Mathematical Optimization: The Key to Unlocking Opportunity in this Time of Transformation in the Electricity Industry

Author: Pavan Racherla, PhD
Date: 4/13/2021

The electricity industry is undergoing a major transformation as it transitions from being almost entirely dependent on the non-renewable resource of fossil fuels to being powered by sustainable resources such as solar and wind. This seismic shift is generating unprecedented opportunities and challenges for players across the industry landscape. Which enterprises will be best positioned to capitalize on the opportunities and conquer the challenges presented by this transformation? Those that utilize mathematical optimization – which has established itself as an essential AI technological tool for electricity companies.

A Changing Industry Landscape

To understand why mathematical optimization is a such a critical technology for energy market players today, we must take a closer look at the changes happening across the industry.

Historically, the electricity industry has been structured vertically with generation at the top, transmission in the middle, and distribution at the bottom. From the viewpoint of an independent regional system operator, this has meant that the day-to-day and real-time scheduling of generators, in response to the anticipated demand for electricity, is generally a deterministic problem (given that fossil-fuel, nuclear, and hydro generators ­– the dominant resources then and now – have configurable power outputs). In short, the supply and demand of electricity can be balanced – in a relatively straightforward manner – when fueled or driven by heretofore conventional energy resources, thereby ensuring the stability of the power grid.

That, however, is all in the past. The advent of Distributed Energy Resources (DERs) – such as solar photovoltaic arrays, wind turbines, and Lithium-ion batteries – has disrupted the picture of verticality described above, causing:

• The demarcation between generation, transmission, and distribution to become increasingly blurred.
• The determinacy of centralized scheduling of conventional energy resources to give way to the indeterminacy of scheduling them in tandem with highly intermittent and geographically variable DERs.

Consequently, organizations across every sector of the industry are experiencing a paradigm shift in their operations, planning, and strategic outlook. Consider, for example, distribution utilities. Traditionally, they have been one-way conduits for electricity – from generators through transmission to consumers. But now, as rooftop solar, Tesla Powerwalls, smart inverters, plug-in electric vehicles, and advanced metering infrastructure have become more commonplace, they are tasked with orchestrating two-way flows of electricity and data. Collectively, these technologies hold the promise of not only a cleaner and smarter power grid, but also allow consumers to become “prosumers” by generating their own electricity and potentially selling the excess.

Meanwhile, according to a recent survey by Accenture, nearly six out of ten utility executives “continue to voice considerable concern about the impact of rising rates of distributed generation on their revenues,” and a good two third of them expect “their company’s role to evolve toward DER integrator and DER-services market facilitator.” This signals a marked departure for utilities from primarily being electricity distributors to providers of a suite of value-added electricity services.

Leveraging New Techniques and Technologies

 Optimal Power Flow (OPF) is a key methodology that can help electricity companies during this transitional period. With OPF, an objective such as the minimization of operating costs and/or other externalities for a given system and timeframe is sought, subject to the accompanying power flow equations and network, and device constraints. For distribution systems, in general, this corresponds to a highly nonlinear, mixed-integer, time-coupled optimization problem. Such a problem is very difficult to solve within operationally relevant timescales (as it’s NP-hard and nonconvex), and neither the feasibility nor the optimality of the solution is assured.

In order to make OPF algorithms more operationally relevant, it is essential to convexify the nonconvex OPF problem, drawing on modern, powerful convex optimization techniques such as linear, second-order cone, and semidefinite programming. In my experience, Gurobi’s state-of-the-art mathematical optimization solver – with its cutting-edge features and continual speed improvements – is by far the best tool available for the convex optimization of electricity networks.

Speed and performance are important not just for optimizing day-to-day operations, but for longer-term planning and decision making too. For instance, consider the task of optimally sizing and siting solar and storage for a distribution system, given some utility-specified objectives. This is a hard optimization problem on multiple fronts:

• Firstly, a typical system serves thousands of customers – each one a candidate location for solar and storage – and the value proposition might vary considerably from one location to another.
• Secondly, the optimization horizon needs to be long enough (for example, a year) to account for the seasonality and day-to-day variability of solar irradiance.
• Thirdly, other operational, financial, and regulatory uncertainties need to be factored in over the project horizon.

Given the astronomical number of possibilities, such mathematical optimization problems clearly demand creative approaches – and Gurobi’s solver is ideally suited to solve such problems.

An Indispensable Tool for Today’s Challenges

During the ongoing transformation of the electricity industry from being powered chiefly by large fossil fuel power plants to small distributed energy resources such as solar photovoltaic arrays and wind turbines, state-of-the-art mathematical optimization solvers like the Gurobi Optimizer will continue to be indispensable tools for players across the industry – from independent system operators to distribution utilities to Green Tech startups.

Here are just some of the problems that can be solved optimally using mathematical optimization technologies:

• Exact load flow
• Unit commitment
• Network reconfiguration
• Transmission expansion
• Electricity markets
• Multi-period optimal power flow with energy storage and inventory control
• Optimal siting and sizing of power sources and energy storage
• Uncertainty modeling
• Microgrid development
• Charging and discharging of plug-in electric vehicles

With mathematical optimization, electricity companies can tackle their toughest problems and unlock new opportunities for improved efficiency and profitability in this time of transformation.

About the Author

Pavan Racherla is a consultant at Energy Grid Analytics LLC, which he founded in 2020. He makes software rooted in mathematical optimization for the electricity industry. He has a PhD in Engineering and Public Policy from Carnegie Mellon University, and has served as a Postdoctoral Research Scientist at NASA Goddard Institute for Space Studies and as a Research Assistant Professor in Electrical Engineering at University of Vermont.