Quantifying hydro-wind-solar energy complementarity is crucial to planning and optimal dispatch of a co-generation system. However

previous evaluation indexes for the complementarity paid less attention to the three-dimensional complementary capacity of hydro-wind-solar energy

and they were often used to either consider only the overall trend or the amount of change in a continuous period of the power output sequence

or they neglected the effect of fluctuating phase differences

lowering the accuracy of quantification in a variety of scenarios. This paper examines the correlation of hydro-wind-solar energy fluctuations in depth

and presents a new multidimensional

multi-timescale complementarity evaluation index by categorizing fluctuation states in consecutive periods. Then

we verify this index for several typical scenarios and show its accuracy in quantifying complementarity of hydro-wind-solar energy sequences

and its superiority by comparing the results with those of the previous complementarity indexes. Finally

application of the new index to regional wind-solar planning is demonstrated in a case study of a comprehensive development base for hydro-wind-solar integrated renewable energy in the Wujiang River basin. For this base

optimal ratios of the wind-solar installed capacities are given in different time scales.