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Incentivizing Energy Trading for Interconnected Microgrids

Hao Wang, Jianwei Huang

arXiv:1609.07576v1cs.GTmath.OC

TL;DR

Autonomous interconnected microgrids need incentives to coordinate energy trading despite self-interested decisions and tightly coupled schedules. The paper uses Nash bargaining with joint scheduling and trading, decomposed optimization, and decentralized information exchange; realistic-data simulations report up to 13.2% lower total system cost and up to 29.4% lower individual microgrid cost.

  • Problem

    Autonomous microgrids have self-interests, while their trading and scheduling decisions are coupled, creating a need for incentives and distributed coordination.

  • Method

    The paper jointly optimizes scheduling and trading using Nash bargaining, decomposes bargaining into scheduling and payment subproblems, and solves them with limited-information decentralized methods.

  • Results

    13.2% total cost reduction is achieved for the interconnected-microgrids system, while an individual participating microgrid achieves a 29.4% cost reduction through energy trading.

  • Takeaways & Limitations

    Energy trading can provide mutual benefits and fair benefit sharing among autonomous microgrids with diverse renewable supply and demand profiles.

Abstract

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In this paper, we study the interactions among interconnected autonomous microgrids, and propose a joint energy trading and scheduling strategy. Each interconnected microgrid not only schedules its local power supply and demand, but also trades energy with other microgrids in a distribution network. Specifically, microgrids with excessive renewable generations can trade with other microgrids in deficit of power supplies for mutual benefits. Since interconnected microgrids operate autonomously, they aim to optimize their own performance and expect to gain benefits through energy trading. We design an incentive mechanism using Nash bargaining theory to encourage proactive energy trading and fair benefit sharing. We solve the bargaining problem by decomposing it into two sequential problems on social cost minimization and trading benefit sharing, respectively. For practical implementation, we propose a decentralized solution method with minimum information exchange overhead. Numerical studies based on realistic data demonstrate that the total cost of the interconnected-microgrids operation can be reduced by up to 13.2% through energy trading, and an individual participating microgrid can achieve up to 29.4% reduction in its cost through energy trading.

I. INTRODUCTION

The paper addresses autonomous interconnected microgrids that must coordinate coupled supply, demand, and trading decisions while preserving self-interested operation. It proposes Nash-bargaining incentives, joint scheduling and trading, and a decentralized solution, with realistic-data simulations showing lower system cost.

  • Motivation: Autonomous microgrids create an underexplored setting because prior work often assumes a common operator or hierarchical coordination.The paper instead considers multiple small microgrids operating independently and in a distributed fashion.
  • Challenges: Incentive mechanisms are needed because self-interested autonomous microgrids interact only when doing so provides additional benefits.Their external trading decisions and internal operating decisions are also coupled with those of other microgrids.
  • Motivation: Different renewable-generation and consumption profiles create opportunities for microgrids to exchange electricity and reduce operating costs.One microgrid may have excess renewable generation while another has a power deficit at the same time.
  • Contributions: The paper jointly optimizes individual power scheduling and energy trading among interconnected microgrids.The model includes local renewable generation, energy storage, and demand-responsive users within the interconnected system.
  • Contributions: A Nash-bargaining incentive mechanism encourages proactive trading and fair benefit sharing among autonomous microgrids.The bargaining problem is decomposed into sequential subproblems for optimal schedules and trading payments, with limited information exchange.
  • Evaluation: 13.2% total cost reduction is demonstrated for the interconnected-microgrids system in numerical studies based on realistic data.The simulations evaluate wind-based renewable generation using data from several Hong Kong locations.

2) Main grid power:

Each microgrid can purchase electricity from or sell excess power to the main grid, subject to prices and physical limits. The resulting main-grid schedule contributes to the microgrid’s energy cost.

