This article takes an integrated view of optimized capacity design and operation of islanded energy hubs. We consider energy hubs that incorporate emerging distributed energy resources as well as energy storage devices and fully support electricity and heat demand of an islanded installation. Both battery and hydrogen storage are incorporated. To explicitly account for the stochasticity in renewable energy generation and load, the energy hub capacity design problem is first expressed as a chance-constrained optimization problem and then reformulated as a robust counterpart problem, where battery charging/discharging responds to stochastic renewable energy generation and load realizations through a control policy. In particular, an affine policy is considered, enabling a linear program formulation of the problem. To reduce conservativeness of the design, an iterative algorithm is proposed, where the interaction between a chance-constrained design problem and a validation problem is achieved through a scalar auxiliary variable. The design result demonstrates a balanced tradeoff between robustness and cost efficiency. After the energy hub has been designed, we propose a bi-level operating strategy, where a day-ahead schedule is optimized at the higher level and model predictive control is used for tracking the schedule in real time at the lower level. Finally, we discuss the potential for increasing the reliability of energy hub systems while decreasing operational cost by sharing energy between multiple energy hubs through networking.

Trajectory sensitivity analysis has been widely used to analyze the dynamic behaviour of complex systems such as power system. It is common to use first-order sensitivities, which have been fully described for hybrid dynamical system. However, second-order trajectory sensitivities have only been analyzed for continuous systems. This paper derives the jump conditions describing the behaviour of second-order trajectory sensitivities at switching and reset events. This enables second-order sensitivity analysis of general hybrid dynamical systems. The jump conditions are illustrated using a simple power system example and the results are compared with first-order sensitivities. It is shown that incorporating second-order sensitivity increases the accuracy of trajectory approximation.

The expanding penetration of nondispatchable renewable resources within power system generation portfolios is motivating the development of demand-side strategies for balancing generation and load. Commercial heating, ventilation, and air conditioning (HVAC) loads are potential candidates for providing such demand-response (DR) services as they consume significant energy and because of the temporal flexibility offered by their inherent thermal inertia. Several ancillary services markets have recently opened up to participation by DR resources, provided they can satisfy certain performance metrics. We discuss different control strategies for providing frequency regulation DR from commercial HVAC systems and components, and compare performance results from experiments and simulation. We also present experimental results from a single ~30 000-m2office building and quantify the DR control performance using standardized performance criteria. Additionally, we evaluate the cost of delivering this service by comparing the energy consumed while providing DR against a counterfactual baseline.

Recently, there has been significant interest in convex relaxations of the optimal power flow (OPF) problem. A semidefinite relaxation globally solves many OPF problems. However, there exist practical problems for which the semidefinite relaxation fails to yield the global solution. Conditions for the success or failure of the semidefinite relaxation are valuable for determining whether the relaxation is appropriate for a given OPF problem. To move beyond existing conditions, which only apply to a limited class of problems, a typical conjecture is that failure of the semidefinite relaxation can be related to physical characteristics of the system. By presenting an example OPF problem with two equivalent formulations, this paper demonstrates that physically based conditions cannot universally explain algorithm behavior. The semidefinite relaxation fails for one formulation but succeeds in finding the global solution to the other formulation. Since these formulations represent the same system, success (or otherwise) of the semidefinite relaxation must involve factors beyond just the network physics.

The level of uncertainty in power systems is increasing due to substantial growth in renewable generation and increasing reliance on cyber-enabled system-wide responsiveness. In order to guarantee dynamic security of networks, power system designers are in need of practical reachability analysis tools that allow them to assess vulnerability of the system to undesirable outcomes and evaluate the impact of parameter uncertainty. This paper describes a novel suite of parameter continuation algorithms that may be applied to large-scale, stiff, hybrid power systems. They allow the impact of parameter uncertainty to be quantified, thereby enabling secure design through efficient exploration of critical parameter values and initial conditions.

As new devices and technologies enter the electrical distribution grid, decentralized control algorithms will become increasingly important. Unlike centralized control where standard optimization procedures can ensure optimal system performance, control algorithms for distributed systems may take a variety of forms. This paper derives a decentralized algorithm that regulates the reactive power output from highly distributed photovoltaic (PV) sources. An objective function is constructed that minimizes voltage deviations and line losses. It is shown that this objective function is minimized by a local control law that regulates the reactive power output of PV inverters. Optimality of the derived control law is tested against central optimization solutions.

