CHAPTER 4 SINGLE OBJECTIVE CENTRALIZED CONGESTION MANAGEMENT

Transcription

1 46 CHAPTER 4 SINGLE OBJECTIVE CENTRALIZED CONGESTION MANAGEMENT 4.1 INTRODUCTION The centralzed congeston management s based on the COPF approach. The COPF requres the submsson of detaled prvate nformaton of the maret partcpants that may nclude ther beneft/cost functons to the ISO. In ths approach ISO maxmzes the total socal welfare and t s also responsble for the relablty and securty of the system. Both the smooth and non- smooth cost functons are consdered for the socal welfare. The voltage and reactve power constrants are ncluded n the model. In ths model the partcpants submt the generaton and demand of ther transactons and cost/ beneft functons to the ISO. The ISO verfes the lne flow and other constrants based on the generaton and demand of the transactons. If the lne flow s greater than the transmsson lne capacty of the partcular lne, then the ISO reduces the lne flow by adustng the generaton and demand of the transactons, whle maxmzng the socal welfare. 4.2 MATHEMATICAL FORMULATION In a perfect compettve maret, the ISO adusts the contracts generaton and demand to maxmze the socal welfare to acheve effcent operaton wth all constrants satsfed. The COPF model equatons are gven n Equaton

2 47 max, T G T E D P P C D B 4.1 Subect to the followng constrants 0 T P D G E T Q Q G E 4.3,,max mn, T G P P P 4.4,,max mn, T G Q Q Q 4.5,,max mn, T G V V V 4.6,,max mn, T E V V V 4.7,,max mn, T E D D D 4.8 max I m L l m T m D, P 4.9 Non smooth generator cost functon sn,mn 2 T G P P f e P c P b a 4.10 Customer beneft functon 2 d T d E d D c D b a PARAMETER SELECTION The SQP soluton s obtaned usng the MATLAB fmncon functon. After a number of trals, t s observed that only after functon evaluatons, the results are obtaned wth constrant satsfacton n SQP. The

3 48 tolerance values for both obectves TolFun and coordnates TolX are assumed as 1x10-5. For the Algorthm, Vmax s taen as 0.25 tmes X u X l, tolerance values for obectves TolFun and coordnates TolX are assumed as 1x10-5 and 1x10-5 respectvely. For IEEE 30 bus system, populaton sze N, and maxmum functon evaluatons F eval are taen as 100 and respectvely. For IEEE 118 bus system, populaton sze N and maxmum functon evaluatons F eval are taen as 250 and respectvely. For IU 62 bus system, populaton sze N and maxmum functon evaluatons F eval are taen as 120 and respectvely. For the algorthm, the tolerance values for both obectves TolFun and coordnates TolX are assumed as 1x10-5. For IEEE 30 bus system, populaton sze N and maxmum functon evaluatons F eval are fxed at 100 and respectvely. For IEEE 118 bus system, populaton sze N and maxmum functon evaluatons F eval are fxed at 250 and respectvely. For IU 62 bus system, populaton sze N and maxmum functon evaluatons F eval are fxed at 120 and respectvely. 4.4 IMPLEMENTATION OF SINGLE OBJECTIVE CENTRALIZED CONGESTION MANAGEMENT In the proposed mproved COPF model, the general scheme for centralzed congeston management of the forward maret s dscussed. Based on the ntal contracts of all the transactons, the congested transmsson lnes and load flow on the transmsson lnes are determned by the ISO usng load flow results. Based on the load flow result the ISO maxmzes the socal welfare wth the constrant that the load flow on the congested lne should be less than the maxmum capacty of the lne. The generaton and demand

4 49 detals that are obtaned durng the optmzaton procedure wll be sent to the ndvdual transacton. Based on the receved generaton and demand, each transacton adusts ts contract generaton and demand Implementaton usng Step : Randomly generate the partcles value between the upper X u and lower X l lmts of generaton and demand of all the transactons. Step : Assgn the ntal generaton and demand partcle value as the Pbest values. Step : Compute the ftness functon of each partcle and compare t wth ts Pbest. The best among the Pbest s the Gbest. Step : Change the velocty and poston of the partcle usng Equatons 2.2 and 2.3 Step : Compare the ftness functon of each partcle wth ts Pbest. If the current value s better than the Pbest, then set the Pbest value equal to the current value and the Pbest locaton equal to the current locaton n the search space. Step : Compare the best current ftness evaluaton wth the populaton s Gbest. If the current value s better than the Gbest, then reset the Gbest to the current best poston and ftness value. Step : Repeat steps to untl the convergence crteron of the maxmum number of evaluatons s met. the ISO. The optmal generaton and demand wll be sent to the transactons by

