## 3 Results and Discussion
For other import prices, the growth of capacity factor was less than 0.08%, since the CCGTs capacity factor depends on both the IC1 import price and CO\({}_{2}\) tax. Figure 3 represents the impact of the CO\({}_{2}\) tax on the total electricity flow in and out of GB over 2030. As is evident from Figure 3a, at a constant IC1 price, increasing the CO\({}_{2}\) tax will cause a reduction in the total amount of electricity exports to France. This is because of the fact that part of the electricity exported to France comes from CO\({}_{2}\) emitting power plants, and increasing the CO\({}_{2}\) tax will affect the power outputs of such plants. In our experiments, when the IC1 price was below \(\tau_{\text{FR},t}\), the cross-border link IC1 imported power to GB and then exported it to France by means of the IC2. At low values of IC1 prices, there were big differences among the total electricity exports from GB to France compared to the change of the CO\({}_{2}\) tax. For example, the difference between the quantity of electricity exports to France was 0.4 TWh as the CO\({}_{2}\) tax increased from 50 to \(\varepsilon\)90/ton. At high IC1 import prices, there was no surplus power to be exported to France, since the electricity price in France was below the IC1 import price. At a constant CO\({}_{2}\) tax price, increasing the IC1 price tended to decrease the electricity exported to France, because a fraction of the electricity exported to France is provided via IC1. Figure 3b depicts the amount of power flow to GB by means of the IC2 line. At fixed IC1 import prices, increasing the CO\({}_{2}\) tax tends to improve the import to GB by means of the cross-border interconnect IC2. The reason is that increasing the CO\({}_{2}\) tax increases the emission costs of gas and coal-fired power plants, and the power required to meet the demand is import via IC1. At a fixed CO\({}_{2}\) tax, raising the IC1 import price causes more imports to GB via IC1. At a constant CO\({}_{2}\) price, increasing the IC1 price diminishes the importance by means of the cross-border link IC1. Except for the IC1 price of \(\varepsilon\)60/MWh, the profiles of the IC1 electricity flow to GB are very close to each other. Figure 1: Contribution of generation technologies in power supply (%) vs. CO\({}_{2}\) tax and the IC1 import price over 2030. Figure 2: _Cont_. Figure 4 shows the frequency of the half-hours during which the IC2 is fully loaded versus the IC1 price and CO\({}_{2}\) tax in 2030. For each IC1 price, the percentage of times (half-hours) that the IC2 power link is fully loaded is not changed much by the variation of CO\({}_{2}\) tax. At a fixed CO\({}_{2}\) tax, increasing the IC1 price increases the percentage of times (half-hours) that the IC2 is on full load. Figure 5 illustrates the minimum and maximum amounts of shedding (in GW) and the maximum IC1 load (in GW) when IC1 was fully loaded at various CO\({}_{2}\) taxes and IC1 import prices for 2030. As is evident from this figure, for all values of the IC1 prices, the minimum and maximum shedding were 0.7 and 1.07 GW, respectively. In addition, the maximum IC1 load tends to decline as the IC1 price increases. It is worthy to mention that shedding phenomena occur during 10 half-hours irrespective of the IC1 import price and the CO\({}_{2}\) tax. During shedding times, \(\pi_{\text{FR},t}\) is greater than \(\pi_{\text{GB},t}\) and according to the Equation (10), the flow through the IC2 becomes zero. At a constant value of CO\({}_{2}\) tax, increasing the IC1 price reduces the number of occasions (half-hours) in 2030 in which IC1 is loaded due to the increased marginal cost of power supply via IC1. Alternatively, when the IC1 price is constant, the higher the CO\({}_{2}\) tax, the higher the number of half-hours within 2030 that IC1 is used (loaded). This is because increasing the CO\({}_{2}\) tax results in a high marginal cost of CO\({}_{2}\) emitting power plants.