There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

This paper recalls a few past achievements in Model Predictive Control, gives an overview of some current developments and suggests a few avenues for future research.

Model Predictive Control

Convex bodies: the brunn–minkowski theory

http://bme2.aut.ac.ir/~towhidkhah/MPC/seminars-ppt/seminar%20MPC/Fazane%20karami/Reference/Architectures%20for%20distributed%20and%20hierarchical%20Model%20Predictive%20Control%20%e2%80%93%20A%20review.pdf

Architectures for distributed and hierarchical Model Predictive Control - A review

Historically, centrally computed algorithms have been the primary means of power system optimization and control. With increasing penetrations of distributed energy resources requiring optimization and control of power systems with many controllable devices, distributed algorithms have been the subject of significant research interest. This paper surveys the literature of distributed algorithms with applications to optimization and control of power systems. In particular, this paper reviews distributed algorithms for offline solution of optimal power flow (OPF) problems as well as online algorithms for real-time solution of OPF, optimal frequency control, optimal voltage control, and optimal wide-area control problems.

https://ieeexplore.ieee.org/ielaam/5165411/8075182/7990560-aam.pdf

A Survey of Distributed Optimization and Control Algorithms for Electric Power Systems

The existence of locally optimal solutions to the AC optimal power flow problem (OPF) has been a question of interest for decades This paper presents examples of local optima on a variety of test networks including modified versions of common networks We show that local optima can occur because the feasible region is disconnected and/or because of nonlinearities in the constraints Standard local optimization techniques are shown to converge to these local optima The voltage bounds of all the examples in this paper are between ±5% and ±10% off-nominal The examples with local optima are available in an online archive (http://wwwmathsedacuk/optenergy/LocalOpt/) and can be used to test local or global optimization techniques for OPF Finally we use our test examples to illustrate the behavior of a recent semi-definite programming approach that aims to find the global solution of OPF

/pdf/local-solutions-of-the-optimal-power-flow-problem-mpqu5fm0vi.pdf

Local Solutions of the Optimal Power Flow Problem

In this paper, a flexible optimization-based framework for intentional islanding is presented. The decision is made of which transmission lines to switch in order to split the network while minimizing disruption, the amount of load shed, or grouping coherent generators. The approach uses a piecewise linear model of AC power flow, which allows the voltage and reactive power to be considered directly when designing the islands. Demonstrations on standard test networks show that solution of the problem provides islands that are balanced in real and reactive power, satisfy AC power flow laws, and have a healthy voltage profile.

Optimization-Based Islanding of Power Networks Using Piecewise Linear AC Power Flow

This article presents a new form of robust distributed model predictive control (MPC) for multiple dynamically decoupled subsystems, in which distributed control agents exchange plans to achieve satisfaction of coupling constraints. The new method offers greater flexibility in communications than existing robust methods, and relaxes restrictions on the order in which distributed computations are performed. The local controllers use the concept of tube MPC – in which an optimisation designs a tube for the system to follow rather than a trajectory – to achieve robust feasibility and stability despite the presence of persistent, bounded disturbances. A methodical exploration of the trades between performance and communication is provided by numerical simulations of an example scenario. It is shown that at low levels of inter-agent communication, distributed MPC can obtain a lower closed-loop cost than that obtained by a centralised implementation. A further example shows that the flexibility in communication...

/pdf/distributed-model-predictive-control-of-linear-systems-with-4sdna5ld7t.pdf

Paul Trodden

Papers

Local Solutions of the Optimal Power Flow Problem

Optimization-Based Islanding of Power Networks Using Piecewise Linear AC Power Flow

Distributed model predictive control of linear systems with persistent disturbances

Model predictive control system design and implementation for spacecraft rendezvous

Cooperative distributed MPC of linear systems with coupled constraints