5 Implementaton usng Step : The requres a seed vector to generate the ntal populaton, usng Gaussan samplng, wth lower X l and upper X u lmts of generaton and demand for all the transacton. Step : The Intal coordnate wse standard devaton vector s set at 0.25 tmes range of each coordnate. Step : The offsprng populaton s generated around the ntal seed vector by samplng a multvarate normal dstrbuton wth a nown covarance matrx and overall standard devaton. Step : The covarance matrx Co determnes Be and De, and s adapted by means of the summaton of the weghted center of mass dfferences. g1 Step : The Global step sze s based on a conugate evoluton path 1 P g, whch s calculated usng Equaton 2.8, and the global step sze g1 s computed usng Equaton 2.9 Step : Steps are repeated untl the maxmum number of functon evaluatons or tolerance of varables and obectve functon s reached. The optmum generaton and demand wll be sent to all the transactons by the ISO. 4.5 RESULTS AND DISCUSSION The IEEE 30 bus system, IEEE 118 bus system and IU 62 bus system case 1 and case 2 are consdered for smulaton. Smulaton s conducted on a Core 2 duo PC 2.93GHz usng MATALAB.

6 IEEE 30 bus system Smooth cost functon Table 4.1 compares the statstcal performances of SQP, and algorthms wth the smooth obectve functon. The statstcal results of socal welfare show the better performance of the algorthm. The total socal welfare obtaned usng the algorthm s better than that of the other algorthms. In Table 4.1, the standard devaton of the algorthm s lesser than that of the other algorthms and t shows the consstency of the algorthm. The load flow caused by the ndvdual transactons on lne for ther best contract s also gven n Table 4.1. It shows that the congeston s cleared. The best contracts of each transacton usng SQP, and algorthms are shown n Table 4.2. It shows that the algorthm gves a better contract than other algorthms whle clearng congeston. Fgure 4.1 shows the socal welfare durng teratons usng for smooth cost functon. From the Fgure 4.1, t s clear that the algorthm for COPF model converges near 100 teratons. Durng ntal perod, the updates ts covarance matrx. Table 4.1 Results of COPF -smooth cost functon IEEE 30 bus Method used Capacty of transmsson lne used by transactons n MW Total capacty used n MW Total Proft n $/hr T1 T2 T3 Best Worst Mean SD SQP COPF COPF COPF

7 52 Table 4.2 Best contracts n MW -smooth cost functon IEEE 30 bus Method used SQP COPF COPF T1 T2 T3 P D P D P D COPF SOCIAL WELFARE, $/hr ITERATION NUMBER Fgure 4.1 Socal welfare durng teratons usng -IEEE 30 bus COPF-smooth cost functon

8 Non-smooth cost functon Table 4.3 shows the statstcal results of and algorthms wth the non-smooth obectve functon. The SQP cannot be appled because of the non-smooth obectve space. The statstcal results show that the socal welfare obtaned usng the algorthm s better than that of the. In Table 4.3, standard devaton of the algorthm s lesser than that of the and t shows the consstency of the algorthm. The load flow caused by the ndvdual transactons on lne correspondng to ther best contract s also gven n Table 4.3. It shows that the congeston s releved. The best contracts of each transacton usng the and algorthms are gven n Table 4.4. It shows that the best contract obtaned usng the algorthm s better than that of the algorthm whle relevng congeston. Fgure 4.2 shows the socal welfare durng teratons usng for non-smooth cost functon and t converges near 100 teratons. Table 4.3 Results of COPF -non-smooth cost functon IEEE 30 bus Method used COPF COPF Capacty of transmsson lne used by transactons n MW Total capacty used n MW Total Proft n $/hr T1 T2 T3 Best Worst Mean SD

