature survey simulating these events confirms that the full prefault demand can not be sustaine.d on the depleted power system4

•

The development of analytical methods for problem of voltage instabi lity and voltage collapse is being investigated for the last two decades. The achievements lie in the domain of static model5 as well as on dynamic voltage collapse models6

. These models predict th (~ proximity of the sys tem near critical state and determine the reactive reserves, etc . However, it is not usually explored about the margin or proximity to the stability limit that is of concern to any system operator. ]n the operation of LPS system, it is pertinent to investigate the voltage stability

. d I 47 margIns an resu ts ..

It is a usual practice that singularity of the Jacobian . fl ' d' . . I f I 8 9 II 13-In power ow In Icates cntlca state 0 vo tage' . . 15. It is also recognized that security assessment has to include an estimation of the proximity of the voltage stability limit for a g iven load condition. It indicates a first hand assessment of a ri sk of voltage instabilit/ . Voltage stability problem can be effecti ve ly tackled by the inherent robustness of the sys tem l 2

, which manifests some resistance to voltage collapse.

*For correspondence

The paper highlights the ro le of security of a power system bus once its degree of weakness is di agnosed. The security assessment has been proposed based on the magnitude of bus real and reactive power sensitivity wi th voltage. A typical LPS system has been simulated to detect the weakest bus first usi ng sensitivity parameter from the power flow technique. Graphical profiles of bus sensitivity and voltage with respect to real and reactive power variations have been exhibited under different operating conditions taking into account the presence of SVc.

Theory

The bas ic equations used in Newton-Raphson load flow method are:

. .. ( I )

.. . (2)

Ivl - Ivl [I + ~Ivil /lelY - old lVI

... (3)

CHANDA el al.: BUS SECUR ITY GOVERNED BY REACTIV E POWER SENSITIVITY IN LPS SYSTEM 26 1

Here the Jacobian is:

rap v ap j

[J]= a8 Ilarvr =[J/ aQ Ivl~ 13

Lao alvl

12] J4

... (4)

To obtain real and react ive power sensitivity the basic load fl ow equation becomes:

... (5)

Hence, the real and reactive power sensitivity of i-th bus are obtained as:

:1:;1 = [J2Jx lv;1

~I~;I = [J 4JX Iv;1

. .. (6)

Eq. (6) represents the real and reactive power

sensitivities of the i-th bus. CJIQ;I a lso indicates the CJV;

CJQ; degree of weakness for the i-th bus as being

CJlv ;1

CJlvl high, --' becomes low indicating minimum change

CJQ;

in Iv ;1 for variation In Q-status of the bus . Thus,

°IQ;1 being higher, the degree of weakness of the i-th OV ;

bus becomes lesser.

Simulation A sample 6-bus, 8-lines interconnected

transmiss ion line model, typically similar to that of a sub-grid in LPS systems (Fig. 1) has been considered in order to validate the developed concept. Table I indicates the p.u . impedances and line charging susceptances of the system.

Analysis of the Jacobian elements has been performed using Newton-Raphson load flow technique; the weakest bus has been detected by observing the magnitude of dQldV for the respective bus (for weakest bus, this value being the minimum).

The fl owchart of the load fl ow method is shown in (Fig. 2).

Testing of weak ness for the buses has been conducted in the simul ated system and the results reveal bus number 6 is the weakes t, and bus number 5 is second in line of degree of weakness for the simulated sys tem: However, it is interes ting to note that at simulated load leve l, the voltage of bus nu mber 6 is better than bus number 5 . This is contrary to the conventional concept that weak bus is diagnosed by lower voltage level. Actual ly, some researches7

.9

.lo

have shown the same concept and opted for checking the Jacobi an against reac ti ve power sensiti vity with respect to bus voltage in order to determine the degree of weakness of a bus , as done in this paper.

Bus number 6 being diagnosed as the weakest bus, the real power sensitivity margins have been obtained for real load increase in the same bus at different power factors , assuming thi s bus to be a reacti ve power constraint bus (Fig. 3a) . With higher load levels, the sensitivity decreases and the critical stability limits are obtained at points 'a', ' b' and 'c' on the respective graph. The voltage magnitude profiles at simulated power factors for corresponding

Table I-Impedances and line charging for six-bus test system

Bus-code Line Line charging Off-nominal p-q impedance Y,,,(2 tap ratio of

Zpq tra nsformer

1-3 0.04+)0.30 )0.010 2-3 0.03+)0.20 jO.OIO 3-4 0.04+)0.20 )0.010 3-5 0.04+)0.20 jO.OIO 4-5 0.03+)0. 15 )0.0 10 5-6 0.06+)0.30 )0.010 1-2 1.05+)0.0 2-6 1.02+)0.0

