Modeling by order reducing the load angle of a three-phase synchronous generator and designing an AOA-PID controller to control the load angle

Document Type : Power Article


Department of Electrical Engineering, Technical and Vocational University (TVU), Tehran, Iran


One of the important factors that are always discussed in the study of power systems is the issue of power system stability. In this paper, the load angle control of a three-phase synchronous steam power plant generator is presented by overcoming the load angle fluctuations in both transient and permanent system conditions and expanding the range of stable generator performance. First, the equations of the linear state space of the steam power plant around the operating point are extracted. Then, based on Hankel single values, the model is approximated to the 6th order and based on that, a proportional, derivative, and integral controller for the load angle is presented. Then, using the arithmetic optimization algorithm, the controller coefficients are adjusted with two approaches reducing the settling time and reducing the overshoot of the step response. The stability of the proposed controller output power was also used using the stability criteria Bode and Nyquist was examined. The simulation results show that the arithmetic optimization algorithm has a better performance in controlling the load angle of the three-phase synchronous generator than the fuzzy controller and genetic and harris hawks algorithms. For example, in comparison with the genetic algorithm, the output power has good stability, and the rise time, settling time and the amount of overshoot in the step response of the proposed algorithm is reduced by 82.97, 82, and 40.18%, respectively.


Main Subjects

[1] Abdolhosseini, Morteza, Rohollah Abdollahi, and Meraj Rajaee. "Designing of PIλ Dδ controller for PMBLDC motor using metaheuristic algorithms." Karafan Quarterly Scientific Journal 17, no. 4 (2021): 149-165.
[2] M. karrari. power systems dynamics and control. Amir Kabir University Publishing. 2015.( inPersian)
[3] S. Korram and H. R. ezadfar, “ A method for calculating accurate the reference value of synchronous generator load angle” The National Conference of New Idea On Electrical Engineering, Esfahan, Iran, Novenber 2015.( inPersian)
[4] P. Kundur. Power System Stability and Control. 1th ed, McGraw-Hill. 1994.
[5] Sumina, D., A. Sala, and R. Malaric. "Determination of load angle for salient-pole synchronous machine." Measurement science review 10, no. 3 (2010): 89.
[6] Čuček, Hrvoje, Damir Sumina, and Nikola Švigir. "Synchronous generator load angle estimation." In Melecon 2010-2010 15th IEEE Mediterranean Electrotechnical Conference, pp. 18-22. IEEE, 2010.
[7] M.R. Aghamohammadi, E, Kazemi and M. shivaei, “Provide a method for estimating the rotor angle of a synchronous generator using parameters that can be measured with PMU” International Conference on Electricity, Power Research Institute, Tehran, Iran, November 2013, pp. 1-6. (inPersian)
[8] Dehghani, M., and S. K. Y. Nikravesh. "Nonlinear state space model identification of synchronous generators." Electric Power Systems Research 78, no. 5 (2008): 926-940.
[9] Gallehdari, Z., M. Dehghani, and S. K. Y. Nikravesh. "Online state space model parameter estimation in synchronous machines." Iranian J. Electrical & Electronic Engineering 10 (2014): 124-132.
[10] Hosseini, Seyed Mehdi, Rohollah Abdollahi, and Mehdi Karrari. "Inclusive design and implementation of online load angle measurement for real-time transient stability improvement of a synchronous generator in a smart grid." IEEE Transactions on Industrial Electronics 65, no. 11 (2018): 8966-8972.
[11] Kovalenko, P. Y., and A. N. Moiseichenkov. "Comparing the techniques of defining the synchronous machine load angle." In Journal of Physics: Conference Series, vol. 870, no. 1, p. 012013. IOP Publishing, 2017.
[12] Sumina, Damir, Bulić, Neven and Vražić, Mario. “Load Angle Control of a Synchronous Generator.” Przeglad Elektrotechniczny 88, 3a (2012): 225-231.
[13] Abdolhosseini, Morteza, and Rohollah Abdollahi. "Design of HHO-PID Controllers for Load Angle of Power Plant Synchronous Generators." International Transactions on Electrical Energy Systems 2022 (2022).
[14] Abualigah, Laith, Ali Diabat, Seyedali Mirjalili, Mohamed Abd Elaziz, and Amir H. Gandomi. "The arithmetic optimization algorithm." Computer methods in applied mechanics and engineering 376 (2021): 113609.
[15] K. R. Padiar. Power system dynamics stability and control. New Delhi : BS Publications. 2008.
[16] S. Korram and H. R. ezadfar, “Use of genetic algorithm in optimal control of real power and load angle of synchronous generator” International conference on recent trends in engineering and materials science, Dubai, UAE, December 2016, pp. 1-15. (inPersian)
[17] Izci, Davut, Serdar Ekinci, Murat Kayri, and Erdal Eker. "A novel improved arithmetic optimization algorithm for optimal design of PID controlled and Bode’s ideal transfer function based automobile cruise control system." Evolving Systems 13, no. 3 (2022): 453-468.
[18] Ahmed, Mohamed, Gaber Magdy, Mohamed Khamies, and Salah Kamel. "Modified TID controller for load frequency control of a two-area interconnected diverse-unit power system." International Journal of Electrical Power & Energy Systems 135 (2022): 107528.