(162e) A Sequential Decision-Making Framework for Long-Term Energy Transition Planning Under Uncertainty

Many countries around the world have set net zero emission targets within the next 30 years in an effort to mitigate the impacts of climate change. Achieving this ambitious goal will require large-scale investments into renewable and low-carbon technologies that will need to be efficiently integrated into our current energy system in order to meet net zero goals at the lowest cost. Energy system models can show how we can expand and operate a given set of technologies in order to meet specific goals. In most previous studies, the developed models have assumed to have perfect information about the future and that a decision maker will only make decisions at the beginning of the time horizon. But in reality, it is uncertain how parameters will change over time, such as the demand for liquid fuels. Also, decision makers are able to re-evaluate their previous decisions and can update their choices based on new information.

Uncertainty in energy system models is commonly studied through sensitivity analysis, allowing a decision maker to see how decisions change as the level of the input parameters change, as was done in the Net Zero America study [1]. While this method is beneficial for observing the effect of varying parameter values on the system, it does not allow for making unique decisions today that address the different parameter levels. Another method to study uncertainty is stochastic programming, which accounts for uncertainty through scenarios. In stochastic programming, there are first stage decisions that are made before any uncertainty is realized and are the same across all scenarios, and there are decisions made in the following stages as uncertainty is realized. In multistage stochastic programming (MSSP), uncertainty is realized successively through multiple stages [2]. Through the use of MSSP, a decision maker is able to make unique decisions today that address the different scenarios.

A common way energy system models are solved is with a forward-looking approach, where a model is solved once over the full horizon, meaning the energy transition is predicted at the beginning of the planning horizon. In reality, an energy transition over a long horizon will involve decisions made in a sequential manner which means that a rolling horizon approach can be applied, where a decision maker’s ability to consider feedback and observe the development of parameters is better represented. With this approach, a decision maker will select which technologies to invest over a given planning horizon, for example over the next 30 years. After a few years, the decision maker is able to re-evaluate their choices and can make new investments considering how parameters have changed as well as new information about the future that they did not know previously.

We develop a linear mixed-integer MSSP model for capacity expansion to study the energy sector for the United States using real data [4]. The system includes 10 liquid fuel producing technologies, 9 electricity generating technologies and 2 intermediate technologies over a multiperiod horizon divided into 5-year time periods. The model is solved to meet liquid fuel and power demand over the horizon at the lowest cost and considers uncertainty in the demand, capital cost of select renewable technologies and policy related to carbon emission reduction. In addition to the MSSP model, we develop a deterministic model (meaning we assume perfect foresight) for the same system. We solve the models separately with a forward-looking and with a rolling horizon approach. This allows us to evaluate the benefit of accounting for (1) uncertainty with MSSP under both solution approaches and (2) a decision makers ability to re-evaluate decisions. We also present additional ways to simulate challenging real-world characteristics such as time delays, lagged capacity installation, or the impact of social acceptance with a rolling horizon approach.

When the models are solved with the forward-looking approach, it is seen that the solution of the stochastic model has larger initial investments into technologies producing electricity and liquid fuel compared to the solution of the deterministic model. This is because the stochastic model makes a single decision today that considers multiple scenarios with varying demand for liquid fuels and electricity. When the rolling horizon approach is used, the stochastic model has a wider variety of technologies installed throughout the time horizon. This is again due to the uncertainty considered in each iteration with the stochastic model, leading to more diverse investments.

We also consider the effect of incorrect parameter predictions for both the forward-looking and the rolling horizon approach. When the investment decisions of the solution obtained using the forward-looking approach are subject to different observed parameter values, the average optimal objective value of the stochastic model is lower and has a smaller standard deviation than the average optimal objective value of the deterministic model. A similar trend is observed when the parameter values are varied with the rolling horizon approach. It is also seen that the average optimal objective value of both the deterministic and stochastic models are lower when paired with the rolling horizon approach compared to the forward-looking approach, which demonstrates that there is a benefit to reoptimizing investment decisions as new information is observed. This trend is seen because there are more diverse investments made when a decision maker is able to reconsider their past choices and make new investments as they observe how parameter values develop compared to their original predictions.

We close with a short but broader discussion of energy system models. The proposed models allow us to study how real-world constraints impact the energy transition in the United States. For example, we study how investment decisions change to focus more on renewable and low-carbon technologies when we enforce net zero emissions by 2050. When we pair our model with a rolling horizon approach to better represent real-world decision making, we observe the benefit of being able to re-evaluate decisions, particularly when predictions about parameter values over the horizon are incorrect.

References

1. Larson, E., Greig, C., Jenkins, J., et al. (2021). Net-Zero America: Potential Pathways, Infrastructure, and Impacts, Final Report Summary. Princeton University.
2. Birge, J.R., Louveaux, F. (1997). Uncertainty and modeling issues. Introduction to Stochastic Programming, 54-61.
3. Rawlings, J.B., Mayne, D.Q. (2009). Model Predictive Control. Model Predictive Control: Theory and Design, 91-107.
4. “U.S. Energy Information Administration - EIA - Independent Statistics and Analysis,” https://www.eia.gov/state/search/#?5=126&r=false.