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Charging and Discharging of Plug-In Electric Vehicles (PEVs) in Vehicle-to-Grid (V2G) Systems: A Cyber Insurance-Based Model

Dinh Thai Hoang, Ping Wang, Dusit Niyato, Ekram Hossain

arXiv:1701.00958v1cs.GTcs.CY

TL;DR

PEV users need V2G information to make cost-effective charging and discharging decisions, but that information can be unavailable. The paper models cyber insurance and online decision-making for PEVs; simulations report lower average cost than the stated alternatives. The authors present insurance as a way to address information risks and improve PEV-user outcomes.

Abstract

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In addition to being environment-friendly, vehicle-to-grid (V2G) systems can help the plug-in electric vehicle (PEV) users in reducing their energy costs and can also help stabilizing energy demand in the power grid. In V2G systems, since the PEV users need to obtain system information (e.g., locations of charging/discharging stations, current load and supply of the power grid) to achieve the best charging and discharging performance, data communication plays a crucial role. However, since the PEV users are highly mobile, information from V2G systems is not always available for many reasons, e.g., wireless link failures and cyber attacks. Therefore, in this paper, we introduce a novel concept using cyber insurance to "transfer" cyber risks, e.g., unavailable information, of a PEV user to a third party, e.g., a cyber insurance company. Under the insurance coverage, even without information about V2G systems, a PEV user is always guaranteed the best price for charging/discharging. In particular, we formulate the optimal energy cost problem for the PEV user by adopting a Markov decision process framework. We then propose a learning algorithm to help the PEV user make optimal decisions, e.g., to charge or discharge and to buy or not to buy insurance, in an online fashion. Through simulations, we show that cyber insurance is an efficient solution not only in dealing with cyber risks, but also in maximizing revenue of the PEV user.

I. INTRODUCTION

V2G systems use PEVs as storage and flexible energy resources, but their performance depends on exchanging timely information with mobile vehicles. The introduction outlines V2G operation and control choices, then situates the paper’s insurance-based contribution among the benefits of V2G.

I. INTRODUCTION

  • The paper proposes cyber insurance to transfer information-related risks and formulates PEV energy-cost optimization as a Markov decision process with an online learning algorithm.The algorithm supports charging, discharging, and insurance-purchase decisions based on the PEV’s current state.Source: §I · p. 1

1) Introduction:

  • V2G can help balance dynamic grid demand by using PEV batteries to store energy and return it to the grid when supply cannot meet demand.PEVs can charge when supply exceeds demand and sell energy back during peak demand.Source: 1) Introduction · p. 2

2) Architecture:

  • V2G connects PEVs through charging stations and aggregators, which mediate energy flow between the grid and vehicles.V2G systems serve as both energy storage and consumers, while communication infrastructure exchanges data among system participants.Source: 2) Architecture · p. 2

3) Smart charging/discharging control:

  • Centralized control can more easily achieve optimal performance, but decentralized control is more preferable in actual systems because PEVs cannot control their own charging and discharging under centralized control.The paper distinguishes operator-controlled charging from decisions made by PEV users themselves.Source: 3) Smart charging/discharging control · p. 3

4) Benefits:

  • V2G can support ancillary services, renewable integration, and improved service quality, while PEV users can earn rewards by managing charging and discharging.PEVs can provide services such as spinning reserves and frequency regulation, and can charge off-peak and discharge during peak hours.Source: 4) Benefits · p. 3

5) Electric vehicle battery:

This section reviews battery trade-offs, V2G communications, security requirements, and proposed defenses. It concludes that existing approaches can mitigate some threats, while cyber insurance can transfer information-unavailability risks and guarantee PEV users the best charging or discharging price.

5) Electric vehicle battery:

  • Heavier vehicle batteries can provide longer travel time, but can limit speed and increase energy use, making weight a design trade-off.The paper describes batteries designed for high power and energy capacity while constrained by space and weight.Source: 5) Electric vehicle battery · pp. 3–4

6) Data communications:

  • Wireless communication is important because operators need PEV demand information and users need V2G infrastructure information to optimize energy costs.The paper notes that ZigBee suits short-range links, while IEEE 802.11p and WiMAX are used for long-range communication.Source: 6) Data communications · p. 4

1) Security requirements:

  • V2G communications must protect confidentiality, authenticity, integrity, and availability; disrupted availability can leave operators with incomplete system information.Denial-of-service attacks are given as one way communications can be disrupted.Source: 1) Security requirements · p. 5

