Heuristics for Lagrangian Relaxation Formulations for the Unit Commitment Problem

The expansion of distributed energy resources (DER), demand response (DR), and virtual bidding in many power systems and energy markets are creating new challenges for unit commitment (UC) and economic dispatch (ED) techniques. Instead of a small number of traditionally large generators, the power system resource mix is moving to one with a high percentage of a large number of small units. These can increase the number of similar or identical units, leading to chattering (switching back and forth among committed units between iterations). This research investigates alternative and scalable ways of increasing the high penetration of these resources.

First, the mathematical formulations for UC and ED models are reviewed. Then a new heuristic is proposed that takes advantage of the incremental nature of Lagrangian relaxation (LR). The heuristic linearizes and distributes the network transmission losses to appropriately penalize line flow and mitigate losses.

Second, a mixed integer programming (MIP) is used as a benchmark for the proposed LR formulation. The impact of similar and identical units on the solution quality and simulation run time of UC and ED was investigated using the proposed formulation.

Third, a system flexibility study is done using DR and a load demand pattern with a high penetration of renewables, creating a high daily ramp rate requirement. This work investigates the impact of available DR on spikes in locational marginal pricing (LMP).

Fourth, two studies are done on improving LR computational efficiency. The first proposes a heuristic that focuses on trade-offs between solution quality and simulation run time. The heuristic iterates over lambda and energy marginal price while the convergence issue is handled using Augmented LR (ALR). The second study proposes a heuristic that penalizes transmission lines with binding line limits. The proposed method can reduce power flow in the transmission lines of interest, and considerably reduce the simulation time in optimization problems with a high number of transmission constraints.

Finally, the effect of a large number of similar and identical units on simulation run time is considered. The proposed formulation scales linearly with the increase in system size.