Kriging based Surrogate Modeling for Fractional Order Control of Microgrids (1408.4612v1)

Abstract: This paper investigates the use of fractional order (FO) controllers for a microgrid. The microgrid employs various autonomous generation systems like wind turbine generator (WTG), solar photovoltaic (PV), diesel energy generator (DEG) and fuel-cells (FC). Other storage devices like the battery energy storage system (BESS) and the flywheel energy storage system (FESS) are also present in the power network. An FO control strategy is employed and the FO-PID controller parameters are tuned with a global optimization algorithm to meet system performance specifications. A kriging based surrogate modeling technique is employed to alleviate the issue of expensive objective function evaluation for the optimization based controller tuning. Numerical simulations are reported to prove the validity of the proposed methods. The results for both the FO and the integer order (IO) controllers are compared with standard evolutionary optimization techniques and the relative merits and demerits of the kriging based surrogate modeling are discussed. This kind of optimization technique is not only limited to this specific case of microgrid control but also can be ported to other computationally expensive power system optimization problems.

• The paper presents a Kriging-based surrogate modeling approach for optimizing fractional order (FO) PID controllers used in microgrid frequency control.
• Kriging models efficiently approximate the complex optimization landscape, significantly reducing the computational time compared to standard genetic algorithms.
• Simulation results show that FO-PID controllers optimized via Kriging provide superior performance and robustness over traditional PID controllers in microgrids.

Kriging-Based Surrogate Modeling Approach for Fractional Order Control in Microgrids

This paper by Indranil Pan and Saptarshi Das presents an advanced control strategy for microgrid frequency stabilization, employing fractional order (FO) controllers, particularly focusing on FO-PID controller design. The microgrid structure described includes diverse generation systems such as wind turbines, solar photovoltaics, diesel generators, and fuel cells, complemented by battery and flywheel storage systems. The paper demonstrates the nuanced benefits of using FO controllers, emphasizing their flexibility and effectiveness over traditional integer order (IO) PID controllers.

Overview of Fractional Order Controllers

The paper positions fractional calculus as an extension of traditional calculus, allowing integration and differentiation of arbitrary real orders rather than using integer orders. This inherent feature of FO controllers offers enhanced control dynamics that can be crucial in dealing with the stochastic nature of microgrids. Fractional order PID controllers are an evolution of standard PID controllers with additional parameters $\lambda$ and $\mu$, representing the fractional integral and derivative orders. The controllers are implemented using higher order rational transfer function approximations, as showcased through Oustaloup's recursive approximation method.

Kriging-Based Surrogate Modeling and Optimization

The paper introduces a kriging-based surrogate modeling approach to address computationally expensive simulations involved in optimizing FO-PID controllers for microgrid control. Kriging models, known for their ability to approximate complex design spaces and cater to both linear and nonlinear trends, are adeptly used as surrogates to reduce computation time while maintaining high accuracy. Through constructing kriging models leveraging various correlation functions, the approach allows for efficient exploration of the optimization landscape, significantly outperforming standard genetic algorithms (GA) as demonstrated in the comparative analysis.

Key Results and Implications

Simulation results indicate that the FO-PID controller exhibits superior performance over PID controllers by reducing frequency fluctuations, enhancing power quality, and increasing robustness under nominal and perturbed conditions. The optimal controller parameters yielded by kriging models contribute to stable, near-optimal solutions consistently across multiple runs, showcasing efficiency and reliability in scenarios with considerable system uncertainties. Statistics confirm that spline correlation models provide the best performance during optimization processes.

The research findings extend beyond microgrid control, providing insights into optimizing other power systems facing similar computational challenges. The utilization of fractional order controllers and surrogate modeling methodologies paves the way for application in diverse dynamic power system optimization problems, including frequency and voltage control, contributing to the enhanced stability and efficiency of contemporary smart grids.

Future Perspectives

Future developments could explore real-time tuning of FO-PID controllers within microgrid architectures, as facilitated by the efficiency gains from kriging-based optimization. This method is particularly suited to applications in dynamic environments where rapid changes necessitate adaptive control strategies. Continuous advancements in fractional calculus, sophisticated surrogate modeling, and global optimization algorithms hold the promise of optimizing control systems with even higher dimensionality and complexity.

In conclusion, Pan and Das's work presents a robust framework for microgrid frequency control, integrating fractional order controllers with kriging-based optimization, signaling promising pathways for future explorations in power systems control and smart grid management.