Architecture and algorithms for privacy preserving thermal inertial load management by a load serving entity

Abstract

Motivated by the growing importance of demand response in modern power system's operations, we propose an architecture and supporting algorithms for privacy preserving thermal inertial load management as a service provided by the load serving entity (LSE). We focus on an LSE managing a population of its customers' air conditioners, and propose a contractual model where the LSE guarantees quality of service to each customer in terms of keeping their indoor temperature trajectories within respective bands around the desired individual comfort temperatures. We show how the LSE can price the contracts differentiated by the flexibility embodied by the width of the specified bands. We address architectural questions of (i) how the LSE can strategize its energy procurement based on price and ambient temperature forecasts, (ii) how an LSE can close the real time control loop at the aggregate level while providing individual comfort guarantees to loads, without ever measuring the states of an air conditioner for privacy reasons. Control algorithms to enable our proposed architecture are given, and their efficacy is demonstrated on real data.

Optimal power consumption for demand response of thermostatically controlled loads

“…For an LSE managing a finite population of TCLs, we formulate and solve the optimal aggregate power consumption design as a finite-horizon deterministic optimal control problem. The contribution of the present paper beyond our previous work 17,18 is that, herein, we analytically solve the continuous-time optimal control problem (Section 4), thereby revealing qualitative insights on how the LSE can use the knowledge of day-ahead price forecast, load forecast, and ambient temperature forecast, for the purpose of energy procurement at least cost. Furthermore, when there is additional constraint on minimum thermostatic switching period, we provide an algorithm (Sections 5 and 6) to recover the optimal binary controls from the corresponding convexified optimal control solutions.…”

“…Details of the simulation setup are described in Section 6. With the initial conditions and parameters of the heterogeneous TCL population as in section V-A in the work of Halder et al, 18 = 1 3 (which was verified to be feasible using (8)), comfort tolerances {Δ i } N i=1 sampled randomly from a uniform distribution over [0.1 • C, 1.1 • C], and for̂(t) and̂a(t) as in Figure 9, the LSE solves the optimal control problem (3)-(6) by first convexifying the controls u i (t) ∈ {0, 1}  → v i (t) ∈ [0, 1] for i = 1, … , N, and then recovering the optimal controls {u * i } N i=1 using Theorem 3. For this computation, we used 1-minute time step for Euler discretization of dynamics (4a), and solved the resulting LP with 1 million 440 thousand decision variables (see Section 3.3) using MATLAB linprog.…”

“…The brick colored curve in Figure 11 corresponds to the real-time aggregate consumption for the TCL population with same T m , and real-time ambient temperature a (t) as in the solid blue curve in Figure 9, for a PID velocity control gain tuple (k p , k i , k d ) used to control the setpoint boundaries as part of a mixed centralized-decentralized control. We refer the readers to section III.1 in the work of Halder et al 18 for details on the real-time setpoint control. The purpose of Figure 11 is to highlight how the solution of the open-loop optimal control problem (3)-(6) can be used by the LSE as a reference aggregate consumption to be tracked in real-time, to elicit demand response.…”

Differential Privacy of Aggregated DC Optimal Power Flow Data

“…In the above procedure, an n-tuple of vectors is also regarded as a matrix of n columns. 6 Since γ ∈ Γ is of rank |S| and {T S θ|∀θ ∈ R N } defines a subspace with ≤ |S| − 1 dimensions, each set of {ξ|∃θ, s.t. γ T ξ = T S θ} in (13) is a subspace with dimension strictly lower than 2N G + 2E.…”

“…Differential privacy, first developed in [1], [2], [3], has been widely used to evaluate the privacy loss for individual users in a dataset. It has recently been used by the researchers in the power systems community for use in applications such as distributed algorithms for EV charging [4], power system data release [5], and load management [6].…”