In this paper, we propose a framework for coordinating distributed energy resources (DERs) connected to a power distribution system, the model of which is not completely known, so that they collectively provide a specified amount of active power to the bulk power system, while respecting distribution line capacity limits. The proposed framework consists of a linear time-varying input-output (IO) system model that represents the relation between the DER active power injections (inputs), and the total active power exchanged between the distribution and bulk power systems (output); an estimator that aims to estimate the IO model parameters; and a controller that determines the optimal DER active power injections so that the power exchanged between both systems equals to the specified amount at a minimum generating cost. We formulate the estimation problem as a box-constrained quadratic program and solve it using the projected gradient descent algorithm. To resolve the potential issue of collinearity in the measurements, we introduce random perturbations in the DER active power injections during the estimation process. Using the estimated IO model, the optimal DER coordination problem to be solved by the controller can be formulated as a convex optimization problem, which can be solved easily. The effectiveness of the framework is validated via numerical simulations using the IEEE 123-bus distribution test feeder.
- active power provision
- distributed energy resource
- parameter estimation
- projected gradient descent
ASJC Scopus subject areas
- Energy Engineering and Power Technology
- Electrical and Electronic Engineering