2) Solutions:

  • Prior V2G security approaches address privacy, authentication, integrity, and jamming, but have limits including reliance on a trusted authority, overhead, or implementation difficulty.The paper also notes that a deception-based approach can be inefficient against powerful jammers with constant power supplies.Source: 2) Solutions · p. 5
  • Cyber insurance transfers information-unavailability risks to an insurer and guarantees PEV users the best charging or discharging price even without V2G information.The proposed coverage is presented as a way to encourage PEV participation and generate revenue for V2G service providers.Source: 2) Solutions · p. 6

III. OVERVIEW OF CYBER INSURANCE

The section presents cyber insurance as a risk-transfer arrangement, describes common concepts and coverage types, and outlines potential benefits to insured users. It frames insurance as complementary to security measures that cannot eliminate cyber risk entirely.

A. Definition, Fundamental Concepts, and Coverage

  • The section presents cyber insurance as a potential response because perfect or near-perfect reliability and cybersecurity protection are described as impossible to achieve.Cyber risks may arise from system failure or cyber attacks affecting connected systems.Source: A. Definition, Fundamental Concepts,… · p. 6

1) Definitions and fundamental concepts:

  • Cyber insurance is described as protection against cyber risks, with definitions varying across Internet, business, and market contexts.In the business context, it transfers network users’ risks to an insurance company in return for a fee.Source: 1) Definitions and fundamental concepts · p. 6
  • The insured pays a premium for protection, while the insurer assumes risks and may compensate losses through an indemnity after a claim.The section identifies the insured, insurer, premium, contract, claim, and indemnity as fundamental concepts.Source: 1) Definitions and fundamental concepts · p. 6

2) Coverage:

  • Cyber insurance policies may cover first-party losses to the insured’s assets, third-party losses, or both.Listed examples include digital-asset loss, theft, security and privacy breaches, third-party data loss, and contractual indemnification.Source: 2) Coverage · p. 6

1) Benefits to the the insured:

  • For insured users, risk transfer can reduce damage, insurers have incentives to protect insured parties, and users may adopt self-protection to lower premiums.These are presented as practical benefits of cyber insurance.Source: 1) Benefits to the the insured: • · p. 6

2) Benefits to insurers:

Cyber insurance offers opportunities for insurers and society, while its implementation requires a staged process for identifying and evaluating risks, contracting, and monitoring. The section also outlines challenges in classifying and assessing cyber risks.

2) Benefits to insurers:

C. Implementation and Effectiveness of Cyber Insurance

  • Cyber insurance has been used in bundled security services since 1990, and TRSecure became the first stand-alone cyber insurance service in 1998.The passage also names later services from Lloyd’s of London, AT&T, and AIG.Source: C. Implementation and Effectiveness of… · p. 7

D. Cyber Insurance Process

  • The four process steps are risk identification, risk evaluation, contract establishment, and implementation and monitoring.Risk identification examines coverage needs and investigates threats and vulnerabilities; risk evaluation assesses likelihood and potential damage; after agreement, the insurer implements protections and monitors and handles claims.Source: D. Cyber Insurance Process · p. 7, 1) Risk identification · p. 7, 2) Risk evaluation · p. 7

1) Risk classification:

  • Cyber-risk classification is intended to provide a foundation for risk evaluation, although empirical information about cyber risks remains limited.The passage points to Table IV for the categories but does not provide their contents.Source: 1) Risk classification · pp. 7–8

2) Risk assessment:

  • A risk assessment matrix can organize focus areas such as frequency, probability, severity, speed of development, and reputational impact.These factors guide assessment of vulnerabilities and the probability of individual risks affecting the insured.Source: 2) Risk assessment · p. 8

3) Interdependent risks:

Cyber insurance must address correlated risks, information asymmetry, moral hazard, and limited premium-setting data. The section also reviews models for insurance decisions, including a classical model based on a risk-averse insured’s utility.

