A computational comparison of 2 mathematical formulations to handle transmission network constraints in the unit commitment problem

Abstract

Summary Until recently, transmission network constraints have been incorporated into the unit commitment (UC) problem (security‐constrained UC [SCUC]) using the classical direct current (DC)–based equation. This paper proposes a new formulation to model network constraints in the UC problem by using the power transfer distribution factor (PTDF). The classical formulation uses the binary commitment status, the power generation, and the voltage‐phase angles as decision variables. For the proposed formulation, the nodal balance equality constraints are modeled using one equality constraint, and the transmission network constraints have been modeled using the PTDF and the active power generation (decision variables). The main advantage of this formulation is the reduction of decision variables in the operation problem in comparison with the classical DC formulation. Transmission losses, using a piecewise linear approximation, are included in the SCUC problem as well. Both formulations are validated and tested on the Institute of Electrical and Electronics Engineers (IEEE) 14‐bus, the IEEE 30‐bus, the IEEE 57‐bus, and the IEEE 118‐bus. The IEEE 14‐bus and IEEE 57‐bus systems are used to compare the loss and the lossless models. The results show that the PTDF‐based formulation, which requires fewer continuous variables and equality constraints than the classical DC formulation, reduces the simulation time without sacrificing optimality. The results also demonstrate the feasibility of the proposed formulation to address the SCUC problem and its potential applicability to medium‐scale and large‐scale power systems.

Estimating B‐coefficients of power loss formula considering volatile power injections: an enhanced least square approach

“…where A ∈ ℝ N × n g is the adjacent matrix of generators with A mn = 1 if generator m is connected to bus n and A mn = 0 otherwise; P D is the vector of all nodal loads; P A ∈ ℝ N and B v ∈ ℝ N × N are constant parameter vector and matrix, respectively, which will be explained later on. Combing (5) and (8), the power loss can be calculated as…”

“…Noticing that power loss is actually equivalent to the difference between total power injections and system load, one can calculate it exactly by solving a set of non-linear AC-power flow (AC-PF) equations or an ACconstrained optimal power flow (AC-OPF) problem [4][5][6]. Nevertheless, due to the intrinsic non-linearity and non-convexity of AC-PF and AC-OPF, solving such problems turns to be computationally challenging, particularly in large-scale decisionmaking problems such as economic dispatch (ED) and unit commitment (UC) [7,8]. Fortunately, since ED or UC problems in practice focus on the active power related issues, DC-power flow (DC-PF) can be used to well approximate the AC-PF.…”

An efficient solution method for integrated unit commitment and natural gas network operational scheduling under “Duck Curve”

“…Thus, one may find similar constraints and functions in other studies such as Refs. 13‐15. However, for the sake of completeness of our work, we present and explain them.…”

Comparison of different model formulations for modelling future power systems with high shares of renewables – The Dispa-SET Balkans model

“…It should be noted that there are already several formulations available in the literature. One such article compares two mathematical formulations of SCUC [48] and demonstrates their potential applicability to medium-scale and large-scale power systems. Meus et al [49] has proven that simplified formulations provide identical results to a traditional binary unit commitment formulation but this assumption only holds for portfolio not restricted by start-up and shut-down limitations.…”