Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · nlin/0409038

Modeling Uncertainties in Aggregated Thermostatically Controlled Loads Using a State Queueing Model

Ning Lu·David P. Chassin·Steve E. Widergren
View original source ↗Read source document ↗Export metadata ↓

Abstract

To study the impacts of price responsive demand on the electric power system requires better load models. This paper discusses the modeling of uncertainties in aggregated thermostatically controlled loads using a state queueing (SQ) model. The cycling times of thermostatically controlled appliances (TCAs) vary with the TCA types and sizes, as well as the ambient temperatures. The random consumption of consumers, which shortens or prolongs a specific TCA cycling period, introduces another degree of uncertainty. By modifying the state transition matrix, these random factors can be taken into account in a discrete SQ model. The impacts of considering load diversity in the SQ model while simulating TCA setpoint response are also studied.

Explore related subjects

nlin.CDnlin.AO

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Ning Lu, David P. Chassin, Steve E. Widergren. 2004-09-19. Modeling Uncertainties in Aggregated Thermostatically Controlled Loads Using a State Queueing Model. https://doi.org/10.1109/tpwrs.2005.846072

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Trigonometric Nosé--Hoover oscillator: chaos, periodic orbits and integrability

We introduce a trigonometric version of the Nosé-Hoover oscillator in which the quadratic mechanical terms and unbounded thermostat coupling are replaced by bounded trigonometric functions. This formulation replaces the harmonic potential by a pendulum-type potential and confines the thermostat interaction to a bounded periodic form. The resulting two-parameter system is naturally defined on the three-dimensional torus and reduces near the origin, to leading order, to the classical polynomial Nosé-Hoover model. We investigate its global dynamics using Poincaré sections, bifurcation diagrams, Lyapunov spectra, Kaplan-Yorke dimensions, and the Lyapunov Integrability Test (LIT). The numerical results reveal the coexistence of regular and chaotic dynamics and characterize changes in dissipative behavior across the parameter plane. We then analyze the two limiting cases associated with the parameter axes. For $a=0$, we construct two functionally independent first integrals on regular domains, whereas for $b=0$ the dynamics reduces to a family of two-dimensional systems on invariant tori, which are analyzed using Darboux polynomials and exponential factors. First-order averaging near the intersection of these integrable limits yields periodic solutions bifurcating from unperturbed periodic orbits and an obstruction to regular $C^1$ first integrals in their neighborhoods. Independently, differential Galois theory applied to the normal variational equation, together with the Ayoul-Zung and Li-Shi criteria, excludes meromorphic $B$-integrability and non-constant meromorphic first integrals near a particular non-equilibrium phase curve for $ab\neq0$. Thus, despite retaining the local structure of the classical Nosé-Hoover oscillator, its trigonometric counterpart exhibits markedly different global dynamics and integrability.

nlin.CD↗
arXiv2026

Experimental detection of energy transfer into the antiphase mode in a branched double pendulum

Multiple pendulum with branching is proposed as a convenient platform to study energy transfer between different modes. The antiphase oscillation mode is localized to the "child" links, which makes it easy to prepare initial conditions without exciting the antiphase mode. A manageable expression for the energy transfer is derived theoretically and evaluated with experimental data.

nlin.CD↗
arXiv2026

A New Route to Chaos through the Geometric Composition of Non-Normal Amplification

Chaos emerges when stretching is repeatedly recycled by reinjection. We uncover a new route to chaos in which the decisive variable is the temporal order of non-normal tangent maps: periodic and chaotic states can share essentially the same one-step stretching statistics while their ordered products acquire opposite Lyapunov growth. We introduce the ordered-product growth rate $h_L$ over $L$ successive tangent maps, which reveals how states indistinguishable at one step separate under geometric composition and identifies the finite composition scale at which chaos emerges. We use this mechanism to establish a new form of global chaos control: minute phase actions reorient the successive non-normal amplification directions so that their geometric composition becomes contracting, suppressing chaos at fixed dissipation without reducing local amplification or targeting a preselected orbit.

nlin.CD↗