**3. Results**

In this section, we present our main results related to cross-drawing the instrumental model and the pollutant-technology model. Additionally, we will discuss how this model can help policy makers make their decisions.

### *3.1. Cross-Drawing the Cost-Risk and Emission-Risk Models and Selecting an Adequate Combination of Non-Pollutant and Pollutant Technologies*

So far, we have one instrumental model that includes all the technologies and constraints, a non-pollutant e fficient frontier that shows higher risk but lower cost than the instrumental e fficient frontier, and a set of several adaptations of a model with pollutant-technologies. Figure 7 represents some of the e fficient frontiers calculated in an emission-risk coordinate axis. Specifically, we depict the instrumental model numbered with 0 and with a dot-dash line, the model adaptations without biomass numbered as 2.c, those without biomass and CSS technologies numbered as 2.d, and those with all the pollutant technologies and with technological constraints numbered as 2.e. It is important to note that the first two adaptations were practically 100% biomass participated, and for this reason, we are not showing them in the graph—they would be located practically where the biomass technology is drawn.

**Figure 7.** Efficient frontiers in an emission-risk plane.

Regarding the pollutant models, the traditional pollutant technologies—coal, natural gas, and oil—show higher levels of emission and risk; model 2.d e fficient frontier appears on the top right side of the figure. If CCS technologies are included, both the emission and the risk levels are drastically reduced; see model 2.c in the figure. In fact, models 2.a and 2.b would be represented over the biomass point in Figure 6. Moreover, the technological constraints are able to lower even more the risk, keeping a similar level of emission—model 2.e.

By representing in the same emission-risk plane our instrumental model, model 0, it is worth comparing it with the pollutant models—the non-pollutant model would be drawn on the coordinate origin. The instrumental model shows a higher level of emission and risk, in terms of emission, than those models allowing biomass and CCS technologies because coal and natural gas participate largely in it, as shown in Figure 2. When approaching the GMC portfolio, these technologies reach their technological limit and, actually, they participate at their maxima in the GMC portfolio.

The efficient frontier of our models is drawn in a cost-risk coordinate axis in Figure 8. Both the instrumental model, model 0, and the pollutant models, models 2.e and 2.d, present smaller levels of risk with similar or lower levels of cost. As stated, pollutant models with biomass, models 2.a and 2.b, would be drawn on the point corresponding to biomass technology that is far out of the graph's limits with a cost variance of 162.84 (standard deviation: 12.76 €/MWh) and with a cost of 96.62 €/MWh.

**Figure 8.** Efficient frontiers in a cost-risk plane.

### *3.2. The CML-Analogous Area*

So far, we have a pollutant-technology efficient frontier from an emission-risk perspective and a point of the emission-risk coordinate axis origin representing all the non-pollutant efficient portfolios. A policy maker could compile a portfolio from the pollutant-technology efficient frontier with the point in the origin to determine a power-generation portfolio with the whole set of technologies. Therefore, it is possible to set the best portfolio given a desired emission factor or a risk limit.

The limits of the pollutant-technology efficient frontier are the GMV and the GME portfolios. The efficient frontier itself connects them together. Combinations of either the GMV or the GME portfolio with any of the non-pollutant efficient portfolios in the origin will fall inside an area delimited by these three portfolios: the GMV portfolio, the GME portfolio, and the non-pollutant efficient portfolio chosen. In Figure 9, this area is the shaded area below and to the left of the pollutant-technology efficient frontier.

Being under the efficient frontier reflects that any point inside that area shows a lower emission factor than the point on the frontier with the same level of risk. This was expected as we are combining a pollutant portfolio with a non-pollutant one. On the other hand, the fact of being to the left of the pollutant efficient frontier indicates that the risk is lower for any emission factor considered. A portfolio inside the CML-analogous area (CML-A) is then more efficient than a portfolio in the efficient frontier with the same emission factor or level of risk.

**Figure 9.** A Capital Market Line (CML)-Analogous analysis.

Focusing on the CML-A, the problem is to determine the best portfolio for a given emission factor or for a given level of risk. It is easy to conclude that the answer must be found on the CML-A borders. Indeed, when determining the best portfolio in the CML-A for a given level of risk, the solution must be that one located on the segmen<sup>t</sup> joining the coordinate axis origin and the GME portfolio that shows that level of risk. Likewise, if we want to determine the best portfolio in the CML-A for a given emission factor, we must find it on the intersection of the segmen<sup>t</sup> joining the GMV portfolio with the coordinate axis origin and the line representing the desired emission factor. In the next section, we present a brief example of these ideas.
