# Power Grid Reliability Evaluation Considering Wind Farm Cyber Security and Ramping Events
## 5 Power System Reliability Assessment
### The Procedures of Reliability Assessment  
Composite power system reliability assessment is based on the sequential Monte Carlo simulation. The step size of the simulation is an hour. In each step, the system states are sampled and evaluated. The power system reliability is estimated by the annual reliability indices. The flow of reliability assessment is detailed as follows:  
(I) Initialize the system reliability model. Establish the basic reliability models of the power system, including the basic power flow data and the physical status of generators and transmission lines.  
(II) Input the system load demand. The chronological curve of load power for 8760 h is generated. The load demand of each bus considers the characteristics of the season and workday.  
(III) System states sampling. The system states contain the physical states of components, the output of WTs, and the cyber security of the wind farm. The events which deteriorate the system reliability are sampled separately. The physical failure of the components and occurrence of WPRs are sampled according to historical probability data. For a cyber-attack event, by sampling the time to compromise and defense the vulnerabilities as Equation (4), the occurrence time and frequency of cyber-attacks can be determined.  
(IV) The assessment of WPRs. If WPRs exists, the ramping rates and durations are sampled by a Gaussian model. According to the ramping rate, the available power capacities of conventional generators are further updated by Equation (13). The load shedding caused by WPRs could be assessed by the basic OPF model. Then the output and the states of WTs are updated for further evaluation.  
(V) The assessment of a cyber-attack. If a cyber-attack exists, the assessment consists of two typical scenarios. For the worst-case attack, the set of system active power margins shown in Equation (5) during the hidden time can be established according to the sampling results in step III. The load shedding caused by cyber-attacks is quantified by the bi-level OPF model Equations (19)-(26). For an IPA, the estimation procedure of time-varying failure rates is illustrated in Figure 4. The impact of an IPA is equivalent to the extra running time of WTs. The bearing states and their remaining life are assessed by the Markov model. When the service time and the remaining life of a WT change, the new WT failure rates should be updated with Equation (10). According to the latest failure rates, the composite system states are evaluated by the basic OPF model.  
(VI) Checking the termination condition. Check if the sampling number meets the stopping criteria. If not, go back to step 2. The state sampling is conducted for 100 years.  
(VII) Reliability indices calculation. When the sampling is sufficient, calculate the annual reliability indices. The reliability indices: The loss of load probability (LOLP) and expected energy not supplied (EENS) are defined as Equations (27) and (28).  
\[LOLP=\frac{1}{Ns}{\sum_{i=1}^{Ns}Ls_{i}} \tag{27}\]  
\[EENS=\frac{8760}{Ns}{\sum_{i=1}^{Ns}Lp_{i}} \tag{28}\]  
where \(NS\) is the total number of samples from the system state space. In the \(i\)th sample, if load curtailment occurs, \(Ls_{i}\) equals 1; otherwise, it equals 0. \(Lp_{i}\) is the load curtailment in the \(i\)th sample, with unit MW.