Learning-based MPC using Differentiable Optimisation Layers for Microgrid Energy Management

In this paper we present a learning-based Model Predictive Control (MPC) algorithm based on differentiable optimisation layers. Recent works show that it is possible to include an optimisation problem as a network layer in a Neural Network (NN) architecture. Here the MPC optimisation problem is integrated on the last layer of a NN which is used to estimate the uncertain parameters of the objective function. The NN is then trained online, end-to-end (E2E), based on previous control actions performance. We show that directly targeting the optimality of the control actions leads to improved control results with respect to the standard method of estimating the uncertain parameters and then perform the optimisation. The effectiveness of the proposed method is illustrated on a microgrid energy management problem where the future profile of the electricity price is not know

Distributed Methods for Estimation and Fault Diagnosis: the case of Large-scale Networked Systems

2011/2012L’obiettivo di questa tesi è il monitoraggio di sistemi complessi a larga-scala. L’importanza di questo argomento è dovuto alla rinnovata enfasi data alle problematiche riguardanti la sicurezza e l’affidabilità dei sistemi, diventate requisiti fondamentali nella progettazione. Infatti, la crescente complessità dei moderni sistemi, dove le relazioni fra i diversi componenti, con il mondo esterno e con il fattore umano sono sempre più importanti, implica una crescente attenzione ai rischi e ai costi dovuti ai guasti e lo sviluppo di approcci nuovi per il controllo e il monitoraggio. Mentre nel contesto centralizzato i problemi di stima e di diagnostica di guasto sono stati ampiamente studiati, lo sviluppo di metodologie specifiche per sistemi distribuiti, larga scala o “networked”, come i Cyber-Physical Systems e i Systems-of-Systems, è cominciato negli ultimi anni. Il sistema fisico è rappresentato come l’interconnessione di sottosistemi ottenuti attraverso una decomposizione del sistema complesso dove le sovrapposizioni sono consentite. L’approccio si basa sul modello dinamico non-lineare dei sottosistemi e sull’approssimazione adattativa delle non note interconnessioni fra i sottosistemi. La novità è la proposta di un’architettura unica che tenga conto dei molteplici aspetti che costituiscono i sistemi moderni, integrando il sistema fisico, il livello sensoriale e il sistema di diagnostica e considerando le relazioni fra questi ambienti e le reti di comunicazione. In particolare, vengono proposte delle soluzioni ai problemi che emergono dall’utilizzo di reti di comunicazione e dal considerare sistemi distribuiti e networked. Il processo di misura è effettuato da un insieme di reti di sensori, disaccoppiando il livello fisico da quello diagnostico e aumentando in questo modo la scalabilità e l’affidabilità del sistema diagnostico complessivo. Un nuovo metodo di stima distribuita per reti di sensori è utilizzato per filtrare le misure minimizzando sia la media sia la varianza dell’errore di stima attraverso la soluzione di un problema di ottimizzazione di Pareto. Un metodo per la re-sincronizzazione delle misure è proposto per gestire sistemi multi-rate e misure asincrone e per compensare l’effetto dei ritardi nella rete di comunicazione fra sensori e diagnostici. Poiché uno dei problemi più importanti quando si considerano sistemi distribuiti e reti di comunicazione è per l’appunto il verificarsi di ritardi di trasmissione e perdite di pacchetti, si propone una strategia di compensazione dei ritardi , basata sull’uso di Time Stamps e buffer e sull’introduzione di una matrice di consenso tempo-variante, che permette di gestire il problema dei ritardi nella rete di comunicazione fra diagnostici. Gli schemi distribuiti per la detection e l’isolation dei guasti sono sviluppati, garantendo la convergenza degli stimatori e derivando le condizioni sufficienti per la detectability e l’isolability. La matrice tempo-variante proposta permette di migliorare queste proprietà definendo delle soglie meno conservative. Alcuni risultati sperimentali provano l’efficacia del metodo proposto. Infine, le architetture distribuite per la detection e l’isolation, sviluppate nel caso tempo-discreto, sono estese al caso tempo continuo e nello scenario in cui lo stato non è completamente misurabile, sia a tempo continuo che a tempo discreto.This thesis deals with the problem of the monitoring of modern complex systems. The motivation is the renewed emphasis given to monitoring and fault-tolerant systems. In fact, nowadays reliability is a key requirement in the design of technical systems. While fault diagnosis architectures and estimation methods have been extensively studied for centralized systems, the interest towards distributed, networked, large-scale and complex systems, such as Cyber-Physical Systems and Systems-of-Systems, has grown in the recent years. The increased complexity in modern systems implies the need for novel tools, able to consider all the different aspects and levels constituting these systems. The system being monitored is modeled as the interconnection of several subsystems and a divide et impera approach allowing overlapping decomposition is used. The local diagnostic decision is made on the basis of the knowledge of the local subsystem dynamic model and of an adaptive approximation of the uncertain interconnection with neighboring subsystems. The goal is to integrate all the aspects of the monitoring process in a comprehensive architecture, taking into account the physical environment, the sensor layer, the diagnosers level and the communication networks. In particular, specifically designed methods are developed in order to take into account the issues emerging when dealing with communication networks and distributed systems. The introduction of the sensor layer, composed by a set of sensor networks, allows the decoupling of the physical and the sensing/computation topologies, bringing some advantages, such as scalability and reliability of the diagnosis architecture. We design the measurements acquisition task by proposing a distributed estimation method for sensor networks, able to filter measurements so that both the variance and the mean of the estimation error are minimized by means of a Pareto optimization problem. Moreover, we consider multi-rate systems and non synchronized measurements, having in mind realistic applications. A re-synchronization method is proposed in order to manage the case of multi-rate systems and to compensate delays in the communication network between sensors and diagnosers. Since one of the problems when dealing with distributed, large-scale or networked systems and therefore with a communication network, is inevitably the presence of stochastic delays and packet dropouts, we propose therefore a distributed delay compensation strategy in the communication network between diagnosers, based on the use of Time Stamps and buffers and the definition of a time-varying consensus matrix. The goal of the novel time-varying matrix is twofold: it allows to manage communication delays, packet dropouts and interrupted links and to optimize detectability and isolability skills by defining less conservative thresholds. The distributed fault detection and isolation schemes are studied and analytical results regarding fault detectability, isolability and estimator convergence are derived. Simulation results show the effectiveness of the proposed architecture. For the sake of completeness, the monitoring architecture is studied and adapted to different frameworks: the fault detection and isolation methodology is extended for continuous-time systems and the case where the state is only partially measurable is considered for discrete-time and continuous-time systems.XXV Ciclo198

