arXiv subjects

Ram Rajagopal

Publications and source records attributed to Ram Rajagopal.

At least 91 records · Page 5Linked to original sources

arXiv2017

Flexible Market for Smart Grid: Coordinated Trading of Contingent Contracts

A coordinated trading process is proposed as a design for an electricity market with significant uncertainty, perhaps from renewables. In this process, groups of agents propose to the system operator (SO) a contingent buy and sell trade that is balanced, i.e. the sum of demand bids and the sum of supply bids are equal. The SO accepts the proposed trade if no network constraint is violated or curtails it until no violation occurs. Each proposed trade is accepted or curtailed as it is presented. The SO also provides guidance to help future proposed trades meet network constraints. The SO does not set prices, and there is no requirement that different trades occur simultaneously or clear at uniform prices. Indeed, there is no price-setting mechanism. However, if participants exploit opportunities for gain, the trading process will lead to an efficient allocation of energy and to the discovery of locational marginal prices (LMPs). The great flexibility in the proposed trading process and the low communication and control burden on the SO may make the process suitable for coordinating producers and consumers in the distribution system.

math.OC↗

arXiv2017

Competition and Efficiency of Coalitions in Cournot Games with Uncertainty

We investigate the impact of coalition formation on the efficiency of Cournot games where producers face uncertainties. In particular, we study a market model where firms must determine their output before an uncertain production capacity is realized. In contrast to standard Cournot models, we show that the game is not efficient when there are many small firms. Instead, producers tend to act conservatively to hedge against their risks. We show that in the presence of uncertainty, the game becomes efficient when firms are allowed to take advantage of diversity to form groups of certain sizes. We characterize the tradeoff between market power and uncertainty reduction as a function of group size. In particular, we compare the welfare and output obtained with coalitional competition, with the same benchmarks when output is controlled by a single system operator. We show when there are $N$ firms present, competition between groups of size $Ω(\sqrt{N})$ results in equilibria that are socially optimal in terms of welfare and groups of size $Ω(N^{2/3})$ are socially optimal in terms of production. We also extend our results to the case of uncertain demand by establishing an equivalency between Cournot oligopoly and Cournot Oligopsony. We demonstrate our results with real data from electricity markets with significant wind power penetration.

cs.GT↗

arXiv2017

Pricing Residential Electricity Based on Individual Consumption Behaviors

The conventional practice of retail electric utilities is to aggregate customers geographically. The utility purchases electricity for its customers via bulk transactions on the wholesale market, and it passes these costs along to its customers, the end consumers, through their rate plan. Typically, all residential consumers are offered the same per unit rate plan, which leads to cost sharing. Some consumers use their electricity at peak hours, when it is more expensive on the wholesale market, and others consume mostly at off peak hours, when it is cheaper, but they all enjoy the same per unit rate through their utility. This paper proposed a method for the utility to segment a population of consumers on the basis of their individual consumption patterns. An optimal recruitment algorithm was developed to aggregate consumers into groups with a relatively low per unit cost of electricity on the wholesale market. It was then proposed that the utility should group together enough consumers to ensure an adequately low forecast error, which is related to risks it faces in wholesale market transactions. Finally, it was shown that by repeated application of this process, the utility could segment the entire population into groups and offer them differentiated rate plans based on their actual consumption behavior. These groupings are stable in the sense that no one consumer can unilaterally improve her outcome.

math.OC↗

arXiv2017

Energy Storage Sharing Strategy in Distribution Networks Using Bi-level Optimization Approach

In this paper, we address the energy storage management problem in distribution networks from the perspective of an independent energy storage manager (IESM) who aims to realize optimal energy storage sharing with multi-objective optimization, i.e., optimizing the system peak loads and the electricity purchase costs of the distribution company (DisCo) and its customers. To achieve the goal of the IESM, an energy storage sharing strategy is therefore proposed, which allows DisCo and customers to control the assigned energy storage. The strategy is updated day by day according to the system information change. The problem is formulated as a bi-level mathematical model where the upper level model (ULM) seeks for optimal division of energy storage among Disco and customers, and the lower level models (LLMs) represent the minimizations of the electricity purchase costs of DisCo and customers. Further, in order to enhance the computation efficiency, we transform the bi-level model into a single-level mathematical program with equilibrium constraints (MPEC) model and linearize it. Finally, we validate the effectiveness of the strategy and complement our analysis through case studies.

