Control Affine Hybrid Power Plant Subsystem Modeling for Supervisory Control Design

TL;DR

The paper develops a control-affine modeling framework for a wind-solar-battery hybrid power plant (HPP) and designs component-wise controllers with safety guarantees to enable supervisory tracking of demand signals. It combines a CBf-QP based wind torque control to enforce limits on the Cp curve, a low-order PI solar model, and an ECM-based battery with ISS and barrier-function constraints, all integrated under a rule-based supervisor (WHOC). The approach demonstrates tracking of a PJM RegA signal in simulation, showing how wind/solar limitations are mitigated by battery support and highlighting remaining challenges in rapid resource changes and setpoint saturation. The work provides a modular, control-affine foundation for supervisory control design in HPPs and suggests future enhancements through predictive/optimization-based schemes and more detailed battery health and temperature effects.

Abstract

Hybrid power plants (HPPs) combine multiple power generators (conventional/variable) and energy storage capabilities to support generation inadequacy and grid demands. This paper introduces a modeling and control design framework for hybrid power plants (HPPs) consisting of a wind farm, solar plant, and battery storage. Specifically, this work adapts established modeling paradigms for wind farms, solar plants and battery models into a control affine form suitable for control design at the supervisory level. In the case of wind and battery models, generator torque and cell current control laws are developed using nonlinear control and control barrier function techniques to track a command from a supervisory control law while maintaining safe and stable operation. The utility of this modeling and control framework is illustrated through a test case using a utility demand signal for tracking, time varying wind and irradiance data, and a rule-based supervisory control law.

Figures (3)

• Figure 1: As $\lambda$ increases beyond the maximum power point, the power curve starts to decrease, indicating a negative $\frac{\partial{C_{p}}}{\partial{\lambda}}$, which would destabilize the closed loop system with control law in (\ref{['eq:tau_control']})
• Figure 2: Equivalent circuit model of a Li-Ion battery with homogeneous RC-circuit cells connected in series and parallel together with an equivalent series resistance, hysteresis voltage, and open open circuit voltage (figure inspiration from 2015Plett_BMS_Vol1, Fig. 2.12)
• Figure 3: Note that in both figures, the sign of the battery power is positive for discharging and negative for charging, which is opposite the sign convention in the dynamics but is used here for easier interpretation. In a), wind and solar resources are seen to be saturated for a majority of the simulation. Battery is able to quickly respond to allow the HPP to maintain good tracking of the demand signal. In b), tracking of the demand signal is illustrated with some difficulty when solar resource availability either ramps up or down quickly due to the irradiance quickly changing ($t = 1.5$ [hr] $\to \ t = 3.0$ [hr]). During periods when there is excess natural resource availability, the HPP is able to track the demand signal without battery contribution and the battery lies dormant.

Theorems & Definitions (5)

• Definition 1: SONTAG1995351
• Definition 2: 2019Ames_ControlBarrierFunctions_TheoryAndApplications2017Ames_ControlBarrierFunctionBasedQuadraticProgramsForSafetyCriticalSystems
• Theorem 1: 2019Ames_ControlBarrierFunctions_TheoryAndApplications2017Ames_ControlBarrierFunctionBasedQuadraticProgramsForSafetyCriticalSystems
• Definition 3: 2022Wei_HighOrderControlBarrierFunctions
• Theorem 2: 2022Wei_HighOrderControlBarrierFunctions