1. Introduction
According to the “European Energy Roadmap 2050” [
1], the European Commission requires the decarbonization of the European Union (EU) energy system with the objective of reducing by 2050 carbon dioxide emissions by 80–95% compared to 1990 levels. This strategic roadmap aims to ensure reliable and economically competitive electricity produced from renewable energy sources (RES) such as wind, solar, and hydro power, accounting for at least 55% of total energy consumption, as well as from low-emission sources, such as nuclear power plants and thermal generating units equipped with carbon capture and storage technologies. The overriding challenge arising from the expected high penetration of renewables in the energy mix is dealing with the variability of generation due to the stochastic nature of wind speed and solar irradiation.
In parallel to decarbonization actions, the European Commission [
2] obliges Member States to ensure a high level of security in electricity supply. This is defined as the ability of an energy system to reliably supply consumers with electricity. In light of the lack of cost-effective energy storage systems and abundant transmission capacity, much of the electricity produced must be used instantly. Hence, there is a need to efficiently balance electricity production with consumption. This is a non-trivial exercise taking into account the richness of the statistical laws governing electrical load (seasonality, short memory, persistence, etc.), which manifest themselves in different time scales.
Before the broad uptake of variable generation technologies, load matching was a standard procedure for transmission system operators (TSO), as the generation of conventional (thermal and hydro) plants could be scheduled accordingly to meet demand fluctuations. In power systems with high penetration of variable resources, load matching is severely hindered by the fact that generation largely depends on unstable and unpredictable weather conditions. This increases the risk of experiencing load mismatches and the need for using costly conventional generation capacity to close production gaps. Developing strategies for managing the RES generation risk becomes of paramount importance to the future viability of clean energy systems.
One strategy to control production intermittencies is to distribute generating capacity across distant sites or different generation technologies. This is called
spatial or
technological risk diversification, respectively. A stream of research studies offers empirical evidence that by interconnecting variable wind or solar generation units located in remote sites it is possible to smooth out the volatility of energy production in each area [
3,
4]. This is explained by the fact that in a well-diversified portfolio the inability to meet load due to the low productivity of one region (or technology) can be overcome by energy produced in another area or by a different-type generator possibly installed in the same region. In order to make optimal use of the spatial variety of clean energy resources, it is essential to consider interconnecting sites over long distances, even across country borders.
The ability to transfer energy across space is a critical factor for the creation of diversified RES portfolios. Traditionally, transmission system operators optimize the electricity supply at the national level using mostly domestic energy sources. However, for the implementation of future decarbonization plans, a crucial role is to be assigned to the European Network of Transmission System Operators for Electricity (ENTSO-E), which is expected to upgrade the interconnection of European countries in order to achieve the EU’s energy and economic policy goals [
5].
With a view to achieving efficient balancing of the energy supply and demand while taking network constraints into consideration, in this paper we present a multi-objective optimization model for efficient deployment of RES generating units. We design portfolios of wind and solar power plants that service the load optimally, in the sense of jointly minimizing renewable energy unavailability and spillover in each country. In parallel to this objective, we investigate the sufficiency of the European transmission system capacity to meet the needs of the overall generation mix. For an empirical assessment of the efficiency of our methodology, we use a rich dataset of daily load measurements, wind/solar capacity factors, and transmission capacity data for 32 European countries [Austria (AT), Belgium (BE), Bulgaria (BG), Bosnia and Herzegovina (BA), Switzerland (CH), the Czech Republic (CZ), Germany (DE), Denmark (DK), Estonia (EE), Greece (EL), Spain (ES), Finland (FI), France (FR), Croatia (HR), Hungary (HU), Ireland (IE), Italy (IT), Lithuania (LT), Luxembourg (LU), Latvia (LV), Montenegro (ME), North Macedonia (MK), the Netherlands (NL), Norway (NO), Poland (PL), Portugal (PT), Romania (RO), Serbia (RS), Sweden (SE), Slovenia (SI), Slovakia (SK), and the United Kingdom (UK)] during the period 2010–2015. These countries were selected based on data availability and their level of connectivity with neighboring countries.
The rest of this paper is organized as follows.
Section 2 provides a literature review of studies related to the risk management of renewable energy resources, and
Section 3 discusses the contributions of this paper beyond the state-of-the-art.
Section 4 develops the multi-criteria linear optimization framework proposed for the allocation of RES portfolio capacity shares, and
Section 5 presents empirical results. Finally,
Section 6 concludes the paper and indicates directions for further research.
