Pressure Fluctuations in Natural Gas Networks caused by Gas-Electric Coupling

The development of hydraulic fracturing technology has dramatically increased the supply and lowered the cost of natural gas in the United States, driving an expansion of natural gas-fired generation capacity in several electrical inter-connections. Gas-fired generators have the capability to ramp quickly and are often utilized by grid operators to balance intermittency caused by wind generation. The time-varying output of these generators results in time-varying natural gas consumption rates that impact the pressure and line-pack of the gas network. As gas system operators assume nearly constant gas consumption when estimating pipeline transfer capacity and for planning operations, such fluctuations are a source of risk to their system. Here, we develop a new method to assess this risk. We consider a model of gas networks with consumption modeled through two components: forecasted consumption and small spatio-temporarily varying consumption due to the gas-fired generators being used to balance wind. While the forecasted consumption is globally balanced over longer time scales, the fluctuating consumption causes pressure fluctuations in the gas system to grow diffusively in time with a diffusion rate sensitive to the steady but spatially-inhomogeneous forecasted distribution of mass flow. To motivate our approach, we analyze the effect of fluctuating gas consumption on a model of the Transco gas pipeline that extends from the Gulf of Mexico to the Northeast of the United States.Comment: 10 pages, 7 figure

Efficient Dynamic Compressor Optimization in Natural Gas Transmission Systems

The growing reliance of electric power systems on gas-fired generation to balance intermittent sources of renewable energy has increased the variation and volume of flows through natural gas transmission pipelines. Adapting pipeline operations to maintain efficiency and security under these new conditions requires optimization methods that account for transients and that can quickly compute solutions in reaction to generator re-dispatch. This paper presents an efficient scheme to minimize compression costs under dynamic conditions where deliveries to customers are described by time-dependent mass flow. The optimization scheme relies on a compact representation of gas flow physics, a trapezoidal discretization in time and space, and a two-stage approach to minimize energy costs and maximize smoothness. The resulting large-scale nonlinear programs are solved using a modern interior-point method. The proposed optimization scheme is validated against an integration of dynamic equations with adaptive time-stepping, as well as a recently proposed state-of-the-art optimal control method. The comparison shows that the solutions are feasible for the continuous problem and also practical from an operational standpoint. The results also indicate that our scheme provides at least an order of magnitude reduction in computation time relative to the state-of-the-art and scales to large gas transmission networks with more than 6000 kilometers of total pipeline

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

Power-to-gas management using robust optimisation in integrated energy systems

A large volume of wind power is curtailed worldwide due to the intermittency and limited transportation capacity of electrical power systems. New technologies, Power-to-Gas via electrolysis, can convert excessive wind power into hydrogen to be transported by natural gas systems. However, the injection of H2 into natural gas pipelines can cause gas quality issues due to changing gas compositions. This paper investigates the impact of injecting H2 converted from wind power on natural gas quality. Two key indexes used to measure gas quality, Wobbe Index and Combustion Potential, are introduced to examine the impact. Then, in order to bring the two indexes into acceptable statutory ranges, H2 is mixed with Liquid Petroleum Gas and Nitrogen. A robust optimization model, considering wind power uncertainties, is thereafter developed to manage the gas mixture, maximize H2 injection. This paper uses the dynamic gas system model to represent real-time pipeline flows, which can better reflect gas flow features over time. The proposed method is demonstrated on a small integrated gas-electricity system. Results illustrate that excessive H2 injection will reduce Wobbe Index but increase Combustion Potential. The robust optimization approach can effectively manage the mixture while ensuring gas quality with an uncertain wind power supply. The proposed method is beneficial to reducing renewable energy curtailment and maximizing H2 injection, benefiting electricity system operators with low operation costs and wind power more penetration.</p

