Edo Abraham

Optimal Active Control and Optimization of a Wave Energy Converter

This paper investigates optimal active control schemes applied to a point absorber wave energy converter within a receding horizon fashion. A variational formulation of the power maximization problem is adapted to solve the optimal control problem. The optimal control method is shown to be of a bang-bang type for a power takeoff mechanism that incorporates both linear dampers and active control elements. We also consider a direct transcription of the optimal control problem as a general nonlinear program. A variation of the projected gradient optimization scheme is formulated and shown to be feasible and computationally inexpensive compared to a standard NLP solver. Since the system model is bilinear and the cost function is not convex quadratic, the resulting optimization problem is not a quadratic program. Results will be compared with an optimal command latching method to demonstrate the improvement in absorbed power. All time domain simulations are generated under irregular sea conditions.

A Graph-Theoretic Framework for Assessing the Resilience of Sectorised Water Distribution Networks

Water utilities face a challenge in maintaining a good quality of service under a wide range of operational management and failure conditions. Tools for assessing the resilience of water distribution networks are therefore essential for both operational and maintenance optimization. In this paper, a novel graph-theoretic approach for the assessment of resilience for large scale water distribution networks is presented. This is of great importance for the management of large scale water distribution systems, most models containing up to hundreds of thousands of pipes and nodes. The proposed framework is mainly based on quantifying the redundancy and capacity of all possible routes from demand nodes to their supply sources. This approach works well with large network sizes since it does not rely on precise hydraulic simulations, which require complex calibration processes and computation, while remaining meaningful from a physical and a topological point of view. The proposal is also tailored for the analysis of sectorised networks through a novel multiscale method for analysing connectivity, which is successfully tested in operational utility network models made of more than 100,000 nodes and 110,000 pipes.

WaterBox: A Testbed for Monitoring and Controlling Smart Water Networks

Smart water distribution networks are a good example of a large scale Cyber-Physical System that requires monitoring for precise data analysis and network control. Due to the critical nature of water distribution, an extensive simulation of decision making and control algorithms are required before their deployment. Although some aspects of water network behaviour can be simulated in software such as hydraulic responses in valve changes, software simulators are unable to include dynamic events such as leakages or bursts in physical models. Furthermore, due to safety concerns, contemporary large-scale testbeds are limited to the monitoring processes or control methods with well established safety guarantees. Sophisticated algorithms for dynamic and optimal water network reconfiguration are not yet widespread. This paper presents a small-scale testbed, WaterBox, which allows the simulation of emerging/advanced monitoring and control algorithms in a fail-safe environment. The flexible hydraulic, hardware, and software infrastructure enables a substantial number of experiments. On-going experiments are related to in-node data processing and decision making, energy optimization, event-driven communication, and automatic control.

Control of water distribution networks with dynamic DMA topology using strictly feasible sequential convex programming

The operation of water distribution networks (WDN) with a dynamic topology is a recently pioneered approach for the advanced management of District Metered Areas (DMAs) that integrates novel developments in hydraulic modeling, monitoring, optimization, and control. A common practice for leakage management is the sectorization of WDNs into small zones, called DMAs, by permanently closing isolation valves. This facilitates water companies to identify bursts and estimate leakage levels by measuring the inlet flow for each DMA. However, by permanently closing valves, a number of problems have been created including reduced resilience to failure and suboptimal pressure management. By introducing a dynamic topology to these zones, these disadvantages can be eliminated while still retaining the DMA structure for leakage monitoring. In this paper, a novel optimization method based on sequential convex programming (SCP) is outlined for the control of a dynamic topology with the objective of reducing average zone pressure (AZP). A key attribute for control optimization is reliable convergence. To achieve this, the SCP method we propose guarantees that each optimization step is strictly feasible, resulting in improved convergence properties. By using a null space algorithm for hydraulic analyses, the computations required are also significantly reduced. The optimized control is actuated on a real WDN operated with a dynamic topology. This unique experimental program incorporates a number of technologies set up with the objective of investigating pioneering developments in WDN management. Preliminary results indicate AZP reductions for a dynamic topology of up to 6.5% over optimally controlled fixed topology DMAs.

Sparse Null Space Algorithms for Hydraulic Analysis of Large Scale Water Supply Networks

AbstractIn this article, a comprehensive review of existing methods is presented and computationally efficient sparse null space algorithms are proposed for the hydraulic analysis of water distribution networks. The linear systems at each iteration of the Newton method for nonlinear equations are solved using a null space algorithm. The sparsity structure of these linear equations, which arises from the sparse network connectivity, is exploited to reduce computations. A significant fraction of the total flops in the Newton method are spent in computing pipe head losses and matrix-matrix multiplications involving flows. Because most flows converge after a few iterations, a novel partial update of head losses and matrix products is used to further reduce computational complexity. Convergence analyses are also presented for the partial-update formulas. A new heuristic for reducing the number of pressure head computations of a null space method is proposed. These savings enable fast near-real-time control of ...

