## 1 Introduction  
On an islanded power system, ensuring the balance between power generation and load demand is very important. When an unpredictable generation unit tripping, \(N\)-1 contingency occurs, the imbalance between generation and load causes a transient frequency dip, which may trigger the involuntary underfrequency load shedding (UFLS) scheme or even cause a complete blackout [1; 2; 3]. This work proposed a complete control strategy that includes four frequency support methods to balance the power generation and load demand. The four methods include the short-term power supports from both generation side and demand side. Generally, the re-dispatch and start-up operations of diesel generators can be executed in a short period of time around several minutes; BESS can provide instantaneous power support in few milliseconds of battery response time [4; 5; 6; 7; 8]. Therefore,the GR and BESS-based methods are good choices to improve frequency stability. On the demand side, the demand response (DR) methods can effectively improve frequency stability by controlling loads. Typically, DR can be categorized into two basic categorizes--price-based demand response (PBDR) and incentive-based demand response (IBDR) [9, 10, 11, 12, 13, 14]. PBDR offers the time-varying electricity rate while IBDR offers the incentive payments or rate discount to DR participants; in exchange, DR participants agree to provide contract-based load-reduction or load-shedding services. In this work, the IBDR methods, including the DLC and EDRP, are used for frequency support. DLC allows utility directly shuts down or cycles participants' certain electrical appliance (e.g., air conditioners and water heaters) on a very short notice [9, 10, 11, 12, 13, 14]. That is, using the load-relay or load-controller, DLC can directly shed the load and provide frequency support when a contingency occurs. As for the EDRP method, it notifies participants 15 min to 2 h ahead and requests for voluntary load-reduction [9, 15]. With the information about the historical demand, electricity price and short-term load forecasting results, the EDRP method can be scheduled to reduce the peak load and thus provide frequency regulation service [9, 14, 16, 17]. The economic analysis in a power utility is significant. Therefore, for the proposed preventive control strategy, the operating costs for each of the four different methods are discussed. For instance, based on the GR method, the fuel cost and start-up cost of diesel generators are considered. For the DLC and EDRP methods, the costs for those methods can be regarded as the incentive payments or rate discount which power utility should pay to the demand-response participants [9], as they belong to the incentive-based demand response. As for the BESS method, the cost for BESS method is determined by the system architecture. In the market-based power system, power utility can regard the BESS cost as the bidding ancillary service payments to BESS provider [18]; whereas in this work, for the island power system operators, the BESS cost should consider the BESS initial investment cost, operation-and-maintenance fees and electricity bill for battery recharging [4, 18]. To simplify the BESS cost analysis, the battery cycle cost, defined as battery investment cost divided by battery lifetime, is utilized in the proposed preventive control strategy [19, 20]. Due to the frequency support requirement is generally highly variable, the battery charging/discharging pattern is usually various and depends on the utility's application, implying that the battery lifetime is hard to be estimated accurately [4, 21]. Therefore, this work has been discussed with Jian-Shan Thermal Power Plant and considers the battery as a back-up power source directly controlled by system operators and the battery lifetime used for this preventive control strategy is assumed to be 5000 cycles. This work is a continuation of our past researches.