Fuzzy Based Load Shedding against Voltage Collapse

Transcription

1 From the SelectedWorks of Almoataz Youssef Abdelazz September, 2012 Fuzzy Based Load Sheddng aganst oltage Collapse Almoataz Youssef Abdelazz Avalable at:

2 MultCraft Internatonal Journal of Engneerng, Scence and Technology ol. 4, No. 3, 2012, pp INTERNATIONAL JOURNAL OF ENGINEERING, SCIENCE AND TECHNOLOGY MultCraft Lmted. All rghts reserved Fuzzy based load sheddng approach aganst voltage nstablty A. Y. Abdelazz 1*, A. T. M. Taha 1, M. A. Mostafa 1, A. M. Hassan 2 1* Electrcal Power and Machnes Department, An Shams Unversty, Caro, EGYPT 2 BAPETCO (Badr el dn Petroleum Company), Caro, EGYPT * Correspondng Author: e-mal: almoatazabdelazz@hotmal.com, Tel Abstract The phenomenon of voltage collapse eclpses a potental hazard for the transmsson and dstrbuton systems. The load sheddng for avodng the exstence of voltage nstablty n power systems s taken as a remedal acton durng emergency states. The load sheddng strategy for power systems wth locaton and quantty of load to be shed s presented n ths paper. Two methods are used for ths purpose. The frst method s based on a mathematcal calculaton of an ndcator of rsk of voltage nstablty. The second method s based on a fuzzy load sheddng based algorthm that uses a voltage stablty ndcator for avertng voltage collapse. Applcatons to the standard IEEE 30-bus system are presented to valdate the applcablty of the two proposed methods. Keywords: Load Sheddng, oltage Instablty, L-ndcator, Fuzzy logc. 1. Introducton oltage stablty s concerned wth the ablty of a electrcal power system to mantan acceptable voltages at all buses of the system after beng subected to a dsturbance from a gven ntal operaton condton [IEEE/CIGRE Jont Task Report, 2004]. Therefore, a power system s sad to have a stuaton of voltage nstablty when a dsturbance causes a progressve and uncontrollable decrease n voltage level. The development and use of accurate methods to predct ncpent voltage nstablty s crucal n preventng such voltage collapse stuatons. At frst a gradual voltage drop n one or several consumer regons may lead to ncrease reactve losses n the system and push transformer taps towards maxmum values. Some generators can reach ther lmts of reactve power. Then voltage drops rapdly and t may drop so far as to cascade trppng of on-lne generators thus causng a complete collapse of the system (Subraman, 2011). When the operatng state s near nstablty, the man obectve s preventon of voltage collapse. If all the control strateges such as reschedulng of generatons, brngng standby generators, swtchng capactor banks, reducton of voltage magntude set pont and other reactve power controls are exhausted, the only alternatve way s load curtalment at some weak buses to avod voltage collapse. The contrbuton of the effect of load sheddng to avod voltage nstablty s reported n El-Sadek (1999) and Quoc (1994). It has been reported n many references (Echavarren, 2006; Balanathan, 1998) that load sheddng actvty s the last lne of defense to secure the system from havng collapse. The am of ths work s to buld a tool to help operators n an emergency by proposng load sheddng actons. The phenomenon of voltage collapse s very complcated. An exact calculaton to estmate voltage stablty lmts s dffcult. Furthermore, when t happens the process evolves very quckly (Quoc, 1994). In order to try to dentfy on-lne a Rsk of oltage Instablty (RI) a rapd ndcator s needed. If necessary, emergency measures to avod all rsks must be quckly proposed. Several authors have worked on load sheddng to avod the rsk of voltage nstablty. In Kessel (1986), a fast calculaton of ndcators of rsk of voltage nstablty has been developed. These ndcators can detect on-lne voltage nstablty and sgnal the tendency towards a crtcal stuaton. Ther values change between zero (no load) and one (voltage collapse). A load sheddng strategy that maxmzes the system reactve securty margn has been developed by (Berg, 1994). The methodology s based on nonlnear optmzaton formulaton. Nanda (1995) developed an energy based approach to under voltage load sheddng. Optmal load sheddng algorthm based on the concept of statc voltage stablty margn and ts senstvty at the maxmum loadng pont or

