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.

Hybrid renewable energy systems: the value of storage as a function of PV-wind variability

“…Kendall's Tau and the Spearman rank coefficient have also been used, but substantial overlap exists in the insights provided by these metrics and the Pearson coefficient for wind-solar complementarity throughout the conterminous United States . Cantor et al assert that correlation is required but not sufficient for complementarity and that the scale of resources must be considered (Cantor et al, 2022a;Cantor et al, 2022b), which we do through the use of the stability coefficient. Jurasz et al provide a comprehensive review of studies that have used-and proposed-a wide range of complementarity metrics, and they note the need for future studies to extend the insights provided by complementarity assessments to practical applications (Jurasz et al, 2020).…”

Discussion of “Assessing temporal complementarity between three variable energy sources through correlation and compromise programming” F.A. Canales et al. Energy 192 (2020) 116637

“…Han et al [8] evaluated the complementarity between solar-wind-hydro time series considering ramp and fluctuations within continuous time windows. The total variation complementarity index proposed by Cantor et al [9], [10] measures the complementarity between multiple time series regarding a constant mean for each function. Finally, the method proposed by Canales et al [11] combines correlation coefficients, compromise programming, and normalization to calculate a total temporal complementarity index 𝑘 𝑡 considering three renewable energy sources' time series.…”

Spatio‐temporal availability of renewable energy sources for Western Paraná

“…8,15,16 Planning for production and democratization of the energy produced is enhanced by the possibility of using more than one energy source, the so-called complementarity. 17,18 The complementarity in space has potential when the energy availability of one or more sources complements each other throughout the same region. In time, there is potential when energy availability presents periods that complement each other over time in the same region.…”

“…Countries must develop a regulatory framework ensuring energy efficiency and integration of the population 8,15,16 . Planning for production and democratization of the energy produced is enhanced by the possibility of using more than one energy source, the so‐called complementarity 17,18 . The complementarity in space has potential when the energy availability of one or more sources complements each other throughout the same region.…”