Saad Dilshad

Type-II Neuro Fuzzy Wavelet Control for Power System Stability Enhancement using STATCOM Rabiah Badar1, Saad Dilshad1 Department of Electrical Engineering COMSATS Institute of Information Technology Islamabad, Pakistan Abstract—Power system stability has become an important issue for secure and reliable operation of power system. This can be improved by using one of the key FACTS controllers, Static Synchronous Compensator (STATCOM) along with a damping controller. FACTS controllers are mainly used for controlling the reactive power flow on the line, but they can also be used for damping low frequency oscillations. This paper presents Type-II NeuroFuzzy Wavelet Control (NFWC) scheme as supplementary control of STATCOM. The proposed control scheme deals with system uncertainties in better way by inclusion of membership function with fuzzy boundaries in antecedent part. Two-areasystem installed with STATCOM is used as test system. The performance of the Type-II NFWC is compared with Adaptive NeuroFuzzy TSK Control (ANFTSKC) and no control scenario. The simulation results show that Type-II NFWC has significantly improved performance in both the transient and steady-state regions. Index Terms— FACTS, power system stability, Type-II NFWC, STATCOM, ANFTSKC, gradient decent, wavelets. I. INTRODUCTION The stability of a reliable and safe power system can be jeopardized by low frequency oscillations ranging from 0.2 to 3 Hz. These oscillations arise in system due to speed mismatch of generating units [1]. If these oscillations are not damped effectively, they may grow with the passage of time leading to partial or complete system blackout. Major blackouts of history caused by these oscillations are reported in literature [2]. Traditionally, Power System Stabilizers (PSSs) have been used to damp out power oscillations, known as Power Oscillation Damping (POD) controller in an interconnected power system. Power system operators have widely implemented PSSs for damping power oscillations to improve the system stability [2, 3]. Over the years of operation, it has been found that PSSs perform better only in vicinity of operating point and their performance is vulnerable to large variations in operating conditions. Flexible AC Transmission Systems (FACTS) controllers are widely used for controlling reactive power flow and system voltage fluctuations. However, they are capable of improving power system stability. FACTS, equipped with supplementary -/16/$31.00 ©2016 IEEE Damping controllers, can be used to damp low frequency oscillations and hence to enhance power system stability. STATCOM is one of the well-known FACTS controllers connected in shunt to the line. It requires lower ratings of passive elements like capacitors and inductors and is capable of working in both inductive and capacitive mode. It injects fully controllable current which in turn generates or absorbs reactive power. If STATCOM voltage is lower than network voltage, STATCOM works as an inductor and it will draw reactive power from the network. If STATCOM voltage is higher than the system voltage, STATCOM works as a capacitor and it will inject reactive power into the system [4]. In stability studies, it has been proved that shunt FACTS controllers are placed slightly off-center towards the sending end with pre-defined direction of real power flow [5]. In literature many control techniques have been proposed for supplementary control of STATCOM like Particle Swarm Optimization [6], Differential Evolution [7], robust PI controller [8], etc. In linear control techniques, system equations are linearized on specific operating conditions with linear models. But linear controllers have problem of performance degradation when operating condition changes. However, nonlinear controllers provide good damping control over wide range of operating conditions. But, their designs are more complex, difficult to implement and often require complete system model. Now-a-days, Adaptive NeuroFuzzy control techniques have emerged to control nonlinear and dynamic systems and to damp power system oscillations [9-11]. NeuroFuzzy controllers have good approximation and control capabilities. However, these NeuroFuzzy controllers use Type-I membership function in antecedent part and linear functions in consequent part which cannot effectively deal with the uncertainties in power system. Therefore, Type-II membership functions were introduced for the control of time-varying plants [12]. In [13], Type-II NeuroFuzzy based STATCOM control is proposed to damp the power system oscillations. However, the consequent part is linear. The linear TSK using conjugate gradient adaptation mechanism may easily get stuck in local-minima. This dilemma can effectively be overcome