3 16 the collapse pont (Amraee, 2007). Bwe (1999) presented an antcpatory load sheddng scheme for loadablty enhancement. In ths technque based on load varaton trends, load sheddng s pre-dctated so that system s secure from voltage collapse. A methodology s descrbed n (Moors, 1999) to determne the locaton of mnmal load sheddng able to stablze the system, egenvector nformaton s used to rank the loads from the vew pont of sheddng effcency. In Taylor (1992), a concept for under voltage load sheddng s presented. In the event of an approachng blackout (collapse), t s dffcult to ensure voltage stablty by reactve power compensaton alone. Hence counter measure requred to avod voltage collapse s the sheddng of loads. Undervoltage load sheddng s powerful countermeasure to mantan voltage stablty for severe contngences (Mnhat, 2008; Casamatta, 2002). Power systems are large networks that are subected to unexpected events and n some cases, the uncertantes are probablstcally represented. Therefore, fuzzy logc technques offer good tools applcable for power system problems (Momoh, 1995; Shankar, 2011). In Saskala (2011), two fuzzy based load sheddng methods that use a voltage stablty ndcator for avertng voltage collapse are proposed. The frst method dentfes the most approprate locatons and uses an analytcal procedure to compute the sheddable load, whle the second drectly predcts the amount of load to be shed at the crtcal buses. In ths paper, two algorthms for determnng the load to be shed and locaton n order to avod rsks of voltage nstablty are presented. The frst method s based on the calculaton of ndcator of rsk of voltage nstablty. The am of ths method s to obtan through load sheddng an ndcator profle lower than a threshold value n order to ensure that the power system wll reman n a state far from voltage nstablty pont. The load bus (locaton) where the ndcator s the hghest s selected n order to carryout load sheddng. A relaton between ndcator changes and load powers to be shed s developed. Wth help of ths relaton the amount of load to be shed can be determned. The second method s based on the fuzzy logc technque whch determnes the sutablty of each bus for load sheddng one by one and the bus wth the hghest sutable value s chosen as the most approprate bus for load sheddng. The amount of load to be shed s then calculated at the chosen bus. The two methods are appled to the standard IEEE 30-bus system. 2. Mathematcal calculaton for load sheddng usng voltage stablty ndcator In Kessel (1986) and Ra (2010), voltage stablty ndcator at bus can be determned by: Where, α L : Set of load buses. α G : Set of generator buses. : Complex voltage of generator bus. : Complex voltage of load bus. F : The hybrd matrx. L F α G = 1, αl Y Y GG GL [ ] = LG Y Y LL (1) Y (2) 1 [ F] = [ ] [ ] Y LL Y LG Y GG, Y LL, Y LG, Y GL : Elements of system admttance matrx [Y]: Bus admttance Matrx. [Y GG ]: Sub-matrx wth dmenson (g x g). [Y GL ]: Sub-matrx wth dmenson (g x (n-g)). [Y LG ]: Sub-matrx wth dmenson ((n-g) x g). [Y LL ]: Sub-matrx wth dmenson ((n-g) x (n-g)). Where, n: Total number of buses, g: Number of generators. A global voltage stablty ndcator of a power system s gven by L, 0 L 1 0: far away from voltage nstablty pont. 1: at voltage stablty pont. The ndcator at bus determned by equaton (1) can be separated nto real and magnary part (3)

4 17 L L R I = α F cos θ ( + δ δ ) G 1 (4) = α G F sn θ ( + δ δ ) (5) Where, δ : oltage angle at generator bus δ : oltage angle at load bus θ : Angle of the hybrd matrx F The voltage stablty ndcator at each bus s a functon of voltage angles and magntudes, the real and magnary parts of ndcators can be expressed as: L R F, ( ) ( ) = (6) 1 δ L I F, = (7) 2 δ The partal dervatve of equatons (4) and (5) wth respect to voltage angle and magntude changes can be determned as: I L I ΔL δ = R R ΔL L δ I L R L Δδ = Δ Δδ Δ [ T ] (8) Matrx [T] s the senstvty matrx between ndcator changes and voltage angle and magntude changes. Ths matrx s very sparse and large number of coeffcents of ths matrx s not needed. The necessary coeffcents to be used for calculatons are those located n the row assocated wth bus J (f bus J s selected to carryout load sheddng) (Quoc, 1994). Coeffcent of matrx [T] can be determned as: L I δ = α G F cos ( θ + δ δ ) ( θ + δ δ ) = R L α G = = δ F F sn cos ( θ + δ δ ) R ( L 1) L I R ( L ) R L α 1 G = = 2 F sn ( θ + δ δ ) I L α G = = 2 L I (9) (10) (11) (12)

5 18 From conventonal Newton-Raphson load flow, we obtan a lnear relaton between msmatches of voltage magntude and phase angles, msmatches of actve and reactve nected power (Ferrera, 1999). Δδ = Δ ΔP ΔQ 1 [ J ] (13) By substtutng from (13) n (8), we get a relatonshp between real and magnary parts of ndcators and nected power as seen below: I ΔL 1 ΔP = [ T ] [ J ] (14) R ΔL ΔQ Where; S S [ S ] = [ T ] [ J ] = 21 S S 22 A relatonshp between changes n ndcators at load bus and power nectons at all load buses can be obtaned: I ΔL = S11 ΔP + S21ΔQ (15) R ΔL = S21 ΔP + S22ΔQ (16) Where [J] s the power flow acoban matrx; [ P] and [ Q] are msmatches of actve and reactve nected power; [S] = [T] [J] 1 senstvty coeffcent matrx (Appendx 1). The actve and reactve loads are not ndependent, one cannot shed actve loads wthout reducng reactve loads. Usually a relaton between actve and reactve load can be obtaned as follows. Here the load power factor s assumed to be constant at each load bus. Q Pf =, α L P ΔQ Pf = ΔP ΔQ = Pf ΔP By substtutng from (17) n (15 & 16), a relatonshp between changes of the ndcator at bus and changes n actve power nected at the same bus can be obtaned as: Where; I ΔL = S11 ΔP + S12 Pf ΔP (18) R ΔL = S21 ΔP + S22 Pf ΔP (19) S S = S11 + S12 S + S 1 2 = Pf Pf Usng equatons (18) and (19), actve and reactve amount of load to be shed can be determned as: ΔL Δ P = (20) 2 2 S 1 + S 2 Δ Q = Pf ΔP (21) (17)