math.OC↗

arXiv2017

Mapping Rule Estimation for Power Flow Analysis in Distribution Grids

The increasing integration of distributed energy resources (DERs) calls for new monitoring and operational planning tools to ensure stability and sustainability in distribution grids. One idea is to use existing monitoring tools in transmission grids and some primary distribution grids. However, they usually depend on the knowledge of the system model, e.g., the topology and line parameters, which may be unavailable in primary and secondary distribution grids. Furthermore, a utility usually has limited modeling ability of active controllers for solar panels as they may belong to a third party like residential customers. To solve the modeling problem in traditional power flow analysis, we propose a support vector regression (SVR) approach to reveal the mapping rules between different variables and recover useful variables based on physical understanding and data mining. We illustrate the advantages of using the SVR model over traditional regression method which finds line parameters in distribution grids. Specifically, the SVR model is robust enough to recover the mapping rules while the regression method fails when 1) there are measurement outliers and missing data, 2) there are active controllers, or 3) measurements are only available at some part of a distribution grid. We demonstrate the superior performance of our method through extensive numerical validation on different scales of distribution grids.

eess.SY↗

arXiv2017

PaToPa: A Data-Driven Parameter and Topology Joint Estimation Framework in Distribution Grids

The increasing integration of distributed energy resources (DERs) calls for new planning and operational tools. However, such tools depend on system topology and line parameters, which may be missing or inaccurate in distribution grids. With abundant data, one idea is to use linear regression to find line parameters, based on which topology can be identified. Unfortunately, the linear regression method is accurate only if there is no noise in both the input measurements (e.g., voltage magnitude and phase angle) and output measurements (e.g., active and reactive power). For topology estimation, even with a small error in measurements, the regression-based method is incapable of finding the topology using non-zero line parameters with a proper metric. To model input and output measurement errors simultaneously, we propose the error-in-variables (EIV) model in a maximum likelihood estimation (MLE) framework for joint line parameter and topology estimation. While directly solving the problem is NP-hard, we successfully adapt the problem into a generalized low-rank approximation problem via variable transformation and noise decorrelation. For accurate topology estimation, we let it interact with parameter estimation in a fashion that is similar to expectation-maximization fashion in machine learning. The proposed PaToPa approach does not require a radial network setting and works for mesh networks. We demonstrate the superior performance in accuracy for our method on IEEE test cases with actual feeder data from South California Edison.

eess.SY↗

arXiv2017

A Sparse Linear Model and Significance Test for Individual Consumption Prediction

Accurate prediction of user consumption is a key part not only in understanding consumer flexibility and behavior patterns, but in the design of robust and efficient energy saving programs as well. Existing prediction methods usually have high relative errors that can be larger than 30% and have difficulties accounting for heterogeneity between individual users. In this paper, we propose a method to improve prediction accuracy of individual users by adaptively exploring sparsity in historical data and leveraging predictive relationship between different users. Sparsity is captured by popular least absolute shrinkage and selection estimator, while user selection is formulated as an optimal hypothesis testing problem and solved via a covariance test. Using real world data from PG&E, we provide extensive simulation validation of the proposed method against well-known techniques such as support vector machine, principle component analysis combined with linear regression, and random forest. The results demonstrate that our proposed methods are operationally efficient because of linear nature, and achieve optimal prediction performance.

stat.ML↗

arXiv2017

Actively Calibrated Line Mountable Capacitive Voltage Transducer For Power Systems Applications

A class of Actively Calibrated Line Mounted Capacitive Voltage Transducers (LMCVT) are introduced as a viable line mountable instrumentation option for deploying large numbers of voltage transducers onto the medium and high voltage systems. Active Calibration is shown to reduce the error of line mounted voltage measurements by an order of magnitude from previously published techniques. The instrument physics and sensing method is presented and the performance is evaluated in a laboratory setting. Finally, a roadmap to a fully deployable prototype is shown.

physics.ins-det↗

arXiv2016

Distribution System Outage Detection using Consumer Load and Line Flow Measurements

