How Sensitive are Optimal Fully Renewable Power Systems to Technology Cost Uncertainty?

AuthorShirizadeh, Behrang

    According to Article 4.1 of the Paris Agreement, the Parties shall endeavor to rapidly reduce greenhouse gas emissions in order to achieve a balance between anthropogenic emissions by sources and removals by sinks in the second half of this century. The electricity sector will have a key role to play, as decarbonisation is easier in this sector than in transport, buildings or agriculture. Renewable energy will be the cornerstone of decarbonisation, making a greater contribution than nuclear energy and fossil fuels with CO2 capture and storage (Rogelj et al., 2018).

    While the feasibility of a 100% renewable electricity system has already been highlighted by many studies (Brown et al, 2018, and references therein), the cost of such a system is heavily debated. Following Joskow (2011), Hirth (2015) and Hirth et al. (2016), many articles have focused on the optimal proportion of renewable energies in the electricity mix. This literature has highlighted the existence of systemic integration costs related to the deployment of variable renewable energies. In particular, a "self-cannibalization" phenomenon was highlighted, linked to the fact that all the solar panels or wind turbines in a given location produce their electricity at the same time. In the absence of affordable storage, these integration costs have two consequences: (i) deployment of renewable energies leads to a significant additional cost, rapidly increasing with the deployment rate; (ii) the right balance must be struck between the different production technologies to minimize this additional cost.

    However, these results of increasing costs and right balance might not hold much longer, due to the rapid decline in storage costs and the fact that recent wind turbines benefit from a flatter production profile than older models (Hirth and Muller, 2016).

    If this phenomenon of increasing costs does not hold any more, it means that the relationship between renewable energy sources is changing from being complements to being substitutes. It would be then possible to identify one or several "robust" energy mixes, in the sense that their overall cost does not vary much, even if the cost of the different technologies finally differs from the initial forecast.

    To shed light on these questions, we build a new open-source model called EOLES (Energy Optimization for Low Emission Systems) and apply it to continental France. EOLES minimizes the total system cost while satisfying energy demand at each hour for a period of up to 18 years. It includes six power generation technologies (offshore and onshore wind, solar, two types of hydro and biogas) and three storage technologies (batteries, pumped hydro and power-to-gas).

    Using this model, we study the sensitivity of the power mix in 2050, through 315 cost scenarios for 2050, varying all key technology costs: onshore and offshore wind by +/-25%; PV, batteries and power-to-gas by +/-50%. Most existing studies are based on a single weather-year or on a few ones, and when a sensitivity analysis on technology costs is performed, it generally varies these costs one-at-a-time. We add to this literature by studying a consecutive 18-years weather period and carefully choosing a representative year for the sensitivity analysis; by testing all combinations of technology costs rather than changing them one-at-a-time; and by calculating the regret from optimizing the energy mix on the basis of cost assumptions that do not materialize.

    The remainder of this paper is organized as follows. In Section 2 we present the EOLES_ elecRES model, the 100% renewable electricity sector version of EOLES family of models. Results are presented in Section 3 while Section 4 provides a discussion and concludes.


    2.1 Model description

    EOLES_elecRES is a dispatch and investment model that minimizes the annualized power generation and storage costs, including the cost of connection to the grid. It includes six power generation technologies: offshore and onshore wind power, solar photovoltaics (PV), run-of-river and lake-generated hydro-electricity, and biogas combined with open-cycle gas turbines. It also includes three energy storage technologies: pump-hydro storage (PHS), batteries and methanation combined with open-cycle gas turbines. These technologies are shown in Figure 1.

    The model considers continental France as a single node. PV and onshore wind are simulated for the 95 counties (departements, an administrative entity corresponding to the European NUTS 3 level). The proportion of the installed capacity in each county remains the same in all simulations, at the level observed in 2017. We consider that this is the best simple method to represent the possible future repartition of these capacities, because it takes into account the local resource (e.g. more PV in the South, more wind in the North), land availability and social acceptability (e.g. little possibility to install wind farms in densely populated areas, in the mountains or in very touristic locations). As detailed in subsection 2.3 below, this scale-up method applies neither to hydro, which is capped by assumption due to the very limited availability of new production sites, nor to offshore wind, for which the repartition of capacities follows the existing offshore projects around France, identified through the "4C offshore" website.

