## 2 Proposed Methodology  
This section describes the proposed bulk system adequacy evaluation methodology for low-carbon energy systems incorporating large-scale generation and demand variability while integrating the cross-correlation between them. The methodology uses time-series data modeling to capture the cross-correlation between wind generation and load variations at each network node, and a probabilistic analytical approach to model the variabilities. The multi-state generation and load models thus obtained can therefore be embedded in commercial CSR software tools. The methodology significantly reduces the number of evaluation scenarios by utilizing a cut-off load strategy that involves a first-pass load-flow run to determine the load level below which load loss probability is negligible, except for islanded contingencies. The proposed methodology models intermittent renewable generation using a nodal negative load modeling technique that utilizes a time-series analysis to incorporate the cross-correlation between variations of the renewable power generation and the demand at a bus. This paper considers wind power as the renewable generation, since penetration of other intermittent renewable sources are less significant than wind power in most bulk power systems. A time-series of net load at each Bus \(i\) is obtained by Equation (1) from historical wind power and load data. The time-series wind and load data can also be estimated using various statistical methods [19; 20]. \[\{L_{net,i}(t)\}_{t=1}^{nT}=L_{i}(t)-W_{i}(t) \tag{1}\]  
where, \(L_{i}(t),\ W_{i}(t)\) are the average load and wind power, respectively, in hour \(t\) at Bus \(i\), \(L_{net,i}(t)\) is the net load in hour \(t\) at Bus \(i\), \(T\) is the evaluation period of one year, and n is the number of years of data used in the evaluation. The nodal net load is the positive data in Equation (1) and can be obtained for the ith bus from Equation (2). \[L_{nod\_i}=\{L_{net,i}(t)\}_{t=1}^{nT}\forall\ L_{net,i}\geq 0 \tag{2}\]  
The effective nodal wind generation model is obtained by creating a discrete probability distribution, \(PW_{i}\) at Bus \(i\) from the data in \(\{-L_{net,i}(t)\}_{t=1}^{T}\), \(\forall\ L_{net,i}>0\), as shown in Equation (3). \[PW_{i}=\left\{C(j),\ Prob\big{(}C_{j}\big{)}\ \big{|}\ j=1,2,\ldots,N_{W}\ \right\} \tag{3}\]  
where, \(C(j)\) is the average wind power in the \(j\)th state, and \(Prob\big{(}C_{j}\big{)}\) is the probability of the wind power residing in the \(j\)th state in the \(N_{w}\)-state discrete probability distribution. A sensitivity study is presented in Section 4 of this paper to show how \(N_{w}\) impacts the CSR indices and number of evaluation scenarios. The generation model \(G_{i}\) at Bus \(i\) is then obtained from the convolution of the two discrete probability distributions shown in Equation (4). \[G_{i}=PW_{i}\beta CG_{i} \tag{4}\]  
where \(CG_{i}\) is the discrete pdf of conventional generation at Bus \(i\), obtained from the convolution \((CG_{i,1}\otimes\ldots\otimes CG_{i,m})\) of the \(m\) conventional units connected to Bus \(i\). It should be noted that the negative load approach substantially reduces the effective net wind generation and, therefore, the multi-state representation of the net load largely dictates the number of evaluation scenarios in the proposed methodology. As mentioned earlier, the methodology to develop the load model reduces the number of evaluation scenarios by utilizing a cut-off load strategy to determine the load level, below which the load loss probability other than islanded contingencies are negligible. The cut-off load \(L_{CO}\) within the nodal net load dataset, \(L_{nod\_i}\), is determined; such that load levels below \(L_{CO}\) do not result in significant loss of load (LOL) at any load buses, except for islanding situations. A preliminary CSR assessment is done using a commercial tool such as the PSSE [21].