Power-to-gas management using robust optimisation in integrated energy systems

A large volume of wind power is curtailed worldwide due to the intermittency and limited transportation capacity of electrical power systems. New technologies, Power-to-Gas via electrolysis, can convert excessive wind power into hydrogen to be transported by natural gas systems. However, the injection of H2 into natural gas pipelines can cause gas quality issues due to changing gas compositions. This paper investigates the impact of injecting H2 converted from wind power on natural gas quality. Two key indexes used to measure gas quality, Wobbe Index and Combustion Potential, are introduced to examine the impact. Then, in order to bring the two indexes into acceptable statutory ranges, H2 is mixed with Liquid Petroleum Gas and Nitrogen. A robust optimization model, considering wind power uncertainties, is thereafter developed to manage the gas mixture, maximize H2 injection. This paper uses the dynamic gas system model to represent real-time pipeline flows, which can better reflect gas flow features over time. The proposed method is demonstrated on a small integrated gas-electricity system. Results illustrate that excessive H2 injection will reduce Wobbe Index but increase Combustion Potential. The robust optimization approach can effectively manage the mixture while ensuring gas quality with an uncertain wind power supply. The proposed method is beneficial to reducing renewable energy curtailment and maximizing H2 injection, benefiting electricity system operators with low operation costs and wind power more penetration.</p

An Equivalent Model of Gas Networks for Dynamic Analysis of Gas-Electricity Systems

The increasing coupling between natural gas and electricity systems by gas-fired generation units brings new challenges to system analysis, such as pressure variations due to consumption perturbations of generation units. The emerging issues require revolutionary modeling and analysis techniques. This paper proposes a novel model to quantify gas pressure variations due to gas-fired power unit ramping and the impact of constraints from natural gas pressure change on ramp rates of gas-fired plants. By utilizing Laplace transform to resolve the governing equations of gas networks, the proposed model can significantly reduce modeling complexity and computational burden. The dynamic behaviors in time scale in s-domain and spatial partial differential equations are transformed into finite difference equations. By introducing the concept of transfer matrices, the relation between states at each node of gas systems can be expressed by transfer parameter matrices. Additionally, a simplified model is introduced to simply the analysis. The explicit expressions of nodal pressure variations in response to demand change are very convenient for analyzing system dynamic performance under disturbances, identifying the most influential factors. The new models are extensively demonstrated on three natural gas networks and benchmarked with traditional simulation approaches. Results illustrate that they produce very close results with the simulation approach, particularly when gas pipelines are long and enter steady states.</p

Model Order Reduction for Gas and Energy Networks

To counter the volatile nature of renewable energy sources, gas networks take a vital role. But, to ensure fulfillment of contracts under these circumstances, a vast number of possible scenarios, incorporating uncertain supply and demand, has to be simulated ahead of time. This many-query gas network simulation task can be accelerated by model reduction, yet, large-scale, nonlinear, parametric, hyperbolic partial differential(-algebraic) equation systems, modeling natural gas transport, are a challenging application for model order reduction algorithms. For this industrial application, we bring together the scientific computing topics of: mathematical modeling of gas transport networks, numerical simulation of hyperbolic partial differential equation, and parametric model reduction for nonlinear systems. This research resulted in the "morgen" (Model Order Reduction for Gas and Energy Networks) software platform, which enables modular testing of various combinations of models, solvers, and model reduction methods. In this work we present the theoretical background on systemic modeling and structured, data-driven, system-theoretic model reduction for gas networks, as well as the implementation of "morgen" and associated numerical experiments testing model reduction adapted to gas network models

Security Analysis of Interdependent Critical Infrastructures: Power, Cyber and Gas

