Slaven Peles

Slaven Peles, Stefan Klus

Most numerical solvers and libraries nowadays are implemented to use mathematical models created with language-specific built-in data types (e.g. real in Fortran or double in C) and their respective elementary algebra implementations. However, the built-in elementary algebra typically has limited functionality and often restricts the flexibility of mathematical models and the analysis types that can be applied to those models. To overcome this limitation, a number of domain-specific languages such as gPROMS or Modelica with more feature-rich built-in data types have been proposed. In this paper, we argue that if numerical libraries and solvers are designed to use abstract elementary algebra rather than the language-specific built-in algebra, modern mainstream languages can be as effective as any domain-specific language. We illustrate our ideas using the example of sparse Jacobian matrix computation. We implement an automatic differentiation method that takes advantage of sparse system structures and is straightforward to parallelize in a distributed memory setting. Furthermore, we show that the computational cost scales linearly with the size of the system.

Shaked Regev, Eve Tsybina, Slaven Peles

We propose a novel computational method for unit commitment UC, which does not require linearized approximation and provides several orders of magnitude performance improvement over current state-of-the-art. The performance improvement is achieved by introducing a heuristic tailored for UC problems. The method can be implemented using existing continuous optimization solvers and adapted for different applications. We demonstrate value of the new method in examples of advanced UC analyses at the scale where use of current state-of-the-art tools is infeasible. We expect that the capability demonstrated in this paper will be critical to address emerging power systems challenges with more volatile large loads, such as data centers, and generation that is composed of larger number of smaller units, including significant behind-the-meter generation.

Shaked Regev, Eve Tsybina, Slaven Peles

We expand our novel computational method for unit commitment (UC) to include long-horizon planning. We introduce a fast novel algorithm to commit hydro-generators, provably accurately. We solve problems with thousands of generators at 5 minute market intervals. We show that our method can solve interconnect size UC problems in approximately 1 minute on a commodity hardware and that an increased planning horizon leads to sizable operational cost savings (our objective). This scale is infeasible for current state-of-the-art tools. We attain this runtime improvement by introducing a heuristic tailored for UC problems. Our method can be implemented using existing continuous optimization solvers and adapted for different applications. Combined, the two algorithms would allow an operator operating large systems with hydro units to make horizon-aware economic decisions.

Slaven Peles, Kalyan S. Perumalla, Maksudul Alam et al.

While interior point methods have been the centerpiece of nonlinear programming tools used in science and engineering, their reliance on linear solvers that can tackle sparse symmetric indefinite and highly ill-conditioned problems made it difficult to implement them effectively on hardware accelerators. At this time, there are few sparse linear solvers that can be used in this context. Here, we present a novel formulation of an interior point method implemented in our HiOp library, which is designed to be able to run entirely on hardware accelerators. This formulation avoids dependence on sparse solvers altogether, which is achieved by compressing the underlying sparse linear problem into a dense one of manageable size. We demonstrate feasibility of this approach and provide a baseline for future interior point method implementations on hardware accelerators. Our investigation is motivated by problems arising in optimal power flow analysis in power systems engineering and our approach is tailored to the broad class of problems arising in that important domain. We also demonstrate utility of modern programming models based on performance portability libraries, namely, Umpire and RAJA. We discuss trade-offs between performance, portability and development cost in the solution space for this non-linear optimization problem. As a result of this research, we demonstrate for the first time that interior point methods for sparse problems can be efficiently realized on modern computing systems where more than 90% of processing power is in GPUs.