APPLICATION OF DIGITAL CELLULAR RADIO FOR MOBILE LOCATION ESTIMATION IIUM Engineering Journal, Vol. 22, No. 1, 2021 Abdul Kareem et al. https://doi.org/10.31436/iiumej.v21i2.1276 ROBUST TUNING OF POWER SYSTEM STABILIZER PARAMETERS USING THE MODIFIED HARMONIC SEARCH ALGORITHM HIBA ZUHAIR ABDUL KAREEM1, HUSAM HASAN MOHAMMED1*, AND AMEER AQEEL MOHAMMED 2 1 Department of Electronic Technologies, 2 Department of Computer Systems, Babylon Technical Institute, Al-Furat Al-Awsat Technical University,51015, Babylon, Iraq *Corresponding author: husam171984@gmail.com (Received: 24th October 2019; Accepted: 18th March 2020; Published on-line: 4th January 2021) ABSTRACT: Power System Stabilizer is used to improve power system low frequency oscillations during small disturbances. In large scale power systems involving a large number of generators, PSSs parameter tuning is very difficult because of the oscillatory modes’ low damping ratios. So, the PSS tuning procedure is a complicated process to respond to operation condition changes in the power system. Some studies have been implemented on PSS tuning procedures, but the Harmony Search algorithm is a new approach in the PSS tuning procedure. In power system dynamic studies at the first step system total statues is considered and then the existed conditions are extended to the all generators and equipment. Generators’ PSS parameter tuning is usually implemented based on a dominant operation point in which the damping ratio of the oscillation modes is maximized. In fact the PSSs are installed in the system to improve the small signal stability in the system. So, a detailed model of the system and its contents are required to understand the dynamic behaviours of the system. In this study, the first step was to linearize differential equations of the system around the operation point. Then, an approach based on the modified Harmony Search algorithm was proposed to tune the PSS parameters. ABSTRAK: Penstabil Sistem Kuasa digunakan bagi meningkatkan sistem kuasa ayunan frekuensi rendah semasa gangguan kecil. Dalam sistem kuasa berskala besar yang melibatkan sebilangan besar penjana, penalaan parameter PSS adalah sangat sukar kerana nisbah corak ayunan redaman yang rendah. Maka, langkah penalaan PSS adalah satu aliran rumit bagi mengubah keadaan operasi sistem kuasa. Beberapa kajian telah dilaksanakan pada prosedur penalaan PSS, tetapi algoritma Harmony Search merupakan pendekatan baru dalam prosedur penalaan PSS. Dalam kajian sistem kuasa dinamik ini, langkah pertama adalah dengan memastikan status total sistem dan keadaan sedia ada diperluaskan kepada semua penjana dan peralatan. Parameter penalaan generator PSS biasa dilaksanakan berdasarkan titik operasi yang dominan di mana nisbah corak ayunan redaman dimaksimumkan. Malah PSS dipasang di dalam sistem bagi meningkatkan kestabilan isyarat kecil dalam sistem. Oleh itu, model terperinci sistem dan kandungannya diperlukan bagi mengenal pasti perihal sistem dinamik. Kajian ini, dimulai dengan melinear sistem persamaan pembezaan pada titik operasi. Kemudian, pendekatan berdasarkan algoritma Harmony Search yang diubah suai telah dicadangkan bagi penalaan parameter PSS. KEYWORDS: power system stabilizer (PSS); power system; harmonic search algorithm 47 IIUM Engineering Journal, Vol. 22, No. 1, 2021 Abdul Kareem et al. https://doi.org/10.31436/iiumej.v21i2.1276 1. INTRODUCTION Small-signal fluctuation stability is a major issue for power system security and reliability. These fluctuations affect the power system’s natural damping [1]. PSS, if well- tuned, will have the ability to function properly in the system [2]. Although these stabilizers have a simple and robust structure, their configuration, even with computer simulation or field testing, involves a highly skilled process for system parameters [3]. These parameters are not readily available and may, during normal operation of the power system, change the values of the parameters [4]. These parameters cannot be measured directly so they should be well estimated [5]. Recently, several heuristic search algorithms have been proposed for tuning, PSS parameters, such as tab search [6] evolutionary programming [7], and Particle Swarm Optimization (PSO) [8] were suggested to evaluate the PSS Parameters. However, these methods failed to determine precise parameters when the system has a specific objective function with a large-scale number of parameters. 2. PROBLEM FORMULATION The power system can be described using a set of first-order nonlinear differential equations[8]: �̇� = 𝑓(𝑥,𝑢) (1) Where �̇� or 𝑥 is the state variables vector, and 𝑢 is the vector of input variables.The linearized models of a power system can be used to design the power system stabilizers. Therefore, the state equation of the power system with stabilizers can be written as [9]: ∆�̇� = 𝐴∆𝑋 + 𝐵𝑈 (2) ∆𝑦 = 𝐶∆𝑋 + 𝐷∆𝑈 (3) where ∆ represents small changes, 𝑋 is the state vector of order n, 𝑦 is the output vector of order m, 𝑈 is the input vector of order r, 𝐴 is a square matrix of states of size n, 𝐵 represents a control matrix with size n × r, 𝐶 refers to the output matrix with size m × n, 𝐷 is the leading matrix with the size m × r. A traditional lead-lag compensator PSS is utilized in this study. The transfer function of the PSS is described by the following equation [10]: 𝑉𝑖 = 𝐾𝑖 𝑠𝑇𝜔 1+𝑇𝜔 (1+𝑠𝑇1𝑖) (1+𝑠𝑇2) (1+𝑠𝑇3𝑖) (1+𝑠𝑇4) ∆𝜔𝑖 (4) where 𝑉𝑖 is the output signal for PSS at 𝑖th machine, 𝐾𝑖 The stabilizer gain, 𝑇𝜔 represents the time constant, ∆𝜔𝑖 speed deviation of 𝑖th machine from the synchronous speed. 3. OBJECTIVE FUNCTIONS The Objective functions are formulated by tuning the PSS parameter and there are three different objective functions that have been used in many studies to set parameters, which will be discussed below: a) The damping factor can be considered as the first objective as follows [11]: 48 IIUM Engineering Journal, Vol. 22, No. 1, 2021 Abdul Kareem et al. https://doi.org/10.31436/iiumej.v21i2.1276 ( max 1≤𝑞≤𝑛𝑞 𝜎𝑞) 𝑦 (5) ( max 1≤𝑞≤𝑛𝑞 𝜎𝑞 − 𝜎0) 𝑦 (6) ( max 1≤𝑞≤𝑛𝑞 𝜎𝑞 − 𝜎0) 1 + ( max 1≤𝑞≤𝑛𝑞 𝜎𝑞 − 𝜎0) 2 + ⋯( max 1≤𝑞≤𝑛𝑞 𝜎𝑞 − 𝜎0) 𝑛𝑦 (7) 𝑀𝑖𝑛𝐹1 = ∑ ( max 1≤𝑞≤𝑛𝑞 𝜎𝑞 − 𝜎0) 𝑦 𝑛𝑦 𝑦=1 (8) where, 𝑛𝑦 are the all operating statuses of the test system, 𝑛𝑞 denotes the number of eigenvalues under 𝑛𝑦, 𝜎𝑞 is the damping factor , 𝜎0 is damping factor constant .When the 𝐹1 ( 𝜎𝑞 is defined as Damping factor) is less than or equal to zero, the response for the maximum damping factor ( max 1≤𝑞≤𝑛𝑞 ) is less than or exactly equal to the expected value 𝜎0,[12]. b) The damping ratio can be considered as the second objective as follows [13]: 𝑀𝑖𝑛𝐹2 = ∑ (𝜁0 − min 1≤𝑞≤𝑛𝑞 𝜁𝑞) 𝑦 𝑛𝑦 𝑦=1 (9) where 𝜁0 represents the predicted damping ratio constant, and 𝜁𝑞 represents the damping ratio. When 𝐹2 is less than or equal to zero, the response is the minimum damping ratio(s) ( min 1≤𝑞≤𝑛𝑞 𝜁𝑞) are more than or exactly the value of 𝜁0 [14]. c) The damping ratio and damping factor can be considered as the third objective as follows [15]: 𝑀𝑖𝑛𝐹3 = ∑ ( max 1≤𝑞≤𝑛𝑞 𝜎𝑞 − 𝜎0) 𝑦 + 𝛼∑ (𝜁0 − min 1≤𝑞≤𝑛𝑞 𝜁𝑞) 𝑦 𝑛𝑦 𝑦=1 𝑛𝑦 𝑦=1 (10) where 𝛼 is the weight for combining both damping ratio and damping factor. 