6 19 Where, ΔL : The change of L ndex requred at crtcal bus- to brng the system away from nstablty pont. Δ L = L T T = threshold value (L threshold ) For each power system, the threshold value of voltage stablty ndcator can be determned after smulatons (off-lne). It s dfferental wth the sngular value of the Jacoban, because the sngular value depends strongly on the system confguraton. It s an advantage of ndcator wth regard to the sngular value. An adequate threshold obvously depends on the system confguraton and the operatng state. 2.1 Algorthm for calculaton of the load to be shed: Let us consder an ntal state Xo of network operaton as shown n Fgure 1. After a calculaton of ndcators at load buses, buses havng ndcator values greater than a fxed threshold ( L L threshold ) are the "crtcal" ones. These buses tend to move towards a crtcal stuaton (voltage nstablty), because voltage nstablty s ntally local phenomenon, but can develop nto voltage collapse that has spread over wde areas. A system has unstable voltage f t ncludes at least one unstable voltage bus. Fgure 1. Schematc representaton of calculaton prncple for load sheddng The am of the method s to determne the load to be shed n order to obtan values for the ndcator lower than the threshold for all load buses. At each teraton of the algorthm see Fgure 2, the bus havng the hghest ndcator value s selected to carry out load sheddng. Ths bus s the most dangerous. In order to decrease the ndcator at ths bus to the threshold value, a load sheddng at ths bus s the most effcent because senstvty between ndcator change and load power change at ths bus s the hghest, wth equatons (20 and 21) the quantty of load to be shed n order to decrease the ndcator value L from ts current value to the threshold value can be obtaned. In the algorthm, at each step, amount of load to be shed at a bus s determned when: Ether the ndcator target value at bus s reached. Or the calculated load power to be shed s greater than the maxmum percentage allowed. The process s repeated untl all ndcator values become lower than or equal to the threshold value.

7 20 Fgure (2) shows a flow chart for the algorthm that s used to calculate the load to be shed usng the L ndcator. Calculaton of voltage nstablty ndcator L, Є α L L L threshold Є α L Determnaton of the load bus havng the hghest ndcator to carryout load sheddng (ex: bus ) Calculaton of senstvtes S 1 & S 2 Determnaton of load to be shed n order to: Ether reduce the ndcator value at bus from the present value to a fxed value Or reach the percentage of load allowed to be shed Calculaton of new state (, δ) of the network after an acton of load sheddng erfcaton wth a load flow calculaton to obtan exact ndcator values after load sheddng L L threshold Є α L STOP Fgure 2. Algorthm for the calculaton of load to be shed

8 21 3. Fuzzy based load sheddng scheme Power systems are large networks that are subected to unexpected events and n some cases, the uncertantes are probablstcally represented. However, t s made clear that some of the uncertan functons are ntrnscally fuzzy n nature and dffcult to handle effectvely by probablty. Fuzzy set theores offer a compromse n the sense of better solutons can be found that cannot be easly determned by other methods and are readly applcable to power system problems (Momoh, 1995; Shankar, 2011). The proposed fuzzy logc system (FLS) determnes the sutablty of each bus for load sheddng one by one and the bus wth the hghest sutable value s chosen as the most approprate bus for load sheddng. The amount of load to be shed s then calculated at the chosen bus. The chosen nput lngustc varables are oltage nstablty L ndex, oltage Magntude (M) and the output varable s Selected Bus for Load Sheddng (SBLS). The rules are summarzed n the fuzzy decson matrx shown n Table 1 and Table 2. The consequents of the rules are shown n the shaded part of the matrx. Havng related the nput varables to the output varable, the fuzzy results are defuzzfed through what s called a defuzzfcaton process, to acheve a crsp numercal value, the most commonly used centrod. The RI values are calculated for the load buses from the power flow soluton. The fuzzy scheme s allowed to determne the sutablty of each bus and the one wth the hghest sutablty chosen for load sheddng. The FIS Edtor dsplays general nformaton about the fuzzy nference system. The FIS Edtor for selected bus for load sheddng and amount of load to be shed s llustrated at Fgure 3 and Fgure 4 respectvely. Fuzzy nference s the process of formulatng the mappng from a gven nput to an output usng fuzzy logc. The mappng then provdes a bass from whch decsons can be made, or patterns dscerned. The process of fuzzy nference nvolves all of the peces that are descrbed n the prevous sectons: membershp functons, fuzzy logc operators, and f-then rules. Fuzzy Rules Matrx Inputs: L (oltage nstablty ndex) Trapezodal membershp functon as shown n Fgure 5 M (oltage Magntude) Trangle membershp functon as shown n Fgure 6. Output: SBLS (Selected Bus Load Sheddng) Trangle membershp functon as shown n Fgure 7. Table 1. Selected bus for load sheddng fuzzy decson matrx Inputs: L (Change n oltage nstablty ndex) Trapezodal Member shp functon M (oltage Magntude) Trangle member shp functon Output: SL (Sheddable load) Trangle member shp functon as shown n Fgure 8. SL: represents a part of real power sheddable load, the reactve component of the sheddable load can be calculated by treatng the power factor constant. The power factor angle s calculated from the specfed real and reactve power load at each bus. Table 2. Sheddable load fuzzy decson matrx In ths formulaton the voltage stablty ndcator L values are lnearly normalzed nto [0, 1] range wth the largest havng value of 1 (voltage collapse) and the smallest havng value of 0 (No load). The L ndex are dvded nto fve categores as shown n Fgure 5 usng fuzzy set notatons: Low ndex (L) trapezodal membershp functon, Low Medum (LM), Medum ndex (M), Hgh Medum ndex (HM) trangular membershp functons, Hgh ndex (H) trapezodal membershp functon, along wth load bus

