- The paper's main contribution is an integrated MIQCP framework that models both electricity transmission and hydrogen pipeline networks with essential physical details.
- It introduces novel relaxations for complex nonlinearities, enabling tractable solutions to a large-scale nonconvex MINLP and yielding near-optimal results.
- Case studies, including an Australian REZ example, demonstrate the framework's ability to optimize techno-economic trade-offs for renewable energy transport.
This paper (2207.03567) presents a novel mathematical framework for the optimal integrated planning of electricity and hydrogen (H₂) infrastructure, specifically for transporting large-scale variable renewable energy (VRE). The core problem addressed is whether it is more cost-effective to transport green energy as electricity (via transmission lines) or as green molecules (via H₂ pipelines) from remote VRE generation sites to demand centers.
Existing literature often examines electricity or H₂ infrastructure planning in isolation, or uses simplified models that neglect crucial physical realities. This paper fills this gap by proposing an integrated framework that considers both electricity transmission (High-Voltage Alternating Current - HVAC and High-Voltage Direct Current - HVDC) and H₂ pipeline networks simultaneously. A key contribution is the inclusion of essential nonlinearities and dynamic effects that significantly impact investment decisions, such as:
- Electricity Network: Voltage drops and losses in HVAC and HVDC lines, losses in HVDC converter stations, reactive power flow and compensation (SVCs).
- Hydrogen Network: Pressure drops in pipelines, time-varying accumulation rates, and linepack (the storage capacity within the pipeline itself).
- Power-to-Gas (PtG) Stations: Electrolyser efficiency, compressor power requirements, and water consumption.
The integrated model includes candidate locations for electrolyser stations and various options for installing HVAC and HVDC lines (with different voltage levels and capacities, including parallel circuits) and H₂ pipelines (with different diameters), along with associated equipment like compressors and reactive power compensators. The decision to install these assets is represented by binary variables. The objective is to minimize the total annualized investment cost of this infrastructure while maximizing the discounted revenue from H₂ sales over a planning horizon.
The inclusion of detailed physical models, particularly the nonlinear power flow equations for HVAC and HVDC, gas flow equations for pipelines, converter loss models, and the dynamic linepack model, results in a large-scale, nonconvex mixed-integer nonlinear programming (MINLP) problem. Such problems are generally computationally intractable to solve to global optimality, especially given the high temporal resolution needed to capture VRE variability (the paper uses half-hourly data for representative periods).
To address this computational challenge, the authors propose a tractable alternative: a mixed-integer quadratically constrained programming (MIQCP) relaxation of the original MINLP. This involves relaxing certain nonconvex equality constraints (like products of variables or square relations) into convex inequality constraints (e.g., rotated second-order cone constraints) and using polyhedral envelopes for other nonlinear terms where necessary. This transformation yields a convex continuous relaxation at each node of a branch-and-bound solver, making the problem solvable by state-of-the-art MIQCP solvers like Gurobi, which was used for the numerical evaluation. While a relaxation does not guarantee the globally optimal solution of the original nonconvex problem, it provides a high-quality lower bound and often yields near-optimal solutions that are feasible in the original space, especially compared to purely linear approximations.
The practical application and effectiveness of the proposed MIQCP model are demonstrated through two case studies:
- Canonical Two-Node System: This paper analyzes the fundamental trade-offs between electricity and H₂ transport based on varying transmission distance (200 km to 1000 km) and VRE capacity (1 GW to 10 GW). The findings provide practical insights:
- HVAC is generally preferred for short distances (< 200 km) across all capacities due to lower terminal costs compared to HVDC converters.
- HVDC becomes competitive for medium to long distances (around 600 km break-even point) and medium capacities (2.5 GW to 5 GW), as its lower line losses and potentially lower total cost for longer routes outweigh the converter station costs.
- H₂ pipelines are favored for medium to long distances (> 400 km) and high VRE capacities (≥ 7.5 GW). This is attributed to their significantly lower transmission losses over distance and the inherent storage capacity provided by linepack, which helps manage VRE variability.
- Real-World Australian REZ Case Study: This paper applies the model to a network of four actual Renewable Energy Zones (REZ) in Queensland, Australia, and one H₂ demand point, using real VRE forecast data. The optimal solution reveals a hybrid infrastructure: a significant HVDC link (2 GW, 570 km), a large double-circuit HVAC link (3 GW, 500 kV, 200 km), and H₂ pipelines (0.5m diameter, total 800 km). No SVCs were required due to the relatively short HVAC segment. The results show that the linepack in the installed pipelines plays a crucial role in smoothing the variable VRE input to meet a more stable H₂ demand profile. The achieved energy transmission factor (percentage of available VRE accommodated) was very high (99.01%), demonstrating the model's ability to design infrastructure that effectively utilizes available renewable resources.
From an implementation perspective, the paper highlights that even with the MIQCP relaxation and the use of representative weeks instead of a full 20-year horizon, the resulting problems are large scale. The canonical 2-node cases involved over 400,000 continuous variables, 28 binary variables, and 900,000 constraints (including 69,000 quadratic), taking 1-3 hours to solve. The Queensland REZ case was even larger, with over 560,000 continuous variables, 44 binary variables, and 1.16 million constraints (including 107,000 quadratic), requiring around 4 days to solve using a powerful solver like Gurobi. This demonstrates the computational complexity of detailed, integrated energy system planning models.
In summary, the paper successfully develops and demonstrates a sophisticated, integrated planning framework that incorporates essential physical details often neglected in previous studies. The use of an MIQCP relaxation makes the complex problem tractable, enabling detailed analysis of the techno-economic trade-offs between electricity and H₂ transport for large-scale VRE integration, providing valuable insights for real-world energy infrastructure planning. The case studies illustrate that the optimal solution is likely a hybrid of electricity and H₂ transport, depending on distance, capacity, and network topology, with hydrogen pipelines offering significant storage benefits via linepack for high-capacity, long-distance transmission.