4. PROPOSED OBJECTIVE FUNCTION The objective functions F1, F2, and F3 produce high frequency or low frequency, which may reduce the life of system devices [16].Therefore, we can overcome the disadvantages mentioned earlier through the following equation [17] : 𝑋 = −(𝜎−𝜎0) √(𝜎−𝜎0) 2+𝜔2 × 100% (11) 𝑀𝑖𝑛𝐹4 = ∑ (𝑋0 − min 1≤𝑞≤𝑛𝑞 𝑋𝑞) 𝑦 𝑛𝑦 𝑦=1 (12) 49 IIUM Engineering Journal, Vol. 22, No. 1, 2021 Abdul Kareem et al. https://doi.org/10.31436/iiumej.v21i2.1276 where X: the constant value for the prospective damping scale Xq: the damping scale for the qth eigenvalue The following equations present the constraints of the PSS parameter design model [18]: { 𝐾𝑚𝑖𝑛 ≤ 𝐾 ≤ 𝐾𝑚𝑎𝑥 𝑇1𝑚𝑖𝑛 ≤ 𝑇1 ≤ 𝑇1𝑚𝑎𝑥 𝑇2𝑚𝑖𝑛 ≤ 𝑇2 ≤ 𝑇2𝑚𝑎𝑥 𝑇3𝑚𝑖𝑛 ≤ 𝑇3 ≤ 𝑇3𝑚𝑎𝑥 𝑇4𝑚𝑖𝑛 ≤ 𝑇4 ≤ 𝑇4𝑚𝑎𝑥 } (13) 5. THE PROPOSED ALGORITHM Harmonic Search Algorithm is one of the simplest and most up-to-date methods, which is the process of finding the optimal solution to the problem. This method was used for the first time in 2001 [19]. Harmony search is inspired by the process of jazz musicians to find the optimal solution. In this algorithm, each solution is called a harmonic and is represented by a vector (N). This algorithm contains the following steps [20]: a) Primary generation (Initial initialization) In the first step, the optimization problem is indicated by the relationship. Also, at this step, the Harmony Memory size (HMS) is calculated. 𝑀𝑖𝑛:{𝑓(𝑥)|𝑥 ∈ 𝑋} (14) 𝑆𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜 ∶ 𝑔(𝑥) ≥ 0 ℎ(𝑥) = 0 (15) where: 𝑓(𝑥) is the objective function, ℎ(𝑥) and 𝑔(𝑥) are the functions of equal and unequal constraints respectively. Also in this step, the HS algorithm parameters are specified. These parameters are [21] : 1) Harmony Memory Size (HMS), or the number of solution vectors in the harmony memory. 2) Harmony Memory Considering Rate (HMCR), HMCR ∈ [0,1]. 3) Pitch Adjusting Rate (PAR) ∈ [0,1]. 4) Stopping criterion or number of improvisations (NI) b) Primary Harmonic Memory Determination At this step, the Harmony matrix (HM) is created from a large number of solution vectors that are created randomly[22]. 𝐻𝑀 = [ 𝑥1 1 𝑥2 1 … 𝑥𝑁−1 1 𝑥𝑁 1 𝑥1 2 𝑥2 2 … 𝑥𝑁−1 2 𝑥𝑁 2 ⋮ 𝑥1 𝐻𝑀𝑆−1 𝑥1 𝐻𝑀𝑆 ⋮ 𝑥1 𝐻𝑀𝑆−1 𝑥2 𝐻𝑀𝑆 ⋮ ⋯ ⋯ ⋮ 𝑥1 𝐻𝑀𝑆−1 𝑥𝑁−1 𝐻𝑀𝑆 ⋮ 𝑥1 𝐻𝑀𝑆−1 𝑥𝑁 𝐻𝑀𝑆 ] (16) c) New harmonic production based on improvisation d) A new harmonic vector 𝑥′(𝑥1 ′ ,𝑥2 ′ ,…. . ,𝑥𝑁 ′ )is produced based on three rules that it describes as improvised: 1) Harmony Memory Considering Rate (HMCR) 50 IIUM Engineering Journal, Vol. 22, No. 1, 2021 Abdul Kareem et al. https://doi.org/10.31436/iiumej.v21i2.1276 2) sound regulation 3) random selection e) Updating Harmony Memory: If the new harmonic vector is better than the worst harmonic vector based on the selected target function, the new harmony is placed inside and the worst harmonic is left out of the set. f) Check the stopping criterion: when the termination criterion is satisfied, the calculations are completed, otherwise, steps 3 and 4 are repeated. 6. MODIFIED HARMONY SEARCH (MHS) The disadvantages of the HS method are the use of PAR and Bandwidth, BW, constant values, which makes it difficult to set up these parameters. Another disadvantage of the HS is that the number of repetitions for which the algorithm needs to find the optimal solution is not appropriate [23]. If PAR is small and BW is large, the algorithm's performance is weak hence increased NI improvements are required to find that optimal solution Fig. 1. Fig. 1: a) change of PAR with iteration number, b) change of BW with iteration