Distributed Frequency Control With Operational Constraints, Part I: Per-Node Power Balance

Abstract

Abstract-This paper addresses the distributed optimal frequency control of multi-area power system with operational constraints, including the regulation capacity of individual control area and the power limits on tie-lines. Both generators and controllable loads are utilized to recover nominal frequencies while minimizing regulation cost. We study two control modes: the per-node balance mode and the network balance mode. In Part I of the paper, we only consider the per-node balance case, where we derive a completely decentralized strategy without the need for communication between control areas. It can adapt to unknown load disturbance. The tie-line powers are restored after load disturbance, while the regulation capacity constraints are satisfied both at equilibrium and during transient. We show that the closed-loop systems with the proposed control strategies carry out primal-dual updates for solving the associated centralized frequency optimization problems. We further prove the closedloop systems are asymptotically stable and converge to the unique optimal solution of the centralized frequency optimization problems and their duals. Finally, we present simulation results to demonstrate the effectiveness of our design. In Part II of the paper, we address the network power balance case, where transmission congestions are managed continuously.

Distributed optimal load frequency control considering nonsmooth cost functions

“…We adopt a second-order linearized model to describe the frequency dynamics of each bus. We assume that the lines are lossless and adopt the DC power flow model [10,8]. For each bus j ∈ N, let θ j (t) denote the rotor angle at node j at time t and ω j (t) the frequency.…”

“…Assumption 1 could be further relaxed, since a nonstrictly convex function can be strictly convexified by using a nonlinear perturbation [21]. (8) allows the cost function f j (P l j ) to be nonsmooth, which is required to be differentiable in the existing literature [8,9,10,11,12,13,14]. Thus, the problem (8) is more general and suitable for a variety of real problems whose regulation costs are not smooth.…”

“…Recently, the so-called reverse engineering methodology is proposed by combining frequency control with optimal operation problems in power systems [4,5,6,7,8]. Under this framework, distributed load frequency control is widely investigated [8,9,10,11,12,13,14]. In [8], an optimal load frequency control problem is formulated and a distributed controller is derived using controllable loads to realize primary frequency control.…”

“…It only requires that the bus dynamics satisfy a passivity condition to guarantee asymptotic stability. In [10,12], the operational constraints including regulation capacity limits and tie-line power limits are considered, which guarantee both steady-state and transient capacity limit constraints. In [14], the distributed load frequency control under time-varying and unknown power injection is inves-tigated, which can recover the nominal frequency even under unknown disturbances.…”

Distributed Stability Conditions for Power Systems With Heterogeneous Nonlinear Bus Dynamics

“…However, with the proliferation of renewable and distributed energy technologies, the power systems will no longer be dominated by a few large SGs, but by massive small devices with various dynamical characteristics [4]. In such a power system with massive heterogeneous dynamics, traditional centralized methods may fail due to the computational burden, communication failures, or even privacy concerns [5]- [7]. Thus, it is necessary to develop distributed stability analytics which is adaptable to heterogeneity and scalability.…”