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This paper introduces a physically-intuitive notion of inter-area dynamics in systems comprising multiple interconnected energy conversion modules. The idea builds on an earlier general approach of setting their structural properties by modeling internal dynamics in stand-alone modules (components, areas) using the fundamental conservation laws between energy stored and generated, and then constraining explicitly their Tellegen's quantities (power and rate of change of power). In this paper we derive, by following the same principles, a transformed state-space model for a general nonlinear system. Using this model we show the existence of an area-level interaction variable, intVar, whose rate of change depends solely on the area internal power imbalance and is independent of the model complexity used for representing individual module dynamics in the area. Given these structural properties of stand-alone modules, we define in this paper for the first time an inter-area variable as the difference of power wave incident to tie-line from Area I and the power reflected into tie-lie from Area II. Notably, these power waves represent the interaction variables associated with the two respective interconnected areas. We illustrate these notions using a linearized case of two lossless inter-connected areas, and show the existence of a new inter-area mode when the areas get connected. We suggest that lessons learned in this paper open possibilities for computationally-efficient modeling and control of inter-area oscillations, and offer further the basis for modeling and control of dynamics in changing systems comprising faster energy conversion processes., Comment: 6 pages, 4 figures, 10th International Conference on Control, Decision and Information Technologies

In this paper we consider a possibility of stabilizing very fast electromagnetic interactions between Inverter Based Resources (IBRs), known as the Control Induced System Stability problems. We propose that when these oscillatory interactions are controlled the ability of the grid to deliver power to loads at high rates will be greatly increased. We refer to this grid property as the dynamic grid loadability. The approach is to start by modeling the dynamical behavior of all components. Next, to avoid excessive complexity, interactions between components are captured in terms of unified technology-agnostic aggregate variables, instantaneous power and rate of change of instantaneous reactive power. Sufficient dissipativity conditions in terms of rate of change of energy conversion in components themselves and bounds on their rate of change of interactions are derived in support of achieving the maximum system loadability. These physically intuitive conditions are then used to derive methods to increase loadability using high switching frequency reactive power sources. Numerical simulations confirm the theoretical calculations, and shows dynamic load-side reactive power support increases stable dynamic loadability regions.

Owners of wind power plants are exposed to financial risk in wholesale electricity markets due to the uncertain nature of wind forecasts and price volatility. In the event of a wind shortfall, the plant may have to repurchase power at a higher price in the real-time market. However, reducing the power offered in the day-ahead market may also be interpreted by regulators as physical withholding. We formulate and solve a mixed-integer quadratic program (MIQP) that prices the uncertain portion of a wind generator's forecast to hedge against uncertainties and which addresses concerns around withholding. We exploit the structure of the MIQP inputs to introduce additional constraints to improve computation time. Additionally, we provide a qualitative approach for generators and regulators to interpret the results of the MIQP. Finally, we simulate a real-world application for a wind farm in New York using past wind forecasts and NYISO prices., Comment: 5 pages, 5 figures. Submitted to the 2024 IEEE PES GM

This paper evaluates market equilibrium under different pricing mechanisms in a two-settlement 100%-renewables electricity market. Given general probability distributions of renewable energy, we establish game-theoretical models to analyze equilibrium bidding strategies, market prices, and profits under uniform pricing (UP) and pay-as-bid pricing (PAB). We prove that UP can incentivize suppliers to withhold bidding quantities and lead to price spikes. PAB can reduce the market price, but it may lead to a mixed-strategy price equilibrium. Then, we present a regulated uniform pricing scheme (RUP) based on suppliers' marginal costs that include penalty costs for real-time deviations. We show that RUP can achieve lower yet positive prices and profits compared with PAB in a duopoly market, which approximates the least-cost system outcome. Simulations with synthetic and real data find that under PAB and RUP, higher uncertainty of renewables and real-time shortage penalty prices can increase the market price by encouraging lower bidding quantities, thereby increasing suppliers' profits., Comment: 2023 ACM E-energy