number 3-or 4. The initial iteration of the HS has large BW and small PAR , which leads to increase the entire solution space of the search algorithm. These values are appropriate for subsequent replies in order to locally search. MHS is similar to HS, with a little difference in that PAR and BW parameter values are dynamically generated in each individual iteration according to the following relationships [24]: 𝑃𝐴𝑅(gn) = 𝑃𝐴𝑅𝑚𝑖𝑛 + 𝑃𝐴𝑅𝑚𝑎𝑥 − 𝑃𝐴𝑅𝑚𝑖𝑛 𝑁𝐼 × 𝑡 (17) where, PAR(t) = Pitch Adjusting Rate for each iteration 𝑃𝐴𝑅𝑚𝑖𝑛= Minimum Pitch Adjusting Rate 𝑃𝐴𝑅𝑚𝑎𝑥= Maximum Pitch Adjusting Rate 𝑁𝐼 = Number of solution vector Iteration 𝑡 = Iteration Number 51 IIUM Engineering Journal, Vol. 22, No. 1, 2021 Abdul Kareem et al. https://doi.org/10.31436/iiumej.v21i2.1276 𝑏𝑤(𝑡) = 𝑏𝑤𝑚𝑎𝑥 × 𝑒 [ 1𝑛[ 𝑏𝑤𝑚𝑖𝑛 𝑏𝑤𝑚𝑎𝑥 ] 𝑁𝐼 ×𝑡] (18) where, 𝑏𝑤(𝑡) = Bandwidth for each iteration 𝑏𝑤𝑚𝑖𝑛= Minimum bandwidth 𝑏𝑤𝑚𝑎𝑥= Maximum bandwidth 7. PSS DESIGN AND SIMULATION RESULTS In this study, the MHS algorithm is used to obtain the optimal design of the PSS parameters for the system of four generators shown in Fig. 2 [25] and compare results with other techniques (Harmony Search, Classic Approach). . Fig. 2: Single-line diagram of the 4-generator system. 7.1 Case 1: The Stability of Four-Generators Without PSS In this case, the system was tested after the fault at bus-3 without PSS to demonstrate the effect of PSS on the stability of this system. According to Table 1, the system is unstable. From Figures 3 and 4, it is observed that the rate of voltage changes and oscillation of the generator’s speed are very high and the system is practically unstable. Table 1: The Four-Generator data without PSS Generators Eigenvalues Frequencies Damping Ratios 1,2,3,4 ±3.994j 0.6354 -0.0134 3,4 ±7.274j 1.1577 0.0668 1,2 ±7.323j 1.655 0.0658 52 IIUM Engineering Journal, Vol. 22, No. 1, 2021 Abdul Kareem et al. https://doi.org/10.31436/iiumej.v21i2.1276 Fig. 3: The bus voltage changes after the fault at bus-3 without PSS Fig. 4: Generator speed changes after the fault at bus-3 without PSS. 7.2 Case 2: The Stability of Four-Generators with PSS Based On (MHS) In this case, PSS is installed on each generator which will guarantee stability of the system and restrain unwanted oscillations. Thus, the PSS parameter is set based on the (MHS) algorithm. The results of the modified harmonic search for the parameters are presented in Table 2. From Fig. 5 and Fig. 6 it is clear that the oscillations due to disturbances are completely repressed and the dynamic state of the system improved. All this happened only after installation of the PSS. Figure 7 explains the convergence of the objective function with MHSA and HSA. From this figure, it is clear that MHSA shows superior performance over HSA. The proposed method obtained the solution after 210 iterations while the HSA reached the solution after 300 iterations. This speed in finding the optimal solution is very important in the stability of the system. Table 2: Optimal Designed Parameters of MHS Generator 4T 3T 2T 1T wT K 1 0.01 0.08 0.01 0.07 10 100 2 0.02 0.1 0.02 0.09 10 127 3 0.01 0.1 0.01 0.1 10 148 4 0.02 0.08 0.02 0.12 10 95 53 IIUM Engineering Journal, Vol. 22, No. 1, 2021 Abdul Kareem et al. https://doi.org/10.31436/iiumej.v21i2.1276 Fig. 5: Voltage changes on the bus number 3 with PSS. Fig. 6: Generator speed changes after the fault at bus 3 with PSS. Fig. 7: Convergence characteristics of HSA and MHSA techniques. Furthermore the above results are compared with those presented in [26] for the 4- generator system. In