APPENDICES APPENDIX A DATA FOR IEEE-30 BUS TEST …

1 APPENDICES APPENDIX - A data FOR IEEE-30 BUS TEST SYSTEM The one line diagram of an IEEE-30 bus system is shown in Fig. 'The System data is taken from references [I471 (1491. The line data . bus data and load flow results are given in Tables , respectively. The generator cost and emission coefficients, transformer tap setting, shunt capacitor data are provided in Table , and , respectively. The B-loss coefficients mauix of the system is given in Table . The data is on I00 MVA base. Fig. One line diagrnrn Table Bus data and Load tlow mults i Bus 1 No. 1 -- 3 4 5 6 7 81 1 - - Bus Voltage Magnitude ( ') 1,045 1,000 "" 1,000 1,010 1 .000 Phase Angle (degrees) Generation 0 I 1 1 ! 12 1 13 Real Power ( ) " 1,000 1 .000 1,071 Reactive Power ( ) @I06 Load 12 -- Real Power ( ) - Reactive Power Limits Reactive Power (p.))]

2 ~.) -. 6 - . -. Qlim (P-U-) - - - - - -. - QN, (p.~.) - - - - - - - - - - - - - - - Table Generator cost and Eminsion coe~cients Table A4. Transformer tap setting data Table Shunt capacitor data Table Generalized loss coeff~cients B,", = [ ] APPENDIX - B data FOR 6 UNIT TEST SYSTEM The system contains six thermal units. 26 buses, and 46 trimmission lines 1421. The load demand is 1263 MW. The cost coefficients of 6 unit test system arc given in Tables The ramp rate limits of corresponding generating units are given in Table The generalized B loss coeficients for the system are shown Table The system data is on 100 MVA base. Table Generating Unit Capacity and Coemcienb p,rnln a( Unit (MW) (MW) (SIMW~~) Table Ramp Rate Limits and Prohibited Operating Zones Table Generalized loss cocflicienta APPENDIX - C data FOR lIUNlT TEST SYSTEM The 15-unit test system contains 15 thermal units whose characleristics are given in Tables , , respectively.

3 The generalized loss cmfiicients an given Table The system data is taken from reference 1421. Table Generating unit with ramp rate limits Table Prohibited operating zones of generating units Table Generalized loss coeflicients Unit I1 (1114 01K112 OM01 4 INX>I 41XX13 4 WL)I 41 OX111 4 IKYII 41 WX13 0 LXXI5 4 IKYl1 -llIlKJZ (I IYKU 0 (XU3 4 INKI? 0 W112 0iKl13 OlXII1 (I INXNI -11 -0 WW2 11 IXINI II IXXII 4llXN13 41 (XXU -0 IXXM -0 11 KXi 11 IIXY IIIXIIII 4 IIIXI2 00(1(11 OWMl 00010 4 IMII 41NJ13 4lIXXN 4 IlYXII IIIKXW UWIH 4IX112 II1X)Il IIIXXXI 4 MI35 0111 11 4lX12Y 4 iKKll 4 UXl5 4) W11l 0 1x134 -1, lXW 4 MI4 ll 1x11 I II(UX0 0 0029 00032 -(I IN11 I -0 (11XI IILXIII 0 INXI1 41 IN126 -11 1x11) .IIIIX>~ -11 (mil II wi7 I~(X~I (1 in114 II (XNI~ II IXII~ n INIIU a I~II~ o1m11 -1) Irxc 41 INXC ulxln 41 (urn 4 MII UIXKKI 4 IXIN 41 IXKM o(1114 (I 1~110 II IYYUI -(I INXK a rm5 4 nnlw ~IXIII 41 (rw n 1~x1: 41 rx,11 elxnl 4 MXII 111KK11 -0 (XKII 11 IN11 1 41 (XKl3 41 (KKK1 (I 1X)I 5 11 lXl17 11 IXIlh IIIXXW -11 (XXh 11 11N17 4, 11 XXl 4lIXNl?))))))))))))))))))

4 41 IN118 .I, *XI) 11 IXHII o am^ a IX~SI~ 41 IXII? .ii II all1 0016~ o msl IIIXI~V 41 IXI:I 11 IXII~ IIIXYII o IXUK 41 (~178 1 4 iKX13 -0 MI2 -11 WXIX 11 1112'4 -1, IKllll 4 IXXIS 0 (XI15 0 WIX: OOIW 1101 Ih 41Xi21 4, IN125 0 IXU11 -0 IN111 41 (1172 -1, lXX13 -11 (KYN -11 W113 I1 11132 -0 (XI13 -0 IXXIX I! IXHIV 0 1Nl7V 0 111 10 OIIZIKI 41 IN127 4) 11114 I,lXNW 4 IXII I 4 IlXIWI -0lKKl3 -0 WXN -00017 4 IINlI I I)IM17 1liX)II 4 IKXIS -0(1123 -00021 41X121 III1141 IIIXXII IIINXU 4 IlY138 OlllhX , n NXI? -11 WXI -OIKNX~ 41 IKXN> 41~~: 4 WXII (I [run 411s% 41~2s 11rn14 OIXXII IIINW atxx)l 11 cwrv 111rn8 IIMM O(KH)I .0(1125 (IIYUII -1111~12 -O~KUI: i~(x~mi (IINNII IIIYLI~ oixnr, ~IMKU -iiirxit 1,111 111 ~IIIIIII OIKIZX UIXK13 11(Kl1<1 (101 1 I <iW\l -U<1114 -OINII7 .(I IXXl2 IllXXl5 dlXl12 4)lXII I I)<Xl1W -1 IIXXN 41 I1 IIII BWX aWW4 -11 IXKII -0 lXK12 41 (XI28 4jlXl2h 4) IKX13 11 IXW3 4 IlXXlB 41 lY178 -011172 41 IXIWII OOl 08 II(112X O(X12X -1) IIU4 O 1213 Prohibited Zones (MW) 1 APPENDIX - D data FOR TAIPOWER 40-UNIT SYSTEM The system data 1s taken from reference [50] whose characteristics am glven In Table The data is on 100 MVA base.))))))))]

