SMALL-SIGNAL STABILITY ASSESSMENT OF THE EUROPEAN POWER SYSTEM BASED ON ADVANCED NEURAL NETWORK METHOD

SMALL-SIGNAL STABILITY ASSESSMENT OF THE EUROPEAN POWER SYSTEM BASED ON ADVANCED NEURAL NETWORK METHOD S.P. Teeuwen, I. Erlich U. Bachmann Univerity of Duiburg, Germany Department of Electrical Power Sytem teeuwen@uni-duiburg.de erlich@uni-duiburg.de Vattenfall Europe Tranmiion GmbH Berlin, Germany udo.bachmann@vattenfall.de Abtract: Thi paper deal with a new method for eigenvalue prediction of critical inter-area tability mode of the European electric power ytem baed on Neural Network (NN). The exiting method for eigenvalue computation are time-conuming and require the entire ytem model that include an extenive number of tate. The ytem feature uitable a input of the NN are elected baed on a new multi tep election technique. After proper training of the NN, the damping and frequency of the ocillation can be predicted very fat and with high accuracy. Hereby, the neural network output decribe the activation of ampling point in the complex plain, which reflect the nearne of eigenvalue. The interpolation of activation reult in region where the eigenvalue are predicted to be located. The method i uitable for on-line application. Copyright 003 IFAC Keyword: Eigenvalue, Ocillation, Neural network, Small ignal mode 1. INTRODUCTION Inter-area ocillation in large-cale power ytem are becoming more common epecially for the European Interconnected Power Sytem UCTE/CENTREL. The ytem ha grown very fat in a hort period of time due to the recent eat expanion. Thi extenive interconnection alter the tability region of the network, and the ytem experience inter-area ocillation aociated with the winging of many machine in one part of the ytem againt machine in other part. Moreover, for certain load flow condition, the ytem damping change widely, (ee) (Bachmann, et al., 1999) and (Breulmann, et al., 000). With deregulation of electricity market in Europe, the utilitie are allowed to ell their generated power outide their traditional border and compete directly for cutomer. For economical reaon, the operator are often forced to teer the ytem cloer to the tability limit. Thu, the operator need different computational tool for ytem tability etimation. Thee tool mut be accurate and fat to allow online tability aement. The computation of the mall ignal tability i a time conuming proce for large network, which include the load flow computation, the linearization at the operating point, and the eigenvalue computation. An alternative method i to ue a Neural Network (NN) trained with off-line data for different load flow and ytem condition. By uing NN, a fat computation of the eigenvalue i poible, providing that the network i properly deigned and trained. Recent NN approache howed highly accurate reult regarding the eigenvalue prediction of largecale power ytem (Teeuwen, et al., 001). But all of them are trained only for narrow operating condition of the power ytem. In fact, when the operating point of a given power ytem change, the correponding eigenvalue may hift ignificantly. Small change, e.g. in the network topology, the current load ituation or the voltage level, may change the poition of the eigenvalue. Thi change in poition lead to the fact that the number of eigenvalue in the weakly damped region i not contant for all conidered ituation. Therefore, the NN ha to be deigned a a robut aement tool

that i not influenced by time of the day, the eaon, and the power ytem topology. The NN introduced in (Teeuwen, et al., 001) predict the eigenvalue itelf. But a NN, which i able to manage all the above-mentioned additional influence, mut be deigned for a varying number of eigenvalue. Hence the NN mut have a variable tructure, which i a difficult tak. To addre thi iue, the aement method propoed in thi paper i baed not on the prediction of eigenvalue per e but on the prediction of region, which could contain one or more dominant eigenvalue with inufficient damping. To generate the training data for the NN, an obervation area i defined within the complex eigenvalue pace. Thi obervation area i located at a low damping level and frequencie where interarea eigenvalue typically occur. Then, the entire obervation area i ampled in the direction of the real and imaginary axe. The ditance between the ample point and the eigenvalue are computed and the ample point are activated depending on whether there are eigenvalue nearby or not. The cloer an eigenvalue to a ample point, the higher the correponding activation. Once thi i computed for the entire et of pattern, the NN i trained with thee activation. After proper training, the NN can be ued in real time to compute the ample activation. Then, the activation are tranformed into a region where the eigenvalue are obviouly located. Thee region are characterized by activation higher than a given limit.. IVESTIGATED POWER SYSTEM The power ytem invetigated in thi tudy i the extended UCTE/CENTREL high voltage European network, including the Eat European and Balkan ytem. It conit of approximately 500 generator, everal thouand line and node, hundred of tranformer, etc. The