In this paper, we suggest that reserves must be computed dynamically to account for wind power volatility. We formalize the notion of dynamic reserves in support of sequential Day-Ahead-Market (DAM) and Real-Time-Market (RTM) clearing and discuss several ways of accounting for wind power uncertainties. Three different wind integration protocols are considered and their impact on stakeholders, and, notably, on the need for dynamic reserves is analyzed. An optimal strategy is proposed which requires the least reserve as long as the bids are truthful and implementable with high confidence. This can be checked by the existing market monitor and/or by a separate risk buro. Concepts are illustrated in part using publicly available information about NYISO., Comment: 2023 IEEE PES general meeting

In this paper, we introduce a method to optimally estimate time-varying frequency bias. Current industry practice is to assume that frequency bias is changing only on annual basis. We suggest that this improved time-dependent bias estimate can be used to reduce the cost of frequency regulation needed to meet industry standards requested by the North American Electric Reliability Corporation (NERC). Optimization of time-varying frequency bias is posed as a parameter estimation (calibration) problem whose implementation utilizes online system measurements. It is further shown how this result can be used to estimate intra-dispatch load deviations. This knowledge is needed to estimate more accurately regulation reserve needed, and to therefore reduce overall regulation cost. Methods can be introduced to give incentives to demand response to participate in frequency regulation. Overall, we show the importance of incorporating knowledge of physics-based models for data-enabled parameter estimation of physical systems.

The emergence of Distributed Energy Resources (DERs) provides both challenges and opportunities for the planning and operations of distribution systems. These resources can be deployed in a manner that is either complementary to or in competition with traditional network operations and planning as the DERs can provide numerous important services to grid operators and utilities. This paper presents a novel method to estimate the trade off between DERs and traditional investments using a dynamic Peak-Load Pricing (PLP) methodology. PLP is a pricing strategy for a time-dependent quantity of a non-storable commodity and is based on the theory of long-run marginal costs. Importantly PLP deals with the trade-off between capacity utilization and consumer welfare. Therefore, the capacity price is set at a point where the cost of investment is exactly offset by the additional social welfare that the investment would bring. Importantly it allows for capital cost recovery with no uplift payments. This dynamic PLP methodology is an interactive planning and operations model based on the Dynamic Monitoring and Decision Systems (DyMonDS) Framework which helps to align physical, information, and economic incentives across many stakeholders within the electric energy system. The DyMonDS framework helps to solve the drawbacks of PLP, which are related to the computational complexity of the PLP models considering different technologies with different payback periods over a long investment horizon. Results show that the dynamic PLP model can accurately value the impact of different technologies in reducing congestion and increasing the number of customers served. This allows the network operator to easily identify which technologies should be chosen in each investment cycle., Comment: Presented at CIGRE US National Committee 2022 Grid of the Future Symposium

This paper concerns the resilience of systems with wind power upon wind reduction by evaluating the potential of corrective actions, such as generation and load dispatch, on minimizing the effects of transmission line failures. Three functions (grid, consumer-centric loss, and resilience impact) are used to statistically evaluate the criticality of initial contingent failures and wind reductions. Our model is learned with Monte Carlo, convex optimization, and adaptive selection, illustrated on the IEEE-30 and IEEE-300 bus systems with both AC and DC models. We highlight the impact of wind reductions and propose physically implementable solutions., Comment: Preprint. Submitted to the 2023 IEEE Power & Energy Society General Meeting (GM). arXiv admin note: substantial text overlap with arXiv:2211.01442

This paper concerns the potential of corrective actions, such as generation and load dispatch on minimizing the effects of transmission line failures in electric power systems. Three loss functions (grid-centric, consumer-centric, and influence localization) are used to statistically evaluate the criticality of initial contingent failures. A learning scheme for both AC and DC grid models combine a Monte Carlo approach with a convex dynamic programming formulation and introduces an adaptive selection process, illustrated on the IEEE-30 bus system., Comment: Pre-print submitted to ACC 2023

