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Fast Relax-and-Round Unit Commitment with Economic Horizons

Shaked Regev, Eve Tsybina, Slaven Peles

Abstract

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.

Fast Relax-and-Round Unit Commitment with Economic Horizons

Abstract

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.
Paper Structure (8 sections, 4 theorems, 8 equations, 6 figures, 2 algorithms)

This paper contains 8 sections, 4 theorems, 8 equations, 6 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. Horizon-Aware Unit Commitment
  3. Mathematical Formulation
  4. Simulation and Results
  5. Hydro-generator commitment
  6. Mathematical Formulation
  7. Simulation and Results
  8. Conclusion and Further Work

Key Result

Theorem 1

$\text{Var}(\Bar{D}_\mathcal{T})-\text{Var}(\Bar{D}^*_\mathcal{T})\leq K^2+2K\sqrt{\text{Var}(\Bar{D}^*_\mathcal{T})}$.

Figures (6)

  • Figure 1: Unit $i$'s typical production cycle. When on, $P_i\in [P_{\min,i},P_{\max,i}]$, though it cannot exceed its ramping power. It can turn off if $P_{t-1,i}-r_{d,i}\leq P_{\min,i}$. The only other decision can be made when the unit is off, to start ramping up. During other periods, it is uncontrollable.
  • Figure 2: RRUC's objective and runtime scaling of with different FPMs. Runtime increases roughly linearly and the objective levels off. This motivates taking a demand sample $D_\delta$ instead of all demands in \ref{['eq:deltaD_UC']}.
  • Figure 3: Objective and runtime scaling of the 3-FPM. The 3-FPM retains accuracy nearly perfectly at scale. The worse objective over 1 day compared to 7 shows likely comes from optimizing for periods outside the time window. RRUC's runtime scales $\approx O(n^{1.5})$ in the number of units. It can solve interconnect sized problems in $\approx 1$ minute.
  • Figure 4: \ref{['alg:hydrocommit']}'s normalized objective and runtime varying the number of days and generators. Its performance is stable as the demand (and number of generators to supply it) increase and in optimizing over longer stretches. Its runtime increases linearly in the number of generators, and slightly faster than linearly in the number of days (or periods) as \ref{['thm:runtime']} guarantees.
  • Figure 5: The normalized objective and runtime of \ref{['alg:ramp']} after running \ref{['alg:hydrocommit']} with comparison to just \ref{['alg:ramp']}. (Top) \ref{['alg:ramp']} maintains accuracy and scales well. (Bottom) Hydro-generation lowers costs more than $3\times$ its relative part of generation.
  • ...and 1 more figures

Theorems & Definitions (6)

  • Theorem 1
  • proof
  • Corollary 1
  • Corollary 2
  • Theorem 2
  • proof