3) Interdependent risks:

  • Because entities’ cyber security depends on other network entities, conventional insurance approaches face interdependent risks; excluding some failures may not prevent infection from spreading.The passage notes that AIG’s 2005 policies excluded electric and telecommunication failures, while worms and viruses could still spread through networks.Source: 3) Interdependent risks · p. 8

4) Adverse selection:

  • Cyber-risk adverse selection is difficult to address because insurers lack the insured’s knowledge of their situation and cyber systems have no safety standardization.The passage contrasts this with insurance settings where certification, such as medical examinations, can document a client’s condition.Source: 4) Adverse selection · pp. 8–9

5) Moral hazard:

  • Contract requirements and promotions are used to address moral hazard, but uniform promotions may not fit clients with different risk levels.The cited discussion says client-discriminating premiums mitigate moral hazard and can maximize overall network security.Source: 5) Moral hazard · p. 9

6) Setting premium:

  • Cyber premiums are difficult to set because actuarial data is unavailable and there is no established standard for cyber-insurance premiums.The passage also identifies underwriting and premium-setting as research challenges.Source: 6) Setting premium · p. 9

7) Other problems:

  • Other proposed mechanisms target information-security event forecasting, stakeholder coordination, and insurer profit; one simulated consumer-pricing mechanism raised a security vendor’s profit by up to 25%.The reported result is attributed to.Source: 7) Other problems · p. 9

F. Cyber Insurance Models

  • The paper frames cyber-insurance models as ways to quantify risks and assess security and risk-management strategies for outcomes affecting insurers and insureds.It introduces a classical model in which a rational, risk-averse insured maximizes a concave utility function.Source: F. Cyber Insurance Models · p. 9, 1) Classical model · p. 9

1) Classical model:

  • In the classical model, the insured accepts full coverage at premium Ω when Ω≤m, where m is the maximum acceptable premium and depends on utility and the loss distribution.The loss distribution is characterized by loss probability p and loss l.Source: 1) Classical model · pp. 9–10

2) Cyber insurance with self-protection:

Cyber-insurance models extend the insured’s choices to include self-protection, insurance, or a hybrid, while interdependent models examine security decisions across agents. The paper then motivates V2G as a potential cyber-insurance market and describes the information-dependent charging and discharging decisions at issue.

2) Cyber insurance with self-protection:

  • With self-protection, an agent chooses protection cost c that affects loss probability p[c]; the cited model’s optimum is either 0 or ct, with investment at ct when protection cost is below threshold c†.With insurance available, the agent may choose insurance instead of protection when its cost is below ct, or use protection alone otherwise.Source: 2) Cyber insurance with self-protection · p. 10

3) Interdependent model:

G. Evolution of Cyber Insurance Market

  • The authors present V2G systems as a potential market for cyber insurers and say cyber insurance can address cyber risks and optimize PEV-user benefits.They connect this proposal to the search for markets beyond conventional Internet security insurance.Source: G. Evolution of Cyber Insurance Market · p. 11

1) PEV charging/discharging and V2G systems:

  • Using V2G information, a PEV user can select the lowest-cost charging station or the highest-profit discharging station; unavailable information can leave charging or discharging costs higher.Charging cost includes travel and charging fees, while discharging profit is revenue minus travel cost; the battery has fixed capacity B divided into B energy levels.Source: 1) PEV charging/discharging and V2G… · p. 11

2) Cyber insurance for PEV charging and discharging:

Cyber insurance transfers the PEV user’s risk of unfavorable prices when charging-station information is unavailable. The model combines insurance choices with charging and discharging decisions and represents the user’s battery, period, and insurance status in its state.

2) Cyber insurance for PEV charging and discharging:

  • Insurance reserves the best charging or discharging price for a coverage period, while the insurer covers extra costs when V2G communication is unavailable.The user pays a premium; the insurer may be a third party or a service offered by a charging-station or aggregator company.Source: 2) Cyber insurance for PEV charging… · pp. 11–12
  • The system model routes energy-price information from charging stations through V2G communication channels to help the user select a station based on battery level.The passage introduces Fig. 5 as the system model for charging, discharging, and cyber insurance.Source: 2) Cyber insurance for PEV charging… · p. 12, Figure 5 · p. 12
  • The PEV user chooses whether to charge, discharge, or do nothing, and whether to buy insurance; coverage guarantees the best price for the next ν periods.The objective is to minimize energy and insurance costs.Source: 2) Cyber insurance for PEV charging… · p. 12

1) State space:

  • The user’s state is the composite variable s = (b, p, i), comprising battery level, time period, and current insurance status.The component ranges are b ∈ {1, . . . , B}, p ∈ {1, . . . , P}, and i ∈ {0, 1}.Source: 1) State space · p. 12

2) Action space:

The action model separates energy decisions from insurance purchase and restricts charging or discharging according to the PEV’s battery level. The immediate cost function assigns heavy costs to doing nothing at an empty battery to discourage energy depletion.

