Power Generation Expansion Considering Endogenous Technology Cost Learning

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1 Antonio Espuña, Moisès Graells and Luis Puigjaner (Editors), Proceedings of the 27 th European Symposium on Computer Aided Process Engineering ESCAPE 27 October 1 st - 5 th, 217, Barcelona, Spain 217 Elsevier B.V. All rights reserved. Power Generation Expansion Considering Endogenous Technology Cost Learning Clara F. Heuberger a,b, Edward S. Rubin c, Iain Staffell a, Nilay Shah b,d and Niall Mac Dowell a,b* a Centre for Environmental Policy, Imperial College London b Centre for Process Systems Engineering, Imperial College London c Department of Engineering and Public Policy, Carnegie Mellon University d Department of Chemical Engineering, Imperial College London niall@imperial.ac.uk Abstract We present a mixed-integer linear formulation of a long-term power generation capacity expansion problem including endogenous learning of technology investment cost. We consider a national-scale power system composed of up to 2 units of 15 different power supply technologies, including international interconnectors for electricity import and export, and grid-level energy storage. We reformulate the non-convex learning curve model into a piecewise linear representation of the cumulative investment cost as a function of cumulative installed capacity. The model is applied to a power system representative of Great Britain for the years 215 to 25. We find that the consideration of technology cost learning rate influences the optimal capacity expansion and has systemic implications on the profitability of the power units. Keywords: power system modeling, capacity expansion planning, unit commitment, technology learning 1. Technology learning in energy system models Energy system models can guide decision-making on power capacity expansion by illustrating different strategies to meet future demands and environmental targets. In addition, such models can elucidate the role and value of technologies within the power system and indicate optimal times of investment. It is in this context, that an accurate representation of technology cost becomes essential to system planning tools. A reduction in technology cost over time and as a function of deployment has been observed for various consumer goods and large-scale power generation technologies. Dedicated R&D investment, manufacturing and process advancements, and government policies are among the identified cost reduction drivers (Grubb et al., 22). We distinguish between exogenous and endogenous representation of cost reduction. The first describes technology cost as time-dependent parameter, whereas the latter refers to the cost as a function of the technology deployment level. The tendency that each doubling of cumulative installed capacity results in a reduction of capital cost at a constant learning rate (LR) was first identified by Solow (Solow, 1957). The cost of the n th unit C n can be determined as a function of the initial unit cost C 1, the cumulative capacity installed x n, and

2 2 C.F. Heuberger et al. the learning rate exponent b, as defined in equation 1 and 2. C n = C 1 x b n (1) LR = 1 2 b (2) Despite cost reduction being identified as an endogenous phenomenon (Kahouli-Brahmi, 28), many energy system models to date apply static or exogenous cost models. The integration of the endogenous learning curve model into large energy system models requires choices being made not only about the factors in equation 1 and 2, but about a cost floor, the starting point for learning, and the experience scope either accounting for local or global cumulative capacity levels (Yeh and Rubin, 212). Optimisation-based energy system models which consider technology learning effects endogenously are for example MESSAGE-MACRO (IIASA, 212) or NEMS (EIA, 214). Due to the large scope and complexity of these models it is challenging to identify effects specifically due to the consideration of technology learning. To provide such insights we present a detailed and comprehensive modelling framework to conduct an explicit and rigorous analysis of technology learning effects in power system models. 2. General problem statement For a national-scale single-node power system, we aim to determine the optimal design, characterised by the unit expansion and retirement, and the optimal schedule, characterised by the generator dispatch, storage, and interconnector operation. From the perspective of a monopolistic system planner, the objective is to minimise total system cost under the given technical, economic, and environmental constraints. The problem is mathematically known as the generation expansion planning (GEP) and unit commitment (UC) model. In addition, the effect of endogenous technology cost learning should be taken into account. A high temporal resolution is required to accurately represent the nature of intermittent renewable power sources (ires), as well as the (in-)flexibility of conventional power generators. We are given the hourly electricity demand, onshore wind, offshore wind, and solar availability, and electricity import prices for the year 215. In addition, detailed performance parameter of power generation, storage units, and transmission losses are known. We assume perfect foresight over the planning horizon, and consider electricity demand to be inelastic and exogenous. Further, we assume that technological change is reflected in the capital cost of the power plant. 3. The ESO-XEL model We extend the work presented in (Heuberger et al., 216) by increasing the time frame from annual to multi-decadal, while maintaining an hourly time discretisation. A k-means clustering approach of the hourly data sets and the relaxation of the integer unit scheduling constraints allows a reduction in solution time of the mixed-integer linear problem (MILP) from days to minutes (approximately 9 %), with an average error of 2.5 % for systemlevel results. Two salient features of the Electricity System Optimisation - Expansion with Endogenous technology Learning (ESO-XEL) model are presented here: the unitwise capacity expansion, and the representation of the technology learning curves.

