arXiv subjects

Pravin Varaiya

Publications and source records attributed to Pravin Varaiya.

At least 19 recordsLinked to original sources

arXiv2023

Mobile Energy Storage in Power Network: Marginal Value and Optimal Operation

This paper examines the marginal value of mobile energy storage, i.e., energy storage units that can be efficiently relocated to other locations in the power network. In particular, we formulate and analyze the joint problem for operating the power grid and a fleet of mobile storage units. We use two different storage models: rapid storage, which disregards travel time and power constraints, and general storage, which incorporates them. By explicitly connecting the marginal value of mobile storage to locational marginal prices (LMPs), we propose efficient algorithms that only use LMPs and transportation costs to optimize the relocation trajectories of the mobile storage units. Furthermore, we provide examples and conditions under which the marginal value of mobile storage is strictly higher, equal to, or strictly lower than the sum of marginal value of corresponding stationary storage units and wires. We also propose faster algorithms to approximate the optimal operation and relocation for our general mobile storage model, and illustrate our results with simulations of an passenger EV and a heavy-duty electric truck in the PJM territory.

eess.SY↗

arXiv2022

Electric Vehicle Battery Sharing Game for Mobile Energy Storage Provision in Power Networks

Electric vehicles (EVs) equipped with a bidirectional charger can provide valuable grid services as mobile energy storage. However, proper financial incentives need to be in place to enlist EV drivers to provide services to the grid. In this paper, we consider two types of EV drivers who may be willing to provide mobile storage service using their EVs: commuters taking a fixed route, and on-demand EV drivers who receive incentives from a transportation network company (TNC) and are willing to take any route. We model the behavior of each type of driver using game theoretic methods, and characterize the Nash equilibrium (NE) of an EV battery sharing game where each EV driver withdraws power from the grid to charge its EV battery at the origin of a route, travels from the origin to the destination, and then discharges power back to the grid at the destination of the route. The driver earns a payoff that depends on the participation of other drivers and power network conditions. We characterize the NE in three situations: when there are only commuters, when there are only on-demand TNC drivers, and when the two groups of drivers co-exist. In particular, we show that the equilibrium outcome supports the social welfare in each of these three cases.

eess.SY↗

arXiv2021

Spatial Pricing in Ride-Sourcing Markets under a Congestion Charge

This paper studies the optimal spatial pricing for a ride-sourcing platform subject to a congestion charge. The platform determines the ride prices over the transportation network to maximize its profit, while the regulatory agency imposes the congestion charge to reduce traffic congestion in the urban core. A network economic equilibrium model is proposed to capture the intimate interactions among passenger demand, driver supply, passenger and driver waiting times, platform pricing, vehicle repositioning and flow balance over the transportation network. The overall optimal pricing problem is cast as a non-convex program. An algorithm is proposed to approximately compute its optimal solution, and a tight upper bound is established to evaluate its performance loss with respect to the globally optimal solution. Using the proposed model, we compare the impacts of three forms of congestion charge: (a) a one-directional cordon charge on ride-sourcing vehicles that enter the congestion area; (b) a bi-directional cordon charge on ride-sourcing vehicles that enter or exit the congestion area; (c) a trip-based congestion charge on all ride-sourcing trips. We show that the one-directional congestion charge not only reduces the ride-sourcing traffic in the congestion area, but also reduces the travel cost outside the congestion zone and benefits passengers in these underserved areas. We further show that compared to other congestion charges, the one-directional cordon charge is more effective in congestion mitigation: to achieve the same congestion-mitigation target, it imposes a smaller cost on passengers, drivers, and the platform. On the other hand, compared with the other charges, the trip-based congestion charge is more effective in revenue-raising: to raise the same tax revenue, it leads to a smaller loss to passengers, drivers, and the platform.

math.OC↗

arXiv2021

Safety Challenges for Autonomous Vehicles in the Absence of Connectivity

Autonomous vehicles (AVs) are promoted as a technology that will create a future with effortless driving and virtually no traffic accidents. AV companies claim that, when fully developed, the technology will eliminate 94% of all accidents that are caused by human error. These AVs will likely avoid the large number of crashes caused by impaired, distracted or reckless drivers. But there remains a significant proportion of crashes for which no driver is directly responsible. In particular, the absence of connectivity of an AV with its neighboring vehicles (V2V) and the infrastructure (I2V) leads to a lack of information that can induce such crashes. Since AV designs today do not require such connectivity, these crashes would persist in the future. Using prototypical examples motivated by the NHTSA pre-crash scenario typology, we show that fully autonomous vehicles cannot guarantee safety in the absence of connectivity. Combining theoretical models and empirical data, we also argue that such hazardous scenarios will occur with a significantly high probability. This suggests that incorporating connectivity is an essential step on the path towards safe AV technology.

