Demand response with moving horizon estimation of individual thermostatic load states from aggregate power measurements

Abstract

We present an optimization-based state estimation method that allows us to estimate the states of individual thermostatically controlled loads (TCLs), such as air conditioners and space heaters, from measurements of the power consumption of small aggregations of TCLs. The state estimator can be used together with a controller to provide ancillary services to power systems such as frequency control. The main advantage of this method is that it is designed to work with existing communication infrastructure. We assume that aggregate power measurements are available from distribution substations every few seconds, while TCL state measurements are available from smart meters only every 20 minutes. We model TCLs as hybrid systems and propose a moving horizon state estimator (MHSE), which is formulated as a mixed-integer linear program. We demonstrate the performance of the MHSE in two case studies: (a) estimation of TCL states in the absence of external control actions, and (b) a power tracking problem with closed-loop control using broadcast control inputs. To demonstrate the robustness of the method, we conduct a parametric analysis with respect to aggregation size and diversity, process noise characteristics, and control trajectory characteristics. The results show that the method generally provides accurate estimates of TCL states, resulting in improved controller performance in most cases, and is implementable in real-time with reasonable computational power.

Market-Based Coordination of Thermostatically Controlled Loads—Part I: A Mechanism Design Formulation

“…Many existing works use a first-order linear system to capture the TCL dynamics [11], [15], [16], where only consists of the room temperature. Although the first-order model is adequate for small TCLs such as refrigerators, it is not appropriate for residential air conditioning systems, which require a 2-D linear system model incorporating both air and mass temperature dynamics [12].…”

“…The optimal solution to this problem is if if otherwise (16) In addition, let us assume that the real time price is 20, and the maximum 5-min energy due to the feeder capacity constraint is 50, i.e., and . According to (16), when , only the 100th user consumes 1 unit of energy, and the aggregated energy is 1.…”

“…According to (16), when , only the 100th user consumes 1 unit of energy, and the aggregated energy is 1. When , the 99th and the 100th user consume 1 unit of energy, respectively, the corresponding aggregated energy is 2, and so forth.…”

“…Some of these DLC methods require fast communications between the aggregator and individual loads. The communication overhead can be reduced using advanced state estimation algorithms [15], [16] that can accurately estimate load state information without frequently collecting measurements from the loads.…”

Large-scale demonstration of precise demand response provided by residential heat pumps

“…Because SM data can be delayed by several hours, cf. II, the current state of a HP cannot be estimated by methods such as [30]. Instead, we consider the binary operational state of HP h as a random variable whose probability of being ON equals its duty-cycle d (h) c (θ out ).…”