by introducing the wavelet NNs in consequent part to improve the convergence speed [14]. The localized property of wavelets is achieved by using wavelet basis functions in the hidden layer. In this paper, a wavelet based Type-II NeuroFuzzy control is presented to improve the steady-state and transient stability of power system using STATCOM. The paper is arranged as follows; Section ІІ gives the mathematical modeling of power system and STATCOM. The detailed mathematical description of Type-II NFWC and its parameters update laws are derived in section ІІI. The simulation results are discussed in section IV. Section V presents the conclusion and future work for this research. II. POWER SYSTEM MODELING INSTALLED WITH STATCOM Fig. 1 shows the n-machine power system with STATCOM installed at node 3. Vo and Ilo is the phasor output voltage and current of the converter, respectively. The nonlinear dynamic model of kth synchronous machine in the form of differential equations is given as, d k (1)  bk dt d k 1  (2)  Pmk  Pek  Dk k  dt Mk dEqk 1  (3)  E fdk   xdk  xdk  I dk  Eqk  dt Tdk dEdk 1  dt Tqk  x dEqk  dt dEdk dt qk   I qk  Edk  xqk   1   I dk  Eqk Eqk   xdk  xdk Tdk  1  Tqok  x qk   I qk  Edk  xqk (4)  Fig. 1. STATCOM with n-machine power system Where, g1  48 and g 2  48 for 48-pulse 2 L 2 C converter. Where, C is the capacitance of the DC bus capacitor, R and L are the resistance and inductance of the coupling transformer, respectively. id and iq are injected STATCOM currents. The network equations of power system installed with STATCOM and reduced at nodes 1-2 are given as [16];  _  _  _   _  0   E1   I 1l   Y13   Y 11 EG  0   (9) _    _  _   _   E 0 Y Y I 22 2 23 l    1      (5)  _ _ I G   Y 31  (6) Here, The output of VSC of STATCOM is written as [15],  V 0  cVDC (cos  j sin )  cVDC   R L  g 2 cos   1  g1 sin  L   id   g1 cos   iq    0    vDC   0  0   0 1 L 0 _ _ EG   E G1  _ E G2 T _ _ _  E1   Y 33 EG  _  ... E Gn   (10) T and T (7) Here, c  nk for Pulse Width Modulation (PWM) inverter with n is the modulation ratio and k is the ratio between AC and DC voltage of converter. For     ,  and  is synchronization and firing angle for PWM inverter, respectively. Reactive power exchange is controlled by adjusting magnitude of phase  . VDC is the DC capacitor voltage. The STATCOM model in dq0 reference frame is given as, R   L  id   d    iq   dt    vDC    g 2 sin  _  _ Y32   E1   0  ed  0   eq  (8)   0  1  L  _ _ _ _  I G   I G1 I G2 ... I Gn  are generator voltages and   currents, respectively. From Fig.1 the voltages at STATCOM terminal and on bus bars 1 and 2 are; _ _ _ _ _ _ E l  jxL I l 0  V0  jxL ( I 1l  I 2l )  cVDC  E i  jxil I il  El i  1, 2 (11) (12)    I 1l  can be found from Fig. 1. Substituting its value in _   I 2l  _ T _ _  Eq. 9 and eliminating  E1 E1  the generator current in   network coordinates can be found as,   jx2l   T T  _   _  _  _   x  Y Y Y _ 31 13  31 1 1   I G   Y 33   _  Y E12  _   EG    _  Y E12  T  V0 (13)        jx1l     Y32   Y 23     Y32       xT    _ KY K0 Where, xT  xL2   x1l  xL  x2l  xL   ' j  x2l  xL   jx  L Y11   xT xT . and YE12    j  x1l  xL   jxL '    Y22  xT xT   After manipulating generator voltages and currents and applying the following transformation, I gi  I Gi e ji The generator currents in machine coordinates are given as; n   Eqi sin  kiG  ( xqi  xdi ) I qi cos  kiG  (14) I dk   K Gik    K cV cos          i 1 0k k kiG   0i DC n   Eqi cos  kiG  ( xqi  xdi ) I qi sin  kiG  I qk   K Gik  (15)   K cV sin          i 1 0k k kiG   0i DC Where,  kiG   k   i   kiG . III. CLOSED LOOP SYSTEM STRUCTURE The overall closed loop system has been shown in Fig. 2. The control block contains the conventional and proposed control strategies such that the output u  ut uT  II  for Adaptive NeuroFuzzy TSK Control (ANFTSKC) and Type-II NFWC, respectively. The control output is modulated with reference output voltage of STATCOM. The plant is multimachine power system installed with STATCOM at middle of the system. The details of proposed Type-II NFWC are presented in the following section. A. Proposed Type-II NFWC The conventional TSK Neurofuzzy structure contains Gaussian membership functions in its antecedent part and linear function in consequent part. In this work, Type-II membership functions have been introduced in antecedent part and the convergence has further been improved by inclusion of wavelets in consequent part. The Type-II Gaussian membership function has fuzziness in its boundaries which can be achieved either by uncertain mean or uncertain standard deviation. In this work, fuzziness has been introduced by uncertain mean. Furthermore, its adaptive behavior for both mean and standard deviation makes it highly dynamic and nonlinear. Thus, membership grade of Type-II