## 3 Results and Discussion
At a constant CO\({}_{2}\) price, as the IC1 price increases from \(\epsilon 20\)/MWh to \(\epsilon 40\)/MWh, the number of cases that IC1 is fully loaded and IC1 is unloaded declines. As the IC1 price rises from 60 to \(\epsilon 100\)/MWh, the number of half-hours in which the IC2 is fully loaded and IC1 is unloaded increases. This is because the demand is not high and the IC1 is not used for power import. IC1 will import and/or export electricity. The number of cases in which IC1 and IC2 power links import and export electricity in and out of GB compared to IC1 price and CO\({}_{2}\) tax were determined. The direction of power flow between France and GB depends upon the relative electricity prices of these states. If \(\pi_{\text{GB},t}\) is higher than that of the neighbors, and GB's power plants cannot meet the demand, the interconnectors will be used for electricity importing to GB. In addition, on the occasions with the IC1 price of \(\epsilon 20\)/MWh and the CO\({}_{2}\) tax of \(\epsilon 50\)/ton, there are 474 half-hours in which \(\pi_{\text{GB},t}\) is higher than \(\pi_{\text{FR},t}\), IC2 imports electricity from France, and IC1 = 0. According to Equation (10), IC2 will not import electricity when \(\pi_{\text{FR},t}\) is higher than \(\pi_{\text{GB},t}\). When \(\pi_{\text{GB},t}\) is higher than \(\pi_{\text{FR},t}\), there are two cases where both IC1 and IC2 links are inactive. Interestingly, power is imported to GB via IC1 at \(\epsilon 20\)/MWh and then is transmitted to France during 595 periods (out of 17520 half-hours) with an electricity price of over \(\epsilon 20\)/MWh. At a constant IC1 price, when the IC1 price is below \(\epsilon 60\)/MWh, increasing the CO\({}_{2}\) tax tends to increase the number of cases such that IC1 > 0 and IC2 > 0. This signifies the role of interconnectors in power import at high CO\({}_{2}\) tax scenarios. Figure 2: Capacity factor of GB’s power generators vs. IC1 import price and CO\({}_{2}\) tax. Figure 3: Impact of CO\({}_{2}\) tax on the total electricity flow from/to GB within 2030: (**a**) electricity flow from GB to France via IC2 link, (**b**) power import from France via IC2 link. Figure 6 displays GB's power system CO\({}_{2}\) emissions in 2030 as a function of the IC1 import price (\(\pounds\)/MWh) and CO\({}_{2}\) price (\(\pounds\)/ton). As is evident in this figure, the amount of emitted CO\({}_{2}\) from the gas and coal-fired power plants at the low IC1 price of \(\pounds\)20/MWh declines as the CO\({}_{2}\) tax increases. For example, the CO\({}_{2}\) emissions reach 7.72 million tons at a carbon tax of \(\pounds\)50/ton, and 7.48 million tons when the CO\({}_{2}\) tax is \(\pounds\)90/ton. In these cases, the CCGT plants emit over 83.5% of the total emissions. The CCGT plants emit ca. 83.05-83.30% of the total emissions. When the IC1 price is set to \(\pounds\)60/MWh, the total power system emissions are 26.47 million tons at the carbon tax of \(\pounds\)50/ton (the contribution of CCGT plants is over 94% of the total power system CO\({}_{2}\) emissions). The reason for having high emission quantities is that IC1 is not importing power, and CCGT plants without CCS supply the required power at a total marginal cost lower than the IC1 price. Further increase of the CO\({}_{2}\) tax to \(\pounds\)70/ton results in a total emission of 7.82 million tons. On such occasions, the required power is supplied by means of the IC1 with a cost below the marginal generation cost of unabated CCGTs. The CO\({}_{2}\) emissions of GB's system at CO\({}_{2}\) tax of 80 and \(\pounds\)90/ton are respectively 7.56 and 7.73 million tons. At IC1 import prices higher than \(\pounds\)60/MWh, the CCGTs with high marginal costs provide the required electricity to GB. At any carbon tax and IC1 price of 80 or \(\pounds\)100/MWh, the unabated CCGTs emit ca. 94.4% of the total CO\({}_{2}\) emissions. Figure 4: Percentage of times that the IC2 power link is fully loaded during 2030. Figure 5: Minimum and maximum shedding and maximum IC1 load when the IC2 is receiving a full load.