3 Power Generation Expansion Considering Endogenous Technology Cost Learning Nomenclature The relevant excerpt of ESO-XEL nomenclature is provided in table 1. Symbol Unit Description a yrs capacity planning periods in years, a A = {1,...,A end } t h operational time periods in hours, t T = {1,...,T end } c - clusters of representative days of each year, c C = {1,...,C end } i, ig, ic, ir, is - technologies, i I = {1,...,I end }, of which ig I are power generating technologies, ic I conventional (thermal), ir I intermittent renewable, and is I storage technologies il - technologies for which learning rate is applied, il I l - line segments for piecewise linear function, l {1,...,L end } yrs step width planning years DIni i - number of available units of technology i for a = 1 DMax i - maximum number of available units of technology i for a = 1 Des i MW/unit nominal capacity per unit of technology i BR i unit/yr build rate of technology i LT Ini i yrs lifetime of initial capacity of technology i for a = 1 LT i yrs lifetime of technology i Xlo il,l MW lower segment x-value of cumulative capacity of piecewise linear cost function Xup il,l MW upper segment x-value Y lo il,l MW lower segment y-value of cumulative CAPEX Yup il,l MW upper segment y-value xs il,a,l R MW position for technology i in year a on line segment l y il,a R cumulative CAPEX for technology i in year a b i,a Z - number of new built units of technology i in year a d i,a Z - number of units of technology i operational in year a, cumulative n ig,a,c,t Z - number of units of technology ig operating in year a at hour t of cluster c o is,a,c,t Z - number of units of storage technology is operating in year a at hour t of cluster c ρ il,a,l [,1] - 1, if cumulative CAPEX of technology il in year a on segment l 3.2. Model formulation Power System Design and Expansion: Equation 3 initialises the number of units of technology type i for the planning year a = 1. In the following planning time steps the number of new build units is constrained by the annual build rate BR i (eqn. 4), and by the maximum capacity/resource potential DMax i (eqn. 5). The unit balance for technology i over the planning horizon a for existing capacity stock and new build units is defined in equations 7-8. d i,a = DIni i i,a = 1 (3) b i,a BR i i,a > 1 (4)

4 Unit cost ( /kw) Unit cost ( /kw) Cumulative cost (bn. ) 4 C.F. Heuberger et al. d i,a DMax i i,a (5) d i,a = d i,a 1 b i,a LT Ini i a d i,a = d i,a 1 + b i,a + b i,a i,a LT Ini i + 1 (6) i, LT Ini i + 1 < a LT i + 1 (7) d i,a = d i,a 1 b LT i,a i + b i,a i,a > LT i + 1 (8) a Piecewise Linear Formulation of the Learning Curve Model: We model a piecewise linear representation of the exponential cost learning curve, following existing efficient mixed-integer linear implementations (Barreto Gómez, 21). To avoid non-linearities by multiplying the technology unit cost with the number of installed units, the presented formulation relates the cumulative investment cost to the amount of cumulative installed capacity, such that CAPEX i = f (d i,a ). ρ il,a,l = 1 il,a (9) l xs il,a,l Xlo il,l ρ il,a,l il,a,l (1) xs il,a,l Xup il,l ρ il,a,l il,a,l (11) a a =1 b il,a = xs il,a,l il,a,a a (12) l y il,a = Y lo il,l + ρ il,a,l Slope il,l (xs il,a,l Xlo il,l ρ il,a,l ) il,a (13) l By selection of the line segment l (equation 9), the x-axis position (constraints 1-12), and the line slope, where Slope il,l = Yup il,l Y lo il,l Xup il,l Xlo, we determine the cumulative investment il,l cost of technology i in year a, y il,a. Figure 1 visualises a nominal learning curve in panel (a), and its piecewise linear representation in panel (b, diamonds) with the corresponding curve of cumulative technology cost (b, squares) (a) Cumulative capacity (GW) (b) xs il,a,l 5 y il,a Slope il,l ρ il,a,l Cumulative capacity (GW) Figure 1: Illustrative technology cost learning curve as (a) a continuous function, and (b) a piecewise linear function of cumulative capacity.

