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Feedback Optimization of Incentives for Distribution Grid Services

Guido Cavraro, Joshua Comden, Andrey Bernstein

Abstract

Energy prices and net power injection limitations regulate the operations in distribution grids and typically ensure that operational constraints are met. Nevertheless, unexpected or prolonged abnormal events could undermine the grid's functioning. During contingencies, customers could contribute effectively to sustaining the network by providing services. This paper proposes an incentive mechanism that promotes users' active participation by essentially altering the energy pricing rule. The incentives are modeled via a linear function whose parameters can be computed by the system operator (SO) by solving an optimization problem. Feedback-based optimization algorithms are then proposed to seek optimal incentives by leveraging measurements from the grid, even in the case when the SO does not have a full grid and customer information. Numerical simulations on a standard testbed validate the proposed approach.

Feedback Optimization of Incentives for Distribution Grid Services

Abstract

Energy prices and net power injection limitations regulate the operations in distribution grids and typically ensure that operational constraints are met. Nevertheless, unexpected or prolonged abnormal events could undermine the grid's functioning. During contingencies, customers could contribute effectively to sustaining the network by providing services. This paper proposes an incentive mechanism that promotes users' active participation by essentially altering the energy pricing rule. The incentives are modeled via a linear function whose parameters can be computed by the system operator (SO) by solving an optimization problem. Feedback-based optimization algorithms are then proposed to seek optimal incentives by leveraging measurements from the grid, even in the case when the SO does not have a full grid and customer information. Numerical simulations on a standard testbed validate the proposed approach.
Paper Structure (13 sections, 1 theorem, 45 equations, 5 figures)

This paper contains 13 sections, 1 theorem, 45 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Grid Modeling
  3. Energy Market and Incentives
  4. An Incentive Mechanism for Grid Services
  5. Quadratic utility functions
  6. Arbitrary power demand
  7. Linear incentive functions
  8. Approximated power exchange
  9. Achieving the Optimal Incentives
  10. A Dual Ascent Method for the Full Information Case
  11. First-Order and Zero-Order Feedback-Based Methods for the Incomplete Information Case
  12. Numerical Illustration
  13. Conclusion

Key Result

Proposition V.1

Consider the dual ascent control scheme eq:DA and define the matrix Then eq:DA converges to the unique minimizer of eq:opt_prob_part if

Figures (5)

  • Figure 1: The incentive function shapes prosumer $n$ surplus. Here, the utility of consumption is quadratic and the incentive function is linear. When $\xi_n$ is negative, the demand is reduced.
  • Figure 2: The incentive function shapes prosumer $n$ surplus. Here, the utility of consumption is quadratic and the incentive function is linear. When $\xi_n$ is positive, the demand increases.
  • Figure 3: Total incentive of customers vs. the number of iterations.
  • Figure 4: Minimum nodal voltage magnitude vs. the number of iterations.
  • Figure 5: Feeder power vs. the number of iterations.

Theorems & Definitions (2)

  • Proposition V.1
  • proof