An outage detection framework for power distribution networks is proposed. Given the tree structure of the distribution system, a method is developed combining the use of real-time power flow measurements on edges of the tree with load forecasts at the nodes of the tree. A maximum a posteriori detector {\color{black} (MAP)} is formulated for arbitrary number and location of outages on trees which is shown to have an efficient detector. A framework relying on the maximum missed detection probability is used for optimal sensor placement and is solved for tree networks. Finally, a set of case studies is considered using feeder data from the Pacific Northwest National Laboratories. We show that a 10\% loss in mean detection reliability network wide reduces the required sensor density by 60 \% for a typical feeder if efficient use of measurements is performed.

eess.SY↗

arXiv2016

Economic information from Smart Meter: Nexus Between Demand Profile and Electricity Retail Price Between Demand Profile and Electricity Retail Price

In this paper, we demonstrate that a consumer's marginal system impact is only determined by their demand profile rather than their demand level. Demand profile clustering is identical to cluster consumers according to their marginal impacts on system costs. A profile-based uniform-rate price is economically efficient as real-time pricing. We develop a criteria system to evaluate the economic efficiency of an implemented retail price scheme in a distribution system by comparing profile clustering and daily-average clustering. Our criteria system can examine the extent of a retail price scheme's inefficiency even without information about the distribution system's daily cost structure. We analyze data from a real distribution system in China. In this system, targeting each consumer's high-impact days is more efficient than target high-impact consumers.

econ.GN↗

arXiv2015

Online Modified Greedy Algorithm for Storage Control under Uncertainty

This paper studies the general problem of operating energy storage under uncertainty. Two fundamental sources of uncertainty are considered, namely the uncertainty in the unexpected fluctuation of the net demand process and the uncertainty in the locational marginal prices. We propose a very simple algorithm termed Online Modified Greedy (OMG) algorithm for this problem. A stylized analysis for the algorithm is performed, which shows that comparing to the optimal cost of the corresponding stochastic control problem, the sub-optimality of OMG is bounded and approaches zero in various scenarios. This suggests that, albeit simple, OMG is guaranteed to have good performance in some cases; and in other cases, OMG together with the sub-optimality bound can be used to provide a lower bound for the optimal cost. Such a lower bound can be valuable in evaluating other heuristic algorithms. For the latter cases, a semidefinite program is derived to minimize the sub-optimality bound of OMG. Numerical experiments are conducted to verify our theoretical analysis and to demonstrate the use of the algorithm.

math.OC↗

arXiv2015

Control of Generalized Energy Storage Networks

The integration of intermittent and volatile renewable energy resources requires increased flexibility in the operation of the electric grid. Storage, broadly speaking, provides the flexibility of shifting energy over time; network, on the other hand, provides the flexibility of shifting energy over geographical locations. The optimal control of general storage networks in uncertain environments is an important open problem. The key challenge is that, even in small networks, the corresponding constrained stochastic control problems with continuous spaces suffer from curses of dimensionality, and are intractable in general settings. For large networks, no efficient algorithm is known to give optimal or near-optimal performance. This paper provides an efficient and provably near-optimal algorithm to solve this problem in a very general setting. We study the optimal control of generalized storage networks, i.e., electric networks connected to distributed generalized storages. Here generalized storage is a unifying dynamic model for many components of the grid that provide the functionality of shifting energy over time, ranging from standard energy storage devices to deferrable or thermostatically controlled loads. An online algorithm is devised for the corresponding constrained stochastic control problem based on the theory of Lyapunov optimization. We prove that the algorithm is near-optimal, and construct a semidefinite program to min- imize the sub-optimality bound. The resulting bound is a constant that depends only on the parameters of the storage network and cost functions, and is independent of uncertainty realizations. Numerical examples are given to demonstrate the effectiveness of the algorithm.

math.OC↗

arXiv2015

Stability of Interconnected DC Converters

This paper addresses stability issues of DC networks with constant power loads (CPL). Common DC networks, such as automotive electrical systems and DC microgrids, typically have a step-up/down converter connected in one side to the main bus and, on the other, to the load. When load is constant power it can generate destabilizing effects if not proper controlled. This paper shows that converters driving CPLs can make the system unstable, even if they are individually stable, depending on network parameters. We mitigate this problem by means of passive components externally connected to the converter/CPL subsystem. The analysis is verified through simulations. We are able to show that certain converter circuit configurations achieve the so called plug-and-play property, which stabilizes the interconnected system for all network parameters. This property is desirable since it is does not require the knowledge of detailed system topology and parameters, which can be time varying and difficult to obtain. This method also contrasts to existing practices of load augmentation, which can lead to severe efficiency losses.

