## 1 Introduction
This approach, however, fails to account for the demand variability. The load duration curve (LDC) is often used in generation system adequacy studies, as the model can capture the load variability, throughout a given period. The LDC is simplified by using a multi-state load model [9] in CSR assessment. The computation time, however, increases in multiples of the number of combinations of the multi-states used in the load and generation models. Existing multi-state load modeling methods to incorporate load variabilities at different buses of emerging power systems result in an increased number of demand scenarios, thereby increasing the number of computations. This paper illustrates a method to determine the optimal number of states in a multi-state load model and presents a methodology to minimize the computation time, using a scenario reduction technique. Although the multi-state generation model can satisfactorily represent the variable output characteristics of a renewable energy source, the model does not retain the chronology of the output events. This creates challenges in incorporating the cross-correlation in variations in supply between multiple nodes, and between supply and demand within a node. Wind speed correlations between different sites, wind penetration levels, and the number of capacity states considered in the wind power model have significant impact on the reliability indices [2]. The cross-correlation between supply and demand will also have a significant impact on system adequacy performance of low-carbon energy systems dominated by intermittent generation sources. For instance, there will be a positive correlation between wind generation and load in winter peaking systems as heating loads increase with wind chill in the winter. On the other hand, the correlation can be strongly negative in the summer as reduced wind on a hot day can cause an increase in the air-conditioning load. The negative load modeling approach [4] subtracts the wind power generation from the load chronologically to obtain the probability distribution of the net load, which incorporates the cross-correlation between the wind generation and the load. A key drawback with this existing method at the system level is that it assumes that the total wind power generated can always be absorbed by the system load, thus ignoring the line congestion problems. This paper, therefore, proposes a novel distributed negative load approach at individual bulk load points connected to wind farms, which allows incorporation of transmission line congestion impacts while incorporating the cross-correlations between wind power and load variations in analytical CSR assessments. The wind generation in excess of the load at each bus is then modeled as a multi-state generation unit. This way, the required correlations can be captured at the individual buses without ignoring the line congestion contingencies in the assessment. The distributed negative load approach incorporates the cross-correlations between the generation and load variations at each bus but does not capture the cross-correlations of the variabilities between multiple buses of the power network. The cross-correlations in all variables can easily be incorporated using a sequential Monte Carlo simulation (MCS) approach. The MCS is implemented to analyze the cross-correlations between multiple wind farms in the CSR studies [10]. A method is proposed to model a combined probability distribution function using the correlation matrix and evaluate the CSR of the network by using the MCS technique [11]. The MCS method in CSR assessment of emerging power systems, however, becomes computationally extensive for capturing all potential scenarios. Additionally, a computer program based on the MCS method is often system-specific, making it difficult to apply to other systems. In contrast, analytical methods involve mathematical models and formulas to directly calculate the reliability indices and can be programmed to be applicable to a wide range of power systems.