In this work, the models are implemented using the software P-graph Studio [25] developed by the team at the University of Pannonia in Hungary. The P-graph framework uses a bipartite graph representation to deal with PNS [16] and PNS-like problems [17]. The P-graph framework is based on five axioms that provide a rigorous mathematical foundation for its component algorithms [15].

In the traditional PNS context, materials are represented by M-type nodes and operations by O-type nodes in the P-graph framework. M-type nodes include raw materials (external inputs), products (exports), and intermediates (internal flows). Different types of nodes are shown in Figure 2.

Figure 2.

M-type and O-type representation

The framework has three component algorithms. First, Maximal Structure Generation (MSG), which generates the non-redundant union of all combinatorially feasible process structures of a PNS problem. The maximal structure is, in effect, a rigorously generated superstructure [26]. The Solution Structure Generation (SSG) algorithm generates all structurally feasible networks for the PNS problem [15]. Each solution structure is a candidate structure embedded in the maximal structure and can be the basis to identify a locally optimal network. Finally, the Accelerated Branch-and-Bound (ABB) algorithm generates the optimal solution structure from the set of structures generated by SSG, coupled with additional cost and flow information [27]. The ABB capitalises on information inherent in all PNS problems and is thus more computationally economical than conventional branch-and-bound techniques for generic mixed-integer programming problems. ABB identifies the optimal solution as well as local optima within the enumerated structures [15]. Such near-optimal solutions are often of great practical engineering value [17].

Any problem that can be mapped into an equivalent PNS problem can be solved with P-graph. For example, Tan et al. [14] showed that the source-sink matching problem often encountered in Process Integration can be expressed in PNS form, including the examples in [28] and [29]. Since it has previously been established that the electricity trading problem can be framed as a source-sink matching problem [5], it logically follows that it can also be solved with P-graph. This work also capitalizes on the PNS-like structure of regional electricity trading [28],[29] as well as the flow of embodied GHG emissions. Figure 3 shows the CMN structure adopted from Tan et al. [14] for regional electricity trading in this work, where sources represent current capacity, and sinks represent future demand. This model is flexible enough and can be applied to any regions that share the same source-sink principle.

Figure 3.

P-graph structure for the allocation of one source to one sink in a CMN

For the model in Figure 3, a CMN with one source (current capacity) and one sink (future demand) is shown. The energy source (represented by ‘raw material’ note) is linked to future demand and excess energy (both are ‘product’ note). Note that the future demand sink is also linked to an external carbon-neutral source (‘raw material’ note), which is used to determine the minimum future demand of renewable energy. Note that two ‘product’ notes are used to present fictitious load sinks that are not present in the actual process flow but refer to emission limits of future demand. The ratio of the ark is the CO₂ intensity of the source, which is used for calculating the CO₂ load between the sources and sinks. The allocation units (‘operating units’) between the sources and sinks are used for determining the amount of energy sources to be sent to the sinks.

To determine the optimal allocation in the P-graph model, an arbitrary fictitious cost is set for carbon-neutral sources, while the cost for the current capacity is set to zero. This cost assignment allows P-graph to minimise the overall costs associated with electricity trading, identifying the most cost-effective solution.

The mathematical formulation involved in the P-graph model is presented in Appendix A-1. The objective function is to minimise the total amount of new renewable energy capacity to be shared by all countries in the system for electricity generation, at the same time allowing future increased demand for electricity with reduced CO₂ intensity to be met [30].

The following sections start with a literature example and continue with two additional case studies. Case Study 1 considers regional transmission between Malaysia to Indonesia, while Case Study 2 focuses on integrating different types of renewables into existing electricity trading systems in Canada.

Table 1 shows the data for a literature example taken from Tan et al. [30]. As shown, three countries have their current capacity (source) and future demand for energy, along with their current and future CO₂ intensity values. It is desired to identify the amount of additional amount of carbon-neutral electricity.

Table 2 shows the solution generated by P-graph, with its superstructure shown in Figure 4. The carbon-neutral electricity generation was identified as 43.57 TWh/y (its total allocation to Countries 1 and 2), with 23.57 TWh/y of excess energy. Both values match the targets identified by CEPA in Tan et al. [30]. Note that P-graph has the ability to generate multiple near-sub-optimal solutions. For instance, Table 3 and Table 4 both display the same amount of carbon-neutral energy (45.71 TWh/y) and excess energy (25.71 TWh/y) as those in Table 2, but with different allocation patterns among the traded countries.

Figure 4.