math.OC↗

arXiv2015

Competition and Coalition Formation of Renewable Power Producers

We investigate group formations and strategic behaviors of renewable power producers in electricity markets. These producers currently bid into the day-ahead market in a conservative fashion because of the real-time risk associated with not meeting their bid amount. It has been suggested in the literature that producers would bid less conservatively if they can form large groups to take advantages of spatial diversity to reduce the uncertainty in their aggregate output. We show that large groups of renewable producers would act strategically to lower the aggregate output because of market power. To maximize renewable power production, we characterize the trade-off between market power and generation uncertainty as a function of the size of the groups. We show there is a sweet spot in the sense that there exists groups that are large enough to achieve the uncertainty reduction of the grand coalition, but are small enough such that they have no significant market power.We consider both independent and correlated forecast errors under a fixed real-time penalty. We also consider a real-time market where both selling and buying of energy are allowed. We validate our claims using PJM and NREL data.

math.OC↗

arXiv2015

Approximation Algorithms for Optimization of Combinatorial Dynamical Systems

This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide computationally tractable solution methods even when the dimension of the system and the number of the binary variables are large. The proposed method employs a linear approximation of the objective function such that the approximate problem is defined over the feasible space of the binary decision variables, which is a discrete set. To define such a linear approximation, we propose two different variation methods: one uses continuous relaxation of the discrete space and the other uses convex combinations of the vector field and running payoff. The approximate problem is a 0-1 linear program, which can be solved by existing polynomial-time exact or approximation algorithms, and does not require the solution of the dynamical system. Furthermore, we characterize a sufficient condition ensuring the approximate solution has a provable suboptimality bound. We show that this condition can be interpreted as the concavity of the objective function. The performance and utility of the proposed algorithms are demonstrated with the ON/OFF control problems of interdependent refrigeration systems.

math.OC↗

arXiv2014

Distributed Online Modified Greedy Algorithm for Networked Storage Operation under Uncertainty

The integration of intermittent and stochastic renewable energy resources requires increased flexibility in the operation of the electric grid. Storage, broadly speaking, provides the flexibility of shifting energy over time; network, on the other hand, provides the flexibility of shifting energy over geographical locations. The optimal control of storage networks in stochastic environments is an important open problem. The key challenge is that, even in small networks, the corresponding constrained stochastic control problems on continuous spaces suffer from curses of dimensionality, and are intractable in general settings. For large networks, no efficient algorithm is known to give optimal or provably near-optimal performance for this problem. This paper provides an efficient algorithm to solve this problem with performance guarantees. We study the operation of storage networks, i.e., a storage system interconnected via a power network. An online algorithm, termed Online Modified Greedy algorithm, is developed for the corresponding constrained stochastic control problem. A sub-optimality bound for the algorithm is derived, and a semidefinite program is constructed to minimize the bound. In many cases, the bound approaches zero so that the algorithm is near-optimal. A task-based distributed implementation of the online algorithm relying only on local information and neighbor communication is then developed based on the alternating direction method of multipliers. Numerical examples verify the established theoretical performance bounds, and demonstrate the scalability of the algorithm.

math.OC↗

arXiv2014

Targeting Customers for Demand Response Based on Big Data

Selecting customers for demand response programs is challenging and existing methodologies are hard to scale and poor in performance. The existing methods were limited by lack of temporal consumption information at the individual customer level. We propose a scalable methodology for demand response targeting utilizing novel data available from smart meters. The approach relies on formulating the problem as a stochastic integer program involving predicted customer responses. A novel approximation is developed algorithm so it can scale to problems involving millions of customers. The methodology is tested experimentally using real utility data.

stat.AP↗

arXiv2014

Distribution System Load and Forecast Model

This short document provides experimental evidence for the set of assumptions on the mean load and forecast errors made in \cite{Sevlian2014A_Outage} and \cite{Sevlian2014B_Outage}. We show that the mean load at any given node is distributed normally, where we compute the mean and variance. We then present an aggregation-error curve for a single day ahead forecaster. Residual analysis shows that beyond 500 customers, gaussian residuals is a reasonable model. We then show the forecaster has uncorrelated errors.

stat.AP↗