Distributed LQR Design for a Class of Large-Scale Multi-Area Power Systems

Abstract

Load frequency control (LFC) is one of the most challenging problems in multi-area power systems. In this paper, we consider power system formed of distinct control areas with identical dynamics which are interconnected via weak tie-lines. We then formulate a disturbance rejection problem of power-load step variations for the interconnected network system. We follow a top-down method to approximate a centralized linear quadratic regulator (LQR) optimal controller by a distributed scheme. Overall network stability is guaranteed via a stability test applied to a convex combination of Hurwitz matrices, the validity of which leads to stable network operation for a class of network topologies. The efficiency of the proposed distributed load frequency controller is illustrated via simulation studies involving a six-area power system and three interconnection schemes. In the study, apart from the nominal parameters, significant parametric variations have been considered in each area. The obtained results suggest that the proposed approach can be extended to the non-identical case.

Probabilistic Decentralised Control and Message Passing Framework for Future Grid

“…Ri with D i being the load dependency factor and R i being the speed droop [14], [15]. According to Equation (6), we can see that y i , which is also referred to as area control error (ACE) [14], is the summation of the frequency deviation ∆f i multiplied by β i and the total tie-line power inflow ∆P tie,i . Augmenting the state vector defined in Equation 5with the performance variable y i , yields the following statespace representation,…”

“…andQ i is the covariance of the noise i k−1 . Conspicuously, the state of control area i is determined by both Equations (12) and (14). For the LFC problem considered in this paper, the aim is to design a control strategy that maintains the frequency and power of local area i around their nominal values.…”

“…For the LFC problem considered in this paper, the aim is to design a control strategy that maintains the frequency and power of local area i around their nominal values. Since complete information about the state of local area i can be only obtained using pdfs as specified in Equations (12) and (14), the control law needs to be ideally derived using a probabilistic framework. This can be achieved by defining the performance measure to be optimised as the Kullback-Leibler divergence (KLD) between the actual joint pdf of the closed loop description of the dynamics of area i and a predefined ideal joint pdf,…”

“…Theorem 1. The pdf of the optimal randomised controller minimising the cost-to-go function (21) subject to the pdfs describing the dynamics of control area i given by Equations (12) and (14), and ideal distributions of area i dynamics and control input given by Equations (27) and (28) respectively, is given by,…”

“…Based on the derived randomised controller (29) and the probabilistic models of the control areas (12) and (14), the details of the message passing methodology and how local controllers harmonise their actions to contribute to the objective of maintaining the frequency of the grid network at its nominal value and meeting demand requirements will be introduced in the next section.…”