Presentations

Abstract:Present Day Ahead (DA) power markets make integer unit commitment decisions and schedule the resulting available capacity across energy and reserves to minimize the costs of (i) balancing energy supply and demand and (ii) securing system reliability. Following the closing of the DA market where financial or virtual bids are allowed, ISOs, whose assessment of demand uncertainty differs from that of the demand bidding market participants (financial, load serving entities etc.), perform an out of market Reliability Unit Commitment (RUC) step that may augment the units committed during the DA market clearing process. 

Whereas system reliability has been reasonably assured in the past through securing exogenously determined levels of reserves to guard against by and large uncorrelated contingencies (N-1 or N-1.5 largest unit capacity), ever increasing volatile renewable generation is introducing spatiotemporally correlated risky generation and demand assets (e.g. Transmission connected wind farms and distribution connected PV) rendering future optimal system reliability assurance a harder task. As such, future DA power markets face much more demanding unit commitment, economic dispatch, and pricing requirements that depend crucially on assessing and managing individual asset risks and their impact on the power system.

We propose a new DA market design that internalizes reserve requirements through probabilistic system reliability constraints including both energy and reserve bids and offers by supply as well as demand with risky capacity availabilities. Uncertain weather and associated power forecasts are modeled through an uncertainty set of spatiotemporally jointly distributed trajectories of asset-specific available capacity. The uncertainty set is designed to provide probabilistic system reliability guarantees. Moreover, demand response – sometimes referred to as acceptable quality of supply — is commoditized by allowing demand to plan on and provide reserves of different types. Thus consumption (and generation) available capacity is modeled in terms of a basket of diversified products consisting of energy as well as reserves (primary, secondary, tertiary, storage-like etc.) and priced accordingly. Most notably, DA market clearing prices are dependent not only on the dual variables of energy balance constraints but also on the dual variables of reliability constraints associated with each trajectory in the aforementioned uncertainty set modulated by the impact of each asset-specific product on the left hand side of the linear reliability constraint.

We will present the proposed market design featuring endogenous reserve requirement determination, discuss the acceptability to stakeholders of expected-marginal-cost-based clearing prices, and speculate on other market pricing alternatives.

Authors:strong> P. Andrianesis, D. Bertsimas, M. Caramanis (presenting author)

Abstract:This presentation will discuss the power system optimization programs at ARPA-E.  Future ISO day-ahead and real-time markets will present new challenges to solving these markets. The GO competition is aimed at solving the OPF problems better and faster. We will discuss the first challenges and the results. The HIPPO project goal is a 10x speed up of the day-ahead MISO market.  It is going into a new phase with additional market designs to solve. PERFORM: is just starting is focused on  risk-aware optimization.

Abstract:Relative to financial markets, current electricity market designs lack sophisticated means of systemic and asset-level risk quantification and trading, thus producing market outcomes incapable of incentivizing cost-efficient risk mitigation. This presentation explores parallels between electricity and financial markets and describes a stochastic market design that allows for (i) explicitly quantifying and limiting the risk of market constraint violations and (ii) introducing such risk-trading instruments as Arrow-Debreu Securities. Taken together, explicit risk quantification and trading make it possible to produce uncertainty- and risk-aware energy and reserve allocations and prices that achieve desirable market design properties (e.g. efficiency, revenue adequacy, cost recovery) in a renewable-rich markets. 

Abstract:The task of finding AC feasible power flow solutions in severely damaged power networks has been a long standing open problem. The crux of the challenge is that as a power network’s configuration departs from its established operating point, the task of adjusting the generator dispatch, voltage profile and system loading to ensure AC feasibility becomes “maddeningly difficult” to do by hand or heuristics. Attempts to automate this process with simple power flow approximations, such as the DC Power Flow model, have met with limited success. In this work we highlight the mathematical properties of the AC Power Flow equations that make solving multi-contingency problems particularly challenging. We then propose novel methods based on convex relaxations to find reasonable operating points in damaged power networks. The resulting approach can find AC feasible power flow solutions to severely damaged networks in seconds and, to the best of our knowledge, represents the first reliable approach to solving the long standing multi-contingency AC power flow problem. The proposed approach has been effective in quantifying the vulnerabilities of real-world power networks to extreme events such as hurricanes and storm surge.

Abstract:The alternating current optimal power flow (AC-OPF) problem is critical to power system operations and planning, but it is generally hard to solve due to its nonconvex and large-scale nature. This paper proposes a scalable decomposition approach in which the power network is decomposed into a master network and a number of subnetworks, where each network has its own AC-OPF subproblem. This formulates a two-stage optimization problem and requires only a small amount of communication between the master and subnetworks. The key contribution is a smoothing technique that renders the response of a subnetwork differentiable with respect to the input from the master problem, utilizing properties of the barrier problem formulation that naturally arises when subproblems are solved by a primal-dual interior-point algorithm. Consequently, existing efficient nonlinear programming solvers can be used for both the master problem and the subproblems. The advantage of this framework is that speedup can be obtained by processing the subnetworks in parallel, and it has convergence guarantees under reasonable assumptions. The formulation is readily extended to instances with stochastic subnetwork loads. Numerical results show favorable performance and illustrate the scalability of the algorithm which is able to solve instances with more than 11 million buses.

