Control and Optimization Methods for Electric Smart Grids

The basic objective of this chapter is to rethink frequency regulation in electric power systems as a problem of cyber system design for a particular class of complex dynamical systems. It is suggested that the measurements, communications, and control architectures must be designed with a clear understanding of the temporal and spatial characteristics of the power grid as well as of its generation and load dynamics. The problem of Automatic Generation Control (AGC) and frequency regulation design lends itself well to supporting this somewhat general observation because its current implementation draws on unique structures and assumptions common to model aggregation in typical large-scale dynamic network systems. We describe how these assumptions are changing as a result of both organizational and technological industry changes. We propose the interactions variable-based modeling framework necessary for deriving models, which relax conventional assumptions when that is needed. Using this framework, we show that the measurements, communications, and control architectures key to ensuring acceptable frequency response depend on the types of disturbances, the electrical characteristics of the interconnected system and the desired technical and economic performance. The simulations illustrate several qualitatively different electric energy systems. This approach is by and large motivated by today’s AGC and its measurement, communications and control architectures. It is with this in mind that we refer to our interactions variable-based frequency regulation framework as “enhanced AGC” (E-AGC). The enhancements come from accounting for temporal and spatial characteristics of the system which require a more advanced frequency regulation design than the one presently in place. Our proposed interactions variable-based aggregation modeling could form the basis for a coordination of interactions between the smart balancing authorities (SBAs) responsible for frequency regulation in the changing industry. Given the rapid deployment of synchrophasors, the proposed E-AGC can be easily implemented.

We consider a set of users served by a single load-serving entity (LSE). The LSE procures capacity a day ahead. When random renewable energy is realized at delivery time, it manages user load through real-time demand response and purchases balancing power on the spot market to meet the aggregate demand. Hence, optimal supply procurement by the LSE and the consumption decisions by the users must be coordinated over two timescales, a day ahead and in real time, in the presence of supply uncertainty. Moreover, they must be computed jointly by the LSE and the users since the necessary information is distributed among them. In this chapter, we present a simple yet versatile user model and formulate the problem as a dynamic program that maximizes expected social welfare. When random renewable generation is absent, optimal demand response reduces to joint scheduling of the procurement and consumption decisions. In this case, we show that optimal prices exist that coordinate individual user decisions to maximize social welfare, and present a decentralized algorithm to optimally schedule a day in advance the LSE’s procurement and the users’ consumptions. The case with uncertain supply is reported in a companion paper.

The main foundations of the emerging Smart Grid are (1) Distributed Energy Resources (DER) enabled primarily by intermittent, nondispatchable renewable energy sources such as wind and solar, and independent microgrids and (2) Demand Response (DR), the concept of controlling loads via cyber-based communication and control and economic signals. While smart grid communication technologies offer dynamic information provide real-time signals to utilities, they inevitably introduce delays in the energy real-time market. In this article, a dynamic, discrete-time model of the wholesale energy market that captures these interactions is derived. Beginning with a framework that includes optimal power flow and real-time pricing, this model is shown to capture the dynamic interactions between generation, demand, and locational marginal price near the equilibrium of the optimal dispatch. It is shown that the resulting dynamic real-time market has stability properties that are dependent on the delay due to the measurement and communication. Numerical studies are reported to illustrate the dynamic model, and a suitable communication topology is suggested.

^∗Based on “Coordinating regulation and demand response in electric power grids using multirate model predictive control,” by H. Hindi, D. Greene, C. Laventall, which appeared in the IEEE Innovative Smart Grid Technologies Conference ISGT 2011, ©2011 IEEE.

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Future “smart electric vehicles,” expected to evolve from emerging electric and plug-in hybrid electric vehicles (EV & PHEV) are becoming increasingly attractive. However, the current electric grid is not considered capable of handling the power demand increase required by a large number of charging stations, especially during peak loads. Furthermore, the envisioned critical infrastructure for such vehicles must include the capability for information exchange involving energy availability, distances, congestion levels and possibly, spot prices or priority incentives. In this chapter, we discuss current trends and challenges in this fascinating and rapidly developing area of research. Our emphasis is on topics related to control, demand-response, infrastructure provisioning, and the communications framework necessary to accomplish all of these “smart” features. As a particular application and a form of case study, we zero in on the design and development of charging stations. We describe a candidate PHEV charging station architecture, and a quantitative stochastic model that allows the analysis of its performance, using queuing theory and economics. The architecture we envision has the capability to store excess power obtained from the grid. Our goal is to promote a general architecture able to sustain grid stability, while providing a required level of quality of service; and to further the development of a general methodology to analyze the performance of such stations with respect to traffic characteristics, energy storage size, pricing and cost parameters.

