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Coalitional game based cost optimization of energy portfolio in smart grid communities

Adriana Chis, Visa Koivunen

arXiv:1705.04118v1math.OCcs.GT

TL;DR

Household energy costs are shaped by intermittent renewable production and the expense of large storage systems. The paper proposes coalitional optimization for sharing and trading energy, reporting up to 20% cost reduction for RESs and ESSs owners and up to 5% for sole consumers.

  • Problem

    RES production is intermittent and high-capacity storage can be costly, motivating cooperation to address these drawbacks.

    Source: §I · p. 1

  • Method

    Two coalitional optimization models let RESs and ESSs owners share and exchange energy, with a second model also selling energy to sole consumers and distributing coalition revenues by Shapley value.

    Source: §I · p. 1, §IV · p. 5

  • Results

    RESs and ESSs owners may reduce costs by 20%, while sole energy consumers may reduce costs by up to 5%.

    Source: §VI · p. 8

  • Takeaways & Limitations

    Selling electricity below the utility price can further reduce owners’ costs while giving sole consumers cost savings.

    Source: §VI · p. 8

Abstract

from arXiv · show

In this paper we propose two novel coalitional game theory based optimization methods for minimizing the cost of electricity consumed by households from a smart community. Some households in the community may own renewable energy systems (RESs) conjoined with energy storing systems (ESSs). Some other residences own ESSs only, while the remaining households are simple energy consumers. We first propose a coalitional cost optimization method in which RESs and ESSs owners exchange energy and share their renewable energy and storage spaces. We show that by participating in the proposed game these households may considerably reduce their costs in comparison to performing individual cost optimization. We further propose another coalitional optimization model in which RESs and ESSs owning households not only share their resources, but also sell energy to simple energy consuming households. We show that through this energy trade the RESs and ESSs owners can further reduce their costs, while the simple energy consumers also gain cost savings. The monetary revenues gained by the coalition are distributed among its members according to the Shapley value. Simulation examples show that the proposed coalitional optimization methods may reduce the electricity costs for the RESs and ESSs owning households by 20%, while the sole energy consumers may reduce their costs by 5%.

I. INTRODUCTION

Renewable generation can reduce grid losses and costs, but its intermittency and the expense of large storage systems motivate cooperation among households. The paper proposes coalitional sharing and energy-trading models, with simulations reporting cost reductions for both resource owners and sole consumers.

I. INTRODUCTION

  • RES intermittency and the high cost of large-capacity storage motivate cooperation, which can improve renewable integration, reduce storage needs, and provide participant savings.Prior work addressed energy trading among microgrids – and game-theoretic energy trading in smart grids –.Source: §I · pp. 1–2
  • The community model includes RESs-and-ESSs owners, ESS-only households, and sole consumers, with a central unit optimizing costs and controlling energy flows.Smart meters predict demand and renewable production profiles over a finite horizon; utility purchases meet demands when community renewable resources are insufficient.Source: §I · p. 1
  • The paper formulates individual optimization and two coalitional models: owners share and exchange energy, then may also sell energy to sole consumers.Sole consumers buy from the coalition at a price below the utility rate but are not coalition participants; the optimization problems are convex and linear.Source: §I · pp. 1–2
  • Coalition revenues are allocated among RESs and ESSs owners by Shapley value according to each member’s contribution.The selected method does not depend on the order in which players join.Source: §I · p. 2
  • The paper extends preliminary results by adding sole consumers, operational costs, penalty terms, and extended simulations.The added consumer group buys energy from the coalition at a price lower than the utility company's price.Source: §I · p. 2
  • 20% total cost reduction for RESs and ESSs owners, including a further 6.5% after sole consumers join; sole consumers save about 5% versus utility purchases.The first coalition yields approximately 13.5% more cost reduction than individual optimization; the second model's total owner savings reach 20%.Source: §I · p. 2

II. SYSTEM MODEL

The system model represents a community of households that exchange energy through a central control unit over a finite, equally spaced time horizon.

II. SYSTEM MODEL

  • Households trade and exchange energy through a central energy control unit over a finite horizon divided into equally long time slots.The model partitions households into M, which includes RES-producing or ESS-owning residences, and P, the sole energy consumers; P = N \ M.Source: §II · p. 2
  • N denotes the community household set, with n indexing households; M and P denote smart residences and sole consumers, respectively.The model assigns indices m to members of M and p to members of P.Source: §II · p. 2
  • Optimization spans T equally long time slots, indexed by t = 1, . . . , T.The stated horizon length is T.Source: §II · p. 2

A. The Energy Model

The energy model balances household demand against renewable generation, grid purchases, storage, and—when collaboration is allowed—energy transfers. Pure consumers can receive community energy but cannot sell electricity back to the grid.