cs.RO↗

arXiv2021

Impact of Congestion Charge and Minimum Wage on TNCs: A Case Study for San Francisco

This paper describes the impact on transportation network companies (TNCs) of the imposition of a congestion charge and a driver minimum wage. The impact is assessed using a market equilibrium model to calculate the changes in the number of passenger trips and trip fare, number of drivers employed, the TNC platform profit, the number of TNC vehicles, and city revenue. Two charges are considered: (a) a charge per TNC trip similar to an excise tax, and (b) a charge per vehicle operating hour (whether or not it has a passenger) similar to a road tax. Both charges reduce the number of TNC trips, but this reduction is limited by the wage floor, and the number of TNC vehicles reduced is not significant. The time-based charge is preferable to the trip-based charge since, by penalizing idle vehicle time, the former increases vehicle occupancy. In a case study for San Francisco, the time-based charge is found to be Pareto superior to the trip-based charge as it yields higher passenger surplus, higher platform profits, and higher tax revenue for the city.

econ.EM↗

arXiv2020

Selling Demand Response Using Options

Wholesale electricity markets in many jurisdictions use a two-settlement structure: a day-ahead market for bulk power transactions and a real-time market for fine-grain supply-demand balancing. This paper explores trading demand response assets within this two-settlement market structure. We consider two approaches for trading demand response assets: (a) an intermediate spot market with contingent pricing, and (b) an over-the-counter options contract. In the first case, we characterize the competitive equilibrium of the spot market, and show that it is socially optimal. Economic orthodoxy advocates spot markets, but these require expensive infrastructure and regulatory blessing. In the second case, we characterize competitive equilibria and compare its efficiency with the idealized spot market. Options contract are private bilateral over-the-counter transactions and do not require regulatory approval. We show that the optimal social welfare is, in general, not supported. We then design optimal option prices that minimize the social welfare gap. This optimal design serves to approximate the ideal spot market for demand response using options with modest loss of efficiency. Our results are validated through numerical simulations.

eess.SY↗

arXiv2020

Off-Street Parking for TNC Vehicles to Reduce Cruising Traffic

This paper considers off-street parking for the cruising vehicles of transportation network companies (TNCs) to reduce the traffic congestion. We propose a novel business that integrates the shared parking service into the TNC platform. In the proposed model, the platform (a) provides interfaces that connect passengers, drivers and garage operators (commercial or private garages); (b) determines the ride fare, driver payment, and parking rates; (c) matches passengers to TNC vehicles for ride-hailing services; and (d) matches vacant TNC vehicles to unoccupied parking garages to reduce the cruising cost. A queuing-theoretic model is proposed to capture the matching process of passengers, drivers, and parking garages. A market-equilibrium model is developed to capture the incentives of the passengers, drivers, and garage operators. An optimization-based model is formulated to capture the optimal pricing of the TNC platform. Through a realistic case study, we show that the proposed business model will offer a Pareto improvement that benefits all stakeholders, which leads to higher passenger surplus, higher drivers surplus, higher garage operator surplus, higher platform profit, and reduced traffic congestion.

math.OC↗

arXiv2020

Market Implementation of Multiple-Arrival Multiple-Deadline Differentiated Energy Services

An increasing concern in power systems is how to elicit flexibilities in demand, which leads to nontraditional electricity products for accommodating loads of different flexibility levels. We have proposed Multiple-Arrival Multiple-Deadline (MAMD) differentiated energy services for the flexible loads which require constant power for specified durations. Such loads are indifferent to the actual power delivery time as long as the duration requirements are satisfied between the specified arrival times and deadlines. The focus of this paper is the market implementation of such services. In a forward market, we establish the existence of an efficient competitive equilibrium to verify the economic feasibility, which implies that selfish market participants can attain the maximum social welfare in a distributed manner. We also show the strengths of the MAMD services by simulation.

eess.SY↗

arXiv2019

Large-Scale Traffic Signal Offset Optimization

The offset optimization problem seeks to coordinate and synchronize the timing of traffic signals throughout a network in order to enhance traffic flow and reduce stops and delays. Recently, offset optimization was formulated into a continuous optimization problem without integer variables by modeling traffic flow as sinusoidal. In this paper, we present a novel algorithm to solve this new formulation to near-global optimality on a large-scale. Specifically, we solve a convex relaxation of the nonconvex problem using a tree decomposition reduction, and use randomized rounding to recover a near-global solution. We prove that the algorithm always delivers solutions of expected value at least 0.785 times the globally optimal value. Moreover, assuming that the topology of the traffic network is "tree-like", we prove that the algorithm has near-linear time complexity with respect to the number of intersections. These theoretical guarantees are experimentally validated on the Berkeley, Manhattan, and Los Angeles traffic networks. In our numerical results, the empirical time complexity of the algorithm is linear, and the solutions have objectives within 0.99 times the globally optimal value.