abstract: Our daily life is becoming more and more reliant on services provided by the infrastructures power, gas , communication networks. Ensuring the security of these infrastructures is of utmost importance. This task becomes ever more challenging as the inter-dependence among these infrastructures grows and a security breach in one infrastructure can spill over to the others. The implication is that the security practices/ analysis recommended for these infrastructures should be done in coordination. This thesis, focusing on the power grid, explores strategies to secure the system that look into the coupling of the power grid to the cyber infrastructure, used to manage and control it, and to the gas grid, that supplies an increasing amount of reserves to overcome contingencies. The first part (Part I) of the thesis, including chapters 2 through 4, focuses on the coupling of the power and the cyber infrastructure that is used for its control and operations. The goal is to detect malicious attacks gaining information about the operation of the power grid to later attack the system. In chapter 2, we propose a hierarchical architecture that correlates the analysis of high resolution Micro-Phasor Measurement Unit (microPMU) data and traffic analysis on the Supervisory Control and Data Acquisition (SCADA) packets, to infer the security status of the grid and detect the presence of possible intruders. An essential part of this architecture is tied to the analysis on the microPMU data. In chapter 3 we establish a set of anomaly detection rules on microPMU data that flag "abnormal behavior". A placement strategy of microPMU sensors is also proposed to maximize the sensitivity in detecting anomalies. In chapter 4, we focus on developing rules that can localize the source of an events using microPMU to further check whether a cyber attack is causing the anomaly, by correlating SCADA traffic with the microPMU data analysis results. The thread that unies the data analysis in this chapter is the fact that decision are made without fully estimating the state of the system; on the contrary, decisions are made using a set of physical measurements that falls short by orders of magnitude to meet the needs for observability. More specifically, in the first part of this chapter (sections 4.1- 4.2), using microPMU data in the substation, methodologies for online identification of the source Thevenin parameters are presented. This methodology is used to identify reconnaissance activity on the normally-open switches in the substation, initiated by attackers to gauge its controllability over the cyber network. The applications of this methodology in monitoring the voltage stability of the grid is also discussed. In the second part of this chapter (sections 4.3-4.5), we investigate the localization of faults. Since the number of PMU sensors available to carry out the inference is insufficient to ensure observability, the problem can be viewed as that of under-sampling a "graph signal"; the analysis leads to a PMU placement strategy that can achieve the highest resolution in localizing the fault, for a given number of sensors. In both cases, the results of the analysis are leveraged in the detection of cyber-physical attacks, where microPMU data and relevant SCADA network traffic information are compared to determine if a network breach has affected the integrity of the system information and/or operations. In second part of this thesis (Part II), the security analysis considers the adequacy and reliability of schedules for the gas and power network. The motivation for scheduling jointly supply in gas and power networks is motivated by the increasing reliance of power grids on natural gas generators (and, indirectly, on gas pipelines) as providing critical reserves. Chapter 5 focuses on unveiling the challenges and providing solution to this problem.Dissertation/ThesisDoctoral Dissertation Electrical Engineering 201

Optimizing Nonlinear Dynamics in Energy System Planning and Control

Understanding the physical dynamics underlying energy systems is essential in achieving stable operations, and reasoning about restoration and expansion planning. The mathematics governing energy system dynamics are often described by high-order differential equations. Optimizing over these equations can be a computationally challenging exercise. To overcome these challenges, early studies focused on reduced / linearized models failing to capture system dynamics accurately. This thesis considers generalizing and improving existing optimization methods in energy systems to accurately represent these dynamics. We revisit three applications in power transmission and gas pipeline systems. Our first application focuses on power system restoration planning. We examine transient effects in power restoration and generalize the Restoration Ordering Problem formulation with standing phase angle and voltage difference constraints to enhance transient stability. Our new proposal can reduce rotor swings of synchronous generators by over 50\% and have negligible impacts on the blackout size, which is optimized holistically. Our second application focuses on transmission line switching in power system operations. We propose an automatic routine actively considering transient stability during optimization. Our main contribution is a nonlinear optimization model using trapezoidal discretization over the 2-axis generator model with an automatic voltage regulator (AVR). We show that congestion can lead to rotor instability, and variables controlling set-points of automatic voltage regulators are critical to ensure oscillation stability. Our results were validated against PowerWorld simulations and exhibit an average error in the order of 0.001 degrees for rotor angles. Our third contribution focuses on natural gas compressor optimization in natural gas pipeline systems. We consider the Dynamic Optimal Gas Flow problem, which generalizes the Optimal Gas Flow Problem to capture natural gas dynamics in a pipeline network. Our main contribution is a computationally efficient method to minimize gas compression costs under dynamic conditions where deliveries to customers are described by time-dependent mass flows. The scheme yields solutions that are feasible for the continuous problem and practical from an operational standpoint. Scalability of the scheme is demonstrated using realistic benchmark data