Load

Fig. I-Sample system for simulation

262 INDIAN 1. ENG. MATER. SCI., AUGUST 2002

Read I . No of buses 2. IYbt!.slmatrix 3. In ilia l bus voltage magnitude. sc.:hed ulcd

active and reacti ve power for each bus

Appl y N-R mclhod to find final bus voltage

No

S IOfe I.H MI hus voltages 2. dP/ d V, in case uf real load change or dQ/d Vi in case of reactive load change at load buses

Yes

Modify the diagonal element of i Ybus l matrix corresponds to the weak bus under simulation for SVC ~dd in induc tive mode of operation Or. SVC add in capaci tive mode of

operation And update init ial bus vallage for next step of SVC add

Increase Qlaad at any weak load bus Or. Increase Pload at the weak load bus And update inil ial bus voltage for next step Qload increase

Fig. 2-Flow chart of the proposed method

0.6

0.4

"? 0 .2 ~

---+-- Un ity power fac to r

. - • - - Lagging power faclor

- - .. . . Lead ing power factor ~ 0 :> ~ -Q.2 ~

-0.4

-Q.6 :&.

-Q.8 '&.

· 1

Q3 0.4 05 O~ O~ O~ O~ 1.1 1.2 1.3 1.4 1.5 1.6 1.7

P-.,.. at bus-6 (in p.u.)

Fig . 3a-dPld V vs. P load at bus-6 (six-bus test system)

changes in real power load are shown in Fig. 3b; it is evident that the bus voltage also decreases in conjunction with decrease in real power sensitivity and approaches the critical points accordingly Ca", ' b" , 'c / ). The corresponding voltage security margins have been marked in Fig. 3b.

Same simulation has been performed in bus number 6 for a simulated load level with and without a SVC

1.2

1.1 .. ... -.~'"=.'-. -. ... ,----.---

• •• . 1J.-,.-:-: ..•• -. _----'IL..-__ .. ' ..

' .. , ..

0.7

0.6

0.3 0.5 0.7 0.9 1.1

P\o;I,iJ al bus·6 (i n p.u.)

-+-- Unily po wer faclor

... • . Lagging power faclor

... .... .. Leadin g powcrfaclor

' .. b' c'

1.3 1.5 1.7

Fig. 3b--Voltage vs. Pload at bus-6 (six-bus test system)

8.5

7.5

6 .5

~

~ 4 .5 c; "0 3.5

2.5

1.5

•

.--+-- Q loOO inc . in S1C p o f 0 .025 p.u.

- -. - - SVC (cap) add in step of Dsvc;0 .0 5 p.o.

- - ... - - SVC (ind) add in step of 8 5\"(;;-0 .05 p.o.

.... __ ,...:::::.....,.c..::Sensitivity

0 .5 +---.---'---r--+~--~- - --,,---0 .1 0 .2 0 .3 0 .4 0 .5 0.6

Q\o..Iad al hw;·f) (in p.u.)

Fig. 4a-dQldV VS. Q load at bus-6 (six-bus test system)

0 .7

in bus number 6 as shown in Fig. 4a (SVC is simulated here as both inductive and capacitive var compensator). For lagging power factor load, addition of SVC in bus number 6 in induction mode decreases reactive power sensitivity of that bus, pushing the bus more towards insecure zone of operation (profile ' m' in Fig. 4a). On the other hand, operation of SVC in capacitive mode is undoubtedly advantageous and it can be observed that at higher reactive demands, even for lower bus reactive power sensitivity, SVC keeps the system within prescribed operational limit [this is evident by comparing sensitivity profiles with SVC (curve number 'n'), with that having no SVC (curve number 'p')] . It can also be observed from Fig. 4b that, profile 'n", (corresponding to profile 'n' in Fig. 4a) offers higher bus Voltages. On the other hand, profile 'p" representing bus voltages with reactive demand increase without SVC, the bus voltage magnitude deteriorates when SVC operating in inductive mode is added in shunt with bus number 6

CHANDA el al_: BUS SECURITY GOVERNED BY REACTIVE POWER SENSITIVITY IN LPS SYSTEM 263

1.2 -

1.1 - '- .

~ I i

i 0_9 ! -g '2. 0.8 ~ E ~ 0.7 -!9 "0 > 0.6 .

0.5

. ... -.. ..

-+-- Qload inc. in s tep 01'0.0251

. - -. _. : : (cap) add in step of " Bs vc =().05 p.u. f

~ -- -&-- - SVC (ind) add in SICp o f I m'

Bs vc =-il.05 p.u .

0.4 - -

o 0.1 0.2 0.3 0.4

Q,.., .. bus-6 (in p.u.)

p'

0.5 0.6 0.7

Fig. 4b-Voltage vs .. Qload at bus-6 (six-bus test system)

1.2

~ 0.8 .:, ~

.D

~ 0.6 ~ 01 .., 0.4

0.2

~ . - . 1*;---".;----:: _"'c-'--~~",cnsi l ivi l y margin

.. ... ' ~,

' ., & ,

'., ." '., '., __ Unily power faClor

- -. - - Lagging power faClor

- - ~ - - Leading power faClor

0+--.--+-.--.--.---.--.--.---.--. o 0.05 0 .1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Q"", al bus-26 (in p.u.)