5 Table Generating units coeff~cients with ramp rate limits APPENDIX - E LINE VOLTAGE STABILITY INDEX The important aspect of voltage stability assessment is lo find the distance (MW/MVAR/MVA) to maxlmum loadabtllty point from the present operating point [115]. Line voltage stahil~ty index 1s used to get accurately the proximity of the operating point to voltage collapse point by the mdcx glven as follows. Let us consider a single line of an lnterconnccted network. where the lines are connected through a grid network. Any of the lines from that network can be considered to have the following parameters as shown In Fig. E. 1. Utlliz~ng the concept of power flow In the line and analyzing with '11' model representation, the real and reactlve power llow equations in terms of transmiss~on llne constants are formulated Fig.

6 One line diagram of a typical transmission system Loads are more often expressed In terms of real (WattsIKW) and reactlve (VArsKVAr) power. Therefore, 11 1s convenient to deal with transmission llne equation in the form of send~ng and receiving end complex power and voltage. Let us treat receiving end voltage as a reference phasor (VR = IVRILO) and let the sending end voltage lead it by an angle S(Vs = IVslL6). Transrnlssion lines are normally operated with a balanced 3 phase load. The analysis can be therefore performed on per phase basis. The complex power leaving the sending- end and entering the receiving end of the transmission line can be expressed on per phase basis [154], as A transmission llne on a per phase basis, can be regarded as a two-pon network, where in the sendlng end voltage, Vs and current.

7 IS are related to the receiving end voltage, VK and current. IR through ABCD constants [I541 as Receiving and sending end currents can hc expressed In terms ofreceivlng and scndlng end voltagcs [I 54) as 1 =Iv .AV BS BY (E 3) Let A, B, D the transmission l~ne constants [I 541 he wrltten as A = IAlial. R - IBILPI. 1) - ID1 LUI (Since A =D) Therefore we can write, Substituting for In in equation ( ) we get, If equation ( ) is expressed In real and rlnaglnarv parts, we can write the real and reactive powers at the receiving end [I 541 as. where A La 1 and B LP I are the transnilsston l~ne constants For the usual n-model, the transmlsslon l~ne constants may be written as follows If the length of the line is medium, then Z is the total series impedance of ltne, Y is the total line charging susceptance. If it is a long transmission line, then Z'Y' A=]+-- 2 B = Z' where (E.]]]

8 12) (E. 13) y IS propagation constant and 1 is the length of~ansrn~ss~on llne The formulae for the receiving end real and reactive powers can he formulated as follows [I 541 These can be rewritten as, (E. I 8) E IEI E~'AISln(p, -a,)= L-Ls~n(p, -8) Q, +--- (E. 19) IBI IBI Then by el~rninatlng 6. by squanng and adding the two equations, we obtain the locus of PH against QR to be a c~rcle with given values ofA and B and for assumed values of ER and jEs/ to be [I 541 as follows. If kth bus is the sending end and m" bus is the receiving end and expanding the above equation we get as follows, The above equation should have the real roots for V,,, for the system to be stable. Hence the following condition should bc satisfied[ 1541 where, LS, is termed as voltage stability index of the line P, and Q, are the real and reactive power rece~ved at the receiving end rn, ALal and BLP are the transmission 11ne constants, Vk and V, are the voltages at the sending end bus k and receiving end bus m.]]]

9 At or near the collapse point, voltage stabil~ty index of one or more line approach to unity. This method is used to assess the voltage stability. APPENDIX - F STANDARD - 5 BUS SYSTEM The Standard 5 bus system is shown in Fig. The System data is taken from reference [154]. The line data and bus data are given in Tables , respectively. The data is on I00 MVA base. Fig. One line diagrnm Table Line dnta Table Bus data APPENDM - G data FOR IEEE-14 BUS TEST SYSTEM The one line diagram of an IEEE-14 bus system is shown in Fig. The System data is taken from reference [147]. The line data , bus data and load flow results are given in Tables and , respectively. The data is on 100 MVA base. C Spchrmxnn Comnprm*ors h G Gcnt~ators Three Wmdi. Transformer Equivalent -r9 e Fig. One line diagram Table Line data 1 I I I Line lmocdanec I Half Line Line 1 I 1 2 F~~~ Bus TO Bus Charging s~~~~~~~~~ ( ) Resistance @-u) Reactance ( ) Tabk Bus data and load flow results Bus No.

10 1 2 3 4 5 6 7 8 9 - 10 11 12 13 - 14 Bus Voltage Ma'nitude ( ) 1 .OW Generation 1:;: (degrees) ~ O-OoO Real Power ( ) Reactive power (p.~) Load Rul Power ( ) 12 (H) Reactive Power Reactive power ( ) .. Qm,m (Pu) - - - - ~.- .- - - - - - - Limits Qmm, (Ku) - - KT'' -- - - - - - Table G3. Transformer tap ~niag data Table Shunt capacitor data TapSctting ' Value ( ) From Bus 4 4 5 To Bus 7 9 6 APPENDIX - H data FOR AN IEEE-57 BUS TEST SYSTEM The System data is taken hm reference [147]. The line data bus data and load flow results for an 1 EEE-57 bus system given in Tables and respectively. The transformer tap setting and shunt capacitor data are provided in Table and , respectively.