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The Near-Optimal Feasible Space of a Renewable Power System Model
Fabian Neumann, Tom Brown
TL;DR
Long-term power-system models typically provide a single least-cost layout, leaving uncertainty about other cost-efficient designs and their socially relevant features. The paper uses MGA to explore the near-optimal feasible space of a fully renewable European electricity model with joint generation, storage, and transmission expansion. Many diverse alternatives exist: a 0.5% cost increase already yields numerous options, while wind, hydrogen storage, and grid reinforcement remain necessary within 10% of optimum.
Problem
Single-solution cost optimization provides limited evidence about diverse near-optimal layouts and features that persist across them.
Method
MGA systematically explores the near-optimal feasible space of a fully renewable European electricity model with detailed spatio-temporal conditions and co-optimized generation, storage, and transmission.
Results
0.5% cost deviation already offers many technologically diverse alternatives, while either wind type, some hydrogen storage, and grid reinforcement are essential within 10% of optimum.
Takeaways & Limitations
Technology-specific boundary conditions can inform discussions about social constraints on renewable deployment and the extent of transmission reinforcement.
Abstract
from arXiv · showhide
Models for long-term investment planning of the power system typically return a single optimal solution per set of cost assumptions. However, typically there are many near-optimal alternatives that stand out due to other attractive properties like social acceptance. Understanding features that persist across many cost-efficient alternatives enhances policy advice and acknowledges structural model uncertainties. We apply the modeling-to-generate-alternatives (MGA) methodology to systematically explore the near-optimal feasible space of a completely renewable European electricity system model. While accounting for complex spatio-temporal patterns, we allow simultaneous capacity expansion of generation, storage and transmission infrastructure subject to linearized multi-period optimal power flow. Many similarly costly, but technologically diverse solutions exist. Already a cost deviation of 0.5% offers a large range of possible investments. However, either offshore or onshore wind energy along with some hydrogen storage and transmission network reinforcement are essential to keep costs within 10% of the optimum.
I. INTRODUCTION
Energy system models usually return one cost-optimal layout, although feasible near-optimal alternatives may better accommodate social acceptance and other difficult-to-quantify considerations. This work applies MGA to systematically explore diverse, similarly costly European power-system layouts and identify persistent investment requirements.
- Energy models typically optimize total cost for fixed inputs but return only one solution, underrepresenting design flexibility.
- Near-optimal solutions can accommodate public acceptance, implementation difficulty, land-use conflicts, and regional inequality at limited additional cost.
- MGA explores structurally different investment choices for one parameter set, complementing methods that vary cost assumptions or other parameters.
- The study targets a European pan-continental electricity model with detailed spatio-temporal conditions and joint generation, storage, and transmission optimization under LOPF constraints.
- The work systematically explores diverse technology mixes and derives rules that keep costs within predefined ranges.
II. METHODOLOGY
The model minimizes annualized generation, storage, transmission, and operating costs subject to linearized multi-period power-flow, resource, storage, network, and emissions constraints. It assumes a static cost-optimal layout for a specified emissions target rather than an investment pathway.
- The objective minimizes total annual system costs from investment capacities and variable generator dispatch.
- Representative snapshots are weighted so their total duration equals one year, producing a convex linear-program formulation with linear optimal-power-flow constraints.
- Generation, storage, and transmission capacities are bounded by geographical potentials and renewable availability factors vary across locations and time.
- Storage charging and discharging are represented by positive power variables bounded by storage ratings, while energy levels remain dispatch-consistent and capacity-limited.
- Network constraints enforce nodal electricity balance and linearized voltage-cycle conditions, with security margins applied to line capacities.
- The formulation limits emissions to a target but excludes investment pathways, reserve power, system stability, and robust scheduling, assuming perfect foresight for the reference year.
B. Modeling to generate alternatives (MGA)
MGA constrains the original feasible space to solutions within a chosen cost increase and systematically explores alternative investment directions. By minimizing or maximizing predefined regional and technological investment groups, it identifies boundaries and rules for near-optimal solutions.
- MGA limits the feasible space to solutions whose objective value is within a specified relative cost increase ϵ of the optimum.
- The structured search minimizes or maximizes predefined groups of generation, storage, and transmission capacity variables rather than using the HSJ algorithm.
- Search groups can be organized by region and technology, such as German onshore wind or total transmission expansion.
- The resulting minima and maxima define boundaries containing all near-optimal solutions and express rules for remaining nearly cost-optimal.
- Because the formulation remains convex, every group capacity between its minimum and maximum has a corresponding near-optimal solution, though not every combination is feasible.
C. Model input data
The model uses a spatially and temporally resolved European power-system dataset with simultaneous expansion of generation, storage, and transmission technologies. Its infrastructure choices are bounded by geographical, network, demand, and security assumptions.
- The PyPSA-Eur dataset represents Europe with 100 nodes and 4380 two-hourly snapshots covering a full year.
- The greenfield model jointly expands transmission, HVDC links, storage, and renewable generators, with gas turbines as the only fossil-fueled plants.
- Run-of-river and pumped-hydro capacities cannot be expanded because of assumed geographical constraints.
- New HVDC corridors are limited to 30 GW, existing AC lines can be reinforced up to four times capacity, and annual power-sector demand is assumed near today’s level.
D. Experimental setup
The experiments vary allowable cost slack and emissions targets while extremizing investment groups across generation, storage, and transmission. They generate a large ensemble of near-optimal solutions at different temporal resolutions.
- The main MGA runs use cost deviations ϵ from 0.5% to 10% and emissions-reduction targets of 80%, 95%, and 100%.
- The alternative objectives minimize and maximize investment groups spanning generation capacity, hydrogen storage, battery storage, and transmission infrastructure.