A. The Energy Model

  • Household demand is known in advance over T and is inflexible; renewable production for RES owners is predicted, while ESS-only households have zero renewable production.Energy exchanges may be positive when a household provides energy and negative when it receives energy; grid purchases are represented separately.Source: A. The Energy Model · p. 2
  • Individual RESs and ESSs owners must meet demand using renewable energy, grid purchases, and storage energy.This is the individual energy-consumption constraint described for households in M.Source: A. The Energy Model · pp. 2–3
  • In the collaborative constraint, households in M can also transfer or receive energy through the community exchange variable.The transfer term is added to the demand balance in the collaborative scenario.Source: A. The Energy Model · p. 3
  • Pure consumers in P can only receive energy from community members, and their consumption constraint accounts for their demand and grid purchases.Their community exchange is restricted to receiving energy.Source: A. The Energy Model · p. 3
  • Grid purchases are nonnegative, and households cannot sell electricity back to the power grid.These conditions bound utility purchases and rule out export to the grid in the proposed model.Source: A. The Energy Model · p. 3

B. The Energy Storage Model

The storage model bounds each ESS by its capacity and charging/discharging rate, accounts for leakage, and tracks stored energy across time slots.

B. The Energy Storage Model

  • Each ESS has a maximum storage capacity, a charging rate equal to its discharging rate, and a leakage factor between 0 and 1, typically much smaller than 1.These parameters characterize the storage limits and energy loss over a time unit.Source: B. The Energy Storage Model · p. 3
  • Storage charge and discharge amounts can be positive or negative and are bounded by the charging/discharging rate.A positive value means energy is charged; a negative value means energy is discharged during that time slot.Source: B. The Energy Storage Model · p. 3
  • The storage state records energy at each time-slot end, follows storage dynamics from an initial state, and must respect the capacity constraint.The initial state is the amount remaining at the end of the previous optimization period.Source: B. The Energy Storage Model · p. 3

III. THE COST MINIMIZATION PROBLEM

The section presents two coalitional cost-minimization models: one for households with renewable and/or storage resources, and another that also includes sole energy consumers. It compares coalition participation with individual optimization and assumes utility prices are known in advance.

III. THE COST MINIMIZATION PROBLEM

  • The two models let resource-owning households share resources and trade energy, with the second also selling to sole consumers; participation may reduce costs versus individual optimization.In the second model, resource owners may reduce costs further, and sole consumers may also save.Source: §III · p. 3
  • The optimization period uses utility electricity prices known ahead for each time slot.The prices are denoted by ξ(t) for t = 1, . . . , T.Source: §III · p. 3
  • The section proceeds from individual household optimization to a coalition of resource owners, then to a coalition that also includes sole energy consumers.Source: §III · p. 3

A. Individual cost minimization problem

The individual model minimizes each household’s costs without cooperation. It accounts for utility electricity purchases, storage degradation, and a penalty intended to prevent renewable energy from being wasted.

A. Individual cost minimization problem

  • Individual costs include utility electricity purchases and, for households in M, storage degradation from charging and discharging.The degradation price π applies per unit of energy charged or discharged.Source: A. Individual cost minimization problem · p. 3
  • Each household m in M optimizes its costs independently, without collaboration with other community members.The stated solution variables are {bm, rm, sm}.Source: A. Individual cost minimization problem · p. 4
  • A penalty discourages renewable energy from being wasted, and ESS-only households use storage alone with wm = 0.The penalty is intended to ensure produced renewable energy is consumed or stored in ESSm.Source: A. Individual cost minimization problem · p. 4

B. Coalitional cost minimization problem for households owning RESs and/or ESSs

The coalition of households owning RESs and/or ESSs jointly optimizes costs by sharing renewable resources and storage. Its model includes energy-transfer and central-control costs, alongside constraints for energy balance and renewable-energy use.

B. Coalitional cost minimization problem for households owning RESs and/or ESSs

  • Households owning RESs and/or ESSs share renewable resources and storage, with a central unit optimizing and controlling energy flows and transfers.The model includes a central-control operating cost and a transfer price τ per unit of energy transferred between households.Source: B. Coalitional cost minimization… · p. 4
  • The coalition jointly minimizes costs for households in M, adding energy-transfer costs to electricity-purchase and storage-degradation costs.Source: B. Coalitional cost minimization… · p. 4
  • The model penalizes renewable energy not consumed or stored and balances energy given away against energy received within M.Its final constraints include (2), (5)–(8), and (14).Source: B. Coalitional cost minimization… · p. 4

C. Coalitional cost minimization problem for the whole community of households

The whole-community model adds sole energy consumers, who buy energy from households owning RESs and ESSs. It sets their community purchase price below the utility price and constrains their costs to remain below utility-only purchases.