Maximal Structure for Literature Example

Within the ASEAN community, several countries have engaged in power trading. One of the upcoming trading networks is the Brunei-Indonesia-Malaysia-Philippines East ASEAN Growth Area (BIMP-EAGA), suggested by the International Energy Agency (IEA) [7]. This case involves four countries, with data provided in Table 5. Currently, all countries are self-sufficient in electricity, with current capacity matching demand. Future emissions limits are based on commitments to the 2015 Paris Agreement, targeting 2030. While all countries are expected to increase electricity demand, their CO₂ intensity is set to decrease, except for Brunei, due to low-tariff electricity and overconsumption [31]. Emission reduction targets include Brunei's 30% reduction by 2030, Indonesia's 29% reduction from business-as-usual (BAU) emissions, Malaysia's 45% reduction in GHG intensity relative to GDP, and the Philippines' 70% reduction relative to a BAU scenario [32]. The countries aim to meet future demand by integrating renewable energy, assumed to have zero carbon intensity in this study.

Currently, there is only one regional transmission line within the area of study, which is from Sarawak (Malaysia) to Kalimantan (Indonesia). A few more interconnectors are proposed within Malaysia (connecting from Sarawak to Sabah), within Malaysia and nearby countries, i.e., Brunei and Sabah to Mindanao (Philippines), as shown in Figure 4 [7].

In the base case, renewables are assumed to be unlimited. The P-graph model results, shown in Table 6 and Appendix A-2, indicate that 289.33 TWh/y of renewable energy should be introduced, with an excess of 140.34 TWh/y from Indonesia, which can be converted into storage for emergency use in the future. This aligns with results obtained using CEPA [11]. Given Indonesia's high future demand, all countries must trade electricity with it to meet both CO₂ emission limits and future demand. Most renewables are allocated to Indonesia, Malaysia, and the Philippines, while none are sent to Brunei due to its decreasing demand; instead, Indonesia supplies 2.8 TWh/y to Brunei. The model does not consider specific renewable sources or transmission capacity limits, only current and future capacity constraints.

From the base case, 289.33 TWh/y of renewables are required for the system, making it important to identify their individual sources. The capacity of renewables from each country is analysed to ensure they can meet future demand. Table 7 summarises the source of the renewables from each country, taken from the International Renewable Energy Agency (IRENA). Future renewable capacities are estimated by extrapolating current trends in renewable energy supply for each country. However, this estimation may not represent the maximum potential capacity, as factors like long-term contracts, grid access, and new installations could increase future capacity [33]. Based on the data reported in IRENA, each country studied has at least one type of renewable energy, which ranges from solar energy, hydropower, biofuels, wind and geothermal [34].

The P-graph model was modified to reflect multiple projected renewable energy sources instead of one unlimited source, as in Figure 3. When renewable energy is supplied within its own country, transmission costs are lower due to the absence of wheeling charges—fees applied by transmission owners for transporting electricity over the grid.

In Scenario 1, as direct transmission lines are still not available among all countries, wheeling is required in order to allow power trading to occur. The wheeling charges are assumed to be 1 USD/TWh since there is no specific import or export price set under power purchase agreements (PPAs). In this scenario, wheeling charges are charged to electricity importers only. An assumption of no limits on transmission capacity for country-to-country transmission was made in this scenario.

The results of the model are shown in Table 8 and Table 9 (the P-graph maximal structure is shown in Appendix A-4). As shown, the main trading occurs between Malaysia, Indonesia, and the Philippines. This is due to the lesser demand of Brunei, making it less involved in direct trading. Its role is more on wheeling electricity to and from the Philippines, Malaysia, and Indonesia.

In comparison of the results of Base Case and Scenario 1, the majority of the distributions are similar, with only a few differences spotted, evidently in the trading among Indonesia, Malaysia, Philippines, and the number of renewables allocated to each country. One of the main differences is that Malaysia's electricity from current capacity to future demand decreased as it relied more on its own renewables (see Table 7), increasing from 112.63 TWh/y to 127.80 TWh/y (see Table 6 and Table 8). This shift reduced Malaysia's dependence on "dirty" energy from 99.27 TWh/y to 84.11 TWh/y.

As for Indonesia, the imported renewable energy reduced from 101.24 TWh/y (Table 6) to 86.07 TWh/y (Table 8). However, with the knowledge of renewable energy sources and the assumption that energy transmitted to their own country will have a lesser cost compared to country-to-country transmission, the renewables from Indonesia will be supplied to them first. With the decrease in renewable energy distributed to them, more electricity is required to be exported to them in order to fulfil their future demand. This is reflected in the increment of electricity imported from Malaysia, which is from 21.85 TWh/y to 115.61 TWh/y to meet future demand due to Malaysia's less carbon-intensive energy mix.