- The primary setup produces 384 near-optimal solutions, with average computational requirements of 6.5 hours and 31 GB of memory per problem.
- A supplementary 3-hourly model evaluates country-wise investment minima and maxima for 1%, 5%, and 10% slacks, producing 1584 additional solutions.
A. Optimal solutions
Optimal fully renewable systems are dominated by wind, with generation concentrated near European coasts and grid expansion linked to wind-farm locations. Tighter emissions targets increase costs non-linearly and shift technology preferences.
- In the 100% reduction optimum, offshore wind supplies more than half of electricity, onshore wind another quarter, and photovoltaics 16%.
- A 95% reduction system uses less onshore wind and more solar than the fully decarbonized system while maintaining the same offshore-wind share.
- A 95% emissions reduction costs roughly a quarter more than an 80% reduction, while zero emissions costs almost 50% more.
- Optimal generation hubs cluster along the North, Baltic, and Mediterranean coasts, while inland regions produce little electricity.
- Solar dominates southern Europe, wind prevails near the North and Baltic Seas, and HVDC routes correlate with wind-farm placement.
B. The near-optimal feasible space
Near-optimal solutions permit substantial technological flexibility, but wind, hydrogen storage, and transmission remain important constraints as systems approach full decarbonization. Country-level alternatives can also omit individual technologies when neighboring countries compensate.
- Method: The analysis uses investment extremization to derive technology-specific rules for solutions within predefined cost slack, although the slack constraint limits solution-space accuracy.
- Generation: Wind remains essential across emission targets, although zero-emission alternatives can omit onshore wind at 4% higher cost or offshore wind at 7.5% higher cost.
- Generation: A 0.5% cost increase creates investment flexibility of roughly ±200 GW for onshore and ±150 GW for offshore wind, while both technologies remain jointly necessary.A fully renewable system costing 10% more still requires more than 500 GW of wind capacity.
- Storage: Hydrogen storage becomes imperative when weather-independent gas-fired flexibility is unavailable, while battery storage is not essential even under complete decarbonization.Reducing hydrogen infrastructure requires excess generation and greater curtailment.
- Transmission: Transmission reinforcement becomes more pivotal with higher renewable shares, yet its volume can range from nearly double today’s capacity to marginal reinforcement within the near-optimal space.At 80% emission reduction, a 2% cost increase can avoid reinforcement; at 100%, some additional capacity remains necessary at a 10% deviation.
- Country-level flexibility: Any one country can omit a generation or storage technology while remaining within 5% of the optimum for a 95% emission reduction target, provided neighbors compensate.
C. Correlations
Near-optimal capacity mixes become more diverse as cost slack increases, with interdependencies among wind, storage, solar, and transmission shaping feasible alternatives. The analysis also relates this space to regional generation concentration and transmission–equity trade-offs.
- Capacity mixes: Fig. 5 compares generation and storage compositions across slack levels and optimization senses, with bar-chart labels identifying the investment-variable group optimized.
- Capacity mixes: Capacity-mix diversity rises as more cost slack is allowed, with lower solar capacity factors contributing substantially to variation in capacity totals.
- Technology correlations: Hydrogen storage is positively correlated with onshore and offshore wind, battery deployment aligns with solar, and transmission expansion accompanies both wind technologies.
- Regional structure: Fig. 7 relates cumulative regional electricity generation to cumulative demand across 100 European regions, while Fig. 6 reports capacity correlations across near-optimal solutions.
- Regional structure: Fig. 8 examines Gini-measured generation equity against transmission volume across four search directions involving transmission and storage.
D. Distributional equity
The study evaluates regional equity using Lorenz curves and Gini coefficients, finding that stronger emission reduction targets favor less equitable cost-efficient solutions. Greater equity remains attainable with limited cost increases by reducing emphasis on transmission expansion.
- Equity and decarbonization: More ambitious emission reduction targets favor less equitable solutions from a cost perspective, although these may conflict with public attitudes.
- Equity measures: Lorenz curves compare cumulative regional electricity generation with cumulative electricity demand to characterize distributional equity.
- Equity measures: The Gini coefficient measures uniformity from the area between the Lorenz curve and identity line; 1 denotes maximum inequality and 0 equal average production and consumption.
- Technology trade-offs: Prior work associates wind-focused systems with less balanced generation and photovoltaic supply with more even regional distribution, a pattern also observed here.
- Technology trade-offs: More regionally equitable solutions are attainable for a limited cost increase when attention shifts away from transmission expansion, whereas using less storage generally discourages equitable generation patterns.This exception does not hold for a zero-emission system in the same way.
IV. CRITICAL APPRAISAL
The analysis is limited to an electricity-sector model and finite spatial-temporal resolution, while also neglecting parametric uncertainty. Despite these boundaries, it identifies a broad near-optimal space and technology-specific conditions relevant to policy discussions.
- Scope boundaries: The study covers only the electricity sector, so stronger sector coupling could produce a different near-optimal feasible space.The authors note that increasing sector coupling may reduce the benefit of transmission and alter the feasible space.
- Resolution: Higher spatial and temporal resolution would better represent transmission-bottleneck curtailment and extreme weather events.The authors identify this as desirable within computational constraints.
- Uncertainty: The analysis neglects parametric uncertainty, although combining MGA with parameter sweeping could produce probabilistic feasible-space boundaries.Such boundaries would represent the probability that component capacities fall within the near-optimal space.
- Policy relevance: The near-optimal feasible decision space is flat, enabling boundary conditions for discussing renewable-resource constraints and transmission reinforcement.These rules support policy discussions beyond a single least-cost solution.
- Findings: A 0.5% cost deviation already yields technologically diverse alternatives, while staying within 10% of optimum requires wind, hydrogen storage, and grid reinforcement.Onshore wind can be omitted at a 4% cost increase and solar at 10%.