Fig. 5-dPldV vs. Pload at bus-26 (IEEE 30 bus test system)

2.5

• •

0.5

__ Qload inc . in slep of 0 .025 p.u .

- - . - - SVC (cap) add in slep of Bsvc =0.0 1 p.u.

- - ... - - SVC (ind» add in Slep o f Bsvc =-0 .0 I p.u.

O+----r---,---,----,---,---,,---.---. o 0.05 0.1 0.15 0.2 0.25 0 .3 0 .35 0.4

Q"", al bus-26 (in p.u.)

Fig. 6-dQldV VS. Qload at bus-26 (IEEE 30 bus test system)

Table 2 - Impedances and line charging for IEEE 30-bus test system

Bus- Line impedance Line charging Off-nominal code Z,," Yrxf2 tap ratio of p-q transformer

1-2 0.01 92+jO.0575 0+jO.0264 1-3 0.0452+jO.1852 0+jO.0204 2-4 0.057+jO. I737 O+jO.0184 3-4 0.0132+jO.0379 0+jO.0042 2-5 0.0472+jO.1983 0+jO.0209 2-6 0.0581 +jO.1763 0+jO.0187 4-6 0.0119+jO.0414 0+jO.0045 5-7 0.0460+jO.1160 0+jO.0102 6-7 0.0267+jO.082 0.0267+jO.082 6-8 0.01 2+jO.042 O+jO.OO85 9-11 0+jO.208 0+jO.0045 9-10 0+jO.11 O+jO 12-13 0+jO.14 O+jO 12-14 0.1231 +jO.2559 O+jO 12-15 0.0662+jO.1304 O+jO 12-16 0.0945+jO.1987 O+jO 14-15 0.2210+jO.1997 O+jO 16-17 0.0824+jO.1932 O+jO 15-1 8 0.1070+jO.21 85 O+jO 18- 19 0.0639+jO.1292 O+jO 19-20 0.0340+jO.068 O+jO 10-20 0.0936+jO.209 O+jO 10-17 0.0324+jO.0845 0.0936+jO.209 10-21 0.0348+jO.0749 O+jO 10-22 0.0727+jO.1499 O+jO 21 -22 0.0116+jO.0236 O+jO 15-23 0.I+jO.202 O+jO 22-24 0.115+jO.179 O+jO 23-24 0.132+jO.27 O+jO 24-25 0.1885+jO.3292 O+jO 25-26 0.2544+jO.38 O+jO 25-27 0.1093+jO.2087 O+jO 27-29 0.2 198+jO.4153 O+jO 27-30 0.3202+jO.6027 O+jO 29-30 0.2399+jO.4533 O+jO 8-28 0.0636+jO.2 O+jO 6-28 0+jO.0214 0+jO.0214 6-9 0+jO.208 0.0+jO.OO65 1.01 55+jO 6-10 O+jO.556 0.9629+jO 4-12 0+jO.256 1.0 129+jO 28-27 0+jO.3960 0.9581+jO

(profile 'm" in Fig. 4b). At any power level, the corresponding sensitivity margins can be observed from Figs 3a and 4a.

The simulations performed on a six-bus test system, have been repeated for the standard IEEE 30 bus test system (Table 2). The results reveal that real and reactive power sensitivities follow almost the same profile like those obtained earlier. Figs 5 and 6 exhibit these profiles with respect to real and reactive

264 INDIAN J. ENG. MATER. SCI.. AUGUST 2002

power changes. The simulati ons also reveal that the change of vo ltage profiles of the weakest bus (bus number 26) in the IEEE 30-bus test system also follows the expected pattern reinforcing the results obtained fo r the six-bus system.

Conclusions The inves ti gat ions show that in a multibus system,

degree of weakness for any bus can be analyzed in a better way from the viewpoint of its real and reactive power sensItIvItI es than only from its voltage magnitude. Further, for the real and react ive power sensi ti vit ies of the bus with respect to voltage decrease with higher load levels, there are specific sensitivity margins at each load level which can be determined on off- line basis for any multi bus power system using the load flow based method proposed in the text. Static Var Compensator (SVC) application in capacitive mode in a weak bus improves the operational capabili ty of such a bus and even enhances the reactive power sensitivity as well as sens i ivity margin of the weak bus within a range of operation. It also enhances the bus voltage offering more voltage security. Installation of SVC is thus recommended for the weak buses in a typical longitudinal power supply system.

Acknowledgement Sincere thanks are due to the University Grants

Commission, Government of India, New Delhi, for sponsoring the Major Research Project based on development of power systems of developing countries.

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