The increasing integration of variable renewable energy sources such as wind and solar will require new methods of managing generation uncertainty. Existing practices of uncertainty management for these resources largely focuses around modifying the energy offers of such resources in the quantity domain and from a centralized system operator consideration of these uncertainties. This paper proposes an approach to instead consider these uncertainties in the price domain, where more uncertain power is offered at a higher price instead of restricting the quantity offered. We demonstrate system-level impacts on a modified version of the RTS-GMLC system where wind generators create market offers valuing their uncertainties over scenario set of day-ahead production forecasts. The results are compared with a dispatch method in which wind energy is offered at zero marginal price and restricted based on the forecast percentile., Comment: 6 pages, 3 figures. Accepted to the 2023 American Control Conference (ACC)

In this paper we propose a co-design of the secondary frequency regulation in systems of AC microgrids and its cyber securty solutions. We term the secondary frequency regulator a Micro-Automatic Generation Control (Micro-AGC) for highlighting its same functionality as the AGC in bulk power systems. We identify sensory challenges and cyber threats facing the Micro-AGC. To address the sensory challenges, we introduce a new microgrid model by exploiting the rank-one deficiency property of microgrid dynamics. This model is used to pose an optimal Micro-AGC control problem that is easily implemented, because it does not require fast frequency measurements. An end-to-end cyber security solution to the False Data Injection (FDI) attack detection and mitigation is developed for the proposed Micro-AGC. The front-end barrier of applying off-the-shelf algorithms for cyber attack detection is removed by introducing a data-driven modeling approach. Finally, we propose an observer-based corrective control for an islanded microgrid and a collaborative mitigation schemes in systems of AC microgrids. We demonstrate a collaborative role of systems of microgrids during cyber attacks. The performance of the proposed cyber-resilient Micro-AGC is tested in a system of two networked microgrids., Comment: The manuscript has been accepted by IEEE Transactions on Smart Grid

This paper points out some key drawbacks of today's modeling and control underlying hierarchical electric power system operations and planning as the hidden roadblocks on the way to decarbonization. We suggest that these can be overcome by enhancing today's information exchange and control. This can be done by revealing and utilising inherent structure-preserving features of complex physical systems, and, based on this, by establishing multi-layered energy modeling. Each module (component, control area, non-utility-owned entities) can be characterized in terms of its interaction variable, and higher level models can be used to understand the interaction dynamics between different modules. Once the structure is understood, we propose nonlinear energy control for these modules which supports feed-forward self-adaptation to ensure feasible interconnected system. Based on these technology agnostic structures it becomes possible to expand today's Balancing Authorities (BA) to multi-layered interactive intelligent Balancing Authorities (iBAs) and to introduce protocols for flexible utilization of diverse technologies over broad ranges of temporal and spatial conditions., Comment: In proceedings of the 11th Bulk Power Systems Dynamics and Control Symposium (IREP 2022), July 25-30, 2022, Banff, Canada

The power interactions of any component in electric energy systems with the rest of the system happen naturally, as governed by the energy conservation principles. There may, however, occur instances when the rate at which power gets generated by one component through local energy conversion is not exactly the same as that absorbed by rest of the system. This is when instabilities get induced. To model and control such instabilities, this paper generalizes the notion of interaction variable used to characterize diverse system components in a unified manner. The same variable captures aggregate system-wide effects and sets reference points for multi-layered distributed output feedback control. It has a physical interpretation of instantaneous power and generalized reactive power. The higher layer design utilizes the interactive energy state-space model to derive intermediate reactive power control, which becomes a control command to the lower layer physical model. This command is implemented using either Feedback Linearizing Control (FBLC) or Sliding Mode Control (SMC), for which sufficient stability conditions are stated. This paper claims that the proposed design is fundamental to aligning dynamic interactions between components for stability and feasibility. Without loss of generality, we utilize a simple RLC circuit with a controllable voltage source for illustrations, which is a simplified representation of any controllable component in microgrids., Comment: Preprint submitted to Automatica (Revision 1)