C. Coalitional cost minimization problem for the whole community of households

IV. THE COALITIONAL GAME MODEL FOR HOUSEHOLDS OWNING RESS AND ESSS

The model treats RES- and ESS-owning households as players in a transferable-utility characteristic game, with coalition worth representing collaborative cost savings. It also defines a broader worth for whole-community coalitions and allocates coalition revenue by Shapley value.

IV. THE COALITIONAL GAME MODEL FOR HOUSEHOLDS OWNING RESS AND ESSS

  • The game’s players are households with renewable production and storage systems, and any non-empty subset may form a coalition.A coalition of all such households is the grand coalition, and coalition worth represents the group’s total revenue.Source: §IV · p. 5
  • For RES- and ESS-owner coalitions, worth is the cost saved compared with the members’ total electricity costs under individual optimization.The optimization uses members’ renewable production and storage systems to minimize electricity cost.Source: §IV · p. 5
  • The broader community worth includes RES- and ESS-owning households together with households that only consume electricity.Source: §IV · p. 5
  • Coalition revenue is allocated among members by Shapley value, according to each player’s contribution and independently of joining order.Each household’s payoff represents its fraction of total coalition revenue achieved through its participation.Source: §IV · p. 5

V. SIMULATION EXAMPLES

The simulations compare individual optimization with coalitional energy sharing and whole-community trading over 31 days. The whole-community method lowers costs for both resource-owning households and sole consumers, with results also varying by sale price and storage capacity.

V. SIMULATION EXAMPLES

  • The 31-day simulations use nine households: three with RESs and ESSs, three with ESSs only, and three sole consumers; most runs assume 5 kWh per ESS.Hourly slots span 24 hours; the sale-price ratio is α=0.9, and the simulations use May 2013 Finnish Nord Pool Spot prices and Helsinki-region weather data.Source: §V · pp. 5–6
  • For a 24-hour example, renewable producers usually supply energy to ESS-only and sole-consuming households, while owners buy from the utility during low-price hours.The displayed profiles cover prices, demand, renewable production, storage levels, exchanges, and grid purchases.Source: §V · p. 6, Figure 1 · p. 6
  • 20%: owners' 31-day cost falls from 32.74e individually to 26.2e with whole-community optimization; owner-only coalition yields 13.5% savings at 28.21e.The whole-community result adds a further 6.5% reduction relative to the owner-only coalitional method.Source: Figure 2 · p. 7, §V · p. 7
  • Over 31 days, sole energy consumers’ cost in this example falls from 31.32e when buying all electricity from the utility to 30.03e under whole-community cost optimization, about 4%.Source: §V · p. 7
  • Whole-community gains turn positive at α ≥0.4; owners' cost reduction peaks at about 20% for α=0.9, while consumers' peaks at about 5% for α=0.8.Higher sale prices increase the amounts owners sell, and the passage links consumer savings to energy purchased from owners.Source: §V · p. 7, Figure 3 · p. 7
  • As community storage capacity rises, owners' monetary gains decrease but remain significant even at large capacities, while sole consumers' gains increase.The individual-optimization benchmark also improves with increased storage capacity, narrowing owners' coalitional gains.Source: §V · p. 7, Figure 4 · p. 7
  • In the whole-community simulation, Shapley-value blocks divide owners' daily savings, with a large share allocated to renewable producers; owners underperform individually on five days.The passage attributes those five days partly to different initial storage levels in the individual and coalitional optimizations; sole consumers receive daily savings by buying below utility prices.Source: §V · pp. 7–8, Figure 5 · p. 8

VI. CONCLUSIONS

The proposed coalitional models let households with renewable generation and storage share resources, with a second model also selling electricity to consumers. Simulations report lower costs for participating owners and savings for sole consumers.

VI. CONCLUSIONS

  • The initial coalition lets RES- and ESS-owning households exchange energy and share renewable energy and storage, reducing their energy costs by roughly 13.5%.The reported reduction is from simulation examples.Source: §VI · p. 8
  • About 6.5% further owner savings brings the total reduction to 20% versus individual optimization; sole consumers save up to 5%.The further reduction comes from the model in which owners also sell electricity to consumers.Source: §VI · p. 8
  • The second model retains resource sharing among RES- and ESS-owning households and adds electricity sales to simple energy consumers at prices below the utility rate.The owners may further reduce their costs through these sales.Source: §VI · p. 8
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