  • Main grid procurement: Microgrids purchase main-grid power when local wind generation is insufficient to meet demand.Purchased power is subject to a maximum amount determined by the main-grid connection’s physical capacity.
  • Main grid sales: Microgrids can sell excess local wind power to the main grid under a feed-in tariff contract.The amount sold is constrained by the maximum allowed main-grid selling capacity.
  • Pricing and cost: Main-grid energy cost depends on scheduled power and time-slot-specific buying and selling prices.The model distinguishes procurement prices from feed-in prices and represents both schedules over the operation horizon.

3) Local power demand:

Local demand is modeled through inelastic and elastic loads, user discomfort, and operational constraints. Energy storage shifts power across time while accounting for capacity, efficiency, degradation, and daily cycling requirements.

  • Load modeling: Inelastic loads cannot be easily shifted, whereas elastic loads such as electric vehicles and HVAC can be scheduled across time.Demand response controls elastic loads subject to total-energy and per-time-slot bounds.
  • Load modeling: Elastic-load scheduling can affect user comfort when actual consumption deviates from preferred consumption.A weighted coefficient represents each user’s sensitivity to consumption deviations.
  • Energy storage: Energy storage smooths intermittent wind generation, shifts energy between low- and peak-load periods, and enables price arbitrage.The model includes storage charging, discharging, and stored-energy variables over the operation horizon.
  • Energy storage: Charging and discharging power are bounded by maximum storage rates in each time slot.These limits constrain the instantaneous charging and discharging decisions.
  • Energy storage: Storage dynamics account for charging and discharging conversion efficiencies and power losses.Charging and discharging efficiencies are modeled separately for each microgrid.
  • Energy storage: Stored energy is constrained by physical capacity and depth-of-discharge requirements, while terminal energy equals initial energy.The equal initial and terminal levels decouple daily storage operation across different days.
  • Energy storage: Storage operation includes an amortized degradation cost for charging and discharging over the device lifetime.The cost represents degradation associated with repeated storage cycling.

B. Single Microgrid’s Cost Minimization Problem

Each microgrid jointly schedules generation, grid exchange, storage, and elastic demand while maintaining power balance. It minimizes operating costs that include energy, storage, and user discomfort costs, with no-trading cost as the benchmark.

  • The operator coordinates power scheduling, battery charging and discharging, and elastic-load shifting.
  • Power balance equates total supply from wind, grid purchases, and battery discharge with grid sales, battery charging, and local loads.
  • Available power cannot exceed the microgrid’s total available power, comprising local wind-power surplus and battery energy.
  • The operating-cost objective includes energy cost, storage-operation cost, and users’ discomfort costs.
  • The convex cost-minimization problem uses generation, grid exchange, elastic-load, and storage charging and discharging variables.
  • The minimized no-trading cost is the noncooperative benchmark for evaluating energy trading.

C. Energy Trading among Microgrids

Interconnected microgrids can trade energy to exploit differences in renewable generation and load profiles. The formulation accounts for market clearing, power balance, payments, and each microgrid’s incentive to reduce its total cost.

  • Different locations create diverse renewable-generation and local-load profiles that provide opportunities for energy exchange.
  • Market clearing constraints govern energy trading and payment among the interconnected microgrids.
  • The power-balance constraint is adjusted for energy exchange, under the assumption that nearby microgrids incur negligible exchange losses.
  • Positive traded energy denotes purchasing, negative traded energy denotes selling, and payment signs distinguish payments made from payments received.
  • Each microgrid minimizes total cost, combining its operating cost with payments made to other microgrids.
  • A microgrid participates only when trading reduces its overall cost relative to its minimized no-trading cost.

D. Nash Bargaining Formulation for Energy Trading

The paper formulates willing microgrids’ energy trading as a Nash bargaining problem. This formulation seeks feasible, individually rational, Pareto-optimal, and fairly shared cost reductions, while motivating a decentralized implementation.

