Determining optimal virtual inertia and frequency control parameters to preserve the frequency stability in islanded microgrids with high penetration of renewables

Highlights

• A method is proposed to determine the proper value of virtual inertia in MGs.

• Tuning the parameters of MG is determined as a multi-objective optimization problem.

• A many-objective optimization algorithm is used to solve the optimization algorithm.

• The characteristics of the ultracapacitor used for emulating inertia are determined.

Abstract

Preserving the frequency stability of low inertia microgrids (MGs) with high penetration of renewables is a serious challenge. To rise to this challenge, the inertia constant of MGs would be virtually increased using energy storages. However, it is important to determine the suitable value of inertia constant for these systems such that the frequency stability is preserved with a lower cost. Frequency droop coefficient of distributed energy resources (DERs) and load frequency controllers’ parameters would also affect the frequency response of MGs. Hence, in this paper, inertia constant is tuned together with frequency droop coefficient of DERs and load frequency controllers’ parameters. Determining these parameters is modeled as a multi-objective optimization problem and, because the number of objectives is higher than three, the problem is solved by a many-objective optimization algorithm. Comparative simulation studies have been done on an MG with different types of DERs to prove that using the proposed strategy for tuning the MG parameters not only the frequency deviation is highly decreased but also the amount of load shedding is considerably diminished. This would increase the customers’ satisfaction. Moreover, considering the inertia constant as a minimization objective, frequency stability would be preserved with a lower cost.

Introduction

Due to the environmental concerns, there is an increasing interest in using renewable energy sources (RESs) for power generation. MGs would provide a suitable infrastructure for integrating RESs to the grid at distribution level. MGs can operate in grid-connected or islanded mode. However, in islanded mode, they would encounter challenges in frequency and voltage control. These problems would be exacerbated in MGs with a high share of power-electronically interfaced DERs; due to the low inertia of the grid. In fact, in low inertia MGs, power imbalances result in rapid changes in frequency that might endanger the stability of the system [1].

To address these stability concerns, some methods have been proposed to increase the inertia of MGs. In Refs. [2], [3], using synchronous condensers have been proposed for this purpose. In addition to contributing to the inertia of the gird, synchronous condensers would participate in reactive power control. Inverter-based DERs would also emulate the inertial response of synchronous generators by injecting a power proportional to frequency derivative to the grid. In Ref. [4], a control method has been proposed for converters to emulate the behavior of synchronous generators. Virtual inertia has been implemented in Ref. [5] to increase the contribution of distributed generators to oscillation damping. To emulate the inertial behavior of synchronous generators, inverter-based DERs require a temporary source of energy similar to the kinetic energy of the rotor of synchronous generators. In Ref. [6], the energy stored in the rotor of doubly fed induction generator (DFIG) based wind turbines and also the ultracapacitor (UC) installed at the dc-link of converters are used as energy sources for inertia emulation. In Ref. [7], HVDC transmission line is controlled to contribute to the inertia of the grid. HVDC links would transfer the inertial power generated by wind farms to the main grid, transfer inertial power from one area of power system to another area or use the energy stored in the DC link to emulate the inertial response. UC is proposed in Ref. [8] to emulate the inertial response of synchronous generators in an isolated power system. Although some studies have been carried out on contribution of inverter-based DERs to the inertia of MGs, to the best of authors’ knowledge, a systematic method for determining the proper value for inertia constant in islanded MGs has not yet been proposed.

In addition to inertia constant, load frequency controllers and frequency droop coefficient of power sources would affect the frequency response of the grid. Fine-tuning the load frequency controllers would reduce the maximum frequency deviation and also bring back the frequency to the nominal value faster. Different methods have been proposed for load frequency control (LFC) in power systems. In Ref. [9] the performance of model predictive controller for LFC in Nordic power system was investigated. Many researchers have focused on tuning the traditional proportional integral (PI)/proportional integral derivative (PID) controllers using evolutionary algorithms. In Ref. [10] bacterial foraging optimization algorithm has been implemented to tune the load frequency controllers of an MG with generation rate constraint (GRC). In Ref. [11] a hierarchical approach based on fuzzy logic has been proposed to improve the quality of frequency control. Electrical vehicles have been implemented in Ref. [12] for frequency control. In Ref. [13], fractional order PID controllers have been proposed for LFC in a multi-area power system. An adaptive set-point modulation technique has been implemented in Ref. [14] to enhance the performance of PI load frequency controllers. To improve the performance of frequency controllers in a three-area thermal power system, in Ref. [15] governors’ frequency droop coefficient (R) have been optimized together with the load frequency controllers’ parameters.

Since the grid inertia constant (H), frequency droop coefficient of DERs and parameters of load frequency controllers all affect the frequency response of MGs, in this paper, tuning these parameters has been suggested to improve the frequency stability of MGs. Based on different criteria that should be met to have a proper frequency response in MGs, a systematic method is proposed for tuning all the parameters, including R, H and the controllers parameters, simultaneously. The main goal of tuning these parameters is to improve the frequency stability of MG. However, this goal should be achieved with the minimum cost. Hence, tuning these parameters has been modeled as a multi-objective optimization problem which considers both stability and economic aspects. Considering the fact that usual multi-objective optimization algorithms, like non-dominated sorting genetic algorithm II (NSGA-II), would not show a good performance in solving optimization problems with more than three objectives [16], a recently developed many-objective knee point driven evolutionary algorithm (KnEA) is implemented for solving this problem. Finally, to select one of the Pareto optimal solutions obtained by KnEA as the final solution, a strategy based on the minimum sum of the normalized objectives is suggested. Also, a method for determining the characteristics of the ultracapacitor required for emulating the determined inertia is proposed.

The rest of this paper is organized as follows: in Section 2, the required equipment for increasing the inertia constant of the MG is studied. In Section 3, the process of tuning the parameters of MG for improving its frequency response is explained. The studied MG is introduced in Section 4. Then, in Section 5, by simulation studies carried out in Matlab/Simulink, the effectiveness of the proposed method is investigated. Finally, the conclusions of this research are presented in Section 6.