Abstract
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.