generator are decribed by 5. order model, while different uer-defined model are employed for the controller. The ytem data i prepared for dynamic invetigation in the time range of econd to a few minute. Alongide the time domain imulation, the oftware package ued allow the calculation of eigenvalue and eigenvector. Fig. 1a-c provide an overview of the inherent ytem dynamic behavior, the o called mode hape. Mode hape depicted in Fig.1 repreent the mot important inter-area mode, which will be invetigated next. The arrow how the direction and the relative intenity of the correponding wing, becaue they repreent the eigenvector correponding to the mechanical motion of generator rotor. The poitioning of arrow to the generator geographical location i arbitrary. However, thi kind of viualization provide an excellent overview about the pread of ocillation. The damping of the firt mode in the bae tate i very good a yet. However, it can change with the operating point over a wide range a hown in Fig.. Eigenvalue 1: f=0.199 Hz, ζ=13,3% Eigenvalue : f=0.9 Hz, ζ=.9% Eigenvalue 3: f=0.368 Hz, ζ=0.9% Fig. 1 Modehape to the three conidered inter-area mode Fig. contain the eigenvalue for 500 different load-flow ituation. It i calculated by varying the active power tranit between different network area, which correpond with different utilitie. To increae the power generation in one area the neceary number of unit were taken into operation. At the ame time in the power receiving area the generation wa reduced by witching off unit. Generally, the load-flow cenario were adjuted baed on practical experience. a) b) c)

Eigenvalue Eigenvalue 1 Eigenvalue 3 Fig. Conidered interarea eigenvalue for 500 load-flow cenario From Fig. follow that all three eigenvalue may experience change ranging up to untable value. Furthermore, the impact of tranaction on the eigenvalue i trongly non-linear. Obviouly, it depend on everal factor and cannot be decribed analytically. 3. NN-BASED APPROACH It i known that NN are able to learn complex nonlinear relationhip. Furthermore, a NN input uually a reduced number of ytem feature are ufficient. A further advantage of the NN i it very fat computation time. The baic idea for NN-baed mall ignal tability aement i hown in Fig. 3. Input: Selected ytem feature Input Layer x 1 x x a x a+1 NN : Non-linear function W ji Hidden Layer Output Layer Fig. 3 NN-baed Small Signal Stability Aement It i clear that eigenvalue calculation uing NN will alway be afflicted with error. Therefore, the accuracy enured by the method mut be adequate for the propoed application. Two baic quetion arie: - How can feature for NN be elected? - How can eigenvalue location be mapped by NN output? The firt quetion i a general one and will be dicued in the next chapter. 1 b b+1 V kj out 1 out out c Output: Mapped eigenvalue location Eigenvalue mapping can be done in different way. Apparently, the coordinate of eigenvalue can be calculated directly by the NN. Thi method ha been proven in (Teeuwen, et al., 001) and i applicable with the following retriction: the locu of different eigenvalue may not overlap each other and the number of eigenvalue mut remain alway contant. Thee follow from the fact that eigenvalue are aigned directly to NN output. Another approach conider fixed rectangular region, which - depending on the ditance between region centroid and eigenvalue - are activated or not. The output of the NN are in thi cae the activation of predefined region (Teeuwen, et al., 003a). Enhancement could be achieved with thi method by making the region width on the abcia variable (Teeuwen, et al., 003b). A more generalized method conider the activation of ampling point without any fixed partitioning of the complex plain into region (Teeuwen, et al., 003c). Thi method will be applied to the ytem decribed in thi paper and will be dicued next. Generally, the advantage of each method, taking into account activation value to be predicted, i the fact that eigenvalue mut not be eparable. Therefore the number of eigenvalue can vary and overlapping doe not lead to problem. The propoed tability aement method require that the obervation area in the complex eigenvalue pace i defined firt. The obervation area i located at the region of inufficient damping, where typical inter-area eigenvalue can be found. In thi tudy, the conidered damping range i choen between 4% and 1.0%. Then, thi area i ampled along the real axi (σ ) with a contant tep width. Thi i done for the given application 5 time for 5 different frequencie f. The ampling tep applied are a follow: 1 σ = 0.015 f = 0.14 Hz The obervation area of inufficient damping i hown in Fig. 4. The ample point are marked by circle. 4% 3% % 1% 0% -1% -% NN A NN B NN C NN D NN E Fig. 4. Partitioning and ampling of eigenvalue plain The ampling reult in a et of 40 ample point. To increae the accuracy of the prediction, the