fuzzy sets are itself fuzzy and can handle nonlinearities in the system [14]. Consider the Gaussian membership function with uncertain mean given as; 2   1  xi  cij   G  ij , cij , xi   exp   , c  c1, c 2 (16) 2  2  ij    Here, x1 , x2 ,..., xm are the inputs to the NeuroFuzzy structure, c is uncertain mean and  is fixed standard deviation. Based on uncertain mean the upper  and lower  membership functions are given below; G (c1ij ,  ij , xi ), xi  c1ij  ij ( x)  1, c1ij  xi  c 2ij G (c 2 ,  , x ), x  c 2 ij ij i i ij  c 1  ij  c 2ij G (c 2ij , ij , xi ), xi  2 ij ( x)   c  1 G (c1 ,  , x ) x  ij c 2ij ij ij i i  2 Where, c1 and c2 are the mean values for lower and upper membership functions, respectively. Fig. 2. Closed-loop system structure The layered structure of Type-II NFWC is shown in Fig. 2. The structure of Type-II NFWC is described by the following IF-THEN rule; IF x1 is A1 j and x2 is A 2 j and  xm is A mj THEN s j is  j (17) Here, s1 , s2 ,..., sn are the output variables, Aij are Type-II membership functions. Layer 1 is the input layer with number of nodes equal to number of inputs. These nodes distribute the input signals. Layer 2 determines the Gaussian membership grade for upper and lower part; each grade value corresponds to one linguistic term. In layer 3, number of nodes describes the number of rules R1 , R2 , R3 ,..., Rn . Each node describes one rule and rule firing strength has been calculated by using T-norm product operator. The output of 3rd layer for jth rule is given below; f j   A1 j ( x1 ) *  A2 j ( x2 ) *  *  Amj ( xm ) (18) f j   A ( x1 ) *  A ( x2 ) *   *  A ( xm ) 1j 2j Where,  j ( xi )  cos(5qij )e Here, qij  xi  bij aij 0.5 qij (20) with aij and bij are the dilation and translation parameters of the wavelet function, respectively. In layer 6 and layer 7 type reduction and defuzzification is done. In a Type-I fuzzy system, the output of the defuzzifier is crisp. But in case of Type-II fuzzy system, an operation similar to Type-I defuzzification is called type reduction. In type reduction, the output of Type-II fuzzy sets are converted to Type-I fuzzy sets and then defuzzifier converts it to crisp output. Thus, the output of the Type-II FWNN is given by; N u p f s j j 1  j N f j 1  j N   (1  p) f j s j j 1 N j 1 (21)  f j mj These  f j , f j  are the inputs for the next layer. In layer 4 each node is wavelet network. There are three sub layers in WNN. The hidden layer contains wavelet functions. The output of WNN is given by; m s j   j  w j   j ( xi ) i 1 (19) Such that, N u f j 1  j N f N sj j 1  j and u   f j 1 N j (22)  f j 1 sj j B. Type-II NFWC Adaptation Mechanism The cost function used to update the parameters of Type-II NFWC is, 1  2 J   yr  y   u 2 (23) 2 2 Where, yr and y are the reference and the actual output of the plant, respectively. ‘ u ’ is the output of the controller. The parameters update rule based on gradient decent algorithm is given by; J (24)   t  1  (t )     is the learning rate and Here,    aij , bij ,  ij , c1ij , c 2ij , w j , p  is adaptation parameter vector. The partial derivative in the update law is calculated by the following chain rules.  J y   u f j  j u f j  j  J    u     (25)  ij j  y u   f j  j  ij f j  j  ij   J y   u f j  j u f j  j  J    u     (26) c1ij j  y u   f j  j c1ij f j  j c1ij   J y   u f j  j J u f j  j     u     (27)  2 c 2ij       y u f c f j  j c 2ij  j    j j ij  u s j  j qij J  J y   u  aij  y u  s j  j qij aij (28)  u s j  j qij J  J y   u  bij  y u  s j  j qij bij (29)  J y  u s j J   u  w j  y u  s j w j (30)  u J  J y   u  (31) p  y u  p y is used as constant. The parameter ‘p’ is the Here, u design factor which determines the contribution of upper and lower membership function in the final output. Using the results of Eq. 25 to Eq. 31 in Eq. 24, the complete update equations are formed. The real power flow is from area 1 to area 2 depending on the selection of loads in both areas. Both generators are installed with PSSs. The STATCOM is connected at bus-2 which is slightly off-centered for optimal location. The length of double-circuit transmission lines is 500km with STATCOM installed at distance of 210 km from bus B1. The loads connected at buses B1 and B3 are 82.8 MW and 1415.4 MW, respectively. The initial loading conditions of the generators 1 and 2 are P1 = 0.8937 pu and P2 = 0.4 pu, respectively. The effectiveness of Type-II NFWC system is evaluated using different fault events for four scenarios; firstly, without STATCOM when switch S is open as shown in Fig. 2, secondly, STATCOM installed in system by closing switch S but without supplementary damping control, thirdly STATCOM installed with ANFTSKC and finally STATCOM installed with Type-II NFWC. A. Case-I: Three Phase Fault A 3-phase, self-clearing