Optimal Control of Transient Flow in Natural Gas Networks

We outline a new control system model for the distributed dynamics of compressible gas flow through large-scale pipeline networks with time-varying injections, withdrawals, and control actions of compressors and regulators. The gas dynamics PDE equations over the pipelines, together with boundary conditions at junctions, are reduced using lumped elements to a sparse nonlinear ODE system expressed in vector-matrix form using graph theoretic notation. This system, which we call the reduced network flow (RNF) model, is a consistent discretization of the PDE equations for gas flow. The RNF forms the dynamic constraints for optimal control problems for pipeline systems with known time-varying withdrawals and injections and gas pressure limits throughout the network. The objectives include economic transient compression (ETC) and minimum load shedding (MLS), which involve minimizing compression costs or, if that is infeasible, minimizing the unfulfilled deliveries, respectively. These continuous functional optimization problems are approximated using the Legendre-Gauss-Lobatto (LGL) pseudospectral collocation scheme to yield a family of nonlinear programs, whose solutions approach the optima with finer discretization. Simulation and optimization of time-varying scenarios on an example natural gas transmission network demonstrate the gains in security and efficiency over methods that assume steady-state behavior

Industrial water management by multiobjective optimization: from individual to collective solution through eco-industrial parks.

Industrial water networks are designed in the first part by a multiobjective optimization strategy, where fresh water, regenerated water flow rates as well as the number of network connections (integer variables) are minimized. The problem is formulated as a Mixed-Integer Linear Programming problem (MILP) and solved by the ε-constraint method. The linearization of the problem is based on the necessary conditions of optimality defined by Savelski and Bagajewicz (2000). The approach is validated on a published example involving only one contaminant. In the second part the MILP strategy is implemented for designing an Eco-Industrial Park (EIP) involving three companies. Three scenarios are considered: EIP without regeneration unit, EIP where each company owns its regeneration unit and EIP where the three companies share regeneration unit(s). Three possible regeneration units can be chosen, and the MILP is solved under two kinds of conditions: limited or unlimited number of connections, same or different gains for each company. All these cases are compared according to the global equivalent cost expressed in fresh water and taking also into account the network complexity through the number of connections. The best EIP solution for the three companies can be determined

Wireless Backhaul Node Placement for Small Cell Networks

Small cells have been proposed as a vehicle for wireless networks to keep up with surging demand. Small cells come with a significant challenge of providing backhaul to transport data to(from) a gateway node in the core network. Fiber based backhaul offers the high rates needed to meet this requirement, but is costly and time-consuming to deploy, when not readily available. Wireless backhaul is an attractive option for small cells as it provides a less expensive and easy-to-deploy alternative to fiber. However, there are multitude of bands and features (e.g. LOS/NLOS, spatial multiplexing etc.) associated with wireless backhaul that need to be used intelligently for small cells. Candidate bands include: sub-6 GHz band that is useful in non-line-of-sight (NLOS) scenarios, microwave band (6-42 GHz) that is useful in point-to-point line-of-sight (LOS) scenarios, and millimeter wave bands (e.g. 60, 70 and 80 GHz) that are recently being commercially used in LOS scenarios. In many deployment topologies, it is advantageous to use aggregator nodes, located at the roof tops of tall buildings near small cells. These nodes can provide high data rate to multiple small cells in NLOS paths, sustain the same data rate to gateway nodes using LOS paths and take advantage of all available bands. This work performs the joint cost optimal aggregator node placement, power allocation, channel scheduling and routing to optimize the wireless backhaul network. We formulate mixed integer nonlinear programs (MINLP) to capture the different interference and multiplexing patterns at sub-6 GHz and microwave band. We solve the MINLP through linear relaxation and branch-and-bound algorithm and apply our algorithm in an example wireless backhaul network of downtown Manhattan.Comment: Invited paper at Conference on Information Science & Systems (CISS) 201

Voltage Stabilization in Microgrids via Quadratic Droop Control

We consider the problem of voltage stability and reactive power balancing in islanded small-scale electrical networks outfitted with DC/AC inverters ("microgrids"). A droop-like voltage feedback controller is proposed which is quadratic in the local voltage magnitude, allowing for the application of circuit-theoretic analysis techniques to the closed-loop system. The operating points of the closed-loop microgrid are in exact correspondence with the solutions of a reduced power flow equation, and we provide explicit solutions and small-signal stability analyses under several static and dynamic load models. Controller optimality is characterized as follows: we show a one-to-one correspondence between the high-voltage equilibrium of the microgrid under quadratic droop control, and the solution of an optimization problem which minimizes a trade-off between reactive power dissipation and voltage deviations. Power sharing performance of the controller is characterized as a function of the controller gains, network topology, and parameters. Perhaps surprisingly, proportional sharing of the total load between inverters is achieved in the low-gain limit, independent of the circuit topology or reactances. All results hold for arbitrary grid topologies, with arbitrary numbers of inverters and loads. Numerical results confirm the robustness of the controller to unmodeled dynamics.Comment: 14 pages, 8 figure

On the flexibility of an eco-industrial park (EIP) for managing industrial water

In a recent paper, a generic model, based on a multiobjective optimization procedure, for water supply system for a single company and for an eco-industrial park was proposed and illustrated by a park involving three companies A, B and C. The best configuration was identified by simultaneously minimizing the fresh water flow rate, the regenerated water flow rate and the number of connections in the eco-industrial park. The question is now to know what the maximal increase/decrease in pollutant flow rates is, so that the eco-industrial park remains feasible, economically profitable and environmentally friendly. A preliminary study shows that the park can accept an increase of pollutant flow rates of 29% in company A, 12% in company B and only 1% in company C; beyond these limits the industrial symbiosis becomes not feasible. The proposed configuration is not flexible with a very limited number of connections. Indeed, the solution implemented for conferring some flexibility to this network is to increase the number of connections within the park. However, connections have a cost, so the increase of their number needs to remain moderate. The number of connections is augmented until the symbiosis becomes unfeasible, or until the gain for each company to participate to the park becomes lower than a given threshold. Several cases are studied by increasing the pollutant flow rates under two different scenarios: 1) in only one company, 2) in two or three companies simultaneously

Dynamic Time-domain Duplexing for Self-backhauled Millimeter Wave Cellular Networks

Millimeter wave (mmW) bands between 30 and 300 GHz have attracted considerable attention for next-generation cellular networks due to vast quantities of available spectrum and the possibility of very high-dimensional antenna ar-rays. However, a key issue in these systems is range: mmW signals are extremely vulnerable to shadowing and poor high-frequency propagation. Multi-hop relaying is therefore a natural technology for such systems to improve cell range and cell edge rates without the addition of wired access points. This paper studies the problem of scheduling for a simple infrastructure cellular relay system where communication between wired base stations and User Equipment follow a hierarchical tree structure through fixed relay nodes. Such a systems builds naturally on existing cellular mmW backhaul by adding mmW in the access links. A key feature of the proposed system is that TDD duplexing selections can be made on a link-by-link basis due to directional isolation from other links. We devise an efficient, greedy algorithm for centralized scheduling that maximizes network utility by jointly optimizing the duplexing schedule and resources allocation for dense, relay-enhanced OFDMA/TDD mmW networks. The proposed algorithm can dynamically adapt to loading, channel conditions and traffic demands. Significant throughput gains and improved resource utilization offered by our algorithm over the static, globally-synchronized TDD patterns are demonstrated through simulations based on empirically-derived channel models at 28 GHz.Comment: IEEE Workshop on Next Generation Backhaul/Fronthaul Networks - BackNets 201