The penetration of distributed generators (DGs) causes voltage unbalance issues in distribution systems. The issues increases the number of objectives in distribution system operation, making it more challenging to achieve optimal operation. Reducing the dimensionality of the objectives by revealing the correlations between objective functions is a practical approach to such challenges. This paper reports reduction of objective functions in an optimal operation problem of unbalanced power distribution systems. Four typical objectives, including voltage unbalance, are considered, and correlations are analyzed by principal component analysis (PCA). In addition, comparisons are made under different constraints. Despite the results revealing two significant conflicts between the objective functions, performing objective reduction using PCA is challenging in many cases. However, the Pareto fronts of some objective functions indicate the existence of reasonable knee points, suggesting that further objective dimensionality reduction may be achieved by integrating some objective functions based on the knee point.