Welcome to PENSA at Princeton University

SAP logoPENSA is the home of the SAP Initiative for Energy Systems Research at Princeton University. Our goal is to bring advanced analytical thinking to the development of new energy technologies, the rigorous study of energy policy, and the efficient management of energy resources.


The Renewables Challenge: Keeping the lights on while managing variability and uncertainty - Talk given to the Princeton Academic Mini Reunion, October 2, 2015.

This talk highlights the cost of uncertainty in renewables that arise due to uncertainty. This is not a simple calculation, because the cost of uncertainty depends on process of how decisions are being made. For example, the cost of day-ahead forecasting errors for wind or solar energy are not as large as hour-ahead forecasting errors, because errors in day-ahead forecasts can be hedged with hour-ahead decisions about gas turbines, while an error in an hour-ahead forecast is harder to handle.

Click here for the presentation.

We finally have our first paper on SMART-ISO. Below is a paper describing the workings of the model (no math!), and the results of a multi-year study funded by DOE on off-shore wind integration done jointly with the University of Delaware:

Hugo P. Simao, W.B. Powell, C. Archer, W. Kempton, “The challenge of integrating offshore wind power in the US electric grid. Part II: Simulation of the PJM market operation,” Working paper, April, 2015.

The modeling of wind for our offshore wind study is described in

C. Archer, Hugo P. Simao, W. Kempton, W.B. Powell, M. Dvorak, “The challenge of integrating offshore wind power in the US electric grid. Part I: Wind Forecast Error,” Working paper, April, 2015.


Jungle of stochastic optimization

Warren Powell gave a tutorial presentation to FERC on stochastic optimization, with an update on our research on the stochastic unit commitment problem. Recent research has formalized industry practice as a "robust cost function approximation" which involves optimizing a parametric modification of the cost function. For a tutorial on stochastic optimization and the stochastic unit commitment problem, click here.





Lab lunchErick Chen, Shuyang Li and Ryan McNellis, undergraduate interns the summer of 2014, present their summer research, covering approximate dynamic programming to model economic behavior, optimizing energy storage using reinforcement learning, and the modeling of wind and solar energy for the PJM grid. Other summer research included monotone ADP for bidding battery storage, and the comparison of stochastic dual decomposition (Benders cuts) against separable, piecewise linear value functions for grid level battery storage.



Solar and uncertaintyUnderstanding uncertainty in the context of uncertainty. Variability of solar is a big issue, but so its the challenge of forecasting it. The problem is that decisions are often made in advance. Gas turbines (on the PJM grid) are planned once every 30 minutes. Steam is planned a day in advance. And energy investments are planned years in advance.

(Click here to download the full pdf).







We are starting to get some very close comparisons between the LMPs (locational marginal prices) produced by SMART-ISO, and those observed in history. Following a major rewrite to model PJM's IT-SCED unit commitment process, we obtained a surprisingly close match in the difficult peak month of July (right). For more on calibration, click here.

Getting a match on the behavior of LMPs means that we had to reasonably match PJM's behavior of day-ahead and real-time planning, with a realistic economic dispatch model (where the LMPs are calculated), with an accurate model of the grid.


Princeton hosted a research team from University Sao Paulo and Unicamp in September, 2013, to compare differences in Brazilthe energy systems of the two countries, compare research agendas, and look for opportunities for future collaboration. The differences are significant - Brazil derives almost 90 percent of its electricity from hydroelectric power. However, dry periods can periodically limit the use of hydro, recently forcing Brazil to generate a significant amount of power from oil, raising their interest in other types of renewable generatioin.






Ph.D. student Daniel Salas developed an approximate dynamic programming algorithm, SMART-Storage, for optimizing grid level storage. This first plot shows the grid without storage, with the orange and red rectangles indicating the lines with the highest congestion. The simulation is testing significant levels of off-shore wind.

Click here for movie (100 meg!)





grid_nostorageIn this second simulation, he can use storage near the off-shore wind generators (shown in green, where the diameter indicates how much is in storage at a point in time), or near major load points (shown in blue). The algorithm adapts to the congestion on the grid. Note the dramatic reduction in the lines that are over capacity (the snapshot is made at the same point in time in the simulation).

Click here for movie (100 meg!).


SMART-Storage can be used to identify the best locations for storage, based on their marginal value over an entire planning period, taking into account near-optimal policies for charging and discharging in response to locational marginal prices.

[This research was funded by the National Science Foundation.]




Daniel Salas presents his work on grid level storage to the group. His work spans stochastic optimization (approximate dynamic programming), stochastic modeling of prices, and modeling of the power grid.





SMART-LSOC is an intelligent load and source controller developed jointly with the Center for Computational Learning Systems at Columbia University, as part of a DOE-funded projected for ConEd of New York City. We compared two approximate dynamic programming policies, a cost function approximation and a policy based on value function approximations, to develop robust policies for executing advance curtailments of buildings in anticipation of grid congestion. The image to the left shows the grid for Queens, NY, with the various primary feeders which may fail from time to time.Click here for the paper.








Deputy director Hugo Simao kicks off the 2013 summer season with a presentation on SMART-ISO, prior to giving this talk at the 2013 FERC Conference in D.C. Three years in development, SMART-ISO is beginning to produce results that accurately capture the historical behavior of PJM.







chilled water

We have begun two projects managing energy systems for buildings. The first is a model of energy flows for Princeton University, which involves optimizing the chilled water energy storage facility with energy from the grid (at spot prices), gas turbine, and a diesel generator. The university operates several boilers and eight chillers. These have to be optimized to meet campus loads while minimizing exposure to real-time spot prices. A separate project involves optimizing steam generation for building loads, given the complex peak-load pricing policy of Consolidated Edison of New York.





NJ capital

Warren Powell met with members of the NJ state legislature and the Bureau of Public Utilities to help Tom Nyquist and Ted Borer from Princeton University explain new rules that might stabilize solar renewable energy credit markets. A multiagent simulator developed by Will Harrel '13 helped to analyze the effect of the newrules.





Warren Scott designed a direct policy search algorithm using his adaptation of the knowledge gradient algorithm for continuous parameters, resulting in a battery storage policy that produced solutions within 5-10 percent of a benchmark optimal policy. Along the way, he demonstrated the equivalence of projected Bellman error minimization and Bellman error minimization using instrumental variables (but neither of these worked as well as direct policy search). Warren defended his dissertation in May.