The existing literature predominantly concentrates on the utilization of the gradient descent algorithm for control systems design in power systems for stability enhancement. In this paper, various flavors of the Conjugate Gradient (CG) algorithm have been employed to design the online neuro-fuzzy linearization-based adaptive control strategy for Line Commutated Converters (LCC) High Voltage Direct Current (HVDC) links embedded in a multi-machine test power system. The conjugate gradient algorithms are evaluated based on the damping of electro-mechanical oscillatory modes using MATLAB/Simulink. The results validate that all of the conjugate gradient algorithms have outperformed the gradient descent optimization scheme and other conventional and non-conventional control schemes.
AC/DC POWER SYSTEM MODEL DESCRIPTION
The LCC-HVDC system represented by an average model is shown in Figure 1. The variables are shown with appropriate subscripts I and R for the inverter and rectifier poles, respectively. The rectifier and inverter poles are average models of 12-pulse converters with equivalent DC voltage and AC current sources. The voltage source generates converter voltage at the DC side, and the current source injects the fundamental component of the current into the AC network. The linear model of the commutation transformer is also included in the average model representation.
CLOSED-LOOP CONTROL SYSTEM DESIGN
The proposed ANFFBLC scheme is a model-free indirect control strategy and requires minimal knowledge of the power system. As shown in Figure 2, the dynamics of the AC/DC power system are identified through an Adaptive Neuro-Fuzzy Identifier (ANFI) using the Wide-Area Measurement System (WAMS)-based measured speed signals of generators. The CG algorithm on-line optimizes the ANFI parameters to minimize the identification error.
SIMULATION RESULTS AND DISCUSSION
The damping performance of HVDC links with damping control is also assessed through performance indexes. Two performance indexes ITSE and ITAE are shown in Figure 5. The ITSE plot represents time-weighted speed deviation error during the transient-state. The best improvement of 55% in the minimization of the transient-state error is achieved by ANFFBLC-HZ in comparison with PID control, while the ITSE plot of ANFFBLC-FR shows 50% improvement over PID.
The ITSE and ITAE indexes shown in Figure 7 represent the damping performance comparison. HVDC links with MIMO ANFFBLC have lesser ITSE index values at any time and more flat profiles as compared to the ITSE plot of the benchmark control systems. As compared to conventional PID control, the ITSE plot for ANFFBLC-HZ depicts 63% improvement in damping the transient-state oscillations.
The article presented an MIMO POD controller for multiple HVDC transmission systems. The ANFFBLC schemes effectively modulate the real power flow through the HVDC system to enhance its damping assistance during perturbed conditions. Excited power oscillations under any disturbance are apprehended by the ANFFBLC on the basis of the measured speed signal of generators. SD and six CG algorithms are employed to optimize the parameters of ANFIS that minimize the identification error and captured the updated plant dynamics without a priori knowledge of the system model. The damping performance is investigated through the multi-machine AC/DC power system exposed to the disturbances of different severity.
Results obtained for a wide range of operating conditions indicate the improved damping performance of different proposed CG-based ANFFBLC schemes as compared to ANFFBLC-SD, conventional PID control, AdapPID and DirINF. Among CG algorithms, the HZ method shows the best optimization capabilities with strong convergence to optimal minima of the optimization function. Rapid identification of the plant model with the HZ method enables ANFFBLC-HZ to derive the desired control output that effectively damped LFO in the power system. The future work includes the implementation of MIMO nonlinear POD control for multiple HVDC links and FACTS controllers, as well as the investigation of the effect on damping the low-frequency oscillations.
Source: Carnegie Mellon University
Authors: Saghir Ahmad | Laiq Khan