9 22 oltage Magntude whch s dvded nto fve categores as shown n Fgure 6, Low (L) below 0.88 p.u trapezodal membershp functon, Low Medum (LM) n range ( ) p.u trangular membershp functons, Medum (M) n range ( ) trapezodal membershp functon, Hgh Medum (HM) trangular membershp functons and Hgh oltage (H) above 1.02 p.u trapezodal membershp functon. Fgure 3. Bus selecton FIS Edtor The framework of proposed method excludes the use of numercal procedures and reles solely on fuzzy logc. The L ndex s calculated at every bus from the results of the load flow soluton. The approach s desgned so as to calculate the amount of sheddable real and reactve power loads at the chosen bus for load sheddng, where the RI value s the largest and exceeds the threshold value. So, the nput varables are change of L ndex requred at crtcal bus to brng the system away from nstablty pont. M of crtcal bus and the output varable s SL, "amount of load to be shed". The Fuzzy Logc System s used to determne the amount of actve and reactve powers to be shed at the chosen load bus. The computed load s allowed to be shed and the above process s contnued tll ether all the L ndcator values are less than a selected threshold value or all the load buses approach ther respectve sheddable lmt. Fgure 4. Load sheddng FIS Edtor

10 23 Fgure 5. The nput varable - (L) membershp functon Fgure 6. The nput varable - oltage Magntude (M) membershp functon Fgure 7. The output varable - Selected bus for load sheddng (SBLS) membershp functon

11 24 Fgure 8. The output varable - Amount of load to be shed (SL) membershp functon 4. Smulaton Results The two suggested methods n ths paper are tested on the IEEE 30 bus standard system (Power System Test Case Archve). The loadng factor s a multpler by whch the actve and reactve powers of PQ buses and the actve power at the P buses are ncreased keepng the voltage magntudes of all the P buses constant. We attempt to change the real power generaton of the alternator, whose MA capacty cannot be altered. Fgure 9. Sngle lne dagram for IEEE 30 bus test system

12 25 The threshold value depends on the power system confguraton and the operatng state. If ths value s chosen too hgh, t does not ensure that the power system s mantaned n the stable state. On the other hand, f t s fxed too low, the loads to be shed may be too excessve. Ths value s determned by a tral and error process. The algorthm s ntally run by arbtrarly choosng a threshold value of 0.8 under heavy loadng condton, whch s ust away from the voltage collapse pont. The voltage magntudes pror to load sheddng may be n the range of p.u. A compromse s made n choosng the threshold value. Once the threshold value s chosen for a gven system, t s treated as a constant for all the loadng condtons. The threshold value for the L ndex s fxed as 0.14 for load varaton and 0.11 for frst level generator outage contngences, whenever any topologcal changes relevant for the voltage stablty n the system under study, the coeffcents of matrx [F] should be updated. Due to operatng constrants there s a maxmum lmt to the load that can be shed at each bus (for example 80% of the ntal load of the bus ) to ensure mnmum servce for consumers. The results are obtaned by usng the Newton-Raphson load flow analyss smulaton n MATLAB Power System Analyss Toolbox, (PSAT) and the MATLAB Fuzzy Logc Toolbox. The followng Fgure 9 represents the sngle lne dagram for IEEE 30 bus test system The system has sx generators, four under load tap changng transformers, two shunt capactor and thrty seven lnes. In the base case the total system load s pu, the swng bus (bus number 1) generates real power of pu, whle the other generators generate 0.4 pu real power. 4.1 Load varaton contngency Table 3 shows the results of the load flow soluton for the IEEE 30-bus system at base case Table 3. Load flow solutons at base case, L crtcal = 0.14 Bus No. oltage Angle L ndex It s shown from Table 3 that the L ndex s smaller than L crtcal, therefore no correctve acton wll be taken. Table 4 shows the results of the load flow soluton for the IEEE 30-bus test system wth a 1.1 loadng factor.

13 26 METHOD 1 (Mathematcal calculaton) Table 4. Load flow solutons at 1.1 loadng factor, Lcrtcal = 0.14 Bus No. BLS BLS ALS ALS Angle Sheddable load oltage L ndex oltage L ndex MW MAR BLS = before load sheddng ALS = after load sheddng It s shown from Table 4 that the L ndex of bus 30 s whch s greater than 0.14 (L crtcal ), therefore bus 30 s the selected bus for load sheddng. After load sheddng of bus 30, the voltage magntude has mproved to p.u. and the L ndex has decreased to METHOD 2 (Fuzzy based load sheddng system) Determnaton of selected bus for load sheddng usng the proposed fuzzy system s shown n Table 5. It s shown from Table 5 that bus No.30 has the hghest value, therefore t s selected as the approprated bus for load sheddng. Fgure 10 shows the FIS system for selected bus for load sheddng at bus 30 wth 1.1 loadng factor. Table 5. Fuzzy output for selected bus of load sheddng at loadng factor 1.1 Bus No. Selected bus for load sheddng

14 27 Table 5 (Cont d). Fuzzy output for selected bus of load sheddng at loadng factor 1.1 Bus No. Selected bus for load sheddng Fgure 10. FIS for Selected Bus for Load Sheddng at Bus (30) wth 1.1 loadng factor Usng the fuzzy based Load sheddng system to determne the amount of load to be shed: The amount of load to be shed 2.93 MW and MAR The voltage profle ncreased at bus 30 to p.u. and the voltage stablty ndcator decreased to Table 6 shows the results of the load flow soluton for the IEEE 30-bus system wth a 1.2 loadng factor.

