## 1 Introduction  
Because of more economic objectives for operation, power grids are being operated around their stability limits nowadays. Cascading events, such as failures because of the protection system and human errors, can lead to catastrophic blackouts, as revealed by the 14 August 2003 blackout [1]. In general, splitting the system into controlled islands is considered as the last resort against a blackout after large disturbances [2]. A suitable under frequency load shedding (UFLS) scheme is the key to preventing frequency collapse in small receiving-end power systems [3; 4; 5]. The concept and model of UFLS schemes for isolated power systems are simple and well known, but it must be robust to prevent frequency collapse against many possible disturbances in the isolated power system. Due to the introduction of electricity markets and to the increasing integration of converter-connected renewable generation [6; 7] (e.g., doubly-fed induction generator, DFIG), permanent magnet synchronous generators (PMSG), and photovoltaic (PV)), the power system dynamic frequency responses have recently undergone significant changes. The performance of the UFLS schemes, which are designed based on experience, cannot be necessarily guaranteed in the modern power system. So, several optimization methods have been extensively investigated to design UFLS schemes [3; 8; 9; 10; 11; 12; 13]. To minimize the amount of shed load, both traditional optimization methods and the evolutionary algorithms have been employed to determine the UFLS relay parameters, i.e., frequency thresholds, step sizes, and time delay. The deterministic optimization algorithms, such as the quasi-Newton method [3], sequential quadratic programming (SQP) [9], and the mixed-integer linear program (MILP) [10] were applied to designing UFLS schemes as effective approaches. Heuristicmethods were also given credit for optimizing UFLS relay parameters. The genetic algorithm (GA) [11] and simulated annealing (SA) [12] were developed for setting UFLS relay parameters successfully. The design methods for UFLS schemes reported in the literature were almost established on the system frequency response (SFR) model, which was first proposed in [13]. Higher adaptability of the model was advanced by reducing the SFR model to a simplified equivalent SFR model expressed by [14]. Consequently, the performances of the optimized UFLS scheme mainly depends on the precision of the parameters of the SFR model or simplified SFR model except for optimizing strategies. [PERSON] et al. used the probability-based approach to analyze the control performance of a traditional UFLS strategy in [15], which is of great significance for promoting the application of traditional UFLS. At the same time, with the rapid development of the modern power system, the complexity of the power system dynamic rose sharply, and the parameters derived by using the conventional static equivalence method were hard to meet the requirements of controlling the scheme design. In recent years, wide area measurement system (WAMS) based adaptive UFLS strategies have been proposed [16]. In particular, [PERSON] and [PERSON]'s research [17; 18] on WAMS-based UFLS have made important contributions. However, due to the limited numbers of the Phasor Measurement Unit (PMU), the traditional UFLS is still the most widely used in practical engineering at the present stage. Therefore, this paper describes the development of a parameter identifying strategy based on particle swarm optimization (PSO) [19; 20] technology. Then, a model for the design of a robust and high-performance UFLS scheme is proposed based on the simplified SFR model with the identified parameters. In order to achieve the efficiency of the UFLS scheme, the PSO algorithm is also applied to optimize the UFLS relay parameters by capturing the trade-off between minimizing the frequency deviation and the amount of the total load needed to be shed.