Comparison of Uncertainties in Membership Function of Adaptive Lyapunov NeuroFuzzy-2 for Damping Power Oscillations

Comparison of Uncertainties in Membership Function of Adaptive Lyapunov NeuroFuzzy-2 for Damping Power Oscillations

Laiq Khan (COMSATS Institute of Information Technology, Pakistan), Rabiah Badar (COMSATS Institute of Information Technology, Pakistan), Saima Ali (COMSATS Institute of Information Technology, Pakistan) and Umar Farid (COMSATS Institute of Information Technology, Pakistan)
DOI: 10.4018/978-1-4666-7258-1.ch009
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The direct focus of this chapter is to explore the potential of online Adaptive NeuroFuzzy Type-2 (ANFT2) control system for damping inter-area oscillations using Static Synchronous Compensator (STATCOM). The nonlinear ANFT2-based direct control scheme is proposed to damp inter-area oscillations by utilizing its model free and universal approximation capabilities. The Gaussian and triangular membership functions with different variations of uncertain mean and standard deviation are considered for ANFT2. The adaptation mechanism utilizes gradient descent-based back-propagation algorithm using Lyapunov stability criteria to update the rule parameters. The performance evaluation of proposed control strategy has been validated using two and three machine power systems. The nonlinear time domain simulations reveal that ANFT2 has excellent damping capabilities as compared to conventional PI control. Simulation results for different performance indices further emphasize the optimal performance of ANFT2 with uncertain mean and variance of triangular membership function in transient and steady state region.
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In a large interconnected power system, the machine angles of a group of machines oscillate against the others due to the imbalance of energy conversion resulting from a three phase fault, load outage and/or any other discrete event. These oscillations either decay with time restoring the system to its original or a new steady-state, depending upon the nature of the fault, or they may grow indefinitely resulting in system collapse. In the former case, the system has sufficient natural damping to diminish the effect of these oscillations with time, whereas, in later case the system cannot damp these oscillations and additional damping control is needed for secure and reliable operation (Mohagheghi, Venayagamoorthy and Harley, 2006; Mohapatra, Panda and Satpathy, 2013). Flexible AC Transmission System (FACTS) is a relatively new technology which optimizes the performance of a power system through one of the many ways like changing the effective reactance of transmission line, exchange of reactive power with transmission network and phase control of injected voltage (Obulesu, et al. 2009; Varma, 2011) etc.

STATCOM is a shunt connected controller, belonging to the second generation of FACTS, which maintains the bus voltage at a constant level by injecting or absorbing reactive power. Due to its efficient performance, STATCOM found extensive applications to optimize power system operation (Abido, 2005; Panda and Padhay 2008; Ganesh, Dahiya and Singh, 2014). Since, the primary objective of the STATCOM is voltage regulation, it may not perform well or even degrade the system performance in terms of damping inter-area oscillations (Gharaveisi, 2009). In order to damp the low frequency electromechanical oscillations, STATCOM is facilitated with some Supplementary Damping Control (SDC) in addition to the voltage control. The supplementary control must provide the STATCOM with the complete information of the system to perform efficiently. Due to highly nonlinear, multivariable and time varying nature of power system, the exact modeling of each component is almost impossible especially those which are not well-defined like different loads and distributed generations (Hiskens and Alseddiqui, 2006). This gives rise to the uncertainties in power system. Therefore, SDC must exploit some technique which could encounter the effect of the uncertainties in the system (Badar and Khan, 2012, 2013a).

Key Terms in this Chapter

Low Frequency Oscillations: Low frequency oscillations are generator rotor angle oscillations having a frequency between 0.1-2.0 Hz and are classified based on the source of the oscillation. The main cause of electrical power oscillations are the unbalance between power demand and available power at a period of time.

Power System Stability: Power system stability can be defined as its ability to operate in an equilibrium state under nominal conditions and to maintain synchronism, when subjected to disturbances, either by restoring the original or new equilibrium state.

Membership Function: The set of elements that have a non-zero membership is called the support of the fuzzy set. The function that ties a number to each element of the universe is called the membership function.

Flexible Alternating Current Transmission Systems (FACTS): is a general term used for consortium of technologies that drastically increases the capacity of the transmission network while maintaining or improving voltage stability and grid reliability.

Artificial Intelligence: The ability of a computer or other machine to perform those activities that are normally thought to require intelligence.

Gradient Descent: is an optimization technique used to find the local minimum of a function taking steps proportional to the negative of the gradient of the function at the current point.

Foot Print of Uncertainty: of a type-2 fuzzy set will be a bounded region consisting of all the points of primary membership of elements.

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