# General situation of arbitrarily distributed solar power generation clusters

We have discussed the ideal situation of n identical systems with the same variability VI in the unrelated state. As a result, the relative variability of the cluster is equal to 1/, /n of the separately installed system.

In addition, we also show the impact on this relationship when the correlation is not equal to 0, and how this correlation evolves according to factors such as distance, time interval and cloud speed.

Generally speaking, the cases of chromatic number smoothing are mainly divided into centralized and decentralized solar (PV) power generation. Centralized solar power generation is similar to some equal point systems arranged in a certain distance and rules.

As a more common type, distributed solar power generation has different systems, and the spacing is arbitrarily distributed, so it has different degrees of pairwise location correlation.

Because each system is not always the same, the output and variability of the power generation cluster may be affected by the size of a single system and the variability of each system, which itself may be the result of spatial smoothing within a large array. Therefore, it is necessary to return to the variability formula based on the power output of each system, where I represents the ith system in the cluster.

Cluster variability refers to the standard deviation of cluster power output change, which is equal to the square root of variance of the sum of power changes of each single system. The variance of the sum is equal to the sum of the covariances of all possible combinations.

In formula , we should pay special attention to that the standard deviation of the change of cluster power output is based on the correlation between the power output of the power station at each location and each location. Using the empirical formula proposed in formula , the correlation coefficient between each location can be measured.