9 54 Table 4.4 Best contracts n MW -non-smooth cost functon IEEE 30 bus Method used T1 T2 T3 P D P D P D COPF COPF SOCIAL WELFARE, $/hr ITERATION NUMBER Fgure 4.2 Socal welfare durng teratons usng -IEEE 30 bus COPF- non-smooth cost functon

10 IEEE 118 bus system Smooth cost functon Table 4.5 compares the statstcal performances of the SQP, and algorthms wth the smooth obectve functon. The statstcal results of socal welfare show the better performance of the algorthm. It shows that the socal welfare obtaned usng the algorthm s better than that of the other algorthms. In Table 4.5, the standard devaton of the algorthm s lesser than that of other algorthms and t shows the consstency of the algorthm. The load flow caused by the ndvdual transactons on lne for ther best contract s also gven and t shows that congeston s cleared. The best contracts of each transacton usng SQP, and algorthms are shown n Table 4.6. It shows that the algorthm gves better contracts than the other algorthms whle clearng congeston. Fgure 4.3 shows the socal welfare wth smooth cost functon durng teratons usng. Table 4.5 Results of COPF -smooth cost functon IEEE 118 bus Method used Capacty of transmsson lne used by transactons n MW Total Capacty used n MW Total proft x 10 3 $/hr T1 T2 T3 T4 T5 T6 Best Worst Mean SD SQP COPF COPF COPF

11 56 Table 4.6 Best contracts n MW -smooth cost functon IEEE 118 bus Transactons T1 T2 T3 T4 T5 T6 SQP COPF COPF COPF P D P D P D SOCIAL WELFARE, $/hr ITERATION NUMBER Fgure 4.3 Socal welfare durng teratons usng -IEEE 118 bus COPF- smooth cost functon

12 Non-smooth cost functon Table 4.7 shows the statstcal results of the and algorthms wth the non-smooth obectve functon. The statstcal results show that the socal welfare obtaned usng algorthm s better than that of the algorthm. In Table 4.7, the standard devaton of algorthm s lesser than that of the and t shows the consstency of the algorthm. The load flow caused by the ndvdual transactons on lne correspondng to ther best contract s also gven n Table 4.7. It shows that the congeston s releved. The best contracts of each transacton usng the and algorthms are gven n Table 4.8. It shows that the algorthm gves better contract than the algorthm, whle relevng congeston. Fgure 4.4 shows the socal welfare wth non-smooth cost functon durng teratons usng. Table 4.7 Results of COPF - non-smooth cost functon IEEE 118 bus Method used Capacty of transmsson lne used by transactons n MW Total Capacty Total Proft x10 3 $/hr used T1 T2 T3 T4 T5 T6 Best Worst Mean n MW SD COPF COPF

13 58 Table 4.8 Best contracts n MW - non-smooth cost functon IEEE 118 bus Transactons T1 T2 T3 T4 T5 T6 COPF COPF P D P D SOCIAL WELFARE, $/hr ITERATION NUMBER Fgure 4.4 Socal welfare durng teratons usng -IEEE 118 bus COPF- non-smooth cost functon

14 IU 62 bus system Smooth cost functon Tables 4.9 and 4.10 compare the statstcal performances of the SQP, and algorthms wth the smooth cost functon for case 1 and case 2. The statstcal results of the socal welfare show the better performance of the algorthm. In Table 4.9 the load flow caused by the ndvdual transactons for case 1 and case 2 for ther best contract s gven and t shows that the congeston s releved. In Table 4.10, the standard devaton of algorthm s lesser than that of the other algorthms and t shows the consstency of the algorthm. Table 4.10 shows that the algorthm gves better value for socal welfare than the other algorthms. The best contracts of each transacton for case 1 and case 2 usng the SQP, and algorthms are shown n Table It shows that the algorthm gves better contract than the other algorthms, whle relevng case 1 and case 2 congestons. Fgure 4.5 and Fgure 4.6 show the socal welfare wth smooth cost functon durng teratons usng for case 1 and case 2 respectvely. Table 4.9 Capacty of the lne -smooth cost functon IU 62 bus Method used SQP COPF COPF COPF T1 T2 Case 1 Case 2 Total capacty Used n MW T1 T2 Total capacty Used n MW