  • The participating set M′ contains microgrids willing to trade; microgrids outside M′ lack benefits and incentives to participate.
  • The Nash bargaining problem determines energy trading and payments for the participating microgrids under the stated system constraints.
  • Each participant’s bargaining benefit is its no-trading disagreement cost minus its total cost after operating and trading payments.
  • The Nash product shares cooperation benefits fairly across microgrids rather than maximizing only their summed performance improvements.
  • Solving the bargaining problem yields trading, payment, and local power-scheduling strategies for participating microgrids.
  • A centralized solution requires complete operational information, which may be infeasible in practice; the paper therefore develops a decentralized method.

IV. PROBLEM ANALYSIS

The bargaining problem is connected to social-cost minimization and can be solved sequentially through energy trading and scheduling followed by payment bargaining. Only microgrids that trade energy participate in payment bargaining, while non-trading microgrids retain their separate-operation costs.

  • Proposition 1 states that the optimal bargaining solution also minimizes the total cost of participating microgrids.This establishes the connection between the bargaining solution and the social optimum for the trading group.
  • Microgrids in M\M′ have no incentive to trade in cases such as local supply-demand balance or system-wide renewable surplus.In these cases, external energy exchange is unnecessary or unavailable as a mutually beneficial trade.
  • The bargaining problem decomposes into sequential energy trading and scheduling, followed by trading-payment optimization.The first stage minimizes social operating cost; the second shares the resulting benefits through payment bargaining.
  • Microgrids with nonzero optimal trading vectors form M′ and participate in payment bargaining.Microgrids outside M′ do not trade and retain operating costs equal to their disagreement points.
  • Centralized solution of P1 and P2 is impractical because autonomous microgrids retain independent decisions and privacy-sensitive internal variables.The framework therefore motivates a decentralized algorithm for solving both problems.

V. DECENTRALIZED SOLUTION METHOD

The decentralized method uses ADMM to solve the social energy-trading and scheduling problem while coordinating microgrid decisions through auxiliary and dual variables. Auxiliary trading variables convert the original multi-block structure into a convergent two-block formulation.

  • ADMM is used to design a decentralized solution for P1 because it supports large-scale problems with non-strictly convex objectives.The method coordinates local microgrid optimization with higher-level updates.
  • Auxiliary energy-trading variables convert the M-block microgrid structure into an equivalent two-block structure.This addresses the lack of guaranteed convergence for multi-block ADMM while retaining equivalent optimization structure.
  • Each microgrid solves its local P1 optimization problem using fixed dual and auxiliary variables.The local variables include generation, storage, demand-response, and energy-trading decisions.
  • The higher-level problem updates auxiliary trading variables and dual variables from the microgrids’ local solutions.Pairwise trading-partner structure allows the higher-level updates to be formulated around microgrid pairs.

B. Solving P2 (Payment Bargaining)

The payment-bargaining problem is solved decentrally with auxiliary payment variables and ADMM-style iterations. Microgrids repeatedly optimize local payments while higher-level updates enforce consistency through dual variables.

  • P2 is solved in a decentralized fashion by introducing auxiliary payment variables π̂_i.The auxiliary variables replace the original payment-consistency constraints.
  • The log transformation of P2’s objective is used to formulate its Lagrangian for decentralized optimization.The dual variables γ and penalty parameter ρ2 are associated with the payment-consistency constraints.
  • At each iteration, every participating microgrid solves its local P2 payment problem using current auxiliary and dual variables.The local problem produces payment decisions π_i,j for subsequent coordination updates.
  • The higher-level P2 problem updates auxiliary payments and dual variables based on the local payment solutions.Payment updates can be organized around pairs of microgrids, with dual updates enforcing agreement.

C. Algorithm Design and Implementation

Algorithm 1 implements the two-stage decentralized solution by iterating between microgrid-local problems and virtual-clearing-house updates. It requires limited communication, and under proper diminishing stepsizes converges to optimal solutions for both P1 and P2.

