Feature subset selection in dynamic stability assessment power system using artificial neural networks

TAÏP CHÍ PHAÙT TRIEÅN KH&CN, TAÄP 18, SOÁ K3- 2015 Feature subset selection in dynamic stability assessment power system using artificial neural networks  Nguyen Ngoc Au 1  Quyen Huy Anh 1  Phan Thi Thanh Binh 2 1Ho Chi Minh city University of Technical and Education 2Ho Chi Minh city University of Technology, VNU-HCM (Manuscript Received on October 30nd, 2014, Manuscript Revised July 08nd, 2015) ABSTRACT This paper presents method of feature Sequential Backward Selection (SBS), subset selection in dynamic stability Sequential Forward Floating Selection assessment (DSA) power system using (SFFS) and Feature Ranking (FR) algorithm artificial neural networks (ANN). In the to feature subset selection. The application of ANN on DSA power system, effectiveness of the algorithms was tested feature subset selection aims to reduce the on the GSO-37bus power system. With the number of training features, cost and same number of features, the calculation memory computer. However, the major results show that SFS algorithm yielded challenge is to reduce the number of higher classification rate than FR, SBS features but classification rate gets a high algorithm. SFS algorithm yielded the same accuracy. This paper proposes applying classification rate as SFFS algorithm. Sequential Forward Selection (SFS), Key words: feature subset selection, dynamic stability assessment, artificial neural networks, and power system. 1. INTRODUCTION sources and transmission systems are not developed to meet the load demand. While Modern power systems are forced to operating the power system is always faced with operate under highly stressed operating unusual circumstances such as a generator conditions closer to their stability limits. The outage, loss of a line, sudden dropping of a large operation of power systems is challenged load, switching of station or substation, and increasingly significant because investment Trang 15 SCIENCE & TECHNOLOGY DEVELOPMENT, Vol.18, No.K3 - 2015 three-phase sudden short circuit, ... Power The intelligent systems for DSA consist of system stability is the ability to regain an four basic steps: database generation, feature equilibrium state after being subjected to a selection, knowledge extraction and model physical disturbance and maintain the validation. In particular, a very important stage continuous supply of electricity to customers. is feature selection because it greatly affects Power system stability is classified [1]: rotor cost, computational time and recognition angle stability, frequency stability and voltage accuracy of DSA system. Feature selection stability. Rotor angle stability is divided into two actually reduces features or variables, just select categories including short-term and long-term. the minimum number of variables but ensure Short-term stability angle is considered transient recognition accuracy. This paper proposed dynamic stability and important contribution in applying FR (Feature Ranking), SFFS power system stability. Long-term stability (Sequential Forward Floating Selection), SFS angle includes small signal stability and (Sequential Forward Selection), SBS frequency stability. (Sequential Backward Selection) algorithm for feature subset selection. The case study was Due to the complexity of the power system, done on GSO-37bus power system diagram with traditional methods to power system analysis the support of simulation software PowerWorld take so much time and cause delays in decision 17. The algorithms of feature subset selection making. However, the relationship between pre- were programmed on Matlab software. fault parameters of the power system state and Multilayer Feed forward Neural Networks post-fault modes of power system stability has (MLFN) is supported by Matlab software. highly nonlinear, extremely difficult to describe this mathematical relationship. In order to 2. METHOD overcome such difficulties, intelligent system, 2.1. Mathematical Model of Multimachine that is ANN, has been proposed for DSA thanks Power System to special abilities in pattern classification [2],[6],[7]. Operating conditions of power The dynamic behavior of a generator power systems have wide range so that it is difficult system can be described by the following perform online calculations. ANN is in need of differential equations [1]: initial off-line data for training. Extensive off- d 2  i (1) line simulation is performed so as to acquire a M i 2  Pmi  Pei dt large enough set of training data to represent the different operating conditions of typical power d i It is known