In this paper, we consider the problem of controlling power consumption dynamics of residential heating, ventilation and air conditioning (HVAC) units so that they follow the grid-side power specifications. In order to do so, we design a novel dynamical energy controller which ensures regulation of the cumulative effects of power imbalances. For this, we derive a novel energy-based model that relates the HVAC physics-based dynamics to both real and reactive power balance at the point of interconnection with the grid. In contrast to several other approaches in the literature, we show that a limited number of HVAC units can meet the stringent performance metrics set by the ARPA-E/NODES program on following the frequency regulation signal, while maintaining consumer comfort. Theoretical and simulation-based model and control validation is provided by making use of real-world HVAC data., Comment: Preprint submitted to IEEE Transactions on Control Systems Technology

Frequent metering of electricity consumption is crucial for demand side management in smart grids. However, metered data can be processed fairly easily by employing well-established nonintrusive appliance load monitoring techniques to infer appliance usage, which reveals information about consumers' private lives. Existing load shaping techniques for privacy primarily focus only on altering metered real power, whereas smart meters collect reactive power consumption data as well for various purposes. This study addresses consumer privacy preservation via load shaping in a demand response scheme, considering both real and reactive power. We build a multi-objective optimization framework that enables us to characterize the interplay between privacy maximization, user cost minimization, and user discomfort minimization objectives. Our results reveal that minimizing information leakage due to a single component, e.g., real power, would suffer from overlooking information leakage due to the other component, e.g., reactive power, causing sub-optimal decisions. In fact, joint shaping of real and reactive power components results in the best possible privacy preservation performance, which leads to more than a twofold increase in privacy in terms of mutual information., Comment: 10 pages, 3 figures, preprint

In recent years, cyber-security of power systems has become a growing concern. To protect power systems from malicious adversaries, advanced defense strategies that exploit sophisticated detection algorithms are required. Motivated by this, in this paper we introduce an active defense method based on dynamic clustering. Our detection strategy uses a moving-target approach where information about the system's varying operating point is first used to cluster measurements according to their transfer function characteristics that change over time. Then, detection is carried out through series of similarity checks between measurements within the same cluster. The proposed method is effective in detecting cyber-attacks even when the attacker has extensive knowledge of the system parameters, model and detection policy at some point in time. The effectiveness of our proposed detection algorithm is demonstrated through a numerical example on the IEEE 24-bus power system.

Providing situational awareness in light of severe coordinated cyber-attacks on power grids, where many measurements may be untrusted, is necessary for reliable monitoring and resilient operation of the grid. In this scenario, the set of good measurements is by itself insufficient for state estimation due to loss of observability. In this paper, we present a resilient state estimation algorithm, based on output clustering. By augmenting the measurement set by respective cluster variables, the system observability is regained, and a reliable state estimate can be computed. We show the numerical performance of our proposed algorithm and its ability to successfully replace corrupted measurements using cluster variables through an example on the IEEE 24-bus power system., Comment: arXiv admin note: substantial text overlap with arXiv:2004.03838

This paper is motivated by the need to enhance today's Automatic Generation Control (AGC) for ensuring high quality frequency response in the changing electric power systems. Renewable energy sources, if not controlled carefully, create persistent fast and often large oscillations in their electric power outputs. A sufficiently detailed dynamical model of the interconnected system which captures the effects of fast nonlinear disturbances created by the renewable energy resources is derived for the first time. Consequently, the real power flow interarea oscillations and the resulting frequency deviations are modeled. The modeling is multi-layered, and the dynamics of each layer (component level (generator); control area (control balancing authority), and the interconnected system) is expressed in terms of internal states and the interaction variables (IntV) between the layers and within the layers. E-AGC is then derived using this model to show how these interarea oscillations can be canceled. Simulation studies are carried out on a 5-bus system., Comment: This paper is accepted to the IEEE PES General Meeting 2019

In this paper, we propose a method for estimating radial distribution grid admittance matrix using a limited number of measurement devices. Neither synchronized three-phase measurements nor phasor measurements are required. After making several practical assumptions, the method estimates even impedances of lines which have no local measurement devices installed. The computational complexity of the proposed method is low, and this makes it possible to use for on-line applications. The effectiveness of the proposed method is tested using data from a real-world distribution grid in Vienna, Austria., Comment: This paper has been accepted to IEEE PES GM 2019