15 28 METHOD 1 (Mathematcal calculaton) Table 6. Load flow solutons at 1.2 loadng factor, Lcrtcal = 0.14 Bus No. BLS BLS ALS Angle ALS Angle Sheddable load oltage L ndex oltage L ndex MW MAR The program ndcates that MW and MAR should be shed but ths amount of the total power to be shed n bus 30 s greater than that allowed (total powers to be shed reach 80% of the ntal base load). Therefore the program decdes to shed only 8.48 MW and 1.52 MAR at ths bus. The voltage profle ncreased at bus 30 to p.u and the voltage stablty ndcator decreased to Method 2 (Fuzzy based load sheddng system) Determnaton of selected bus for load sheddng usng the proposed fuzzy system s shown n Table 7. It s shown from Table 7 that bus No.30 has the hghest value, therefore t s selected as the approprated bus for load sheddng. Fgure 11 shows the FIS system for selected bus for load sheddng at bus 30 wth 1.2 loadng factor. Table 7. Fuzzy output for selected bus of load sheddng at loadng factor 1.2 Bus No. Selected bus for load sheddng

16 29 Table 7 (cont d). Fuzzy output for selected bus of load sheddng at loadng factor 1.2 Bus No. Selected bus for load sheddng Fgure 11. FIS for Selected Bus for Load Sheddng at Bus (30) wth 1.2 loadng factor Usng the fuzzy based load sheddng system to determne the amount of load to be shed: Amount of load to be shed 5.89 MW and MAR The voltage profle ncreased at Bus 30 to p.u and the voltage stablty ndcator decreased to Table 8 shows the results of the load flow soluton for the IEEE 30-bus system wth a 1.3 loadng factor. Method 1 (Mathematcal calculaton) Table 8. Load flow solutons at 1.3 loadng factor, Lcrtcal = 0.14 Bus No. BLS BLS ALS ALS Angle Sheddable Load oltage L ndex oltage L ndex

17 30 Table 8 (cont d). Load flow solutons at 1.3 loadng factor, Lcrtcal = 0.14 Bus No. BLS BLS ALS ALS Angle Sheddable Load oltage L ndex oltage L ndex MW MAR The program ndcates that MW and MAR should be shed but ths amount of the total power to be shed n bus 30 s greater than that allowed (total powers to be shed reach 80% of the ntal base load). Therefore the program decdes to shed only 8.48 MW and 1.52 MAR at ths bus. After solvng load flow, t s found that bus 26 wth hghest ndcator therefore n the next step (the next maxmum value ndcator) s selected to carry out load sheddng as shown n Table 9. Table 9. Load flow solutons for the next step of load sheddng Bus No. BLS Angle BLS ALS ALS Sheddable Load oltage L ndex oltage L ndex MW MAR

18 31 As shown from Table 9 after load sheddng of buses 26 and 30, the voltage magntude has mproved to p.u and p.u. and the L ndex has decreased to and respectvely, so the total amount of power to shed to stablze the system equals to 10 MW and MAR. Method 2 (Fuzzy based load sheddng system) Determnaton of selected bus for load sheddng usng the proposed fuzzy system s shown n Table 10. It s shown from Table 10 that bus 30 has the hghest value, therefore t s selected as the approprated bus for load sheddng. Fgure 12 shows the FIS system for selected bus for load sheddng at bus 30 wth 1.3 loadng factor. Table 10. Fuzzy output for selected bus of load sheddng at loadng factor 1.3 Bus No. Selected bus for load sheddng Fgure 12. FIS for Selected Bus for Load Sheddng at Bus (30) wth 1.3 loadng factor

19 32 Usng the fuzzy based load sheddng system to determne the amount of load to be shed: Amount of Load to be shed 8.74 MW and MAR whch exceeds the maxmum permssble value to shed power at bus 30, therefore the program decdes to shed only 8.48 MW and 1.52 MAR at ths bus. Determnaton for the next selected bus for load sheddng usng the proposed fuzzy system s shown n Table 11. It s shown from Table 11 that bus No.26 has the hghest value; therefore t s selected as the approprated bus for load sheddng. Fgure 13 shows the FIS system for selected bus for load sheddng at bus 26. Table 11. Fuzzy output for selected bus of next stage load sheddng at loadng factor 1.3 Bus No. Selected bus for load sheddng Fgure 13. FIS for Selected Bus for Load Sheddng at Bus (26) wth 1.3 loadng factor The next maxmum value ndcator s selected to carry out load sheddng as shown n Table 12 for bus 26.

20 33 Table 12. Load flow solutons for the next step of load sheddng Bus No. BLS BLS ALS ALS Angle Sheddable Load oltage L ndex oltage L ndex MW MAR As shown from Table 12 after load sheddng of buses 26 and 30, the voltage magntude has mproved to p.u and p.u. and the L ndex has decreased to and respectvely, so the total amount of power to shed to stablze the system equals 10.8 MW and 1.93 MAR. 4.2 Generator outage contngency The results of calculaton of oltage nstablty ndcator at contngences for generaton unt outages are shown n Table 13 Table 13. oltage nstablty ndcator for contngences of generaton unt outages Case No. Contngency L ndcator 1 G1 (Generator outage) Fal to coverage 2 G8 (Generator outage) G13 (Generator outage) G5 (Generator outage) G11 (Generator outage) G2 (Generator outage) In the IEEE 30; three generator buses were chosen namely G2, G5 and G8 for frst level outage contngency analyss G2 Outage contngency: Table 14 shows the results of the load flow soluton for the IEEE 30-bus system wth G2 outage.

