Total variation as a metric for complementarity in energy resources time series

Complementarity has become an essential concept in energy supply systems. Although there are some other metrics, most studies use correlation coefficients to quantify complementarity. The standard interpretation is that a high negative correlation indicates a high degree of complementarity. However, we show that the correlation is not an entirely satisfactory measure of complementarity. As an alternative, we propose a new index based on the mathematical concept of the total variation. For two time series, the new index φ is one minus the ratio of the total variation of the sum to the sum of the two series' total variation. We apply the index first to an auto-regressive (AR) process and then to various Colombian electric system series. The AR case clearly illustrates the limitations of the correlation coefficient as a measure of complementarity. We then evaluate complementarity across various space-time scales in the Colombian power sectors, considering hydro and wind projects. The complementarity assessment on a broad temporal and geographical scale helps analyze large power systems with different energy sources. The case study of the Colombian hydropower systems suggests that φ is better than ρ because (i) it considers scale, whereas ρ, being non-dimensional, is insensitive to the scale and even to the physical dimensions of the variables; (ii) one can apply φ to more than two resources; and (iii) ρ tends to overestimate complementarity.