Risk-limiting power grid control with an ARMA-based prediction model

Abstract

Abstract-This paper is concerned with the risk-limiting operation of electric power grids with stochastic uncertainties due to, for example, demand and integration of renewable generation. The main contribution is incorporating autoregressive-moving-average (ARMA) type prediction models for the underlying uncertainties into chance-constrained, finitehorizon optimal control. This uncertainty model leads to a more (compared to existing work in literature) careful treatment of correlation in time which is significant especially in renewable generation yet has attracted limited attention. The paper first discusses how the resulting chance-constrained optimization problems can be solved computationally and demonstrates the effects of the use of the proposed prediction models through simulation-based case studies with realistic data.

Stochastic linear Model Predictive Control with chance constraints – A review

“…. ., t + N − 1 and for all i > 1 in (13), and K k|t = K =− a/b for all k ≥ 0 in ( 14) and ( 16)) we obtain that, for all k ≥ t e k+1 = w k (27) which implies that Var{e t+k } = W and that e t ∈ [− w, w] for all k ≥ 0. Neglecting the recursive feasibility issues for simplicity, to enforce (8) for all possible realizations of w t+k .…”

“…The use of chance constrained optimization and stochastic MPC has been considered as a promising solution in a number of application domains, such as water reservoir management [5][6][7], temperature and HVAC control in buildings [8][9][10][11][12][13][14][15][16][17], process control [18][19][20][21][22], power production, management, and supply in systems with renewable energy sources [23][24][25][26][27][28][29][30][31][32][33][34], cellular networks management [35], driver steering, scheduling, and energy management in vehicles [36][37][38][39][40][41][42][43][44], path planning and formation control [45][46][47][48], air traffic control [49], inventory control and supply chain management [50][51]…”

On the comparison of stochastic model predictive control strategies applied to a hydrogen-based microgrid

“…CC-MPC uses an explicit probabilistic modeling of the system disturbances to calculate explicit bounds on the system constraint satisfaction. For instance, [26] presents a chanceconstrained two-stage stochastic program for unit commitment with uncertain wind power output and [27] shows an autoregressive-moving-average (ARMA) type prediction model for the underlying uncertainties (load/generation) into chance-constrained finite-horizon optimal control. An application of this technique in the context of the drinking water network of the city of Barcelona is reported in [28].…”

Comprehensive decoupled risk-limiting dispatch

“…problem with ramping constraints, energy storage and congested networks. Reference [11] incorporated auto-regressivemoving-average type prediction models into the risk-limiting control, while reference [12] considered optimal curtailing of intermittent sources. A risk-limiting optimal power flow problem for power systems with high penetration of wind power was formulated in reference [13].…”