The Interval Stability of an Electricity Market Model

Abstract

Combined with the electric power market dynamic model put forward by Alvarado, an interval model of electricity markets is established and investigated in this paper pertaining to the range of demand elasticity with suppliers and consumers. The stability of an electricity market framework with demand elasticity interval is analyzed. The conclusions characterizing the interval model provided are derived by constructing a suitable Lyapunov function and using the theory of interval dynamical system in differential equations and matrix inequality theory and so forth. Applying the corollary obtained can judge the system stability by available data about demand elasticity. The obtained results are validated and illustrated by a case example.

Stability of the Stochastic Model for Power Markets with Interval Parameters

“…If = 0, then the model gets rid of random factors and becomes a deterministic model, which agrees with the theorem in [24]. So we can see that the mean interval stable Theorem 8 and Corollary 9 are a generalization of [24,25].…”

“…Then, the stability determine condition of model (12) can be simplified as max ( T 33 3 33 ) < 0; that is to say, all eigenvalues of 3 are negative, which is consistent with Theorem 2 in [10] and theorem in [25]. If = 0, then the model gets rid of random factors and becomes a deterministic model, which agrees with the theorem in [24]. So we can see that the mean interval stable Theorem 8 and Corollary 9 are a generalization of [24,25].…”

“…Finally, the validity of results is verified by using exact power market examples and stimulation analysis in Matlab. The results generate conclusions about power market certainty models [8], interval models [24], and stochastic models [25].…”

“…The random excitation can be deemed as power demand stochastic fluctuation caused by objective factors, and these fluctuation are presumed to be Gaussian Wiener process generally. (12), it can be simplified to the deterministic dynamic model proposed by Alvarado in [8], the interval dynamic system model in [24] and the stochastic dynamic model for power market in [25], respectively. Therefore, the model for power market (12) considering both the randomness of power demand and interval features of demand elasticity for suppliers and consumers, is a generalization of deterministic model, interval model and stochastic model proposed by Alvarado, instead of only considering one of the interval or stochastic features.…”

“…In [22,23], -moment stability of power system is also discussed. In the power market, considering that demand elasticity is uncertain and ranging within interval, a power market interval model is described, and the conditions to determine the interval stability are provided in [24]. In [25], a class of power market stochastic dynamic model is presented, and the conditions to determine the mean stability are provided considering the randomness of the electricity demanding.…”