A number of standard power system models implement non-windup limits on control blocks in ways that can lead to trajectory deadlock. This deadlock behaviour takes the form of infinitely fast switching, due to incompatibility between the conditions that govern switching on either side of the switching surface. Solutions can only be continued in a Filippov sense. The paper explores this phenomenon in the context of a standard voltage regulator model, and an industry-standard model of a doubly-fed induction generator that is widely used to represent wind turbine generators. Two approaches to preventing deadlock are considered: the first employs a deadband, while the second uses feedback.

This paper discusses conceptual frameworks for actively involving highly distributed loads in power system control actions. The context for load control is established by providing an overview of system control objectives, including economic dispatch, automatic generation control, and spinning reserve. The paper then reviews existing initiatives that seek to develop load control programs for the provision of power system services. We then discuss some of the challenges to achieving a load control scheme that balances device-level objectives with power system-level objectives. One of the central premises of the paper is that, in order to achieve full responsiveness, direct load control (as opposed to price response) is required to enable fast time scale, predictable control opportunities, especially for the provision of ancillary services such as regulation and contingency reserves. Centralized, hierarchical, and distributed control architectures are discussed along with benefits and disadvantages, especially in relation to integration with the legacy power system control architecture. Implications for the supporting communications infrastructure are also considered. Fully responsive load control is illustrated in the context of thermostatically controlled loads and plug-in electric vehicles.

The paper explores the meaning of smart grid, concluding that the term is closely linked with enhanced sensing, actuation and control of power systems. It is suggested that such cyber-physical systems would be more meaningfully described as responsive grids. The paper provides a brief historical perspective of the decision-making that underlies existing, seemingly inflexible, grid structures. It emphasizes the future needs for responsive grids, as a consequence of inevitable growth in renewable generation and newer types of loads such as plug-in electric vehicles. The paper considers the cyber-infrastructure requirements for supporting controllability of highly distributed generation and load resources.

Uncertain parameters impact the dynamic behaviour of many important nonlinear systems. Assessing the significance of parameter uncertainty is often vitally important, but traditional techniques are computationally challenging. A recent approach uses trajectory sensitivities to form a first-order approximation of perturbed trajectories. These approximate trajectories are generally quite accurate, though their quality reduces in the vicinity of the stability boundary. The paper proposes a modification that improves the accuracy of sensitivity-based approximations of marginally-stable trajectories. This modified approach generates approximate trajectories by considering the intersection of the perturbed trajectory with a hyperplane that progresses with the nominal trajectory.

The large disturbance behaviour of power systems often involves complex interactions between continuous dynamics and discrete events. The paper proposes a differential-algebraic-discrete (DAD) model structure which captures those interactions in a systematic way. It is shown that the model is a realization of a general hybrid system model. The DAD model opens up opportunities for the application to power systems of hybrid system results in stability analysis and control. The paper presents a practical approach to implementing the DAD model structure.

A number of facts about quadratic load flow problems y=f(x)=0, x/spl isin/R/sub x//sup n/, y/spl isin/R/sub y//sup n/ is proved. The main results are the following: If any point x belongs to a straight line connecting a pair of distinct solutions in the state space R/sub x//sup n/, the Newton-Raphson iterative process goes along this line. If a loading process y(/spl beta/) reaches a singular point of the problem, the corresponding trajectory of state variables x(/spl beta/) in R/sub x//sup n/ tends to the right eigenvector nullifying the Jacobian matrix at the singular point. In any singular point of the quadratic problem, there are two solutions which merge at this point. The maximum number of solutions on any straight line in state the space R/sub x//sup n/ is two. Along a straight line through two distinct solutions of a quadratic problem, this problem can be reduced to a single scaler quadratic equation which locates these solutions. In addition, a number of other properties is reported. New proofs of them are given. There is a point of singularity in the middle of a straight line connecting a pair of distinct solutions in the state space R/sub x//sup n/. A vector co-linear to a straight line connecting a pair of distinct solutions in R/sub x//sup n/ nullifies the Jacobian matrix at the point of singularity in the middle of the line.

As systems become more heavily loaded, nonlinearities play an increasingly important role in power system behavior. Modeling must accurately reflect component and system response. Analysis tools should combine to work reliably even under extreme system conditions, providing accurate predictions of power system behavior. The paper considers some power system modeling issues and presents an overview of the source of nonlinearities in power systems. It then considers industry accepted analysis techniques, as well as those techniques that are more research orientated. The influence of nonlinearities on these tools is explored.