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Home Energy Management under Tiered Peak Power Charges

David Pérez-Piñeiro, Sigurd Skogestad, Stephen Boyd

Abstract

We consider the problem of operating a battery in a grid-connected home to minimize electricity cost, which includes an energy charge and a tiered peak power charge based on the average of the $N$ largest daily peak powers over a month. With perfect foresight of loads and prices, the minimum cost can be found by solving a mixed-integer linear program (MILP), which provides a lower bound on achievable cost. We propose a model predictive control (MPC) policy that uses simple forecasts of prices and loads and solves a small MILP at each time step. Numerical experiments on data from a home in Trondheim, Norway, show that the MPC policy achieves a cost within $1.7\%$ of the prescient bound.

Home Energy Management under Tiered Peak Power Charges

Abstract

We consider the problem of operating a battery in a grid-connected home to minimize electricity cost, which includes an energy charge and a tiered peak power charge based on the average of the largest daily peak powers over a month. With perfect foresight of loads and prices, the minimum cost can be found by solving a mixed-integer linear program (MILP), which provides a lower bound on achievable cost. We propose a model predictive control (MPC) policy that uses simple forecasts of prices and loads and solves a small MILP at each time step. Numerical experiments on data from a home in Trondheim, Norway, show that the MPC policy achieves a cost within of the prescient bound.
Paper Structure (48 sections, 20 equations, 12 figures, 7 tables)

This paper contains 48 sections, 20 equations, 12 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Related work
  3. Energy management.
  4. Peak power charges.
  5. Outline
  6. Home energy system
  7. Power balance
  8. Storage device
  9. Cost function
  10. Energy charge.
  11. Peak power charge.
  12. Total cost.
  13. Policies
  14. Information pattern.
  15. Prescient policy.
  16. ...and 33 more sections

Figures (12)

  • Figure 1: Grid-connected home with storage; $l_t$ is net load, $p_t$ grid power, $c_t$ charging power, and $d_t$ discharging power.
  • Figure 2: Hourly loads from a home in Trondheim, Norway. Top. Three-year period 2020--2022. Bottom. One week in January 2022.
  • Figure 3: Day-ahead prices $\lambda_t^\mathrm{da}$ for Trondheim, Norway. Top. Three-year period 2020--2022. Bottom. One week in January 2022.
  • Figure 4: Prescient policy with 40 kWh storage over 2022. Tier thresholds shown as dashed lines. Top left. Load. Top right. Grid power. Bottom left. Charge level. Bottom right. Average peak power $z_k$.
  • Figure 5: Prescient policy over one week in July 2022. Electricity prices $\lambda_t^\mathrm{tou} + \lambda_t^\mathrm{da}$ shown as dotted lines. Top left. Load. Top right. Grid power. Bottom. Charge level.
  • ...and 7 more figures