  • Algorithm 1 solves P1 and P2 through lower-level microgrid computations and higher-level virtual-clearing-house updates.The two stages are executed sequentially, with iterations continuing until their terminal conditions are satisfied.
  • The virtual clearing house is a non-profit communication and computing module that can protect microgrid privacy.It broadcasts auxiliary and dual-variable updates while receiving trading schedules and payment schedules from participating microgrids.
  • Each microgrid communicates with the virtual clearing house instead of directly communicating with every other microgrid.This reduces information-exchange overhead and allows one-to-many technologies such as LTE to support coordination.
  • Algorithm 1 converges to the optimal solutions of P1 and P2 under proper stepsizes such as ρ1(k)=1/k→0 and ρ2(k)=1/k→0.The convergence argument relies on convexity and the resulting two-block ADMM formulations.

VI. SIMULATION EVALUATIONS

Simulations evaluate energy trading, power scheduling, demand response, storage, and payments for three interconnected microgrids using realistic wind and electricity-price data. Energy trading improves renewable utilization and reduces system and participating-microgrid costs.

  • Simulation setup: Three microgrids use local wind-generation profiles derived from January 18, 2013 meteorological data at three Hong Kong locations, with main-grid prices from ISO New England.The profiles correspond to Tate’s Cairn, Tai Po Kau, and Sai Kung.
  • Optimal energy trading: Microgrids exchange energy actively across the 24-hour horizon, with Microgrid 1 usually selling excess wind power and Microgrids 2 and 3 purchasing during low-generation periods.Microgrid 1 purchases from Microgrid 3 at hour 7 after a sudden wind-power drop.
  • Optimal power scheduling: Energy trading reduces main-grid purchases and increases direct transfers of local wind power among microgrids.Microgrid 2 purchases less from the main grid, while Microgrids 1 and 3 sell less to it because they sell more wind power to Microgrid 2.
  • Demand response: Flexible loads shift from high-price peak periods to off-peak periods with greater aggregate renewable generation.Peak prices occur during hours 11–20, while aggregate renewable output is higher during hours 1–10.
  • Energy storage: At the beginning of the day, all microgrids charge more energy into storage with trading than without trading.Trading enables microgrids to store more renewable power for meeting later peak loads.
  • Optimal payment: 13.2%: Total interconnected-microgrid cost decreases from 1637.8 to 1422.4, while every microgrid benefits after operating costs and trading payments are combined.Microgrid 1’s combined cost falls from 243.8 without trading to 172.1 with trading, a 29.4% decrease.
  • Conclusion: The conclusion reports that realistic meteorological-data simulations demonstrate the effectiveness of the proposed energy-trading mechanism.Future work will consider the power-grid operator’s role in microgrid energy trading.

APPENDIX

The appendix explains that Nash bargaining can be solved sequentially because energy-trading and scheduling variables decouple from payment variables. The first problem minimizes social cost and identifies trading participants; the second determines payments by maximizing the Nash product.

  • Sequential decomposition: For trading microgrids, the bargaining problem separates energy-trading and power-scheduling variables from trading-payment variables.This decoupling permits a sequential solution.
  • Bargaining objective: The Nash bargaining problem minimizes aggregate operational cost and maximizes the social welfare of the participating microgrids.These properties follow from the appendix’s objective characterization.
  • First step: social-cost minimization: The first optimization problem minimizes the social cost of the entire microgrid system and determines optimal energy-trading and scheduling decisions.The formulation uses variables for generation, grid exchange, trading, demand response, and storage.
  • Participant identification: Microgrids with nonzero optimal energy-trading vectors form the participating set M′, while remaining microgrids have zero trading and make or receive no payments.The full-system cost minimization is used to determine M′ without knowing it beforehand.
  • Second step: payment allocation: The second optimization problem determines trading payments for participating microgrids subject to the bargaining constraints.Only microgrids in M′ bargain over the associated payments.
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