math.OC↗

arXiv2019

A Queuing Approach to Parking: Modeling, Verification, and Prediction

We present a queuing model of parking dynamics and a model-based prediction method to provide real-time probabilistic forecasts of future parking occupancy. The queuing model has a non-homogeneous arrival rate and time-varying service time distribution. All statistical assumptions of the model are verified using data from 29 truck parking locations, each with between 55 and 299 parking spots. For each location and each spot the data specifies the arrival and departure times of a truck, for 16 months of operation. The modeling framework presented in this paper provides empirical support for queuing models adopted in many theoretical studies and policy designs. We discuss how our framework can be used to study parking problems in different environments. Based on the queuing model, we propose two prediction methods, a microscopic method and a macroscopic method, that provide a real-time probabilistic forecast of parking occupancy for an arbitrary forecast horizon. These model-based methods convert a probabilistic forecast problem into a parameter estimation problem that can be tackled using classical estimation methods such as regressions or pure machine learning algorithms. We characterize a lower bound for an arbitrary real-time prediction algorithm. We evaluate the performance of these methods using the truck data comparing the outcomes of their implementations with other model-based and model-free methods proposed in the literature.

cs.LG↗

arXiv2019

Regulating TNCs: Should Uber and Lyft Set Their Own Rules?

We evaluate the impact of three proposed regulations of transportation network companies (TNCs) like Uber, Lyft and Didi: (1) a minimum wage for drivers, (2) a cap on the number of drivers or vehicles, and (3) a per-trip congestion tax. The impact is assessed using a queuing theoretic equilibrium model which incorporates the stochastic dynamics of the app-based ride-hailing matching platform, the ride prices and driver wages established by the platform, and the incentives of passengers and drivers. We show that a floor placed under driver earnings pushes the ride-hailing platform to hire more drivers and offer more rides, at the same time that passengers enjoy faster rides and lower total cost, while platform rents are reduced. Contrary to standard economic theory, enforcing a minimum wage for drivers benefits both drivers and passengers, and promotes the efficiency of the entire system. This surprising outcome holds for almost all model parameters, and it occurs because the wage floors curbs TNC labor market power. In contrast to a wage floor, imposing a cap on the number of vehicles hurts drivers, because the platform reaps all the benefits of limiting supply. The congestion tax has the expected impact: fares increase, wages and platform revenue decrease. We also construct variants of the model to briefly discuss platform subsidy, platform competition, and autonomous vehicles.

math.OC↗

arXiv2019

Optimal Resource Procurement and the Price of Causality

This paper studies the problem of procuring diverse resources in a forward market to cover a set $\bf{E}$ of uncertain demand signals $\bf{e}$. We consider two scenarios: (a) $\bf{e}$ is revealed all at once by an oracle (b) $\bf{e}$ reveals itself causally. Each scenario induces an optimal procurement cost. The ratio between these two costs is defined as the {\em price of causality}. It captures the additional cost of not knowing the future values of the uncertain demand signal. We consider two application contexts: procuring energy reserves from a forward capacity market, and purchasing virtual machine instances from a cloud service. An upper bound on the price of causality is obtained, and the exact price of causality is computed for some special cases. The algorithmic basis for all these computations is set containment linear programming. A mechanism is proposed to allocate the procurement cost to consumers who in aggregate produce the demand signal. We show that the proposed cost allocation is fair, budget-balanced, and respects the cost-causation principle. The results are validated through numerical simulations.