This chapter develops a modeling framework for studying the impact of variability and uncertainty in wind-based electricity generation on power system frequency. The focus is on timescales involving governor response (primary frequency control) and automatic generation control (AGC) (secondary frequency control). The framework includes models of synchronous generators, wind-based electricity sources, the electrical network, and the AGC system. The framework can be used to study the impact of different renewable penetration scenarios on system frequency performance metrics. In order to illustrate the framework, a simplified model of the Western Electricity Coordinating Council (WECC) system is developed.

¹Research in this article was carried out at Washington State University (WSU) while the author was a visiting scholar at WSU.

We describe a dynamical mechanism of cascading failure in a system of interconnected power grids. This mechanism is based on the discovery of (SusukiY et al. (2011) J Nonlinear Sci 21(3):403–439), an emergent and undesirable phenomenon of synchronous machines in a power grid, termed the Coherent Swing Instability (CSI). In this phenomenon, most of the machines in a sub-grid coherently lose synchronism with the rest of the grid after being subjected to a local and finite disturbance. By numerical analysis of a system of weakly interconnected power grids, we present a phenomenon of coupled swing dynamics in which the CSI happens for all of the power grids in a successive manner. We suggest that a small disturbance in one grid can grow, spill to the other grids, and cause the whole system to fail. This mechanism enables the development of dynamically relevant tools for monitoring and control of wide-area disturbances, which become feasible when the physical power network is overlaid with an information network, like the smart grid.

The concept of fault-coverage and how it affects the availability of a dynamic grid is explained through a two-area power system represented by an aggregated swing model. Fault-coverage is intended to serve as a criterion for decisions in redundancy management to benefit system availability upon occurrence of a disturbance due to loss of equipment. The criterion allows the incorporation of formal measures of uncertainties associated with real-time fault diagnosis, as well as formal control performance measures. Also investigated is the effect of the availability of a modern grid’s supporting structure on the availability of the grid, with focus on a network of measurement units. The focus stems from the recognition of a greater need for real-time diagnosis and control in a modern power grid. A redundancy architecture design problem is formulated based on a Markov model of a measurement network, and a solution is presented that minimizes the number of phasor measurement unit (PMU) restorations and the usage of communication links to a PMU while maintaining a prescribed data availability at any PMU. A 3-bus/3-PMU network is used as an example to explain the formulation and the solution of the redundancy architecture design problem.

This chapter discusses the challenges and the possibilities offered by controlling a data center as a node of the smart-grid. The communication between the grid and the data center takes the form of a time-varying and power-consumption-dependent electricity price. A model that considers both the computational and the physical characteristics of a data center, as well as their interactions, is proposed. Two control approaches are discussed. The first control approach does not consider the interaction between the computational and the thermal characteristics of a data center. We call such a control approach uncoordinated. The second controller considers the coupling between the computational and the thermal characteristics. We call such a control approach coordinated. Simulation results, discussed at the end of the chapter, show that the coordinated control approach can lead to larger income for data center operators than the uncoordinated approach.

This chapter investigates measures of centrality that are applicable to power grids. Centrality measures are used in network science to rank the relative importance of nodes and edges of a graph. Here we define new measures of centrality for power grids that are based on its functionality. More specifically, the coupling of the grid network can be expressed as the algebraic equation YU = I, where U and I represent the vectors of complex bus voltage and injected current phasors; and Y is the network admittance matrix which is defined not only by the connecting topology but also by the network’s electrical parameters and can be viewed as a complex-weighted Laplacian. We show that the relative importance analysis based on centrality in graph theory can be performed on power grid network with its electrical parameters taken into account. In the chapter the proposed electrical centrality measures are experimented with on the NYISO-2935 system and the IEEE 300-bus system. The centrality distribution is analyzed in order to identify important nodes or branches in the system which are of essential importance in terms of system vulnerability. A number of interesting discoveries are also presented and discussed regarding the importance rank of power grid nodes and branches.