21 34 Method 1 (Mathematcal calculaton) Table 14. Load flow solutons at G2 unt outage, Lcrtcal = 0.11 Bus No. BLS BLS ALS ALS Sheddable Load oltage L ndex oltage L ndex MW MAR The program decdes to shed 8.48 MW and 1.52 MAR at bus 30. So the voltage profle ncreased at bus 30 to p.u and the voltage stablty ndcator decreased to Method 2 (Fuzzy based load sheddng system) Determnaton of selected bus for load sheddng usng the proposed fuzzy system, therefore bus 30 s selected as the approprated bus for load sheddng. Usng the fuzzy based load sheddng system to determne the amount of load to be shed: Amount of load to be shed 5.3 MW and 0.95 MAR The voltage profle ncreased at bus 30 to p.u and the voltage stablty ndcator decreased to G5 Outage contngency: Table 15 shows the results of the load flow soluton for the IEEE 30-bus system wth G5 outage. Method 1 (Mathematcal calculaton) Table 15. Load flow solutons at G5 unt outage, Lcrtcal = 0.11 Bus No. BLS BLS ALS ALS Sheddable Load oltage L ndex oltage L ndex MW+ 5 MAR

22 35 Table 15 (cont d). Load flow solutons at G5 unt outage, Lcrtcal = 0.11 Bus No. BLS BLS ALS ALS Sheddable Load oltage L ndex oltage L ndex MW MAR The program decdes to shed only 8.48 MW and 1.52 MAR at bus 30. After solvng load flow, t s found that bus 5 wth hghest ndcator therefore n the next step (the next maxmum value ndcator) s selected to carry out load sheddng as shown n Table 15. After load sheddng of buses 30 and 5, the voltage magntude has mproved to p.u and p.u. and the L ndex has decreased to and respectvely, so the total amount of power to shed to stablze the system equals to 33.3 MW and 6.52 MAR. Method 2 (Fuzzy based load sheddng system) Determnaton of selected bus for load sheddng usng the proposed fuzzy system, therefore bus 30 and 5 are selected as the approprated buses for load sheddng. Usng the fuzzy based load sheddng system to determne the amount of load to be shed: Amount of load to be shed from bus 30 = 5.85 MW MAR Amount of load to be shed from bus 5 = MW+ 3.8 MAR After load sheddng of buses 30 and 5, the voltage magntude has mproved to p.u and 0.98 p.u., the L ndex has decreased to and respectvely, so the total amount of power to shed to stablze the system equals to 33.3 MW and 6.52 MAR G8 Outage contngency: Table 16 shows the results of the load flow soluton for the IEEE 30-bus system wth G8 outage. Method 1 (Mathematcal calculaton) Table 16. Load flow solutons at G8 unt outage, Lcrtcal = 0.11 Bus No. BLS BLS ALS ALS Sheddable Load oltage L ndex oltage L ndex

23 36 Table 16 (cont d). Load flow solutons at G8 unt outage, Lcrtcal = 0.11 Bus No. BLS BLS ALS ALS Sheddable Load oltage L ndex oltage L ndex MW MAR MW MAR The program decdes to shed only 8.48 MW and 1.52 MAR at bus 30. After solvng load flow, t s found that bus 26 wth hghest ndcator therefore n the next step (the next maxmum value ndcator) s selected to carry out load sheddng as shown n Table 16. After load sheddng of buses 30 and 26, the voltage magntude has mproved to p.u and p.u., the L ndex has decreased to and respectvely, so the total amount of power to shed to stablze the system equals to MW and MAR Method 2 (Fuzzy based load sheddng system) Determnaton of selected bus for load sheddng usng the proposed fuzzy system, therefore bus 30 and 26 are selected as the approprated buses for load sheddng. Usng the fuzzy based load sheddng system to determne the amount of load to be shed: Amount of load to be shed from bus 30 = 7.73 MW MAR Amount of load to be shed from bus 26 = 2.8 MW MAR After load sheddng of buses 30 and 26, the voltage magntude has mproved to p.u and p.u. and the L ndex has decreased to and respectvely, so the total amount of power to shed to stablze the system equals to MW and 3.22 MAR. It s notced from the prevous results that the fuzzy based load sheddng method s most approprate to compute the sheddable load, and t drectly predcts the amount of load to be shed at the selected bus. Also ths scheme shows an mprovement n the bus voltage profle, n addton to enhancng the voltage stablty of the system. 5. Performance Evaluaton A comprehensve set of results consstng of the M and L ndex at all the load buses over a range of load powers, before and after load sheddng are gven n Fgures (14) and (15). It s evdent from two Fgures (14) and (15) that there s an mprovement both n voltage profle and voltage stablty. The results ndcate that both the methods brng the system far away from the regon of voltage nstablty.

24 37 oltage (p.u) B3 B4 B6 B7 B9 B10 B12 B14 B15 B16 B17 B18 B19 B20 B21 B22 B23 B24 B25 B26 B27 B28 B29 B30 Bus No. (A) BLS oltage ALS oltage (Mathematcal Method) ALS oltage (Fuzzy Method) L ndex BLS Lndex ALS Lndex (Mathematcal Method) ALS Lndex (Fuzzy Method) B3 B4 B6 B7 B9 B10 B12 B14 B15 B16 B17 B18 B19 B20 B21 B22 B23 B24 B25 B26 B27 B28 B29 B30 Bus No. (B) oltage (p.u) BLS oltage ALS oltage (Mathematcal Method) ALS oltage (Fuzzy Method) B3 B4 B6 B7 B9 B10 B12 B14 B15 B16 B17 B18 B19 B20 B21 B22 B23 B24 B25 B26 B27 B28 B29 B30 Bus No. (C)