5 Unit cost ( /kw) Capacity Installed (GW) Carbon Intensity (t CO2 /MWh) Power Generation Expansion Considering Endogenous Technology Cost Learning 5 4. Case study on the British power system The ESO-XEL model is applied to the power system of Great Britain (GB), in the years 215 to 25. In 215, GB s power capacity is composed of 12 % nuclear, 26 % coal, 4 % gas, 8 % wind, 2 % solar, 5 % hydro, and 7 % other types of power generating capacity (Department of Energy & Climate Change, 215). The annual power demand in 215 reached 33 TWh, with a peak of 53 GW. A legally binding economy-wide carbon emission target of 8 % reduction by 25 compared to 199 levels is interpreted as requiring complete decarbonisation of the power sector in the same time frame. Current reserve and power quality standards are to be maintained, requiring a sufficient amount of dispatchable power generators. Power outages are limited to a maximum of.5 % of annual demand. The planning periods a are chosen as 5-yearly intervals. The compression of the hourly granular input parameters into 11 clusters of 24 hours each reduces the number of variables from to (235 integers). Using IBM CPLEX 12.3 within GAMS , this problem is solved to a 3 % relative optimality gap in.2 hours on an Intel i7-477 CPE, 3.4 Ghz machine with 8 GB RAM Scenario definition and input data The cost learning effects for all power plants are based on global experience until the present date. Additionally, we consider knowledge spill-over, meaning that GB technology unit cost are influenced by global capacity increase. Estimates from the EIA and IEA global energy scenarios (EIA, 216; IEA, 214) in conjunction with technology-specific learning rates (Rubin et al., 215) build the basis for the applied cost reduction curves. We consider a base scenario assuming static technology cost at the left-most value in figure 2 (a), and a scenario taking cost reduction into account according to the learning curves shown in figure 2 (a). Remaining parameters are equivalent in both cases (a) Installed capacity (GW) Lead-acid battery Solar Wind-Offshore Wind-Onshore BECCS CCGT-PostCCS Coal-PostCCS CCGT (b) (c) Nuclear Coal IGCC CCGT OCGT Coal-PostCCS CCGT-PostCCS BECCS Wind-Onshore Wind-Offshore Solar Intercon. (FR, NL) Intercon. (IE) Pumped-hydro Lead-acid battery Carbon Intensity Figure 2: (a) Global technology learning curves; (b) optimal capacity mix for static cost, and (c) for a scenario considering cost learning as shown in (a). Bars correspond to the left axis of panels (b) and (c), lines correspond to the right axis. Integrated Gasification Combined Cycle (IGCC), Combined Cylce Cycle Gas Turbine (CCGT), Open Cycle Gas Turbine (OCGT), Carbon Capture and Storage (CCS), Bio-energy and CCS (BECCS).

6 6 C.F. Heuberger et al The effect of cost learning consideration Figure 2 (b) illustrates the optimal capacity stack for each planning year in the case of static technology cost. Considerable capacity expansion is required to meet increasing electricity demands, while reducing the overall carbon intensity (23:.5 t CO2 /MWh). The systemic effects of considering endogenous technology cost reduction are visualised in figure 2 (c). Investment in offshore wind capacity becomes increasingly economical, such that in 25 the amount of offshore wind capacity amounts to 3 GW compared to 18 GW in the base case. Optimal solar PV capacity deployment reduces from 25 to 1 GW in 25. The optimal investment timing of interconnector capacity moves from 23 to 22; additional 6 GW are installed. Consequently, the deployment of battery storage capacity is delayed, however the cost reduction stimulates continuous deployment up to 25. Decarbonisation proceeds more quickly under cost learning (23:.4 t CO2 /MWh). 5. Conclusion We have presented the efficient integration of piecewise linear cost functions into a largescale mixed-integer linear model, to address the issue of endogenous technology cost learning in power systems. A case study on the British power system confirms a significant effect on the optimal investment timing and competitiveness of individual technologies. This contribution enables the analysis of technology-specific policy support, as well as lock-in or crowd-out effects of technologies within a national-scale power system. References Barreto Gómez, T. L., 21. Technological Learning in Energy Optimisation Models and Deployment of Emerging Technologies. Phd, Swiss Federal Institute of Technology Zurich. Department of Energy & Climate Change, 215. Electricity: Chapter 5, Digest of United Kingdom Energy Statistics (DUKES), URL EIA, 214. The Electricity Market Module of the National Energy Modeling System: Model Documentation. URL EIA, 216. International Energy Outlook 216: DOE/EIA-484. Grubb, M., Koehler, J., Anderson, D., 22. Induced Technical Change in Energy and Environmental Modeling: Analytic approaches and policy implications. Annual Review of Energy and the Environment 27 (1), Heuberger, C. F., Staffell, I., Shah, N., Mac Dowell, N., 216. Levelised Value of Electricity - A Systemic Approach to Technology Valuation. In: 26th European Symposium on Computer Aided Process Engineering. Vol. 38. pp IEA, 214. Energy Technology Perspectives 214: Harnessing Electricity s Potential. URL IIASA, 212. Energy Modeling Framework: Model for energy supply strategy alternatives and their general environmental impact (MESSAGE), URL Kahouli-Brahmi, S., 28. Technological learning in energy environment economy modelling: A survey. Energy Policy 36 (1), Rubin, E. S., Azevedo, I. M. L., Jaramillo, P., Yeh, S., 215. A review of learning rates for electricity supply technologies. Energy Policy 86, Solow, R. M., Technical change and the aggregate production function. The Review of Economics and Statistics 39 (3), 312. Yeh, S., Rubin, E. S., 212. A review of uncertainties in technology experience curves. Energy Economics 34 (3),