Another observation found was that both the renewables for Indonesia and the Philippines are depleted to fulfil their own future demands, as there will be no wheeling charges if it is self-supplied. Also, renewables for Brunei are untouched, as the total amount of renewable generation is relatively negligible compared to its future demand. Thus, on an economic scale, it is not worth it if Brunei’s renewables were to be included in the trading matrix. This may not be the most optimal distribution as this may deplete the renewable potentials of said countries, which will make their commitments to the regional electricity trading system more difficult to fulfil in the long run, as it will limit their own development. To make this work, a strong and robust management of the system has to be in place so as not to put any particular country at a disadvantage.

In the development of renewable energy generation, a common barrier found was transmission system constraints. Unlike conventional power sources, renewables like solar, hydro, and wind must be generated at specific locations. These sites are often far from population centres with high electricity demand, which necessitates greater investment in transmission infrastructure [35].

Hence, Scenario 2 presents an improvised version of Scenario 1, which costs for country-to-country transmission will also include source-to-grid costs, borne by the importer. Similar to Scenario 1, it is assumed that source-to-grid costs are assumed to be constant for all sources, with an arbitrary value of 1 USD/TWh for fixed operational cost in this scenario. The results generated by P-graph are shown in Table 10 and Table 11, and the P-graph results are shown in the appendix. The total amount of both renewables' excess energy remains identical to the previous scenario, i.e. 140.34 TWh/y and 289.33 TWh/y, respectively.

Comparing Scenarios 1 and 2, one of the main differences observed is in terms of the export of Brunei. In the earlier scenario, Brunei have been exporting its electricity to Indonesia, whereas in Scenario 2, Brunei exports to the Philippines instead. Another difference seen is how the Philippines does not supply electricity to itself in the earlier scenarios, but they now self-supply 26.63 TWh/y of electricity in Scenario 2. In this scenario, the interconnector of 3.8 TWh/y exported to Philippines from Brunei is beneficial to the entire system as electricity trading between Malaysia and Philippines can be wheeled through Brunei, wherein in the scenario of the Base Case and Scenario 1, an additional interconnector must be built between Brunei and Philippines with no net transmission between them for trading between Philippines, Indonesia, and Malaysia.

Lastly, from Table 11, it is observed that only one source of renewable energy is being introduced, i.e. hydropower from Malaysia, due to the introduction of transmission cost and wheeling charges in this scenario. As the total amount of renewables, as calculated previously, is 289.33 TWh/y and the total amount of hydropower from Malaysia is 469.63 TWh/y, this source can supplement the network’s needs. Aside from that, instead of depleting the renewable sources from Indonesia and the Philippines as suggested in Scenario 1, there will be a surplus in renewable energy supply for all sources with this selection of distribution. Also, by having two sources of renewables, an investment of a higher capital cost for electricity transmission infrastructure is required. Hence, to be able to cut cost at the same time fulfil the network’s requirement, hydropower from Malaysia is the main and only renewable source chosen in this scenario.

Alberta, along with other Canadian provinces, engages in inter-provincial electricity trade. While Alberta and Ontario have deregulated wholesale electricity markets, Alberta stands out with the highest refining capacity [36]. Alberta imports and exports electricity primarily with British Columbia, Saskatchewan, and Montana [37]. According to Alberta Electric System Operator's (AESO) [38], the province's electricity capacity in 2030 is projected to shift towards renewables and away from coal (Table 12). Natural gas will remain the dominant non-renewable source, supplemented by hydropower, wind, and solar. All cogeneration, combined cycle, simple cycle, and coal-to-gas facilities will use natural gas. The projected electricity capacity for Alberta in 2030 is detailed in Table 12.

Table 13 presents the maximum electricity generation data by source for Alberta in 2030, calculated assuming 8,760 h/y of operation. Capacity factors from 2015 to 2019 [37], [39], [40], [41], [42] were estimated by comparing the actual electricity generation to the maximum electricity generated at full capacity, based on data from the Alberta Utilities Commission (AUC). The mean capacity factor for each resource was calculated from these five years. An exception is made for solar, which was minimally utilised until 2018; thus, only 2018 [37] and 2019 [40] data are considered for it. The actual maximum electricity is obtained by multiplying the maximum electricity generated at full capacity by the capacity factor.

Alberta’s electricity demand in 2030 is assumed to be the peak demand in AESO’s reference case in its published Long-term Outlook in 2019 [38]. Alberta aims for a maximum of 209 Mt-CO₂-e in total GHG emissions by 2030 under the Paris scenario [43], with electricity generation expected to account for 16% of this total [44]. The main targets of the P-graph model are shown in Table 14.