25 B3 B4 B6 B7 B9 B10 B12 B14 B15 B16 B17 B18 B19 B20 B21 B22 B23 B24 B25 B26 B27 B28 B29 B30 L ndex BLS Lndex ALS Lndex (Mathematcal Method) ALS Lndex (Fuzzy Method) Bus No. (D) olatge (p.u) B3 B4 B6 B7 B9 B10 B12 B14 B15 B16 B17 B18 B19 B20 B21 B22 B23 B24 B25 B26 B27 B28 B29 B30 Bus No. (E) BLS oltage ALS oltage (Mathematcal Method) ALS oltage (Fuzzy Method) (F) Fgure 14. M and L ndex for IEEE 30 bus system A: BLS and ALS M at loadng factor 1.1 B: BLS and ALS L ndex at loadng factor 1.1 C: BLS and ALS M at loadng factor 1.2 D: BLS and ALS L ndex at loadng factor 1.2 E: BLS and ALS M at loadng factor 1.3 F: BLS and ALS L ndex at loadng factor 1.3

26 39 (A) (B) (C)

27 40 (D) (E) Fgure 15. M and L ndex for IEEE 30 bus system A: BLS and ALS M at G2 unt outage B: BLS and ALS L ndex at G2 unt outage C: BLS and ALS M at G5 unt outage D: BLS and ALS L ndex at G5 unt outage E: BLS and ALS M at G8 unt outage F: BLS and ALS L ndex at G8 unt outage (F)

28 41 The buses at whch load sheddng s to be carred out and the net sheddable load for a vable range of load factors and generator outage contngency for IEEE-30 bus test system are ncluded n Table 17 and Table 18. Test System IEEE- 30 Bus Test System IEEE- 30 Bus Loadng Factor Table 17. Bus locatons and sheddable loads n load varaton contngency Net Sheddable load Selected Bus for Load Sheddng Mathematcal Method Fuzzy Method Mathematcal Fuzzy Method MW MAR 2.93 MW MAR MW MAR 5.89 MW MAR MW MAR 10.8 MW MAR 30 & & 26 Generator Outage Table 18. Bus locatons and sheddable loads n generator outage contngency Net Sheddable load Selected Bus for Load Sheddng Mathematcal Method Fuzzy Method Mathematcal Fuzzy Method G MW MAR 5.3 MW+ 0.95MAR G MW MAR MW MAR 30 & 5 30 &5 G MW MAR MW MAR 30 & & 26 The entres n the Table 17 and Table 18 serve to adequately valdate the fuzzy results through a comparson wth that of mathematcal method 6. Concluson Two algorthms for load sheddng to avod voltage collapse have been presented n ths paper. A smple and new method s developed to determne the locaton and quantty of load to be shed n order to prevent the system voltage from gong to the unstable stuaton. The values of the sheddable load powers are computed by mathematcal and fuzzy logc technques. It s observed that the net sheddable loads from the mathematcal method are slghtly hgher than that obtaned by the fuzzy logc method. Both of the mathematcal and the fuzzy logc technques show consderably mprovement n oltage Profle (P) besdes enhancng oltage Stablty (S). Nomenclature RI Rsk of oltage Instablty. FLS Fuzzy Logc System. M oltage Magntude. SBLS Selected Bus for Load Sheddng. SL Sheddable load. PSAT Power System Analyss Toolbox. FL Fuzzy Logc. T Threshold alue. LF Loadng Factor. BLS Before Load Sheddng. ALS After Load Sheddng FIS Fuzzy Inference System Appendx Appendx 1 - (Formaton of senstvty matrx [S]) Formaton of ndcator Matrx [T]: ΔL I ΔL R 1 = 1 = α α G G F F cos sn I R ( δ ) ( ) + θ δ Δδ L 1 Δδ Δ ( δ + θ δ ) Δδ + L Δδ I L R ( L 1) Δ

29 42 Formaton of power flow acoban Matrx [J]: P Q P + = 2 Q = 2 P = Q δ Q = P δ 2 Y Y 2 Y cosθ Y snθ snθ cosθ Appendx 2 - (IEEE -30 bus test system data) There are three Tables (Table (2.A), Table (2.B) and Table (2.C)) present the data used n the analyss for the system. Table (2.A). Lne data From To R (p.u) X (p.u) B/2 (p.u) TAP

30 43 Table (2.A) (cont d). Lne data From To R (p.u) X (p.u) B/2 (p.u) TAP Table (2.B). Generator data Bus No. oltage (p.u) Pg (p.u) Qg (p.u) Qmax (p.u) Qmn (p.u) Slack bus Table (2.C). Shunt capactor data Bus No. Shunt capactor (p.u) References Amraee T., Ranbar A.M., Mozafar B., Sadat N., An enhanced under-voltage load-sheddng scheme to provde voltage stablty, Electrc Power Systems Research, ol. 77, pp Arya L., Pande. and Kothar D., A technque for load sheddng based on voltage stablty consderaton, Internatonal Journal of Electrcal Power and Energy Systems, ol. 27, No. 7, pp Balanathan, R., Pahalawaththa, N.C., Annakkage, U.D., Sharp, P.W., Undervoltage load sheddng to avod voltage nstablty, generaton, transmsson and dstrbuton, IEE Proceedngs, ol. 145, No. 2, pp Berg G.J., Sharaf T.A System loadablty and load shed, Electr Power Syst Res, ol. 28, pp Bwe P.R., Tare R.S., Kelapure S.M., Antcpatory load sheddng scheme for loadablty enhancement, IEE Proc Gen Trans Dstrbut, ol. 146, No. 3, pp Casamatta F., D. Cro, D. Lucarella, S. Massucco, R. Salvat and M. Sforna, 'Management of Interruptble Loads for Power System Securty and Operaton', IEEE Power Engneerng Socety Summer Meetng, ol. 2, July 2002, pp Echavarren F.M., Lobato E., Rouco L., A correctve load sheddng scheme to mtgate voltage collapse, Electrcal Power and Energy Systems, ol. 28, pp El-Sadek M. Z., Mahmoud G. A., Dessouky M. M. and Rashed W. I., Optmum load sheddng for avodng steady state voltage nstablty, Electrc Power System Research, ol. 50, No. 2, pp Ferrera J.R., Lopes J.A.P., Sarava J.T., Identfcaton of preventve control procedures to avod voltage collapse usng genetc algorthms, Power Systems Computaton Conference (PSCC), Trondhem, Norway.

