by Brian N. Maurizi, PhD; Electricity Trader, Saracen Energy Advisors

~ I received a PhD in Theoretical Mathematics, but I had always been interested in energy and commodity markets. Toward the end of graduate school, I knew that I wanted a career outside academics, and I was most interested in the energy industry. Immediately upon finishing, I started a job at a large energy company, specifically a “merchant generator” in the electric power industry. I quickly learned that the organized wholesale power markets are fascinating!

These markets are centered around an optimization problem called Security Constrained Economic Dispatch. Every day, every power plant in the territory (which could cover over 10 states and tens of millions of people) submits their generation offers – how many megawatts they can generate at what price. Similarly, the utility companies submit their usage forecasts – how many megawatts they will use. The objective function of the optimization is to minimize the cost to generate all the needed megawatts, the decision variables are the commitment and dispatch of each power plant, and the constraints are that all the usage must be met (no blackouts allowed!), and the resulting power flows must not overload any transmission lines. This optimization has thousands of decision variables, and tens of thousands of constraints. Furthermore, the unit commitment problem contains variables that do not continuously vary but instead are just a “on” or “off” decision (a so-called mixed integer problem), specifically the decision of whether to turn on a power plant and run it at least at the minimum production level, or to leave it off. These mixed integer problems are known to have no completely general recipe for a solution which performs any better than random guessing; in the case of SCED the situation is at least not completely general, so we can do better than random guessing, but the difficulty of the problem is very real. In short, just the daily operation of the power grid and power markets involves interesting theoretical and applied mathematical issues.

These issues are going to get more challenging and interesting as the grid evolves, primarily because the growing role of renewable energy brings challenges with it. Quite simply, the wind does not always blow, and clouds (or night!) can quickly reduce solar production, so we need to build a grid that can integrate intermittent energy sources while still keeping the lights on with a combination of battery power and dispatch-able sources like hydroelectric, nuclear, or traditional fossil fuels, to name a few. Any industry where you can go from the mathematics of constrained optimization to global political issues in two paragraphs is not going to be boring I suspect!

So, where do I fit into this picture?

I am an electricity trader, and I work at a company that buys power transmission contracts called Financial Transmission Rights. Essentially, we lease space on transmission lines for months or even years. We buy these leases in centralized competitive auctions that happen on a monthly basis. The leases make (or lose) money based on the price difference between the location where we are sourcing the power from and where we are moving it to. So, for example, we might buy a lease to move 50 megawatts of power from St. Louis to Indianapolis, every hour of every day during the month of January 2020, for $2 per megawatt-hour. Then, if power prices in Indianapolis end up being more than $2 above those in St. Louis, we will make money. What is involved in deciding which leases to bid on and how much to pay, you might ask? Well, everything related to the power grid: weather patterns, power lines, power plants, fuel prices, public policy, and more. We write software and build models to make predictions, and we watch the markets every day to see if our predictions are correct.

How has my mathematics background prepared me for a career in power trading? Well, full disclosure first: during the entirety of graduate school, I pretty much only used computers for checking email and typing up my thesis. Ok, and one numerical analysis class. I did not know how linear regressions worked or what a SQL query was. So, if you are thinking of a career in industry but you feel a bit behind in your knowledge of the toolset, well you are probably not doing any worse than I was!

That is what I did not have, but what I DID have as a mathematics PhD was far more important. First and foremost, humility and a love of and willingness to learn. Second, my PhD work had taught me how to be highly self-directed, have a high degree of focus, continue trying different techniques until a problem was solved, and think critically. I was never limited by my understanding of the math, so I could focus on the problem at hand, whether it was Brownian motion (a common tool used to model asset prices) or multivariate Gaussian models. My boss could tell me “Go figure out how this forecasting model works” and then leave for a week. I was capable of doing it, and of then telling him that it was significantly deficient in some key area and how I thought it could be improved.

Something that bears particular mention is software design. Wherever you go in industry, it is highly likely you will find yourself writing code, because there is no other way to efficiently process large amounts of information. I believe that mathematicians are supremely prepared to be excellent software designers, because fundamentally computer science is a very close cousin to mathematics. The basic architecture of the computer, the Von Neumann architecture, is of course named after John Von Neumann, a famous and prolific mathematician. Early innovators in computer science were very often mathematicians, such as Alan Turing. The theorems, objects and structures that mathematicians design have a close parallel in how it feels to design a piece of software, with many interacting modules and interfaces. The rules that govern a piece of software are very exacting and precise, just like mathematics. That being said, software design is a serious field of engineering and there is a great deal to learn; it should be approached with a humble and open mind. Fortunately it is well worth your time to learn as much as you can about software design – the payoff to being a better software designer is highly nonlinear. A much better software designer might not be just 50% more productive or valuable, they could be 10x or 100x more valuable. And it’s fun too!

Working in “industry” does bring out new types of challenges as well. In academics, you can choose to some extent your area of research. In industry, ultimately a company needs to be profitable, and your role is to be a part of that. Thus you cannot choose the problems you work on, you need to work on whatever is currently holding back your profitability. This can be a great driver for learning new things – needing to solve whatever problem comes your way means that you will learn many things, simply because you are shoved into it. For me, this has been everything from specialized file formats and parallel programming, to the geology and industrial activity in various US regions. And let’s not forget, some of the most powerful mathematical insights have been gained by committing to solving a problem and then following the trail wherever it leads. Information Theory, Cantor’s work on infinite cardinals, Probability theory, arguably these all arose out of solving a highly “applied” problem.

If you are someone who is willing to keep learning many new things, and take on whatever problems are thrown at you, a career outside academics generally and the power industry specifically might be perfect for you.