2) Action space:

  • The energy action a1 is 0 for neither charging nor discharging, 1 for charging, and 2 for discharging; insurance action a2 is 0 or 1 for not buying or buying.The insurance choice is available in any period, while the energy action depends on the current state.Source: 2) Action space · p. 12
  • When battery level is full, the available energy actions are {0, 2}; at intermediate positive levels, they are {0, 1, 2}.Discharging is unavailable when battery level is zero.Source: 2) Action space · p. 12

3) Immediate cost function:

  • At an empty battery, doing nothing incurs a heavy cost, with h2 > h1 for insured versus uninsured users, to discourage energy depletion.Fig. 6 distinguishes insurance-available (IA) and insurance-unavailable (IU) cases.Source: 3) Immediate cost function · p. 12, Figure 6 · p. 13
  • The objective is to find policy Ψ∗ that minimizes the PEV user’s expected average cost over the long run.The passage identifies state st and action at as those at time period t.Source: 3) Immediate cost function · p. 12

C. Optimal Policy with Learning Algorithm

Because cyber risks are random and their probabilities are intractable to estimate, the paper develops an online learning approach for selecting PEV actions. It parameterizes randomized policies and uses average-cost and differential-cost relations to formulate a policy gradient.

C. Optimal Policy with Learning Algorithm

  • Random cyber risks make their per-period probabilities difficult to estimate, preventing construction of the transition matrix and motivating an online learning algorithm for PEV decisions.The algorithm is simulation-based.Source: C. Optimal Policy with Learning… · p. 13

1) Parameterized policy:

  • Under a randomized parameterized policy, the user selects action a in state s with probability µΘ(s, a), and the objective is to minimize its average cost Ψ(Θ).The parameterized policy and cost formulation assume an aperiodic Markov chain with a recurrent state and bounded, twice-differentiable transition probabilities and costs.Source: 1) Parameterized policy · p. 13

2) Policy gradient method:

  • The average cost is defined under parameter vector Θ as an expected long-run cost, and the differential cost relates that average to immediate cost across states.The policy-gradient section presents a gradient expression for average cost and identifies its proof as being in Appendix A.Source: 1) Parameterized policy · p. 13, 2) Policy gradient method · pp. 13–14

3) An idealized gradient algorithm:

The paper first gives an idealized gradient update whose convergence depends on suitable step sizes and Markov-chain assumptions. It then describes an online gradient estimate accumulated between recurrent-state visits and states a convergence result for the learning algorithm.

3) An idealized gradient algorithm:

  • With a suitable step size and Assumption 1, the idealized update makes the average-cost gradient approach zero and the cost converge.The update subtracts the step-size-scaled gradient from parameter vector Θ.Source: 3) An idealized gradient algorithm · p. 14

4) Learning algorithm:

  • Exact average-cost gradients are infeasible to compute for large state spaces, so the learning algorithm estimates gradients and updates parameters online..Source: 4) Learning algorithm · p. 14
  • The algorithm updates Θ at visits to recurrent state s∗, using a gradient estimate accumulated between successive visits and a step size satisfying Assumption 3.The estimated gradient is based on a cumulative sum between those visits.Source: 4) Learning algorithm · p. 14
  • Under Assumptions 1 and 2 and a suitable step size satisfying Assumption 3, Proposition 2 states that ψ(Θm) converges.The proof is given in Appendix B.Source: 4) Learning algorithm · p. 15

5) Online learning algorithm:

The paper modifies its learning algorithm to update parameters at each time step, then evaluates online PEV decisions under information unavailability and changing conditions. Simulations report lower costs with the learning algorithm and examine how insurance and operating conditions affect outcomes.