Optimal active control of a wave energy converter

This paper investigates optimal active control schemes applied to a point absorber wave energy converter within a receding horizon fashion. A variational formulation of the power maximization problem is adapted to solve the optimal control problem. The optimal control method is shown to be of a bang-bang type for a power take-off mechanism that incorporates both linear dampers and active control elements. We also consider a direct transcription of the optimal control problem as a general nonlinear program. A variation of the projected gradient optimization scheme is formulated and shown to be feasible and computationally inexpensive compared to a standard NLP solver. Since the system model is bilinear and the cost function is non-convex quadratic, the resulting optimization problem is not a convex quadratic program. Results will be compared with an optimal command latching method to demonstrate the improvement in absorbed power. Time domain simulations are generated under irregular sea conditions.

Lower-Order

We propose an optimization-based method for designing a lower order Luenberger-type state estimator, while providing L2-gain guarantees on the error dynamics when the estimator is used with the higher order system. Suitable filter parameters can be computed by modelling the bilinear system as a linear differential inclusion and solving a set of bilinear matrix inequality constraints. Since these constraints are nonconvex, in general, we also show that one can solve a suitably defined semi-definite program to compute a bound on the level of suboptimality. The design method also allows one to explicitly take account of linear parameter uncertainties in order to provide a priori robustness guarantees. The H-infinity estimator not only has lower real-time computational requirements compared with a Kalman filter, but also does not require knowledge of the noise spectrum. For a numerical example, we consider the estimation of the radiation force for a wave energy converter, where a low-order model is used to approximate the radiation dynamics.

H_\infty

Water utilities can achieve significant savings in operating costs by optimising pump scheduling to improve efficiency and shift electricity consumption to low-tariff periods. Due to the complexity of the optimal scheduling problem, heuristic methods that cannot guarantee global optimality are often applied. This paper investigates formulations of the pump scheduling problem solved using a branch and bound method. Piecewise linear component approximations outperform non-linear approximations within application driven accuracy bounds and demand uncertainties. It is shown that the reduction of symmetry through the grouping of pumps significantly reduces the computational effort, whereas loops in the network have the opposite effect. The computational effort of including convex, non-linear pump operating, and maintenance cost functions is investigated. Using case studies, it is shown that linear and fixed-cost functions can be used to find schedules which, when simulated in a full hydraulic simulation, have performances that are within the solver optimality gap and the uncertainty of demand forecasts.

Filter Design for Bilinear Systems with Bounded Inputs

Many sequential mathematical optimization methods and simulation-based heuristics for optimal control and design of water distribution networks rely on a large number of hydraulic simulations. In this paper, we propose an efficient inexact subspace Newton method for hydraulic analysis of water distribution networks. By using sparse and well-conditioned fundamental null space bases, we solve the nonlinear system of hydraulic equations in a lower-dimensional kernel space of the network incidence matrix. In the inexact framework, the Newton steps are determined by solving the Newton equations only approximately using an iterative linear solver. Since large water network models are inherently badly scaled, Jacobian regularization is employed to improve the condition number of these linear systems and guarantee positive definiteness. After presenting a convergence analysis of the regularized inexact Newton method, we use the conjugate-gradient (CG) method to solve the sparse reduced Newton linear systems. Since CG is not effective without good preconditioners, we propose tailored constraint preconditioners that are computationally cheap because they are based only on invariant properties of the null-space linear systems and do not change with flows and pressures. The preconditioners are shown to improve the distribution of eigenvalues of the linear systems and so enable a more efficient use of the CG solver. Since contiguous Newton iterates can have similar solutions, each CG call is warm-started with the solution for a previous Newton iterate to accelerate its convergence rate. Operational network models are used to show the efficacy of the proposed preconditioners and the warm-starting strategy in reducing computational effort.

Exploring Optimal Pump Scheduling in Water Distribution Networks with Branch and Bound Methods

This paper investigates low-order observer design for bilinear systems with input constraints. A bilinear Luenberger-type observer with an H-infinity performance measure is formulated and the resulting synthesis problem is posed as a matrix inequality optimization for a linear parameter varying system. The resulting (nonconvex) bilinear matrix inequality problem is then solved with an LMI-based algorithm to find low-order nominal and robust quadratically stable observers. The performance of these observers are compared with that of a Kalman filter. In addition to alleviating the need to know the noise spectrum and its lower real-time computational burden, the H-infinity filter is shown to be robust to model uncertainties. The online radiation force estimation problem for a wave energy converter with bilinear dynamics is considered as an example.