Total Variation-Based Metrics for Assessing Complementarity in Energy Resources Time Series

Abstract

The growing share of intermittent renewable energy sources raised complementarity to a central concept in the electricity supply industry. The straightforward case of two sources suggests that to guarantee supply, the time series of both sources should be negatively correlated. Extrapolation made Pearson’s correlation coefficient (ρ) the most widely used metric to quantify complementarity. This article shows several theoretical and practical drawbacks of correlation coefficients to measure complementarity. Consequently, it proposes three new alternative metrics robust to those drawbacks based on the natural interpretation of the concept: the Total Variation Complementarity Index (ϕ), the Variance Complementarity Index (ϕ′), and the Standard Deviation Complementarity Index (ϕs). We illustrate the use of the three indices by presenting one theoretical and three real case studies: (a) two first-order autoregressive processes, (b) one wind and one hydropower energy time series in Colombia at the daily time resolution, (c) monthly water inflows to two hydropower reservoirs of Colombia with different hydrologic regimes, and (d) monthly water inflows of the 15 largest hydropower reservoirs in Colombia. The conclusion is that ϕ outperforms the use of ρ to quantify complementarity because (i) ϕ takes into account scale, whereas ρ is insensitive to scale; (ii) ρ does not work for more than two sources; (iii) ρ overestimates complementarity; and (iv) ϕ takes into account other characteristics of the series. ϕ′ corrects the scale insensitivity of ρ. Moreover, it works with more than two sources. However, it corrects neither the overestimation nor the importance of other characteristics. ϕs improves ϕ′ concerning the overestimation, but it lets out other series characteristics. Therefore, we recommend total variation complementarity as an integral way of quantifying complementarity.