5) Online learning algorithm:

  • Storing parameter and gradient values between successive visits can slow processing, so the authors rewrite the update and derive an algorithm that updates Θ at each time step.The algorithm defines κ as a positive constant, ρ_t as the step size, and eψ_t as the estimated average cost at time step t.Source: 5) Online learning algorithm · p. 15

1) Cost due to V2G communication infrastructure unavailability:

  • With infrastructure information, PEV users can choose stations with better energy prices, substantially lowering charging cost and increasing discharging profit compared with having no information.The paper calls this benefit the “value of information.”Source: 1) Cost due to V2G communication… · p. 16, Figure 8 · p. 16

2) Benefits of cyber insurance to the V2G system:

  • Average cost converges to approximately 3 for the learning algorithm, versus 4.7 for IP and 4.6 for WP, a reduction of approximately 34.5%.The learning algorithm’s policy buys insurance almost all the time at a premium of 1 MU while balancing charging, discharging, and doing nothing.Source: 2) Benefits of cyber insurance to the… · p. 16, Figure 9 · p. 17
  • As energy-consumption rate rises, all policies’ average total costs increase, but the learning algorithm achieves the lowest cost across the tested cases.Below a consumption rate of 0.3, its average total cost becomes negative because discharging profit exceeds charging cost.Source: 2) Benefits of cyber insurance to the… · p. 17, Figure 10 · p. 17
  • With a 1 MU premium, increasing information-unavailability probability from 0.1 to 0.9 raises WP average total cost, while IP and learning-algorithm costs remain unchanged.The learning algorithm always buys insurance in this setting, maintaining high discharging profit.Source: Figure 11 · p. 17, 2) Benefits of cyber insurance to the… · p. 18
  • As the premium rises, IP and learning-algorithm average total costs increase; above 7 MUs, the learning algorithm’s cost approaches WP’s.When information-unavailability probability is 0.1, the learning algorithm’s insurance-buying rate falls if the premium exceeds 5 MUs.Source: 2) Benefits of cyber insurance to the… · p. 18, Figure 12 · p. 18

V. FUTURE RESEARCH DIRECTIONS OF CYBER INSURANCE IN V2G SYSTEMS

The paper outlines future research directions for V2G cyber insurance, including self-protection, multiple insurers, pricing, and communication through cognitive radios. Its conclusion reports that simulations show the learning algorithm minimizes charging cost and maximizes discharging profit, with convergence supported by proof and simulation.

A. Self-protection Strategy

  • The modeled user chooses only whether to buy insurance, while a practical policy could also choose self-protection, such as backup storage or a backup communication channel.The paper proposes comparing self-protection, insurance, and doing nothing.Source: A. Self-protection Strategy · p. 18

B. Multiple Insurers

  • With multiple insurers, differing policies, station locations, user energy demands, and travel routines leave insurer selection and premium setting as open questions.The paper suggests stochastic geometry and graph theory as possible tools.Source: B. Multiple Insurers · p. 18

C. Smart Cyber Insurance Pricing

  • When energy and insurance providers are separate, conflicting interests complicate premium setting; bundling is proposed as a pricing strategy that can improve provider profit and offer users more attractive services.The paper notes that bundled services may give users more charging stations and better insurance prices.Source: C. Smart Cyber Insurance Pricing · p. 18

D. Cyber Insurance for V2G systems with Cognitive Radios

  • In cognitive-radio V2G networks, communication depends on primary-user demand, so resulting information unavailability can expose PEV users to losses that cyber insurance may protect against.Source: D. Cyber Insurance for V2G systems… · p. 19

VI. CONCLUSION

  • The proposed learning algorithm makes online charging, discharging, and insurance decisions, and simulations show it minimizes charging cost and maximizes discharging profit; convergence is supported by proof and simulation.The paper also reports that unavailable infrastructure information is associated with high charging cost and low discharging profit for the PEV user.Source: §VI · p. 19

APPENDIX A THE PROOF OF PROPOSITION 1

The proof material identifies the average-cost gradient and derives a stationary-distribution identity, then establishes convergence of the parameter updates to a zero-gradient limit under the stated assumptions.

APPENDIX A THE PROOF OF PROPOSITION 1

  • The proof identifies the average-cost gradient and derives an identity equating the stationary-distribution-weighted transition probabilities with the stationary probability of the next state.The derivation is part of the proof of Proposition 1.Source: Appendix A · p. 19

APPENDIX B THE PROOF OF PROPOSITION 2

  • The convergence proof rewrites the updates and shows that the average-cost estimate and ψ(Θ) converge to a common limit.The argument notes that the error term vanishes and the perturbation is summable.Source: Appendix B · pp. 19–20
  • ∇ΘC(Θ∞) = 0: the parameter sequence reaches a zero-gradient limit under the stated assumptions and suitable step size.The update is identified as a gradient method with diminishing errors,.Source: Appendix B · p. 20
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