2. Literature Review
The problem of managing the risk of electricity generation from variable energy sources is receiving increasing attention from researchers in various scientific areas. A significant body of literature recommends the geographical dispersion of RES power plants as a means of diversifying away the production uncertainty of a particular site (termed volumetric risk). Other studies have considered geographical diversification through the distribution of capacity among different generation technologies (e.g., wind and solar) in order to mitigate resource-specific variability.
Thomaidis et al. [
4] applied Markowitz’s [
6] portfolio theory to select optimal RES aggregation plans in the southern Iberian Peninsula (Spain). Based on simulated wind and solar generation data, they computed the efficient frontier of optimal harvesting plans that maximize energy supply for a certain level of generation risk, as measured by the daily variability of renewable energy production. Their empirical results indicate the potential of pooling resources to stabilize the aggregate energy supply while reducing the intensity of the harvesting plan. Out of 4474 total candidate sites, efficient portfolios only committed 34 grid nodes for solar and 42 nodes for wind power plant development. The key element in diversifying volumetric risk is the complementarity of wind and solar energy fields, which is the topic of the present study. Using meteorological simulations for the period 1980–2015, Santos-Alamillos et al. [
7] applied mean variance analysis to explore different scenarios for the re-allocation of wind and solar capacity in Europe. Their empirical study identified three main geographical areas of key importance for achieving the portfolio objectives. These regions are the Iberian Peninsula (due to its strong wind and solar potential), the United Kingdom and Scandinavia (due to their rich wind resources), and the Northern Mediterranean region (characterized by good wind and solar potential). They concluded that a “better” re-distribution of RES capacity could lead to an increase of approximate of
in the energy yield or a reduction of
in production variability, as compared to the 2014 allocation of renewable generating units.
Based on measurement data from ten weather stations on the Corsican coast, Cassola et al. [
8] concluded that the division of the island into three zones and the interconnection of carefully selected generation sites could lead to a reduction in the variability of the wind energy supply along with an improvement in the overall energy yield. The benefits of geographical diversification of volumetric risk were found to be substantial, despite the relatively small area of the island. In the study of Roques et al. [
9], wind capacity data for five European countries (Austria, Denmark, France, Germany and Spain) were examined in a mean variance analysis framework. Their study took into account constraints on the transmission of energy across borders. The empirical results show that insufficient grid connectivity of European countries significantly reduces the efficiency of wind energy harvesting plans. Based on this finding, the authors stress the importance of improving the cross-border interconnections to ensure the future decarbonization of European power systems.
As mentioned earlier, the reliability of power systems depends on real-time balancing of energy production and demand. As both renewable energy generation and load are volatile, researchers have attempted to investigate the feasibility and cost-effectiveness of developing power systems composed exclusively of renewable energy sources. Based on wind and solar meteorological data, Rodriguez et al. [
10] generated technically and economically optimal scenarios for a simplified pan-European power system composed of RES and backup conventional capacity. An optimization model was developed to identify renewable generation mixes that minimize the amount of reserve power and of installed and transmission capacity. Their cost analysis prescribed 50% of the total energy supply to be covered by RES, with the share of wind power being as high as 97%. Under the considered levels of electricity demand, their optimal plan assumed approximately 600 GW of installed wind capacity, 60 GW of solar power, 320 GW of conventional capacity, and a five-fold increase in existing transmission capacity. Jacobson et al. [
11] explored the feasibility of creating generation mixes based exclusively on wind, solar, and hydro energy with the ability to match demand despite their intermittent output. Empirical evidence suggests that there is an abundance of different generation mixes that could attain energy equilibrium in 139 countries by 2050 in a cost-effective way. Energy storage in the form of heat or hydrogen and demand-side management strategies to control peak load levels are particularly important in achieving this objective. Heide et al. [
12] investigated the seasonal behavior of wind and solar energy production in Europe with the goal of turning the mirror seasonality of these energy sources into an optimal generation mix with the ability to meet load efficiently, which is one of the objectives of the present study as well. Their analysis indicated that in the ideal scenario of a 100% clean power system, 55% of the total energy supply should be provided by wind farms and the rest by solar power generating units, while for lower levels of RES penetration the share of wind power should be increased.