that:   i (2) systems. As a pattern classifier, once trained, dt neural networks not only have extremely fast By substituting (2) in (1), therefore (1) becomes: solutions but also get the ability to update new patterns or new operating conditions by d i M i  Pmi  Pei (3) generalizing the training data, improving dt recognition accuracy [7]. Where: i: rotor angle of machine i; i: rotor speed of machine i; Pmi: mechanical power of Trang 16 TAÏP CHÍ PHAÙT TRIEÅN KH&CN, TAÄP 18, SOÁ K3- 2015 machine i; Pei: electrical power of machine i; Step4. Subset feature evaluation. M : moment of inertia of machine i. i Step 5. Subset feature selection. The state of the power system is stable 2.2.2. Data generation, initial feature set when the rotor angle deviation of any two selection. generators not exceeding 1800, and is unstable when the rotor angle deviation of any two A large number of samples are generated generators exceed 1800. Status of power system through off-line simulation and the stable status was performed according to the proposed rules is evaluated for each fault under study. Data for in [1],]4],[5], as follow: each bus or line fault occurring in the test systems are recorded in which samples of data 0 If ij < 180 then Stable are kept in a database. The input is the vector of (4) system state parameters that characterize the 0 If ij  180 then Unstable current system state, usually called feature, they can be classified into pre-fault, fault-on and post- 2.2. Feature subset selection fault features. 2.2.1. General Description Pre-fault features [2]: steady-state The MLNF-based DSA power system can operating parameters such as voltage magnitude be formulated as a mapping yi = f (xi) after and angle of buses, P, Q load, generation and line learning from a stability database flow qualities Pflow, Qflow, Pload, Qload, Vbus, and n before disturbance occurs (P , Q ,  ,). D{xi , yi}i1. Where xi is feature; It is n- gen gen bus dimensional input vector that characterizes the Fault-on features [6]: variables that system operating state; and yi is output vector. characterize at fault-on state of power system The feature subset selection consists of selecting occur such as changes in nodal powers, in power a d dimensional feature vector z. Where d < flows in transmission line, voltage drops in the n; The d selected features represent the original nodes at instance of fault (Pflow, Qflow, Pload, data in a new knowledge base Qload, Vbus,). d Dnew {zi , yi}i1, and the new mapping Post-fault features [4]: variables that ynewi=fnew(zi). Thus, feature selection is actually describe system dynamic behavior after taking away unnecessary features and selecting disturbance occurs such as relative rotor angle, a candidate subset of features that get rich rotor angular velocity, rotor acceleration, rotor information with highly accurate identification kinetic energy, and the dynamic voltage of model. This process includes the following trajectory, steps: The problem of transient stability is usually Step 1. Data generation, initial feature set divided into two main categories: assessment selection. and prediction. Transient stability assessment usually focuses on the critical clearing time Step 2. Candidate feature subset selection. (CCT). In transient stability prediction, the CCT Step 3. Training and testing classification rate. is not of interest [11]. In this aspect, the progress Trang 17 SCIENCE & TECHNOLOGY DEVELOPMENT, Vol.18, No.K3 - 2015 of power system transient due to the occurrence x i  m i (5) z i  of disturbance is monitored. The key question in  i transient stability prediction is: the transient Where: m is mean value of data.  is standard swings are finally ‘Stable’ or ‘Unstable’ [3], i i deviation of data. [10]-[12]. Vector output variables represent the stable conditions of the power system. Need of 2.2.3. Candidate feature subset selection. fast DSA power system after the fault is stable or This step is the process of searching for unstable, so the output variables are assigned to potential subset features. The search strategy is label binary variable y [10, 01]. Class 1 [10] is divided into a global search and local search. stable class and class 2 [01] is unstable class. Global search strategy has the great advantage The use the post-fault variables can be too that for optimal result, but expensive long for operators to take timely remedial computation time. Therefore, the optimal search actions to stop the extremely fast transient strategy is not appropriate when a large number instability development process. of input variables. In the case of large input feature, local optimization search strategy will