Search arXivSearch

arXiv · 2010.07600

Modeling electricity demand, welfare function and elasticity of electricity demand based on the customers risk aversion behavior

Abstract

Nowadays, attitudes towards electricity customers have been changed, so that they are no longer considered static players. The customers behavior identification is vital for establishing modern power systems. This paper utilizes the customers risk aversion coefficient to model their consumption behavior. Through the coefficients, the value of electricity consumption is measured employing the concept of the utility function. The utility function is an essential concept in microeconomics that measures customers preferences and interprets how a rational consumer would make consumption decisions. Based on the utility function, an economic load model and the customers welfare function are formulated. The load model is utilized to estimate price elasticity, and income elasticity of electricity demand. The results illustrated as the risk aversion coefficient increases, the consumers achieve more satisfaction from the consumption. Electricity consumption will be complement (substitute) if the risk aversion coefficient is greater (lower) than the unit. For the unit risk aversion coefficient, the cross-price elasticity will be zero, which means the consumption is independent of the other period demand. The results illustrated electricity price increment neutralizes the income increment effect on consumption. Hence, to study electricity consumption, the price and income variations should be considered, simultaneously.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Amir Niromandfam, Saeid Pashaei Choboghloo. 2020-10-15. Modeling electricity demand, welfare function and elasticity of electricity demand based on the customers risk aversion behavior. https://arxiv.org/abs/2010.07600

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

KEEP EXPLORING

Related papers

Constrained Feedback Control of Nonlinear Systems via Approximate HJB and Control Barrier Functions

This paper presents a two-stage framework for constrained feedback control of input-affine nonlinear systems. Offline, an approximate value function for the unconstrained problem is computed, for example using Hamilton--Jacobi--Bellman (HJB)-based policy iteration. Online, the proposed quadratic program (QP) minimizes the pre-Hamiltonian evaluated using the approximate value-function gradient subject to safety constraints enforced by control barrier functions (CBFs). This architecture decouples performance optimization from constraint enforcement, allowing constraints to be modified without recomputing the value function. As in CBF-QP architectures based on control Lyapunov functions (CLFs), safety is enforced as a hard constraint; however, the performance objective targets approximate optimality rather than a prescribed Lyapunov decay. Numerical results on a linear 2-state hovercraft and a nonlinear 9-state spacecraft attitude-control problem show agreement with the constrained open-loop optimal control problem (OCP) benchmark in the linear case, and performance close to the OCP benchmark, improving on CLF-based controllers, in the nonlinear case.

eess.SY

Rao-Blackwellized Stein Gradient Descent for Joint State-Parameter Estimation

We present a filtering framework for online joint state estimation and parameter identification in nonlinear, time-varying systems. The algorithm uses a Rao-Blackwellization technique to infer joint state-parameter posteriors efficiently. In particular, conditional state distributions are computed analytically via Kalman filtering, while model parameters, including the measurement-noise covariance, are approximated using particle-based Stein Variational Gradient Descent (SVGD), enabling stable real-time inference. To handle parameters subject to physical constraints, we further introduce constrained variants that enforce them through an alternating direction method of multipliers (ADMM) splitting of the SVGD update, including nonlinear equality constraints that standard particle filters cannot readily handle. We derive a stability bound that relates the approximation error in the parameter posterior to the resulting error in the marginal state distribution. Performance of the proposed filters is validated on three case studies: a fed-batch bioreactor with Haldane kinetics and a damped pendulum, both under physical constraints, and a neural-network-augmented dynamic system. The examples cover parameter estimation under inequality and equality constraints and online neural-network training within a dynamical model.

eess.SY

Firing Rate Neural Network Implementations of Model Predictive Control

Human and animal brains perform planning to enable complex movements and behaviors, a process that can be effectively described using model predictive control (MPC). How could the brain physically implement MPC? In this work, we translate model predictive controllers into firing rate neural networks, offering insights into the nonlinear neural dynamics that underpin planning. We propose a constructive method; no training is required. This is done first applying the projected gradient method to the dual problem to derive a baseline neural network implementation. We then use factorization and contraction analysis to systematically generate alternative network architectures; in other words, we systematically generate hypotheses for how planning is done in the brain via neural dynamics. Finally, we present numerical simulations to study different neural networks performing MPC to balance an inverted pendulum on a cart (i.e., balancing a stick on a hand), including one example in which imposing sparse connectivity (a property observed in brain networks) does not degrade control performance.

eess.SY