this reference, the parameters were obtained using the sensitivity analysis method. Table (3) shows the results of the special system values with stabilizer in the two studies. From Fig. 8-9 and Table 3, it is very clear that the performance of the PSS 54 IIUM Engineering Journal, Vol. 22, No. 1, 2021 Abdul Kareem et al. https://doi.org/10.31436/iiumej.v21i2.1276 designed using MHSA is far better compared to the PSS designed using Sensitivity Approach (TSA) and Harmony Search. Fig. 8: Voltage changes at bus 3 after fault in the three-phase system. Fig. 9: the changes of the first generator speed. Table 3: Eigenvalues of the System 4 Generators for Modified Harmony Search Method and Trajectory Sensitivity Approach Generators Eigenvalues Frequencies Damping Ratios MHS -2.138±J5.738 0.856 0.397 -2.714±J6.736 0.891 0.391 -1.130±J4.214 0.637 0.268 Trajectory Sensitivity Approach (TSA)[26] -1.938±J5.738 0.913 0.319 -2.165±J5.936 0.945 0.343 -0.530±J3.504 0.558 0.149 8. CONCLUSION Transient and small-signal stability are critical in power system operation and control studies due to their impact on consumers. Thus power system stabilizers could be used to solve this issue. A modified harmonic search algorithm was proposed to tune the PSS parameters to overcome the drawbacks of the previously suggested algorithms. The MHS results show that adjusted stabilizers have improved performance. The proposed method was applied to a system of four generators. The MHS algorithm results were compared 55 IIUM Engineering Journal, Vol. 22, No. 1, 2021 Abdul Kareem et al. https://doi.org/10.31436/iiumej.v21i2.1276 with the results of the sensitivity analysis method, which was previously suggested for this purpose. The comparison indicates the superiority of this algorithm to obtain the optimal parameters to set the stabilizer. REFERENCES [1] Elazim SMA, Ali ES. (2016) Optimal power system stabilizers design via cuckoo search algorithm. International Journal of Electrical Power & Energy Systems.75:99-107. [2] Chitara D, Niazi KR, Swarnkar A, Gupta N. (2018) Cuckoo search optimization algorithm for designing of a multimachine power system stabilizer. IEEE Transactions on Industry Applications.54(4):3056-3065. [3] Chaib L, Choucha A, Arif S. (2017) Optimal design and tuning of novel fractional order PID power system stabilizer using a new metaheuristic Bat algorithm. Ain Shams Engineering Journal.8(2):113-125. [4] Radmehr M, Mohammadjafari M, GhadiSahebi MR. (2018) LOC-PSS Design for Improved Power System Stabilizer. Journal of Applied Dynamic Systems and Control.1(1):47-54. [5] Ray PK, Paital SR, Mohanty A, Eddy FYS, Gooi HB. (2018) A robust power system stabilizer for enhancement of stability in power system using adaptive fuzzy sliding mode control. Applied Soft Computing.73:471-481. [6] Ali ES. (2014) Optimization of power system stabilizers using BAT search algorithm. International Journal of Electrical Power & Energy Systems.61:683-690. [7] Pattanaik JK, Basu M, Dash DP. (2019) Dynamic economic dispatch: a comparative study for differential evolution, particle swarm optimization, evolutionary programming, genetic algorithm, and simulated annealing. Journal of Electrical Systems and Information Technology.6(1):1. [8] Sambariya DK, Prasad R. (2015) Optimal tuning of fuzzy logic power system stabilizer using harmony search algorithm. International Journal of Fuzzy Systems.17(3):457-470. [9] Kumar A. (2015) Power system stabilizers design for multimachine power systems using local measurements. IEEE Transactions on Power