Found that, pre-fault input features are spend less time searching because the search variables that are too difficult to find a clear process is not through the entire search space. signal for sampled dataset learning. Post-fault input features will prolong a warning of 2.2.3.1. Local optimization search strategies instability power system. Fault-on input features - Sequential Forward Selection – SFS [8]: are proposed in [6] to overcome the drawbacks The SFS method begins with an empty set (k=0), such as analysis since the changes in the value of adds one feature at a time to selected subset with the parameters of input variables are a clear (k+1) features so that the new subset maximizes signal for dataset learning. So, this paper did the cost function J(k+1). It stops when the selected mining of fault-on input features (V , P , bus load subset has the d desired number of features, k<d. Qload, Pflow, Qflow) as a database for training neural networks. -Sequential Backward Selection-SBS [8]: The SBS method begins with all input features The output variables represent the dynamic D (k=D), removes one feature at a time to behavior of power system at fault-on. By selected subset with (k-1) features so that the observation from off-line simulation, these resultant subset maximizes the cost function J(k- binary output variables indicate the status of the 1). The algorithm stops when the resultant feature power system to comply with the law (4). set has the d desired number of features, k<d. The quantitative variables have different - Sequential Forward Floating Selection- units of measurement; the value of the variables SFFS [8]: The SFFS is one of two algorithms of in the different ranges will affect the calculation Floating Search Algorithm (FSA) that are SFFS results in recognition. Data normalization and SBFS (Sequential Backward Floating methods commonly applied in accordance with Selection). The SFFS algorithm the search starts the following formula: with an empty feature set and uses the SFS algorithm to add one feature at a time to the Trang 18 TAÏP CHÍ PHAÙT TRIEÅN KH&CN, TAÄP 18, SOÁ K3- 2015 selected feature subset. Every time a new feature Between-class scatter matrix that describes the is added to the current feature set, the algorithm scatter of the class means about the total mean tries to backtrack by using the SBS algorithm to is: remove one feature at a time to find a better c Ni T S  (m m)(m m) (11) subset. The algorithm terminates when the size b N i i of the current feature set is larger than the d i1 S is the covariance matrix of the feature vector desired number of features. m with respect to the global mean. Its trace is the -Feature Ranking-FR [2],[4]: This is a sum of variances of the features around their simple method which uses less computing time. respective global mean. Sm is: By evaluating cost function of a single feature, S = S +S (12) then it is ranked by ordering the best of them and m w b select for a good feature. Goal is to find a feature subset for which the within-class spread is small and the between- 2.2.3.2. Cost function [8, 9] class spread is large. The cost function is: Let the n data samples be x1 , . . . , xn. The 1 sample covariance matrix, Sm, is given by (6): J  trace{Sw Sm} (13) N th 1 T Formula (14), that was written for the k single S  (x  m)(x  m) (6) m  n n feature, is Fisher distance function: N n1 The sample mean of all data: S (k ) J (k )  b (14) S (k ) 1 N w m   xn (7) The value of J is bigger means that the feature is N n1 more important. The sample mean of class c : i 2.2.4. Training and testing classification rate 1 (8) To test the studied methods without loss of mi   xn Ni xnci generality, the database is randomly partition into k subsets that are D1, D2, , Di,, Dk, each Where: c is the number of class; N is the number i equal size. The model is trained on all the of sample mean of class c ; N is the number of i subsets except for one that is tested to measuring all samples. of validation accuracy. Training and testing are SW, within-class scatter Matrix, is: performed k times. The validation accuracy or classification rate is computed for each of the k c 1 Ni validation sets and averaged to get a final cross- Sw   Si (9) N i1 N validation accuracy. Classification rate of 1 training or testing is determined by the formula T (10) Si  (xn  mi )(xn  mi ) (15): Ni x c n n r(%)  r .100 (15) Si: is the covariance matrix for class i. N Trang 19 SCIENCE & TECHNOLOGY DEVELOPMENT, Vol.18, No.K3 - 2015 Where: nr is the number of sample for training or (37+25+25+56+56). The number of output testing with right result; N is the number of variables is 2 (class 