obervation area i divided into maller obervation ection (row of ample point) whereby each row of ample point ue it own NN. Hence, 5 independent NN are ued. After the obervation area i ampled, the ample point need to be activated according to the poition of the eigenvalue. Thu, the ditance between the eigenvalue and the ample i ued to compute activation for the ample point. The eigenvalue are defined by their real component σ and their frequency f ev their location ( σ,. The ample point are defined by f ). Then, the ditance between a given eigenvalue and a given ample i computed a follow: d = σ σ ev f f ev + (1) kσ k f Becaue σ and f ue different unit and cannot be compared directly, both are caled. Hence, σ and f are divided by the contant for the real part and k f for the frequency, repectively. The imum ditance poible between an eigenvalue and the cloet ample point occur when the eigenvalue i located exactly in the geometrical center of 4 neighboring ample point. Thi i hown in Fig. 5. ( σ, f ) Fig. 5. Definition of the imum ditance d According to Fig. 5 and Equation (1), the imum ditance can be computed a d σ = k σ k σ f + k f ev () Baed on thi imum ditance, the activation value a for a ample i defined a a linear function depending on the ditance between a ample point and an eigenvalue: a d σ Eigenvalue d 1 0.5 = d 0 d 0 d d d > d (3) Thi activation a i computed for a given ample point with repect to all eigenvalue reulting from one pattern. f The final activation value act for the given ample point i the ummation of all activation a act = n i= 1 a (4) whereby n i the number of conidered eigenvalue. The imum ditance () and the activation function (3) lead to the minimum activation for a ample point when an eigenvalue i nearby: act 0.5 (5) The ucce of the prediction depend trongly on the choice of the caling parameter. Thee parameter impact both the training proce of the NN and the accuracy of the predicted region a well. Therefore, ome experience are neceary to apply the propoed method to particular power ytem. 3. FEATURE SELECTION The firt tep for creating any artificial intelligence baed mall ignal tability aement ytem, however, i the election of feature ued a input. A an important iue to be conidered i the fact that the elected feature mut be exchanged between utilitie, i.e. it i required that utilitie are willing to offer thee quantitie to their partner utilitie. Large cale power ytem include many feature uch a tranmiion line flow, generated power, demand, etc.. It i obviou that for a large ytem, the feature et i too large for any effective NN training, ee (Teeuwen, et al., 001). Hence, feature extraction or election technique mut be utilized. Even for election, the feature cannot be treated all together. Therefore, in thi tudy a Multi Step Selection (MSS) technique ha been ued. It i hown in Fig. 6. The number of potential feature in thi tudy reache approximately nine thouand. Therefore feature are divided into five group. Table 1 how the aignment of feature to the group. The group are formed on the bai of phyical knowledge. Then, the Principal Component Analyi (PCA) i utilized to reduce the dimenion of feature vector, which i equal to the number of invetigated load-flow cenario, i.e. exactly 500 (number of pattern). Thi reduction i neceary becaue the applied k-mean clutering algorithm in the ubequent tep how a better performance with maller feature vector. The clutering algorithm put together imilar feature, which contain redundant information. Therefore, only one feature i choen from each cluter for further proceing, which i treated according to the election of ingle group. In the end 50 feature remain a input for the NN. Thi number i till high and could be further reduced. However, conidering poibly miing feature in real ytem caued for example by ignal tranmiion failure, ome redundancy ha to be provided. The remaining 50 feature belong to different phyical quantitie and are pread over the whole network.

Group1 Group... Group5 Reduction of feature dimenion by Principal Component Analyi Clutering by k-mean activation level of 0.5, which i called limit urface. The interection of the activation urface and the limit urface lead to a region, which i called predicted region (Fig. 7b). Activation Surface Limit Surface + Reduction of feature dimenion by Principal Component Analyi Clutering by k-mean a) 50 elected feature Fig. 6. Applied MSS Feature Selection Method Table 1 Grouping of feature Feature Occurrence in the Network Feature Group Sum of active and reactive power in each high voltage utility 58 1 Rotating energy of generator per utility 9 1 Active power tranfer through line.089 Reactive power tranfer through line.089 3 Magnitude of nodal voltage.016 4 Phae angle of nodal voltage.016 5 Active power of generator 468 6 Reactive power of generator 468 6 Kinetic energy of generator 468 1 5 APPLICATION AND RESULTS The ample point activation were computed for the eigenvalue of the 500 calculated load-flow cenario. Thu, the deired input and output of the NN were given. Then the data et were normalized and huffled randomly before the 5 NN ha been trained independently. The training wa carried out with a ubet of training data, wherea a maller part of the data wa kept back for teting. Once the NN are trained properly, the NN output value repreenting the activation of the ampling point, need to be tranformed