Systems.31(3):2163-2171. [10] Bouchama Z, Essounbouli N, Harmas MN, Hamzaoui A, Saoudi K. (2016)Reaching phase free adaptive fuzzy synergetic power system stabilizer. International Journal of Electrical Power & Energy Systems.77:43-49. [11] Islam NN, Hannan MA, Shareef H, Mohamed A. (2017)An application of backtracking search algorithm in designing power system stabilizers for large multi-machine system. Neurocomputing.237:175-184. [12] Ke D, Chung CY. (2016) Design of probabilistically-robust wide-area power system stabilizers to suppress inter-area oscillations of wind integrated power systems. IEEE Transactions on Power Systems.31(6):4297-4309. [13] Soliman HM, Yousef HA. (2015) Saturated robust power system stabilizers. International Journal of Electrical Power & Energy Systems.73:608-614. [14] Yaghooti A, Buygi MO, Shanechi MHM. (2015) Designing coordinated power system stabilizers: A reference model based controller design. IEEE Transactions on Power Systems.31(4):2914-2924. [15] Farah A, Guesmi T, Abdallah HH, Ouali A. (2016) A novel chaotic teaching–learning-based optimization algorithm for multi-machine power system stabilizers design problem. International Journal of Electrical Power & Energy Systems.77:197-209. [16] Soliman M. (2015) Robust non-fragile power system stabilizer. International Journal of Electrical Power & Energy Systems.64:626-634. [17] Rahmatian M, Seyedtabaii S. (2019) Multi-machine optimal power system stabilizers design based on system stability and nonlinearity indices using Hyper-Spherical Search method. International Journal of Electrical Power & Energy Systems.105:729-740. [18] Peres W, Júnior ICS, Passos Filho JA. (2018) Gradient based hybrid metaheuristics for robust tuning of power system stabilizers. International Journal of Electrical Power & 56 IIUM Engineering Journal, Vol. 22, No. 1, 2021 Abdul Kareem et al. https://doi.org/10.31436/iiumej.v21i2.1276 Energy Systems.95:47-72. [19] Wang G-G, Gandomi AH, Zhao X, Chu HCE. (2016) Hybridizing harmony search algorithm with cuckoo search for global numerical optimization. Soft Computing.20(1):273-285. [20] Gao K-Z, Suganthan PN, Pan Q-K, Chua TJ, Cai TX, Chong C-S. (2016) Discrete harmony search algorithm for flexible job shop scheduling problem with multiple objectives. Journal of Intelligent Manufacturing.27(2):363-374. [21] Rezaie H, Kazemi-Rahbar MH, Vahidi B, Rastegar H. (2019 )Solution of combined economic and emission dispatch problem using a novel chaotic improved harmony search algorithm. Journal of Computational Design and Engineering.6(3):447-467. [22] Wang L, Hu H, Liu R, Zhou X. (2019) An improved differential harmony search algorithm for function optimization problems. Soft Computing.23(13):4827-4852. [23] J. Yi, L. Gao, X. Li, and J. Gao, ‘An efficient modified harmony search algorithm with intersect mutation operator and cellular local search for continuous function optimization problems’, Applied Intelligence, vol. 44, no. 3, pp. 725–753, 2016. [24] Yi J, Gao L, Li X, Gao J.( 2016) An efficient modified harmony search algorithm with intersect mutation operator and cellular local search for continuous function optimization problems. Applied Intelligence.44(3):725-753. [25] C. Canizares et al., ‘Benchmark models for the analysis and control of small-signal oscillatory dynamics in power systems’, IEEE Transactions on Power Systems, vol. 32, no. 1, pp. 715–722, 2016. [26] Yuan SQ, Fang DZ. (2009) Robust PSS parameters design using a trajectory sensitivity approach. IEEE Transactions on Power Systems.24(2):1011-1018. 57