31 44 IEEE/CIGRE Jont Task Force Report Defnton and classfcaton of power system stablty, IEEE Trans. On Power Systems, ol. 19, No.2, pp Kessel P. and Glavtsch H., Estmatng the voltage stablty of a power system, IEEE Transactons on Power Delvery, ol. 1, No. 3, pp Nanda A, Crow M.L., An energy based approach to under voltage load sheddng, Electr Power Syst Res, ol. 32, pp Mnhat A. R., Othman M. M., Idrs M. K., Hamzah N., Zakara Z. and Musrn I., Mult-step load sheddng scheme for voltage securty assessment consderng system dsturbances, 7 th WSEAS Internatonal Conference on Applcaton of Electrcal Engneerng (AEE 08), Trondhem, Norway, July 2-4. Momoh J. and Tomsovc K., Overvew and lterature survey of fuzzy set theory n power systems, IEEE Transactons on Power Systems, ol. 10, No. 3, pp Moors C., an Cutsem T., Determnaton of optmal load sheddng aganst voltage nstablty, Power Systems Computaton Conference (PSCC), Trondhem, Norway. Power System Test Case Archve. Avalable from: Downloaded 30 th August, Ra P. A. and Sudhakaran M., Optmum load sheddng n power system strateges wth voltage stablty ndcators, Scentfc Research, ol. 2, pp Sadat N., Amraee T. and Ranbar A. M., A global partcle swarm-based smulated annealng optmzaton technque for under-voltage load sheddng problem, Appled Soft Computng, ol. 9, No. 2, pp Saskala J. and Ramaswamy M., Fuzzy based load sheddng strateges for avodng voltage collapse, Appled Soft Computng, ol. 11, pp Shankar S. and Ananthapadmanabha T., Fuzzy approach to crtcal bus rankng under normal and lne outage contngences, Internatonal Journal on Soft Computng, ol. 2, No. 1, pp Subraman C., Dash S.S., Pat S. and Arunbhaskar M., oltage collapse predcton and optmal locaton for stablty enhancement n power systems based on sngle contngency scenaro, European Journal of Scentfc Research, ol.50, No. 4, pp Taun T.Q., Fandno J., Hadsad N., and Sabon-Nadere J. C. and u H., Emergency load sheddng to avod rsks of voltage nstablty usng ndcators, IEEE Transactons on Power Systems, ol. 9, No. 1, pp Taylor C. W., Concept of under voltage load sheddng for voltage stablty, IEEE Transactons on Power Delvery, ol. 7, No. 2, pp Bographcal notes Almoataz Y. Abdelazz was born n Caro, Egypt, on September 14, He receved the B. Sc. and M. Sc. degrees n electrcal engneerng from An Shams Unversty, Caro, Egypt n 1985, 1990 respectvely and the Ph. D. degree n electrcal engneerng accordng to the channel system between An Shams Unversty, Egypt and Brunel Unversty, England n He s currently a professor of electrcal power engneerng n An Shams Unversty. He was the head of consultant engneers of the electrcal group n the General Drectorate for Proects & Mantenance, Kng Saud Unversty, Ryadh, KSA from 2005 to Hs research nterests nclude the applcatons of artfcal ntellgence to power systems and protecton and new optmzaton technques n power systems operaton and plannng. He has authored or coauthored more than 100 refereed ournal and conference papers. Dr. Abdelazz s a member of the edtoral board and a revewer of techncal papers n several ournals. He s also a member n IET and the Egyptan Sub-Commttees of IEC and CIGRE`. Dr. Abdelazz has been awarded An Shams Unversty Prze for dstnct researches n 2002 and for nternatonal publshng n 2010, A. T. M. Taha was born n Egypt n He receved the B.Sc. and M. Sc. degrees n electrcal engneerng from An Shams Unversty, Caro, Egypt, and the Ph.D. degree n electrcal engneerng from Poly-technque Academy, Bella Russa, n He s currently an Assstant Professor n the Department of Electrc Power and Machnes, An Shams Unversty. Hs research nterests nclude power system analyss. M. A. Mostafa was born n Egypt n He receved the B.Sc. and M.Sc. degrees n electrcal engneerng from An Shams Unversty, Caro, Egypt, and the Ph.D. degree n electrcal engneerng from An Shams Unversty wth ont supervson from Dalhouse Unversty, Halfax, NS, Canada, n He s currently a Professor n the Department of Electrc Power and Machnes, An Shams Unversty. Hs research nterests nclude power system analyss. A. M. Hassan was born n Ryadh, KSA n He receved the B. Eng. Degree n electrcal engneerng from An-Shams Unversty n Caro, Egypt n He s now workng for the M. Sc. degree n electrcal engneerng from An-Shams Unversty n Caro, Egypt. Currently he s an electrcal engneer n Badr el dn Petroleum Company (BAPETCO). Hs research nterests nclude the applcaton of artfcal ntellgent technques to power systems operaton, protecton and plannng. Receved May 2012 Accepted August 2012 Fnal acceptance n revsed form August 2012