One-Dimensional Electric Water Heater Modeling for Thermal Stratification
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Solution Overview
Problem
Existing water heater control systems struggle to accurately model and manage thermal stratification in vertically oriented cylindrical tanks, which affects energy storage and demand response capabilities, and lack effective condition-based maintenance due to insufficient temperature monitoring and complex computational requirements.
Innovation Solution
A one-dimensional modeling approach using a stack of disks to represent the water volume and annular segments for the tank wall, coupled with differential equations to estimate temperature distribution and water draw flow rate, allowing for more accurate energy storage tracking and condition-based maintenance.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a detailed three-dimensional model is used to accurately represent thermal stratification, then measurement precision and energy storage tracking accuracy are improved, but device complexity and computational requirements increase significantly
Solution Approach 1:
The water tank is divided into multiple discrete vertical segments or zones along its height, with each segment representing a specific temperature layer. This segmentation allows the system to capture thermal stratification effects without requiring a continuous three-dimensional model, reducing computational complexity while maintaining measurement precision for energy storage tracking.
Solution Approach 2:
The patent transitions from a three-dimensional modeling approach to a one-dimensional vertical zoning model. By representing the tank as stacked horizontal layers with distinct temperature characteristics, the system achieves adequate thermal stratification representation with significantly reduced computational requirements and simpler device architecture.
2Adaptability or versatility
If remote control and demand response capabilities are implemented, then adaptability and grid integration are improved, but device complexity and control system requirements increase
Solution Approach 1:
The water heater control system is designed to perform multiple functions: traditional temperature control, energy storage tracking, and demand response participation. By integrating these functions into a single control architecture that uses the same vertical zoning model for both operational control and grid interaction, the system achieves high adaptability without proportionally increasing device complexity.
Solution Approach 2:
The system implements feedback mechanisms where temperature measurements from the vertical zones are continuously monitored and used to adjust heating element operation. This feedback loop enables both maintaining water temperature within desired ranges and responding to grid demand signals, achieving versatility through a relatively simple closed-loop control structure.
3Productivity
If thermal stratification is leveraged for energy storage, then productivity and demand response effectiveness are improved, but measurement precision requirements and computational complexity increase
Solution Approach 1:
The vertical zoning of the water tank creates discrete energy storage zones that can be individually characterized and monitored. Each zone's thermal energy content can be calculated based on its temperature and volume, allowing the system to track total energy storage with good accuracy using simple one-dimensional measurements rather than complex three-dimensional temperature field monitoring.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This solution provides more accurate energy storage estimation and operational status monitoring, enabling effective demand response and condition-based maintenance, while reducing computational complexity and requiring only limited inputs from conventional thermostats.
Implementation Method 1
A typical electric water heater includes a water storage tank with one or more heating elements
Implementation Method 2
Heated water loses density, causing it to tend to rise upward
Implementation Method 3
this flow pattern is reinforced by entry of cold water near the bottom of the tank and extraction of hot water from the top of the tank
Data Source
AI summary
A water heater that includes a cylindrical storage tank, at least one heating element, and at least one temperature sensor is modeled using a one-dimensional model that includes: a vertical stack of disks representing the water volume in the cylindrical storage tank, and a stack of annular segments surrounding the vertical stack of disks. The stack of annular segments represents the cylindrical wall of the cylindrical storage tank. The one-dimensional model may be used by a condition-based maintenance system comprising an electronic data processing device configured to detect a failure mode present in the water heater based on an output of the water heating model component. Some illustrative failure modes include insulation disturbance, heating element failure, excessive sediment buildup, or a drip tube rupture.