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.
Effect of nonuniformity on the continuous representation of electromechanical dynamics in large power systems