1 [10]: stable class, class 2 sample for training or testing. [01]: unstable class). From simulated results and based on the law (4), there were 240 samples The expected value (EV) of classification rate of with 120 stable samples and 120 unstable the model was proposed in [6] by the formula samples. Sample set was normalized by formula (16): (5). Full feature set was randomly divided into 6 EV  0.9 (16) feature subsets. Each feature subset had 40 2.2.5. Training and testing classification rate samples (20 stable samples and 20 unstable and subset feature evaluation samples). So, each training subset had 200 samples (100 stable samples, 100 unstable Applying feature subset selection samples) and testing subset had 40 samples (20 algorithms were described as above to selecting stable samples, 20 unstable samples). feature subsets. Each feature subset was trained and tested, the classification rates are calculated 3.2 Results of feature subset selection by the formula (15). In this paper, four search algorithms that are Feature subset is selected with conditions SFS, SBS, SFFS and FR, were proposed that have smaller a number of features, agree to applying to feature subset selection. In which, the formula (16) and get higher classification the SFS, SBS, SFFS algorithms had been applied rate. in [2]. The objective function (13) was applied for these three algorithms in this study. FR 3. RESULTS - DISCUSSION algorithm had been applied in [2],[4] with Fisher 3.1 Feature set, samples for training distance function (15). Figure 1 shows the results of distance measuring value by SFFS, SFS and The off-line simulation was implemented to SBS algorithm. Figure 2 shows the results collection data for training. In this study, the ranked from large to small according to Fisher's GSO-37bus system, that is the standard system distance measuring the value of each single in the simulation program of PowerWorld 17 feature. software, [5], was used as case study. It consists of 37 buses, 9 generators; three different voltage 24 levels are 345kV, 138kV and 69kV, 25 loads, 14 22 transformers, 42 transmission lines. Load level 20 is one hundred percent rated load. Fault types are 18 balanced three-phase, single line to ground, line 16 J value J to line, double line to ground at buses and along 14 SFFS SFS transmission lines. Setting fault clearing time is 12 SBS 25ms [5] with all faults. 10 8 8 10 12 14 16 18 20 Input and output variables are x[Vbus, Feature (d) Pload, Qload, Pflow, Qflow] and y[10,01]. Figure 1 distance calculated value of SFFS, SFS and Totalof input variables is 199 SBS algorithm. Trang 20 TAÏP CHÍ PHAÙT TRIEÅN KH&CN, TAÄP 18, SOÁ K3- 2015 Table 1. The measured distance (J value) of SFFS and SFS algorithm of feature subsets with 98 d=13 and d=20. 96 Feature J value J value (SFS) 94 (d) (SFFS) 92 13 15.42795 15.42502 90 Classification 88rate (%) SFFS 20 23.54927 23.48542 SFS 86 SBS Fisher 1.4 84 8 10 12 14 16 18 20 Feature (d) 1.2 1 Figure 3 clasification rate of testing feature subsets by MLNF. 0.8 J value 0.6 updating algorithm was selected. These functions are supported in neural networks tool 0.4 of R2011b Matlab software. Programs were 0.2 performed by laptop with CPU Inter CoreTM i3- 0 0 50 100 150 200 380M, 2GB DDR3 Memory, 500GB HDD. Feature (d) Figure 3 shows classification rate of testing Figure 2 Fisher's distance measuring value. feature subsets with algorithms by MLNF. Table 3 Training time and testing classification Table 2. Calculating time of SFS, SFFS, SBS rate of algorithms with d=12 and d=199. algorithm with d=20 and FR with d=199. feature Training r(%) SFFS SBS FR (d) time (s) SFS SFS 12 2.03 95.0 Time (s) 1.15 2.58 117.5 0.14 SBS 12 2.18 92.1 Fisher 12 2.16 87.9 Total 199 7.61 95.8 3.3 Results of training From Table 3, we can observe that SFS MLNF had three layers: one input layer, algorithm got higher classification rate than one hidden layer and one output layer. Hidden others. So, Suggested method-based SFS layer has 10 neurals with activate function algorithm applied to select 12 top of features tansig. Activate function purelin was used for (VbusWeber69, VbusBLT138, output layer. Levenberg-Marquardt optimization PloadSHIMKO69, PloadHALE69, based for weight and bias QloadPATTEN69, QloadAMANDA69, QloadBLT138, PloadBLT69, Trang 21 SCIENCE & TECHNOLOGY DEVELOPMENT, Vol.18, No.K3 - 2015 QloadLYNN138, PflowRAY138-BOB138, According to Table 2, with 20 features, it PflowBOB138-BLT138, PflowBLT69- can see that calculating time of FR algorithm is BLT138) in order to reduce the number of inputs the shortest time with 0.14s. Calculating time of to MLFN. However, we expected to check SBS algorithm