Abstract:The security-constrained AC optimal power flow problem (SCACOPF) is a critical piece in the daily operations of power systems. We will present a solution methodology for SCACOPF problems that uses nonlinear programming, interior-point algorithms, and parallel computing to solve realistic SCACOPF instances in realtime. We will outline our primal decomposition approach and discuss its mathematical advantages and challenges as well as its current distributed-memory asynchronous (lock free) parallel implementation. In the second part of the talk, we will discuss opportunities for considerable improvements of realtime ACOPF optimization capabilities that can be obtained from the computing power increase expected from the emerging GPU processors. To this end, we will present challenges in utilizing effectively such computing hardware for the solution of large-scale ACOPF problems.

Abstract:Time-and-Level-of-Use (TLOU) is a recently proposed pricing policy for electric energy, extending Time-of-Use with the addition of a capacity that users can book for a given time frame, reducing their expected energy cost if they respect this self-determined capacity limit. In this presentation we will present the principles of TLOU and provide an overview of the work done on mathematical optimization approaches for various aspects of TLOU and its potential impact on power systems operations.

Restriction: Please note that I am hosting an ENRE Online Event on Thu 10 Dec for 1000-1130 Eastern time, and that I am on a PhD defense on Fri 11 Dec for 0900-1300 Eastern time. Please schedule my talk to avoid those conflicts. 

Abstract:We consider a storage device, such as a pumped storage hydro generator, that has a state-of-charge together with mutually exclusive charging and generating modes and which is purchasing or selling electricity. We develop valid inequalities for a simplified storage model that uses binary variables to represent the charging and generating modes and also consider an objective that evaluates the net benefit of traded electricity and stored energy. We present conditions for the optimum of the continuous relaxation of the formulation to have binary values for the charging and generation mode variables and demonstrate the result numerically with a small example system. We also numerically verify that the valid inequalities can significantly improve the computation time for large-scale systems compared to existing models in the literature. This is joint work with Yonghong Chen and Bing Huang.

Abstract:Although electricity distribution grids and water distribution systems are traditionally operated independently, these systems are interconnected and interdependent. The interdependency is chiefly manifested through the electricity consumption of electric-driven water pumps. The coordination of the two networks can bring about benefits to both systems in terms of economic and sustainable operation. This talk presents optimization methods for managing resources across power and water distribution networks while simultaneously accounting for the coupling between the two infrastructures. The principal challenge arises from the nonconvex water network hydraulics. Novel successive linearization methods provide an efficient solution to the problem. Case studies illustrate the benefits with respect to decoupled designs and are verified by the benchmark software EPANET.

Abstract:We study optimization for data-driven decision-making when we have historical observations of the uncertain parameters (e.g., demand) within the optimization model together with concurrent observations of covariates (e.g., seasonality, weather forecast).  Given a new covariate observation, the goal is to choose a decision (e.g., generator schedules) that minimizes the expected cost conditioned on this observation.  We investigate three data-driven frameworks that integrate a machine learning prediction model within a stochastic programming sample average approximation (SAA) for approximating the solution to this problem.  The frameworks we investigate are flexible and accommodate parametric, nonparametric, and semiparametric regression techniques.  We derive conditions on the data generation process, the prediction model, and the stochastic program under which solutions of these data-driven SAAs are consistent and asymptotically optimal, and also derive convergence rates and finite sample guarantees.  Computational experiments validate our theoretical results and demonstrate the potential advantages of our data-driven formulations over existing approaches.   Potential applications in energy and extensions will be briefly discussed.

Abstract:JuDGE is an open-source Julia package that solves multi-stage stochastic programming models for capacity expansion. It applies a form of Dantzig-Wolfe decomposition to decouple a scenario tree into nodes representing different states of the world. The first part of the talk will briefly cover the theory underlying JuDGE and describe some recent applications of JuDGE to problems in electricity transmission expansion planning and long-term planning for 100% renewable electricity systems. The second part of the talk will be more tutorial in nature, demonstrating the features of the package, and how to download and apply it to capacity planning problems.

Abstract:In this talk, we introduce methods that remove the barrier for applying neural networks in real-life power systems, and unlock a series of new applications. More specifically, we introduce a framework for (i) verifying neural network behavior in power systems and (ii) obtain provable worst-case guarantees of their performance. Up to this moment, neural networks have been applied in power systems as a black-box; this has presented a major barrier for their adoption in practice. Using a rigorous framework based on mixed integer linear programming, our methods can determine the range of inputs that neural networks classify as safe or unsafe; and, when it comes to regression neural networks, our methods allow to obtain provable worst-case guarantees of the neural network performance. Such methods have the potential to build the missing trust of power system operators on neural networks, and unlock a series of new applications in power systems and other safety-critical systems.

