Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

An Electricity Market with Reactive Power Trading: Incorporating Dynamic Operating Envelopes

Zeinab Salehi, Elizabeth L. Ratnam, Yijun Chen, Ian R. Petersen, Guodong Shi, Duncan S. Callaway

Abstract

Electricity market design that accounts for grid constraints such as voltage and thermal limits at the distribution level can increase opportunities for the grid integration of Distributed Energy Resources (DERs). In this paper, we consider rooftop solar backed by battery storage connected to a distribution grid. We design an electricity market to support customers sharing rooftop generation in excess of their energy demand, where customers earn a profit through peer-to-peer (P2P) energy trading. Our proposed electricity market also incorporates P2P reactive power trading to improve the voltage profile across a distribution feeder. We formulate the electricity market as an optimization-based problem, where voltage and thermal limits across a feeder are managed through the assignment of customer-specific dynamic operating envelopes (DOEs). The electricity market equilibrium is referred to as a competitive equilibrium, which is equivalent to a Nash equilibrium in a standard game. Our proposed market design is benchmarked using the IEEE 13-node test feeder.

An Electricity Market with Reactive Power Trading: Incorporating Dynamic Operating Envelopes

Abstract

Electricity market design that accounts for grid constraints such as voltage and thermal limits at the distribution level can increase opportunities for the grid integration of Distributed Energy Resources (DERs). In this paper, we consider rooftop solar backed by battery storage connected to a distribution grid. We design an electricity market to support customers sharing rooftop generation in excess of their energy demand, where customers earn a profit through peer-to-peer (P2P) energy trading. Our proposed electricity market also incorporates P2P reactive power trading to improve the voltage profile across a distribution feeder. We formulate the electricity market as an optimization-based problem, where voltage and thermal limits across a feeder are managed through the assignment of customer-specific dynamic operating envelopes (DOEs). The electricity market equilibrium is referred to as a competitive equilibrium, which is equivalent to a Nash equilibrium in a standard game. Our proposed market design is benchmarked using the IEEE 13-node test feeder.
Paper Structure (10 sections, 2 theorems, 10 equations, 4 figures, 1 algorithm)

This paper contains 10 sections, 2 theorems, 10 equations, 4 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Electric Grid Constraints
  4. Market With Reactive Power Compensation
  5. Nash Equilibrium
  6. Numerical Simulations
  7. Simulation Setup
  8. Numerical Simulations
  9. Conclusion
  10. Proof of Theorem \ref{['theorem7']}

Key Result

Theorem 1

Suppose $f_i(\cdot)$, $\phi_i(\cdot)$, and $-h_i(\cdot)$ are concave functions for $i \in \mathcal{N}$, and Slater's condition holds for eq_competitive_7 and eq4. Given feasible initial conditions $\mathbf x_i(0)$ for $i \in \mathcal{N}$, the following statements hold.

Figures (4)

  • Figure 1: Modified IEEE 13-node test feeder. Left: A prosumer $i$ is zoomed in.
  • Figure 2: Active power prices $\lambda^\ast(t)$ (¢/kWh) and reactive power prices $\gamma^\ast(t)$ (¢/kVarh), over a 24-hour period (48 time steps of length $0.5$ hour).
  • Figure 3: Some elements of the DOE limit price vector $\boldsymbol\beta^\ast(t)$ (in ¢/(kV)$^2$) over a 24-hour period (48 time steps of length $0.5$ hour). The $k$-th element of $\boldsymbol \beta^\ast(t)$ is denoted by $\beta^\ast_{k}(t)$. The other $17$ elements are close to zero and not depicted.
  • Figure 4: Nodal voltages $v_j(t)$ (p.u.) for each of the $12$ nodes, $j\in \{1, \dots, 12\}$. The gray area indicates the voltage range without reactive power trading across the grid.

Theorems & Definitions (7)

  • Definition 1: as in mahmoodi2023capacity
  • Definition 2
  • Theorem 1
  • proof
  • Remark 1
  • Theorem 2
  • proof