3. Contribution to the State-of-the-Art
In this paper, we attempt to enhance the portfolio selection strategy by seeking to minimize on a daily basis the mismatch between (wind and solar) energy production and the demand for electricity. The optimization process explicitly takes into account various scenarios about the cross-border transmission capacity. By introducing
load tracking as a portfolio selection target, we derive capacity allocation plans with optimal control over generation variability, especially large deviations from the target demand. Using a bi-objective mathematical programming framework, we derive the Pareto set of optimal RES generation mixes for various interconnection scenarios and levels of decision-maker aversion to energy deficits or surpluses. The relative efficiency of these sets is quantified by means of the
hypervolume indicator. As a final step, we carry out a sensitivity analysis to determine the contribution of each country to the achievement of the production goals. Our empirical study is based on a panel of 32 countries and 2191 operational days. Even an experimental setup of such a moderate size results in to very large multi-objective optimization problems, including roughly 2.5 million decision variables and 1.5 million constraints. To address the computational challenges associated with the scale of the problem, we resort to advanced linear programming solvers such as MOSEK ([
13]).
Our paper extends the existing literature in many directions. First of all, optimal portfolios are not exclusively selected based on the aggregate productivity profile (as in recent literature [
4,
7,
8,
9,
12]) but also with reference to the load patterns observed in each country. Gearing renewable energy generation towards load often has a dramatic effect on the composition of the RES mix. Further inclusion of cross-border transmission capacity in the optimization model places additional constraints on the energy harvesting plan, pushing it towards more intense capacity allocations. For instance, empirical results show that the optimal solution in cases of limited network connectivity and poor domestic RES energy supply entails up-scaling of the installed wind and solar capacity to meet demand.
The experimental setup adopted in this paper does not explicitly take into account energy production costs, as is traditional in similar works (see, e.g., [
10]). Instead, we restrict our attention to the potential of clean energy resources to maintain the stability of the European power system. In other words, our cost function measures deviations from the load level of each country. We thereby avoid cases in which the optimization process indicates efficient capacity allocation plans with an increased share of conventional (mostly thermal) power plants due simply to their lower investment and maintenance costs. This design choice allows us to fully investigate the extent to which wind and solar resources could gradually replace fossil fuels under existing and future European grid configurations. Even in the current setup, production, and investment costs are indirectly taken into account by the two objectives of the optimization program, as detailed in
Section 4. In particular, the first objective function (1a) tries to minimize the need for conventional (mostly) thermal capacity to cover energy deficits created in each operational hour by inadequate renewable energy supply. The second optimization criterion (1b) attempts to restrict excessive renewable installed capacity by controlling the amount of wind and solar generation that exceeds the load and consequently has to be curtailed from the grid.
6. Conclusions and Future Research
The purpose of this paper was to explore the extent to which clean energy resources (wind and solar) can serve the need for electricity on a continental scale and become a viable alternative to fossil fuels. Using a panel of 32 European countries, we derived optimal allocation plans for RES capacity that take into account the statistical features of domestic load as well as the possibility of transmitting electricity across borders. The bi-objective optimization model developed in this paper highlights the importance of creating spatially and technologically diversified portfolios to address increasing load under the current configuration of the European power grid. Specifically, the results of our empirical study suggest that investments in RES capacity must unavoidably be proportional to the level of domestic electricity demand due to limitations in transmission capacity, regardless of the richness of resources in each country. However, it is clear that expanding transmission capacity and mixing wind and solar resources could help system operators to improve the overall efficiency of the generation plan. This strategy has tangible benefits in terms of obviating unnecessarily large installation of RES generating units, reducing the spillover of clean energy, and minimizing the need for conventional (mostly thermal) capacity. Above all, our study stresses the fact that it is essential in order to meet the European Commission’s objectives regarding the reduction of pollutant emissions [
1] to both upscale wind and solar generating capacity in each country and to invest strategically in a pan-European cooperative for the sharing of clean energy resources.
This study can be extended in many possible directions. One challenge is to consider other forms of renewable energy, such as hydro or biomass, as part of the generation mix. Although in principle these generation technologies are dispatchable and could be used for peak shaving, they are not a viable alternative for each country. Furthermore, the incorporation of hydropower stations in the optimization framework is not a trivial task, as in each time iteration it is necessary to take into account the available water resources based on the limited reservoir capacity of each stations. It might be interesting to consider energy storage methods (batteries, pumped storage power plants) that could shift possible surpluses created by extensive RES production in time and space during periods of low domestic demand and network congestion. Nonetheless, the adoption of these technologies on a grid scale is challenging from a both technical and an economic point of view.
The results of this and similar studies on renewable energy harvesting are unavoidably sensitive to the models and techniques used to quantify wind and solar resources in each country. An assumption made in this paper is that past capacity factor realizations are reflective of the future profile of wind and solar energy generation. In this regard, the outcomes of climatology research could be quite insightful in terms of providing typical patterns of the wind or solar resources in each country as well as in identifying possible “structural breaks” that might be infused in the underlying probability laws due to global climate change.