Abstract:Inspired by recent end-to-end data-driven approaches for power systems operation, power electronics control, and building automation, we consider the problem of optimal and constrained control for unknown systems. A novel data-enabled predictive control (DeePC) algorithm is presented that computes optimal and safe control policies using real-time feedback driving the unknown system along a desired trajectory while satisfying system constraints. Using a finite number of data samples from the unknown system, our proposed algorithm uses a behavioral systems theory approach to learn a non-parametric system model used to predict future trajectories. We show that, in the case of deterministic linear time-invariant systems, the DeePC algorithm is equivalent to the widely adopted Model Predictive Control (MPC), but it generally outperforms subsequent system identification and model-based control. To cope with nonlinear and stochastic systems, we propose salient regularizations to the DeePC algorithm, which are founded on recent advances in distributionally robust optimization. We illustrate our results with experimental and simulation case studies from autonomous energy systems.

Abstract:Bilevel mixed-integer programs arise naturally in problems concerning power systems resilience. The Benders Decomposition method attempts to solve such problems by decomposing into a master problem and inner sub-problem(s), and solving them iteratively. In each iteration, a stronger relaxation of the master problem is solved by adding a Benders cut which involves a product-sum of variables in the master problem and values of dual variables in the inner problem. However, the classical method performs poorly when the inner problem consists of binary variables and non-linear constraints. In this work, we suggest a new heuristic to address this limitation by modifying the so-called Generalized Benders Decomposition. Our approach involves modifying the right-hand side of the Benders cut to be a value determined by the sum of values of a subset of inner dual variables. We show how the size of this subset can be selected to achieve a reasonable tradeoff between solution accuracy and computational effort. We also discuss how to strengthen the modified Benders cut by using the reduced cost of inner problem’s dual linear relaxation and leveraging the properties of power system restoration.

This work is joint with Devendra Shelar and Ian Hiskens.

Abstract:We investigate the problem of estimating the state of a network from heterogeneous sensors with different sampling and reporting rates. In lieu of a batch linear least-squares (LS) approach – well-suited for static networks, where a sufficient number of measurements could be collected to obtain a full-rank design matrix – we propose an online algorithm to estimate the possibly time-varying network state by processing measurements as and when available. The design of the algorithm hinges on a generalized LS cost augmented with a proximal-point-type regularization. With the solution of the regularized LS problem available in closed-form, the online algorithm is written as a linear dynamical system where the state is updated based on the previous estimate and based on the new available measurements. Conditions under which the algorithmic steps are in fact a contractive mapping are shown, and bounds on the estimation error are derived for different noise models. Numerical simulations, including a power system case, are provided to corroborate the analytical findings.

Abstract:Online optimization is a powerful framework in machine learning that has seen numerous applications to problems in distributed systems, robotics, autonomous planning, and sustainability. At Caltech, we began by applying online optimization to design sustainable data centers a decade ago; and now we have used tools from online optimization to develop algorithms for demand response, energy storage management, electric vehicle charging, and beyond. In this talk, I will highlight both the applications of online optimization and the theoretical progress that has been driven by these applications. Over the past decade, the community has moved from designing algorithms for one-dimensional problems with restrictive assumptions on costs to general results for high-dimensional non-convex problems that highlight the role of constraints, predictions, delay, and more. In particular, I will present a new connection between online optimization and adversarial control has emerged, and I will highlight how advances in online optimization can lead to advances in the control of time-varying linear dynamical systems.

Abstract:Distributed energy resources have been almost exclusively deployed and operated under a decentralized decision-making process. In this paper, we assess the evolution of a power system with centrally planned utility-scale generation, transmission, distribution, and distributed resources. We adapt a capacity expansion model to represent both centralized and decentralized decision-making paradigms under various electricity rate structures. This paper shows that a centralized planning approach could save 7% to 37% of total system costs over a 15-year time horizon using a Western United States utility as a case study. We show that centralized decision-making deploys substantially more utility-scale solar and distributed storage compared to a decentralized decision-making paradigm. We demonstrate how a utility could largely overcome the complications of decentralized distributed resource decision-making by incentivizing regulators to develop electricity rates that more closely reflect time- and location-specific, long-run marginal costs. The results from this analysis yield insights that are useful for long-term utility planning and electric utility rate design.

Abstract:Development & commercialization of novel energy technologies takes time. New technologies will enter evolving future electricity systems and compete with a range of extant resources, introducing considerable uncertainty for developers, researchers, and funders. Given limited resources, which avenues for cost or performance improvement are most important for future commercial success and societal impact? This presentation will discuss how optimization models of long-term electricity system capacity expansion and wide-scale parametric uncertainty analysis can be employed to evaluate the “technology design space” for novel low-carbon technologies and provide insights to guide R&D efforts and funding and policy decisions. Results from a recently completed evaluation of long duration energy storage will be presented. Extensions of this general approach to evaluate design choices for flexible carbon capture and geothermal energy systems will also be described.