fault of 10 cycles is applied on line L1 at t=0.1 sec. Figure 3 shows the interarea mode of oscillations and power flow on line L4. The results show the poorly damped oscillatory behavior for no supplementary control. Furthermore, the installation of STATCOM introduces rather negative damping to the system and ANFTSKC also does not make any significant improvement. However, installation of Type-II NFWC significantly improves the performance in transient region. Figure 3a shows the comparative results for rotor speed deviation. The injected voltage by STATCOM when installed with no supplementary control, installed with ANFTSKC and Type-II NFWC are shown in Fig. 3c. B. Case II: Series of Faults The performance of Type-II NFWC control scheme is examined by applying series of faults. A 3-phase fault of duration 12 cycles is applied on line L4 at t=0.1 sec. The 3phase fault is removed by permanent line outage restoring the system at a different operating point. The operating condition is further varied by 50% reduction in load 2 at t=5 sec. IV. SIMULATION RESULTS AND ANALYSIS (a) The two-area system with two machines and 3 buses has been considered to validate the performance of Type-II NFWC. The two area system with STATCOM connected at bus 2 is shown in Fig. 2. The SIMULINK SimPowerSystem toolbox is used to implement the test system and simulate results. The rated capacity of Machine 1 is 700 MVA and Machine 2 is 1400 MVA and output voltages are 13.8kV. The two generators with output voltage of 13.8kV are connected through transmission line with 3-phase step-up transformers. (b) (a) (c) Fig. 3. Case-I Three phase fault (b) (a) (c) Fig. 6. Case-III: Rapidly changing operating conditions (b) (c) Fig. 4. Case-II Series of faults The simulation results for speed deviation, power flow on line L3 and STATCOM injected voltage are shown in Fig. 4a, 4b and 4c, respectively. The results show that Type-II NFWC provides better damping as compared to no control and ANFTSKC and maintains its performance for wide range of operating conditions resulting from structural variations in the system. Figure 4b shows that initially, there was a power flow of 500 MW in steady state on line L3. After fault clearance by line outage the power flow through line L3 increases to almost 1000 MW which then reduces to 700 MW after load reduction. Proposed Type-II NFWC has significant performance in transient and steady-state regions. C. Case III: Rapid Variations in Operating Conditions The robustness of Type-II NFWC scheme is examined by a more stressed scenario of 3-phase fault and line outage. In this case, the system undergoes two consecutive faults without retrieving from the effect of first fault. A 3-phase fault is applied on L4 at t=0.1 sec to t=0.3 sec. The line L4 is removed from the system just after the fault duration at t=0.315 sec and reclosed at t=0.448 sec. This leads to sudden variations in operating conditions of the system. Figure 5 shows that the damping of Type-II NFWC is much better than ANFTSKC and no control. The results show that the performance improvement margin increases for Type-II NFWC in more tough scenarios. Table 1 shows the quantitative results for different performance indices (PI) to get further insight; the performance improvement is calculated with respect to STATCOM without supplementary control case using formula given in [11]. The ITAE and IAE PIs depict the controller behavior in steady-state region, whereas, ITSE and ISE categories the controller performance in transient region. The results show that Type-II NFWC has significantly improved performance in both transient and steady-state regions as compared to ANTSKC and no control, however, the performance improvement margin is large in transient region. V. CONCLUSION This papers presents a wavelet based Type-II NeuroFuzzy control scheme as a supplementary damping control for STATCOM. The two-area system is considered for study of proposed control scheme under several fault conditions. Both the nonlinear time domain simulation results and performance indices confirm the significant performance improvement for application of Type-II NeuroFuzzy control. TABLE I. PERFORMANCE IMPROVEMENT [%] Type-II NFWC Case Control Algo. ANFTSKC Case PI IAE I II III I II 17.39 36.18 ISE 17.59 50.00 ITAE 26.07 30.23 ITSE 31.74 54.52 III 20.88 9.71 29.45 9.62 45.86 15.52 33.52 31.56 26.94 8.75 20.06 12.69 49.64 22.78 36.86 37.22 It can be concluded that the inclusion of Type-II membership function with wavelets in the consequent part drastically improves the controller performance. Type-II NeuroFuzzy control with both uncertain mean and variance can be an interesting future dimension of this work. REFERENCES [1] P. 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