Quantum Optimization for the Future Energy Grid: Summary and Quantum Utility Prospects

Abstract

In this project summary paper, we summarize the key results and use-cases explored in the German Federal Ministry of Education and Research (BMBF) funded project "Q-GRID" which aims to assess potential quantum utility optimization applications in the electrical grid. The project focuses on two layers of optimization problems relevant to decentralized energy generation and transmission as well as novel energy transportation/exchange methods such as Peer-2-Peer energy trading and microgrid formation. For select energy grid optimization problems, we demonstrate exponential classical optimizer runtime scaling even for small problem instances, and present initial findings that variational quantum algorithms such as QAOA and hybrid quantum annealing solvers may provide more favourable runtime scaling to obtain similar solution quality. These initial results suggest that quantum computing may be a key enabling technology in the future energy transition insofar that they may be able to solve business problems which are already challenging at small problem instance sizes.

Figures (9)

• Figure 1: The discount matrices $z_{c,t}$ found by the investigated solvers for $N_c = 100$. Blue indicates a discount and red corresponds to a penalty. White means no discount given at all. Despite their effects on the overall consumption (see Fig. \ref{['fig:ex100-consumption']}) being the same, the discount matrices are significantly different from one another. It is apparent that the Gurobi solver provides a more greedy approach to discount allocation than Leap, thereby indicating a larger impact of the regularization. Nevertheless, a similar pattern is observable in the last three solutions.
• Figure 2: The effect of the DSP solution for problem size $N_c = 100$. The plot shows the aggregated consumption with and without (Base) discounts in place, as well as the grid CO2 intensity. The solutions of all solvers produce the same (effectively) consumption change. Times with high CO2 emissions produce an effective decrease in consumption and vice versa, as expected.
• Figure 3: A cumulative distribution plot of the relative savings of the customers. Gurobi provides a more greedy discount allocation approach by providing discounts to relatively few customers. On the other hand, Leap distributes similar discounts to all customers. Remember: We do not optimize for this metric. This is just an observation of the different strategies and can be interpreted as a measure of the fairness of the optimization algorithms with respect to different customers.
• Figure 4: The investigated metrics for different problem sizes and different solvers. The runtime of all solvers has been set to be equal for a certain problem size, but grows with $N_c$. The top row shows the global metrics, which tell the most about how the solver performed. The relative energy error is the central objective that we try to minimize, while the energy error gives an overview of the performance with regard to all optimization targets.
• Figure 5: The time to solution of Gurobi on the Single-Problem showcases the exponential difficulty of the problem, especially when self-reliance is considered.