Model-based optimal control of variable-speed air conditioners in response to dynamic pricing in smart grids

Abstract

Today's electrical grids are facing great challenges due to the harmful power imbalance between the supply and demand sides. The increasing penetrations of intermittent and unpredictable renewable resources, such as wind and solar energy, exacerbate this imbalance. Demand response (DR) is a cost-effective method to address this imbalance issue. With the assistance of smart grid technologies, such as smart meters and smart home energy manage systems (HEMSs), electricity end-use customers at the demand side are informed and enabled to take DR actions to reduce/shift power consumption and improve the grid reliability. Dynamic electricity pricing is the major DR program adopted by electric utilities and grid operators to encourage electricity end-users to take DR actions. Buildings, as the major electricity consumers worldwide, have great responsibilities and potential to provide DR resources. Centralized heating ventilation and air conditioning (HVAC) systems and decentralized HVAC equipment, such as air conditioners (ACs) and heap pumps, account for a large proportion of the total electricity use in buildings. Their power consumption has a direct impact on power grids. In the context of smart grids, building HVAC systems and equipment need to be not only energy-efficient, but also grid-friendly and grid-responsive to address the power imbalance issue effectively. Unlike centralized HVAC systems in commercial buildings, which are enabled to fulfill automatic DR control by advanced building automation systems (BAS), residential HVAC equipment is still facing challenges to make automatic DR during peak demand periods. Although DR control of residential ACs has been widely studied, the residential ACs in the previous studies were almost all single-speed ACs with on-off control. On-off control carries the great disadvantage of undesired current peaks during state transitions. Single-speed ACs are also being gradually replaced by inverter ACs, which have greater energy efficiency in partial-load conditions. Inverter ACs can operate within a wide range of frequencies (20 to 100 Hz), which is accompanied by large variations in power consumption. The control algorithms of inverter ACs are more complicated than those of single-speed ACs. Two types of dynamic retail electricity pricings are widely used by most utilities in the United States: day-ahead pricing (DAP) and real-time pricing (RTP). For DAP, the prices for specific hourly intervals are announced to the end-consumers 1 day ahead. For RTP, the electricity prices are provided every 5 minutes based on the current electricity supply and demand of grid nodes. To conclude, the present thesis aims to develop model-based DR control methods for residential variable-speed ACs in response to two types of dynamic pricings, i.e. DAP and RTP. Two types of model-based optimal DR control methods are developed in response to two major dynamic electricity pricings, respectively: 1) Indirect model-based optimal control method in response to hourly day-ahead prices (DAP) via temperature set-point reset; 2) Direct model predictive control method in response to 5-minute real-time pricing (RTP) via operating frequency adjustment. Both DR control methods are developed based on the system model and the predictions of the influential variables, including the weather conditions, occupancy and RTPs. The system concerned in the present study is an integrated system consisting of an air-conditioned room and a variable-speed AC. Thus, simplified models for both room thermal dynamics and energy performances of AC are needed. A semi-physical (grey-box) dynamic room thermal model is developed and validated for predicting the indoor air temperature under dynamic operating conditions. For the computational efficiency, the dynamic room thermal model is transformed from the form of ordinary differential equations (ODE) to stochastic discrete-time state-space representation. Random white Gaussian noise is added in the system model considering the uncertainties arising from the exogenous input variables and make the model more realistic. The state space model can be used to formulate convex optimization problems which in general can be conveniently solved by using state-of-the-art optimization techniques. The model parameters can be learnt by making effective use of the data available in the today's smart in-home sensors. Due to the simple structure and moderate computation load, the developed room thermal model is suitable for developing model-based optimal control of residential ACs in response to dynamic DR signals. A simplified energy performance model of variable-speed ACs is developed and validated to characterize the AC performances under various operating frequencies and environmental conditions. The proposed simply structured energy performance model of variable-speed ACs can be readily used by electrical researchers and engineers for either model-based DR control in smart HEMSs or DR potential estimation of a single variable-speed AC or a large population of variable-speed ACs. A model-based optimal control method is developed for variable-speed ACs in response to hourly DAP, which adopts a two-level hierarchy structure. The high-level controller, i.e., the supervisory controller, is used to output the optimal set-point scheduling for the low-level local PID controller. The local PID controller is used to track the optimal set-points. Optimal scheduling of indoor air temperature set-points is formulated as a nonlinear programming problem which seeks the preferred trade-offs among electricity costs, thermal comfort and peak power reductions. Genetic algorithm (GA) is used to search the optimal solution of the nonlinear programming problem. The test results show that the proposed model-based optimal control method can reduce the whole electricity costs and the peak power demands during DR hours while meeting thermal comfort constraints. Besides, sensitivity analyses on the trade-off weightings in the optimization objective function demonstrate that electricity costs, occupant comfort and peak power reductions are sensitive to the weightings and the use of the weightings is effective in achieving the best trade-off. An MPC method is also proposed to directly control the operating frequency of variable-speed ACs in response to 5-minute RTP, which differs from the indirect DR control method (i.e., indoor air temperature set point reset). The major advantage of MPC is to take account of all the influential variables, such as weather conditions, occupancy, and dynamic electricity pricing, at the controller design stage while satisfying the system operating constraints. A simplified room thermal model in the stochastic state-space representation and performance maps of an inverter AC are integrated into the MPC controller for online prediction of the thermal response of an air-conditioned room. Two types of MPC controllers are designed for comparison, including an ordinary MPC controller without DR function and a DR-enabled MPC controller. The test results show that compared to the conventional PID controller, the MPC controller can implement automatic and optimal precooling based on the predictions of dynamic weather conditions and occupancy. Besides, the DR-enabled MPC controller demonstrates great improvements in both peak power reduction and electricity cost savings and is thus more grid-friendly and cost-efficient. To conclude, in order to make the residential variable-speed ACs grid-responsive and DR-enabled, two types of model-based optimal control methods are developed in response to two commonly used dynamic electricity pricings, i.e., DAP and RTP. The proposed DR control methods help to reduce the power consumptions during peak demand periods, reduce the electricity costs for end-use customers, and improve the grid reliability.