the results to larger systems due to prop'erties of the projection algorithm. First, the number of hidden nodes must

Transcription

1 M.E. Aggune, M.J. Dambrg, M.A. El-Sharkawi, R.J. Marks II and L.E. Atlas, "Dynamic and static security assessment f pwer systems using artificial neural netwrks", Prceedings f the NSF Wrkshp n Applicatins f Artificial Neural Netwrk Methdlgy in Pwer Systems Engineering, April 8-10, 1990, Clemsn University, pp DYNAMIC AND STATIC SECURITY ASSESSMENT OF POWER SYSTEMS USING MTIFICIAL NEURAL NEmORXS H.E. Aggune, H.J. Dambrg, L A. El-Sharkawi, R.J. Harks XI, L.E. Atlas Department f Electrical ~ngineering university f Washingtn Seattle, WA What fllws is a summary f sme f the authrsf wrk n tw types f security prblems. In this wrk we used a layered perceptrn with tw training algrithms, a prjectin algrithm and aa errr backprpagatin algrithm. The prjectin algrithm is based n the least squares apprximatin technique and the errr backprpagatin n the steepest descent technique. 1. Dynamic Security Preliminary results were btained frm studies f the dynamic security f a 9 buses, 3 generatrs, and 14 transmissin lines test system. Our first study analyzed the relatinship between system stability and the utput pwer f generatr 3, the excitatin f generatr 3, the apparent pwer f lad 8, and the availability f lines 9 and 10. The results were reprted in [I]. Sme f these results are shwn in Figures 1 and 2. Basically, the accuracy f classificatin and the ability f the ANN t generalize were very gd. Hwever, we encuntered difficulties in extending the results t larger systems due t prp'erties f the prjectin algrithm. First, the number f hidden ndes must be at least as large as the number f training data pints. Secnd, as the number f hidden ndes grew, the prjectin algrithm became unstable due t the prblem f inverting an ill-cnditined matrix Our secnd examinatin f the dynamic security f this system used the errr backprpagatin training algrithm [2]. While this apprach requires fewer ndes in the ANN, the training time is lnger because it is iterative. This secnd study examined the security f the system with respect t the utputs P3 and 43 f generatr 3, the apparent pwer utput S2 f generatr 2, and the status f line LO. he ANN used had 4 input ndes, three representing

2 the quantities P3, Q3, and S2 and 1 fr a cnstant bias input. The hidden layer had 10 ndes and the utput had ne nde. f training.sets were used, each f 1000 pints m allwed dmain in the three dimensinal P3 x 43 x 52 space. One set was chsen at randm ver this dmain using -a unifrm distributin. The ther training set was selected t emphasize the security regin bundaries. Each training set was used separately t train an ANN. In bth cases, cnvergence required a few hundred iteratins thrugh the set as shwn in Figure 3. T assess the classificatin accuracy f each trained ANN, we perfrmed an exhaustive query and Figure 4 shws the perfrmance curves. Fr-bth cases the classificatin accuracy is seen t be very gd. The additinal accuracy that appears t be achieved by the bundary enhancing training set is prbably nt.imprtant. Rather, the significance f this result is that the ANN is able t give a gd representatin f the security bundary fr a cmplex relatinship, infrmatin that can help the dispatcher perate near the bundary with mre'cnfidence than is available at present. 2. Static security ~hisysectin prvides a brief review f the wrk reprted in [3].,The test system.was cmpsed f 8 buses, 4 generatrs, and 14 transmissin lines. The gal was t represent the security relatinship invlving the lads at buses 6 and 8 and transmissin line number 4. The ANN chsen had 3 input neurns, ne fr each f P6, Q6 and Sai- and ne cnstant value, r bias input neurn. There was ne hidden layer with 10 neurns and ne utput neurn. With-.line 4 perating, the netwrk was trained t mnitr the values f P6, 46 and S8 and t indicate when cnstraints wuld-be vilated if line 4 were t fail. That is, line 4 was the nly element in the cntingency list. Traieng was accmplished with the errr backprpagatin algrithm and tw different training sets. The first set was a tw-dimensinal case where S8 was fixed at 100% f its nminal value. Tw thusand training pints were selected randmly in the P6, 46 plane. Figures 5 and 6 indicates the relatinship between the true and predicted security regin. Abaut 2% f the 6561 pints ver which the ANN was tested were misclassified. The false secure and false insecure indicatins were abut equal in number. d training set explred all 3 input variables. The S8 was allwed t have the discrete values f O%, 0% f nminal 10 and P6 and 46 were again

3 selected randmly fr each f these S8 values. A ttal f 1469 training pints was used. When tested, the ANN was fund t generalize smthly between the fixed values f S8 used in training as shwn in Figures 7 and 8. In bth cases, the perfrmance f the ANN was judged very gd fr the cmplex relatinships being classified. 3, The Current Challenge: slving Full Scale Prblems The basic challenge we see at present fr develping useful tls is ne f scale. Pwer systems are typically cnsidered "large scale systems. Hence, an ANN apprach must ultimately accmmdate this prblem f scale in sme manner, The prblems that we think will need t be faced are t determine : hw large an ANN is required and what its architecture must be, hw much data is required fr training and if that training can be accmplished in reasnable time, whether the training data (prbably frm ff-line studies) can be generated with reasnable effrt, a methd fr testing the trained ANN t measure its classificatin accuracy and develp the cnfidance f the dispatcher, if warranted, and hw t update the ANN s it cntinues t be current. 4. References [I] M. E. Aggune, et al., "Preliminary Results n Using Artificial Neural Netwrks fr Security Assessment.ll PICA Cnference, pp , May [2] M. A. El-Sharkawi, et al., "Dynamic Security Assessment f Pwer Systems Using Back Errr Prpagatin Artificial Neural Netwrks," Secnd Smpsium n Expert Systems ~pllicatin t Pwer Svstems, pp , July [3] M. E, Aggune, et al., "Artificial Neural Netwrks fr Pwer System static security Assessment." IEEE Prceedinas f the Internatinal Svm~sium n Circuits and Systems, Vl. 1, pp , May 1989,

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