This chapter discusses strategies to coordinate charging of autonomous plug-in electric vehicles (PEVs). The chapter briefly reviews the state of the art with respect to grid level analyses of PEV charging, and frames PEV coordination in terms of whether they are centralized or decentralized and whether they are optimal or near-optimal in some sense. The bulk of the chapter is devoted to presenting centralized and decentralized cost-optimizing frameworks for identifying and coordinating PEV charging. We use a centralized framework to show that “valley filling” charge patterns are globally optimal. Decentralized electricity cost minimizing frameworks for PEV charging can be framed in the context of non-cooperative dynamic game theory and are related to recent work on mean field and potential games. Interestingly, in this context it can be difficult to achieve a Nash equilibrium (NE) if electricity price is the sole objective. The decentralized algorithm discussed in this chapter introduces a very small penalty term that damps unwanted negotiating dynamics. With this term, the decentralized algorithm takes on the form of a contraction mapping and, in the infinite system limit, the NE is unique and the algorithm will converge to it under relatively loose assumptions.

The supervisory control and data acquisition (SCADA) network provides adversaries with an opportunity to perform coordinated cyber attacks on power system equipment as it presents an increased attack surface. Coordinated attacks, when smartly structured, can not only have severe physical impacts, but can also potentially nullify the effect of system redundancy and other defense mechanisms. This chapter proposes a vulnerability assessment framework to quantify risk due to intelligent coordinated attacks, where risk is defined as the product of probability of successful cyber intrusion and resulting power system impact. The cyber network is modeled using Stochastic Petri Nets and the steady-state probability of successful intrusion into a substation is obtained using this. The model employs a SCADA network with firewalls and password protection schemes. The impact on the power system is estimated by load unserved after a successful attack. The New England 39-bus system is used as a test model to run Optimal Power Flow (OPF) simulations to determine load unserved. We conduct experiments creating coordinated attacks from our attack template on the test system and evaluate the risk for every case. Our attack cases include combinations of generation units and transmission lines that form coordinated attack pairs. Our integrated risk evaluation studies provide a methodology to assess risk from different cyber network configurations and substation capabilities. Our studies identify scenarios, where generation capacity, cyber vulnerability, and the topology of the grid together could be used by attackers to cause significant power system impact.

This chapter deals with power distribution engineering measurements and the processing of those measurements. The concept proposed is the use of synchronized measurements. The synchronization is accomplished through the use of a global positioning satellite signal – thus, time stamping measurements. The synchronized measurements are in phasor detail. The use of these measurements in a state estimator is proposed, described, and illustrated. Possible uses of this technology include: control of distribution system components; fault detection and management; energy management.

In a smart grid, robust energy management algorithms should have the ability to operate correctly in the presence of unreliable communication capabilities, and often in the absence of a central control mechanism. Effective distributed control algorithms could be embedded in distributed controllers to properly allocate electrical power among connected buses autonomously. By selecting the incremental cost of each generation unit as the consensus variable, the incremental cost consensus (ICC) algorithm is able to solve the conventional centralized economic dispatch problem (EDP) in a distributed manner. However, the communication time-delay may cause instability of the system and should be considered during the design process. The mathematical formulation of the ICC algorithm with time-delay is presented in this chapter. Several case studies are also presented to show the system characteristics of the ICC algorithm with time-delay.

This paper presents an adaptive wide-area interarea mode damping controller for power systems using synchrophasor data. A key consideration in the control design is the time delay in computing the phasor quantities and the variable communication network latency for controllers to use remote synchrophasor data. The adaptive switching controller comprises several phase compensators, each designed for a specific data latency. Based on the latency of the arriving synchrophasor data, the adaptive controller will select the appropriate compensator to use. The design is illustrated with a two-area power system. Applications to large power systems will be discussed.

In this chapter, we present a set of results on the design of dynamic controllers for electromechanical oscillation damping in large power systems using Synchronized Phasor Measurements. Our approach consists of three steps, namely – (1) Model Reduction, where phasor data are used to identify second-order models of the oscillation clusters of the system, (2) Aggregate Control, where state-feedback controllers are designed to achieve a desired closed-loop transient response between every pair of clusters, and finally (3) Control Inversion, where the aggregate control design is distributed and tuned to actual realistic controllers at the generator terminals until the interarea responses of the full-order power system matches the respective inter-machine responses of the reduced-order system. Although a general optimization framework is needed to formulate these three steps for any n-area power system, we specifically show that model reference control (MRC) can be an excellent choice to solve this damping problem when the power system consists of two dominant areas, or equivalently one dominant interarea mode. Application of MRC to such two-area systems is demonstrated through topological examples inspired by realistic transfer paths in the US grid.