*Article* **Inertia Dependent Droop Based Frequency Containment Process**

#### **Kaushik Das 1,\*, Müfit Altin 2, Anca D. Hansen 1 and Poul E. Sørensen 1**


Received: 20 March 2019; Accepted: 24 April 2019; Published: 30 April 2019

**Abstract:** Presently, there is a large need for a better understanding and extensive quantification of grid stability for different grid conditions and controller settings. This article therefore proposes and develops a novel mathematical model to study and perform sensitivity studies for the capabilities of different technologies to provide Frequency Containment Process (FCP) in different grid conditions. A detailed mathematical analytical approach for designing inertia-dependent droop-based FCP is developed and presented in this article. Impacts of different droop settings for generation technologies operating with different inertia of power system can be analyzed through this mathematical approach resulting in proper design of droop settings. In contrast to the simulation-based model, the proposed novel mathematical model allows mathematical quantification of frequency characteristics such as nadir, settling time, ROCOF, time to reach the nadir with respect to controller parameters such as gain, droop, or system parameters such as inertia, volume, of imbalance. Comparative studies between cases of frequency containment reserves (FCR) provision from conventional generators and wind turbines (WTs) are performed. Observations from these simulations are analyzed and explained with the help of an analytical approach which provides the feasible range of droop settings for different values of system inertia. The proposed mathematical approach is validated on simulated Continental Europe (CE) network. The results show that the proposed methodology can be used to design the droop for different technology providing FCP in a power system operating within a certain range of inertia.

**Keywords:** inertia; wind power; droop; frequency control; primary control; frequency containment process