15 60 Table 4.10 Total proft - smooth cost functon IU 62 bus system Case 1 Case 2 Method Used Proft x10 3 $/hr Proft x10 3 $/hr SD Best Worst Mean Best Worst Mean SD SQPCOPF COPF COPF Table 4.11 Best contracts n MW - smooth cost functon IU 62 bus Case/ Transacton 1/T1 1/T2 2/T1 2/T2 SQP COPF COPF COPF P D P D P D

16 SOCIAL WELFARE, $/hr ITERATION NUMBER Fgure 4.5 Socal welfare durng teratons usng -IU 62 bus COPF case 1- smooth cost functon SOCIAL WELFARE, $/hr ITERATION NUMBER Fgure 4.6 Socal welfare durng teratons usng -IU 62 bus COPF case 2-smooth cost functon

17 Non-smooth cost functon Table 4.12 and 4.13 show the statstcal results of the and algorthms wth the non-smooth obectve functon for case 1 and case 2. The statstcal results show better performance of the algorthm. In Table 4.12, the load flow caused by the ndvdual transactons for case 1 and case 2 correspondng to ther best contract s gven and t shows that the congeston s cleared. Table 4.13 shows that the socal welfare obtaned usng algorthm s better than that of the algorthm. In Table 4.13, standard devaton of algorthm s lesser than that of the and t shows the consstency of algorthm. The best contract of each transacton usng the and algorthms for case 1 and case 2 are gven n Table It shows that the algorthm gves better contract than the other algorthms, whle clearng case 1 and case 2 congestons. Table 4.15 compares the average CPU tme requred for IEEE 30 bus, IEEE 118 bus and IU 62 bus systems to converge to the optmal soluton wth the SQP, and algorthms. From Table 4.15, t s clear that the average CPU tme requred for the algorthm to converge to the optmal soluton s approxmately 33.3% of the average CPU tme requred for SQP and 66.6% of CPU tme requred for the algorthm. For the COPF model, the algorthm gves better socal welfare than the and SQP at a comparatvely lesser CPU tme. Fgure 4.7 and Fgure 4.8 show the socal welfare wth non-smooth cost functon durng teratons usng for case 1and case 2 respectvely.

18 63 Table 4.12 Capacty of the lne - non-smooth cost functon IU 62 bus Method used T1 Case 1 Case 2 Total Total T2 capacty T1 T2 capacty Used n MW Used n MW COPF COPF Table 4.13 Total proft - non-smooth cost functon IU 62 bus Case 1 Case 2 Method Used Proft x10 3 $/hr Proft x10 3 $/hr SD Best Worst Mean Best Worst Mean SD COPF COPF

19 64 Table 4.14 Best contracts n MW - non-smooth cost functon IU 62 bus Case/ Transacton 1/T1 1/T2 2/T1 2/T2 COPF COPF P D P D Table 4.15 Comparson of average CPU tme COPF Method used Obectve Test System Model SQP functon n secs n secs n secs IEEE 30 Smooth COPF Non smooth COPF IEEE 118 Smooth COPF Non smooth COPF Practcal Indan Utlty 62 Smooth Non smooth COPF COPF Case Case Case Case

20 SOCIAL WELFARE, $/hr ITERATION NUMBER Fgure 4.7 Socal welfare durng teratons usng -IU 62 bus COPF case 1- non-smooth cost functon SOCIAL WELFARE, $/hr ITERATION NUMBER Fgure 4.8 Socal welfare durng teratons usng -IU 62 bus COPF case 2- non-smooth cost functon

21 66 A sngle obectve centralzed congeston management approach usng an AC load flow s proposed for the forward electrcty maret. In the proposed mproved centralzed model, the total socal welfare s maxmzed wth the smooth and non-smooth cost functons by the ISO, and the congeston s releved by adustments n the ntal contracts. The SQP, and algorthms are used. Testng on the IEEE 30 bus, IEEE 118 bus and IU 62 bus systems shows that the proposed mproved sngle obectve centralzed model s effectve. The algorthm gves better socal welfare at comparatvely lesser average CPU tme than the other algorthms. The convergence characterstcs of the varous test systems show that the total socal welfare of the COPF model usng the algorthm converges near 100 teratons.