An Online Learning Method for Microgrid Energy Management Control*

We propose a novel Model Predictive Control (MPC) scheme based on online-learning (OL) for microgrid energy management, where the control optimisation is embedded as the last layer of the neural network. The proposed MPC scheme deals with uncertainty on the load and renewable generation power profiles and on electricity prices, by employing the predictions provided by an online trained neural network in the optimisation problem. In order to adapt to possible changes in the environment, the neural network is online trained based on continuously received data. The network hyperparameters are selected by performing a hyperparameter optimisation before the deployment of the controller, using a pretraining dataset. We show the effectiveness of the proposed method for microgrid energy management through extensive experiments on real microgrid datasets. Moreover, we show that the proposed algorithm has good transfer learning (TL) capabilities among different microgrids

Resilient Microgrid Energy Management Algorithm Based on Distributed Optimization

This article proposes a fully distributed energy management algorithm for dc microgrids, resilient to different faults. Specifically, we employ distributed model-predictive control to deal with the uncertainty that characterizes the microgrid operation. The optimization problem is solved at each time step through a distributed optimization algorithm, which has three main advantages: 1) agents of the network require a small computational power; 2) local information is not shared among the network nodes, hence preserving a certain level of privacy; and 3) it is suitable for implementation in large-scale systems. The resilience property of the algorithm stems from additional constraints that are enforced in order to store in the system enough energy to sustain the microgrid in the case of utility grid or line fault. Simulation results show that the algorithm is suitable to schedule the operation of agents that are always connected to the microgrid (e.g., loads) as well as agents that may be connected and disconnected (e.g., electric vehicles)

Fault diagnosis for uncertain networked systems

Fault diagnosis has been at the forefront of technological developments for several decades. Recent advances in many engineering fields have led to the networked interconnection of various systems. The increased complexity of modern systems leads to a larger number of sources of uncertainty which must be taken into consideration and addressed properly in the design of monitoring and fault diagnosis architectures. This chapter reviews a model-based distributed fault diagnosis approach for uncertain nonlinear large-scale networked systems to specifically address: (a) the presence of measurement noise by devising a filtering scheme for dampening the effect of noise; (b) the modeling of uncertainty by developing an adaptive learning scheme; (c) the uncertainty issues emerging when considering networked systems such as the presence of delays and packet dropouts in the communication networks. The proposed architecture considers in an integrated way the various components of complex distributed systems such as the physical environment, the sensor level, the fault diagnosers, and the communication networks. Finally, some actions taken after the detection of a fault, such as the identification of the fault location and its magnitude or the learning of the fault function, are illustrated

A novel learning-based MPC with embedded profiles prediction for microgrid energy management

This paper presents a novel algorithm for microgrid energy management based on a differentiable learning-based Model Predictive Control (MPC) for jointly optimising profiles prediction and control performance. Specifically, we propose an algorithm for the online training of a Neural Network (NN) that predicts the unknown parameters of the MPC optimisation problem during control operation. Since the training is performed online at each time step the controller adapts to possible changes in the system parameters, while avoiding the offline training phase. Differently to standard methods in the literature, the proposed NN is trained by minimising a performance-based loss, i.e. the total cost of the energy trading with the utility grid. Simulation results show that the proposed approach outperforms the traditional approach minimising an estimation-only MSE loss, both when the model parameters are perfectly known and when they are uncertain

Decentralized state estimation for the control of network systems

The paper proposes a decentralized state estimation method for the control of network systems, where a cooperative objective has to be achieved. The nodes of the network are partitioned into independent nodes, providing the control inputs, and dependent nodes, controlled by local interaction laws. The proposed state estimation algorithm allows the independent nodes to estimate the state of the dependent nodes in a completely decentralized way. To do that, it is necessary for each independent node of the network to estimate the control input components computed by the other independent nodes, without requiring communication among the independent nodes. The decentralized state estimator, including an input estimator, is developed and the convergence properties are studied. Simulation results show the effectiveness of the proposed approach

Reducing false alarm rates in observer-based distributed fault detection schemes by analyzing moving averages

In this paper, we first analyze the possible limitations of a model-based fault detection method grounded on a partition-based distributed Luenberger observer. The corresponding fault detection test consists of comparing, for each time instant, the output prediction error with a suitable bound, computed analytically in a distributed and scalable way As a result, we highlight the presence of an often restrictive tradeoff between false-alarm and missed-detection rates. To overcome this significant drawback, we resort to a method based on the analysis of moving averages of residuals. Tests on an academic case study show the effectiveness of this approach