into eigenvalue location. For thi purpoe all activation value were ued to etup an activation urface, which i contructed by linear interpolation between all row and column of ample point a hown for a elected pattern in Fig. 7a. Then, a plain urface i drawn at the minimum 4 % 3 % % 1 % 0 % Predicted eigenvalue region True eigenvalue poition Fig. 7. (a) Activation urface contructed by ample point interpolation and limit urface, (b) View from above: predicted region in the complex pace If the NN i trained properly, the true eigenvalue poition will be within thi predicted region a hown in Fig. 7b. For a more ound error evaluation, the predicted region are compared with the poition of the eigenvalue for all pattern. If an eigenvalue i located inide a region, the prediction yield correct. If an eigenvalue i located outide the correponding region or no range and therefore no region i contructed for thi eigenvalue, the error i called fale dimial. If a range i contructed, but no correponding eigenvalue exit within the obervation area, the error i called fale alarm. The error rate for both kind of error are calculated according to Eq. (6) number of fale dimial or fale alarm E [%] = 100 (6) number of pattern Table contain the reult for the invetigated ytem. b)

Table Error rate for NN Training and Teting Reult Training Tet Predicted region matche eigenvalue poition 99, % 97,5 % Fale dimial 0,8 %,5 % Fale alarm 0,0 % 0,0 % Fale alarm wa never regitered. Fale dimial occurred in.5% of all cae, which, however, doe not necearily mean that thi prediction are not utilizable. The eigenvalue were alway located near the predicted region. By uing a lightly modified activation function, it i poible to reduce the error rate. Thereby, however, the expane of the predicted region will increae. Therefore, for an evaluation of the propoed method the width of the region in frequency and damping mut be conidered too. Fig. 8 how the definition of region width ζ and reg, repectively. f reg 6. CONCLUSIONS Thi paper introduce a new method of eigenvalue prediction for mall-ignal tability aement. The method i flexible in term of the network condition and can manage a variable number of eigenvalue without lo of accuracy. The area of interet in the complex eigenvalue pace i ampled and the ample point are ued to obtain an activation urface after proper NN training. Thi activation urface can be ued to contruct a region. In other word, the eigenvalue are located within the predicted region, which i given by the prediction tool. It ha been hown that the method i applicable with good accuracy to the European interconnected power ytem. One of the key advantage of thi new technique reult from the fact that only a few elected ytem feature are neceary for eigenvalue prediction. However, in large-cale ytem the feature election mut be treated with well-founded method. Thi paper propoe a multi tep election technique, which applie principal component analyi and the k-mean clutering algorithm to preelect feature group. The NN baed eigenvalue prediction i very fat and, therefore, i applicable for on-line dynamic tability aement. REFERENCES Fig. 8. Definition of the width of a predicted region in damping ( ) and frequency ( ) ζ reg f reg The mean and tandard deviation of ζ and reg were computed for all pattern, which include f reg eigenvalue in the obervation area. Table 3. contain the reult Table 3 Width of predicted eigenvalue region Region Training Tet width Average STD Average STD ζ reg 1,038% 0,430% 1,035% 0,49% f reg 0,055Hz 0,03Hz 0,055Hz 0,04Hz Auming that the eigenvalue will alway be expected in the center of the predicted region, the method provide an average accuracy of ±0.5% for damping and ±0.03 Hz for frequency. By proper modification of the activation function the accuracy could be further increaed at the expene of error rate. Therefore both iue mut be compromied according to the current requirement Bachmann, U., Erlich I., Grebe, E. (1999). Analyi of interarea ocillation in the European electric power ytem in ynchronou parallel operation with the Central-European network, IEEE PowerTech, Budapet Breulmann, H., Grebe, E., Löing, et. al. (000). Analyi and Damping of Inter-Area Ocillation in the UCTE/CENTREL Power Sytem, CIGRE 38-113, Teeuwen, S.P., Ficher, A., Erlich, I., El-Sharkawi, M.A. (001). Aement of the Small Signal Stability of the European Interconnected Electric Power Sytem Uing Neural Network, LESCOPE 001, Halifax, Canada Teeuwen, S.P., Erlich, I., El-Sharkawi, M.A. (003a). Neural Network baed Claification Method for Small-Signal Stability Aement, accepted paper for IEEE PowerTech 003, Bologna, Italy Teeuwen, S.P., Erlich, I., El-Sharkawi, M.A. (003b). Advanced Method for Small-Signal Stability Aement baed on Neural Network, accepted paper for ISAP 003, Lemno, Greece Teeuwen, S.P., Erlich, I., El-Sharkawi, M.A. (003c). Small-Signal Stability Aement baed on Advanced Neural Network Method, accepted paper for IEEE PES General Meeting 003, Toronto, Canada Teeuwen, S.P., Erlich, I., El-Sharkawi, M.A. (00). Feature Reduction for Neural Network baed Small-Signal Stability Aement, PSCC 00, Sevilla, Spain