math.OC↗

arXiv2019

Mechanism Design for Demand Response Programs

Demand Response (DR) programs serve to reduce the consumption of electricity at times when the supply is scarce and expensive. The utility informs the aggregator of an anticipated DR event. The aggregator calls on a subset of its pool of recruited agents to reduce their electricity use. Agents are paid for reducing their energy consumption from contractually established baselines. Baselines are counter-factual consumption estimates of the energy an agent would have consumed if they were not participating in the DR program. Baselines are used to determine payments to agents. This creates an incentive for agents to inflate their baselines. We propose a novel self-reported baseline mechanism (SRBM) where each agent reports its baseline and marginal utility. These reports are strategic and need not be truthful. Based on the reported information, the aggregator selects or calls on agents to meet the load reduction target. Called agents are paid for observed reductions from their self-reported baselines. Agents who are not called face penalties for consumption shortfalls below their baselines. The mechanism is specified by the probability with which agents are called, reward prices for called agents, and penalty prices for agents who are not called. Under SRBM, we show that truthful reporting of baseline consumption and marginal utility is a dominant strategy. Thus, SRBM eliminates the incentive for agents to inflate baselines. SRBM is assured to meet the load reduction target. SRBM is also nearly efficient since it selects agents with the smallest marginal utilities, and each called agent contributes maximally to the load reduction target. Finally, we show that SRBM is almost optimal in the metric of average cost of DR provision faced by the aggregator.

cs.GT↗

arXiv2019

Making intersections safer with I2V communication

Intersections are hazardous places. Threats arise from interactions among pedestrians, bicycles and vehicles, more complicated vehicle trajectories in the absence of lane markings, phases that prevent determining who has the right of way, invisible vehicle approaches, vehicle obstructions, and illegal movements. These challenges are not fully addressed by the "road diet" and road redesign prescribed in Vision Zero plans, nor will they be completely overcome by autonomous vehicles with their many sensors and tireless attention to surroundings. Accidents can also occur because drivers, cyclists and pedestrians do not have the information they need to avoid wrong decisions. In these cases, the missing information can be computed and broadcast by an intelligent intersection. The information gives the current full signal phase, an estimate of the time when the phase will change, and the occupancy of the blind spots of the driver or autonomous vehicle. The paper develops a design of the intelligent intersection, motivated by the analysis of an accident at an intersection in Tempe, AZ, between an automated Uber Volvo and a manual Honda CRV and culminates in a proposal for an intelligent intersection infrastructure. The intelligent intersection also serves as a software-enabled version of the `protected intersection' design to improve the passage of cyclists and pedestrians through an intersection.

cs.CY↗

arXiv2018

Estimating Phase Duration for SPaT Messages

A SPaT (Signal Phase and Timing) message describes for each lane the current phase at a signalized intersection together with an estimate of the residual time of that phase. Accurate SPaT messages can be used to construct a speed profile for a vehicle that reduces its fuel consumption as it approaches or leaves an intersection. This paper presents SPaT estimation algorithms at an intersection with a semi-actuated signal, using real-time signal phase measurements. The algorithms are evaluated using high-resolution data from two intersections in Montgomery County, MD. The algorithms can be readily implemented at signal controllers. The study supports three findings. First, real-time information dramatically improves the accuracy of the prediction of the residual time compared with prediction based on historical data alone. Second, as time increases the prediction of the residual time may increase or decrease. Third, as drivers differently weight errors in predicting `end of green' and `end of red', drivers on two different approaches may prefer different estimates of the residual time of the same phase.

stat.AP↗

arXiv2017

Sharing Storage in a Smart Grid: A Coalitional Game Approach

Sharing economy is a transformative socio-economic phenomenon built around the idea of sharing underused resources and services, e.g. transportation and housing, thereby reducing costs and extracting value. Anticipating continued reduction in the cost of electricity storage, we look into the potential opportunity in electrical power system where consumers share storage with each other. We consider two different scenarios. In the first scenario, consumers are assumed to already have individual storage devices and they explore cooperation to minimize the realized electricity consumption cost. In the second scenario, a group of consumers is interested to invest in joint storage capacity and operate it cooperatively. The resulting system problems are modeled using cooperative game theory. In both cases, the cooperative games are shown to have non-empty cores and we develop efficient cost allocations in the core with analytical expressions. Thus, sharing of storage in cooperative manner is shown to be very effective for the electric power system.

eess.SY↗

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

Analysis of Solar Energy Aggregation under Various Billing Mechanisms

Ongoing reductions in the cost of solar photovoltaic (PV) systems are driving their increased installations by residential households. Various incentive programs such as feed-in tariff, net metering, net purchase and sale that allow the prosumers to sell their generated electricity to the grid are also powering this trend. In this paper, we investigate sharing of PV systems among a community of households, who can also benefit further by pooling their production. Using cooperative game theory, we find conditions under which such sharing decreases their net total cost. We also develop allocation rules such that the joint net electricity consumption cost is allocated to the participants. These cost allocations are based on the cost causation principle. The allocations also satisfy the standalone cost principle and promote PV solar aggregation. We also perform a comparative analytical study on the benefit of sharing under the mechanisms favorable for sharing, namely net metering, and net purchase and sale. The results are illustrated in a case study using real consumption data from a residential community in Austin, Texas.

eess.SY↗