This paper addresses the problem of minimum cost resilient actuation-sensing-communication co-design for regular descriptor systems while ensuring selective strong structural system's properties. More specifically, the problem consists of determining the minimum cost deployment of actuation and sensing technology, as well as communication between the these, such that decentralized control approaches are viable for an arbitrary realization of regular descriptor systems satisfying a pre-specified selective structure, i.e., some entries can be zero, nonzero, or either zero/nonzero. Towards this goal, we rely on strong structural systems theory and extend it to cope with the selective structure that casts resiliency/robustness properties and uncertainty properties of system's model. Upon such framework, we introduce the notion of selective strong structural fixed modes as a characterization of the feasibility of decentralized control laws. Also, we provide necessary and sufficient conditions for this property to hold, and show how these conditions can be leveraged to determine the minimum cost resilient placement of actuation-sensing-communication technology ensuring feasible solutions. In particular, we study the minimum cost resilient actuation and sensing placement, upon which we construct the solution to our problem. Finally, we illustrate the applicability the main results of this paper on an electric power grid example.

Large-scale integration of plug-in electric vehicles (PEV) in power systems can cause severe issues to the existing distribution system, such as branch congestions and significant voltage drops. As a consequence, smart charging strategies are crucial for the secure and reliable operation of the power system. This paper tries to achieve high penetration level of PEVs with the existing distribution system infrastructure by proposing a smart charging algorithm that can optimally utilize the distribution system capacity. Specifically, the paper proposes a max-weight PEV dispatch algorithm to control the PEV charging rates, subject to power system physical limits. The proposed max-weight PEV dispatch algorithm is proved to be throughput optimal under very mild assumptions on the stochastic dynamics in the system. This suggests that the costly distribution system infrastructure upgrade can be avoided, or failing that, at least successfully deferred. The proposed PEV dispatch algorithm is particularly attractive in integrating the renewable energy sources in the distribution system, by successfully absorbing their intermittency., Comment: 9 pages, 5 figures

This paper presents an information-theoretic approach to address the phasor measurement unit (PMU) placement problem in electric power systems. Different from the conventional 'topological observability' based approaches, this paper advocates a much more refined, information-theoretic criterion, namely the mutual information (MI) between the PMU measurements and the power system states. The proposed MI criterion can not only include the full system observability as a special case, but also can rigorously model the remaining uncertainties in the power system states with PMU measurements, so as to generate highly informative PMU configurations. Further, the MI criterion can facilitate robust PMU placement by explicitly modeling probabilistic PMU outages. We propose a greedy PMU placement algorithm, and show that it achieves an approximation ratio of (1-1/e) for any PMU placement budget. We further show that the performance is the best that one can achieve in practice, in the sense that it is NP-hard to achieve any approximation ratio beyond (1-1/e). Such performance guarantee makes the greedy algorithm very attractive in the practical scenario of multi-stage installations for utilities with limited budgets. Finally, simulation results demonstrate near-optimal performance of the proposed PMU placement algorithm., Comment: 8 pages, 7 figures

The concept of plug-in electric vehicles (PEV) are gaining increasing popularity in recent years, due to the growing societal awareness of reducing greenhouse gas (GHG) emissions, and gaining independence on foreign oil or petroleum. Large-scale deployment of PEVs currently faces many challenges. One particular concern is that the PEV charging can potentially cause significant impacts on the existing power distribution system, due to the increase in peak load. As such, this work tries to mitigate the impacts of PEV charging by proposing a decentralized smart PEV charging algorithm to minimize the distribution system load variance, so that a `flat' total load profile can be obtained. The charging algorithm is myopic, in that it controls the PEV charging processes in each time slot based entirely on the current power system states, without knowledge about future system dynamics. We provide theoretical guarantees on the asymptotic optimality of the proposed charging algorithm. Thus, compared to other forecast based smart charging approaches in the literature, the charging algorithm not only achieves optimality asymptotically in an on-line, and decentralized manner, but also is robust against various uncertainties in the power system, such as random PEV driving patterns and distributed generation (DG) with highly intermittent renewable energy sources., Comment: 12 pages, 9 figures