    The model is written in GAMS and solved using the CPLEX solver. The code and data are available on GitHub.1 EOLES uses only linear optimization. Non-linear constraints might improve accuracy, in particular when studying unit commitment, but they entail significant increase in computation time. Palmintier (2014) has shown that linear programming provides an interesting trade-off, with little impacts on cost, CO2 emissions and investment estimations, but a speed-up by up to x1500.

    Figure 2 provides an illustrative output of the model, i.e. the optimal dispatch for a week in winter and for a week in summer, for each hour of the week.

    The remainder of this section presents the main equations (2.2) and the input data (2.3). A detailed description of all sets, parameters and variables of the model is available in Appendix 4.

    2.2 Model equations

    Objective Function

    In EOLES, dispatch and investment are determined simultaneously by linear optimization, minimizing the discounted sum of CAPEX (capital expenditure) and OPEX (operational expenditure).

    The objective function, shown in Equation (1), is the sum of all costs over the chosen period, including fixed investment costs, fixed O&M costs (which are both annualized) and variable costs. For some storage options, in addition to the CAPEX related to charging capacity per k[W.sub.e], another type of CAPEX is introduced: a capex related to energy capacity, per kW[h.sub.e]

    [Please download the PDF to view the mathematical expression] (1)

    where [Q.sub.tec] represents the installed capacities of production, VOLUM[E.sub.str] is the volume of energy storage in MWh, [S.sub.str] is the capacity of storage in MW, [annuity.sub.tec] is the annualized investment cost, fO & M and vO & M respectively represents fixed and variable operation and maintenance costs and [G.sub.tec,h] is the hourly generation of technology tec.

    To calculate the annualized capex ([annuity.sub.tec] in the objective function), we use the following equation:

    [Please download the PDF to view the formula] (2)

    where DR is the discount rate.

    Adequacy equation

    Electricity demand must be met for each hour. If power production exceeds electricity demand, the excess electricity can be either sent to storage units or curtailed (equation 3).

    [Please download the PDF to view the formula] (3)

    where [G.sub.tec,h] is the power produced by technology tec at hour h and STORAG[E.sub.str,h] is the energy entering the storage technology str at hour h.

    Renewable power production

    For each variable renewable energy (VRE) technology, the hourly power production is given by the hourly capacity factor profile multiplied by the installed capacity available for each hour (equation 4).

    [Please download the PDF to view the formula] (4)

    where [G.sub.vre,h] is the electricity produced by each VRE resource at hour h, [Q.sub.vre] is the installed capacity and c[f.sub.vre,h] is the hourly capacity factor.

    Energy storage

    Energy stored by storage option str at hour h+1 is equal to the energy stored at hour h plus the difference between the energy entering and leaving the storage option at hour h, accounting for charging and discharging efficiencies (equation 5):

    [Please download the PDF to view the formula] (5)

    where STORE[D.sub.str,h] is the energy in storage option str at hour h, while [Please download the PDF to view the formula] and [Please download the PDF to view the formula] are the charging and discharging efficiencies.

    Secondary reserve requirement

    Three types of operating reserves are defined by ENTSO-E (2013), according to their activation speed. The fastest reserves are Frequency Containment Reserves (FCRs), which must be able to be on-line within 30 seconds. The second group is made up of Frequency Restoration Reserves (FRRs), in turn divided into two categories: a fast automatic component (aFRRs), also called 'secondary reserves', with an activation time of no more than 7.5 min; and a slow manual component (mFRRs), or 'tertiary reserves', with an activation time of no more than 15 min. Finally, reserves with a startup-time beyond 15 minutes are classified as Replacement Reserves (RRs).

    Each category meets specific system needs. The fast FCRs are useful in the event of a sudden break, like a line fall, to avoid system collapse. FRRs are useful for variations over several minutes, such as a decrease in wind or PV output. Finally, the slow RRs act as a back-up, slowly replacing FCRs or FRRs when the system imbalance lasts more than 15 minutes.

    In the model we only consider FRRs, since they are the most impacted by VRE...

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