The demand of Alberta's trading partners in 2030 was estimated based on expected changes in their electricity generation capacity. By 2030, electricity generation is expected to increase by 50% in British Columbia [45] and by 55.6% in Saskatchewan compared to 2018 [46]. For Montana, a 10% increase from 2019 power demand based on the increment of the demand in North America in the same period is assumed [47]. Alberta’s exports to these regions in 2018 and 2019 are scaled accordingly to estimate their 2030 demand.

Emission limits regions are estimated based on Alberta’s targeted emission intensity of 286.61 t/GWh by 2030 (= 33.44 x 1,000,000 / 116,674.44 t/GWh; see Table 14). For Alberta's import potential, the maximum annual electricity imports from each trading partner from 2011 to 2019 were identified using data from AUC.

Table 15 shows the electricity trading data of Alberta by 2030. Table 16 lists the carbon intensity values for each fuel source, based on their lifecycle GHG emissions from the World Nuclear Association [48]. The average carbon intensities of Alberta's trading partners are assumed to remain constant, as shown in Table 17.

In Scenario 1, the addition of more hydropower or wind capacity to the power mix of Alberta is studied. The GHG intensity of the additional renewable resource is set at 26 t CO₂-e/GWh which is the same as that of hydropower or wind. Optimal solutions and near-optimal solutions were obtained. Figure 5 presents the maximal structure for the case study. Table 18 shows the electricity generation of Alberta by source with respect to three different feasible solutions. Table 18, Table 19, Table 20 and Table 21 show the exports of Alberta by resource for feasible solutions 1, 2 and 3 respectively. Optimal solution results show that the minimum additional hydropower or wind required in the system is equal to 36,023.20 GWh/y.

Figure 5.

Canadian Provinces Case Study - Maximal Structure

Scenario 2 focuses on the increased solar capacity in Alberta. The intensity of the additional resource is adjusted to 85 t CO₂-e/GWh, which is equivalent to that of solar. Table 22 shows the electricity generation of Alberta by source with respect to three different feasible solutions. Table 23, Table 24 and Table 25 show the exports of Alberta by resource for feasible solutions 1, 2 and 3 respectively. The minimum required amount of additional renewable electricity of solar is 41,157 GWh/y.

Lastly, Scenario 3 evaluates the need for nuclear power to meet the model's targets if Alberta decides to incorporate nuclear technology into its power generation. This is considered in the P-graph model by adjusting the GHG intensity of the additional resource to be 29 t- CO₂-e/GWh, equivalent to that of nuclear power generation. Table 26 shows the electricity generation of Alberta by source with respect to three different feasible solutions. Table 27, Table 28 and Table 29 show the exports of Alberta by resource for feasible solutions 1, 2 and 3 respectively. To meet the model's targets, a minimum of 36,253.17 GWh/y of electricity from nuclear resources is required.

The case study data in Table 13 shows that Alberta’s total maximum electricity generation capacity in 2030 is projected to be 88,346.87 GWh/y (sum of all entries in the last row), falling short of the required 116,674.44 GWh/y (see Table 14). Therefore, additional capacity or increased imports are essential, regardless of GHG emission limits. The solutions obtained for the scenarios had some commonality. It is noticed that natural gas is the only resource not utilised fully, due to its high GHG intensity, and being the only non-renewable resource. Imports from Saskatchewan are avoided due to its high GHG intensity of 660 t CO₂-e/GWh, while British Columbia and Montana are prioritised for their lower intensities. To meet the 2030 demand and emission targets, Alberta would need an additional 36,023.20 GWh/year from hydropower or wind, or 41,157 GWh/year from solar. This equates to adding about 13,009 MW of wind, 17,559 MW of hydropower, or 28,913 MW of solar capacity.

Given Alberta’s forecasted capacity of 4,979 MW from these renewables by 2030, such additions seem impractical due to their low-capacity factors and intermittent nature [51]. Hydropower depends on water availability, wind power on wind speeds, and solar power on daylight, with Alberta’s lower sunlight levels further reducing solar capacity factors [43].

Nuclear energy presents a more feasible option. Alberta would need a minimum of 36,253.17 GWh/y to reach the targets of the model. With a global mean capacity factor of 82.5% [48], Alberta would require approximately 5,016 MW of nuclear capacity. Alberta has significant nuclear potential, notably with the Athabasca basin’s uranium reserves [52]. However, traditional large nuclear units face challenges due to the need for substantial reserve capacity and transmission upgrades [53].

In April 2021, Alberta signed the Memorandum of Understanding (MOU) joining three other provinces in an agreement to support the development of small modular reactors (SMRs) as a source of clean energy [54]. SMRs are nuclear reactors that produce a maximum of 300 MW of electricity, and according to the MOU, have the potential to improve the safety, economic and environmental advantages of nuclear energy [55]. SMRs could be key in helping Alberta achieve its electricity demand and emission targets should the province decide to pursue the technology in the future.