is the longest time with 117.5s. whether SFS is biased to any different Calculating time of SFFS algorithm is 2.58s and classifiers. Linear Discrimination Analysis was longer 2,2 times than calculating time of SFS used as the classification algorithm to our testing algorithm. Calculating time of SFFS algorithm is it. The linear classifier (LC) is one of the 1.15s. Calculating time of SBS algorithm is simplest discrimination analysis types. This much longer calculating time of SFS, SFFS and classify function is also supported by Matlab FR algorithm. This can explain that the SBS software. Figure 4 shows classification rate of algorithm has to through the space search with testing feature subsets with algorithms by LC. the entire feature set. SFFS algorithm has longer calculating time than SFS’s time calculating 94 because beside of forward search, SFFS algorithm has to backward search. The shortest 92 calculating time of FR algorithm has a reason SFFS 90 SFS that FR algorithm calculated measuring distance SBF 88 Fisher values only one time respectively for each feature. 86 Figure 3, classification rates of SFS and Classification rate (%) rate Classification 84 SFFS algorithm are the same. SFFS and SFS 82 algorithm give better results than SBS and FR 80 algorithm. Classification rates of SFS and SFFS 8 10 12 14 16 18 20 Feature (d) algorithm are more 1,3% to 2,9% than SBS algorithm and more 4,6% to 8,3% than FR Figure 4 Classification rate of testing feature subsets algorithm. by LC According to Table 3, SFS algorithm, 3.4 Discussion subset has 12 features that its classification rate Figure 1 shows the results of distance got 95% by MLFN. Comparing with feature set measuring value by SFFS, SFS and SBS has 199 features, SFS algorithm’s feature algorithm. Figure 2 shows the results ranked number was reduced 16,5 times, its training time from large to small according to Fisher's distance was reduced 3,74 times. Classification rate of measuring value of each single feature by FR that feature set has 199 features is 95,8%. By algorithm. In which, the same distance comparing the calculated results found that SFS measuring values were caculated by SFS and algorithm has the same results as SFFS SFFS, but that have very small value difference algorithm. These results can be explained that in at subsets with 13 features and 20 features as step backward search SFFS algorithm only Table 1. removes one feature for each execution algorithm could not search deep enough to find Trang 22 TAÏP CHÍ PHAÙT TRIEÅN KH&CN, TAÄP 18, SOÁ K3- 2015 better features. SFS algorithm is simpler than 4. CONCLUSION SFFS algorithm. This paper presents the method of feature Classification rates of SFS and SFFS subset selection in dynamic stability assessment algorithm are also the same and got better results power system using artificial neural networks. than SBS and FR algorithm by LC. MLFN got This paper proposed applying four feature subset higher classification rate than LC for the same selection algorithms that are FR, SFS, SBS, and feature subset selection algorithm. The SFS has SFFS. The effectiveness of the algorithms was the 12 selected features that its classification rate tested on the GSO-37bus power system. With got 95% by MLFN. This result was also the same number of feature, the calculation considered acceptable for some previous studies results show that SFS algorithm yielded higher applying pattern recognition to power system classification rate than FR, SBS algorithm. SFS stability. For instance, classification rate got algorithm yielded the same classification rate as 95% [11], 93,6% [12]. SFFS algorithm. Lựa chọn tập biến trong đánh giá ổn định động hệ thống điện sử dụng mạng thần kinh nhân tạo  Nguyễn Ngọc Âu 1  Quyền Huy Ánh 1  Phan Thị Thanh Bình 2 1Trường Đại học Sư Phạm Kỹ Thuật Thành Phố Hồ Chí Minh 2Trường Đại học Bách Khoa, ĐHQG-HCM TÓM TẮT Bài báo trình bày phương pháp lựa chọn kiếm tiến (SFS), tìm kiếm lùi (SBS), tìm kiếm tập biến trong đánh giá ổn định động (DSA) kết hợp tiến lùi (SFFS), xếp hạng (FR) để lựa hệ thống điện sử dụng mạng thần kinh nhân chọn tập biến. Hiệu quả của các giải thuật đã tạo (ANN). Trong ứng dụng ANN đánh giá ổn được kiểm tra với sơ đồ hệ thống điện GSO- định động hệ thống điện, lựa chọn tập biến 37bus. Kết quả tính toán cho thấy với cùng nhằm mục đích giảm số biến đầu vào, giảm biến đặc trưng (Feature), giải thuật SFS có chi phí và bộ nhớ máy tính . Tuy nhiên, thách độ chính xác nhận dạng cao hơn giải thuật thức lớn là cùng với việc giảm số lượng biến FR và SBS, giải thuật SFS và SFFS có kết nhưng độ chính xác nhận dạng phải cao. 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