Virtual water usage sensor for tank water heater and method

Abstract

Virtual water usage sensors for tank water heaters and methods associated therewith. The virtual water usage sensors estimate water usage in a water heater based on inlet water temperature data and tank water temperature data to allow the water usage to be measured without having to add a flow meter to the tank water heater to directly measure water mass flow from the water heater. Inlet water temperature data can be obtained from a temperature sensor located directly at the inlet of the tank water heater or at remote locations along the water lines upstream from the water heater, such as along a community water supply line or at a water treatment facility. The water usage estimates may be incorporated with a model predictive controller that forecasts water demand using a hybrid machine learning model to dynamically adjust heating schedules of the water heater based on the forecast water demand.

Description

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit of provisional U.S. Patent Application No. 63 / 765,943 filed Mar. 3, 2025, the contents of which are incorporated herein by reference.BACKGROUND OF THE INVENTION

[0002] The invention generally relates to virtual water usage sensors, methods of estimating hot water usage in a tank water heater, and tank water heating systems.

[0003] Electrification of residential hot water systems is an increasingly adopted strategy for reducing greenhouse gas emissions, as electric water heaters can utilize electricity generated from low-carbon sources, including renewable energy. Heat pump water heaters, a form of electric water heater, can further provide improved efficiency by transferring heat from ambient air to stored water, thereby delivering greater thermal energy per unit of electrical input relative to conventional gas-fired or electric resistance-based water heaters. Although electric water heating has distinct benefits, widespread deployment of electric water heaters introduces challenges to electrical grid operation. Renewable energy generation is inherently variable, and distribution infrastructure is often designed around historical load profiles that did not account for large-scale electrification. Uncoordinated operation of electric water heaters may contribute to peak demand events, localized feeder congestion, and increased infrastructure upgrade requirements.

[0004] Load-shifting capabilities may be implemented to enhance coordination of electric water heaters with grid conditions. In certain existing implementations, load control may involve temporarily disabling heating operations during designated periods. However, such approaches don't account for anticipated hot water usage and may result in reduced hot water availability during or following a load-shifting event. As a result, occupants may experience insufficient hot water during normal usage activities, such as showering or bathing. This issue may be more pronounced in heat pump water heaters, as the heat pump component generally provides a lower heating rate than electric resistance elements. Accordingly, improved prediction or estimation of hot water demand may facilitate more effective load-shifting while maintaining desired water temperature levels.

[0005] Residential tank-type electric water heaters typically measure only the temperature of the water inside the water tank. However, with afore mentioned load-shifting capabilities becoming increasingly important, it is desirable for water heaters to be able to shift their heating schedules, for example, to protect either the local power distribution equipment (e.g. electrical panel) and / or the utility level power distribution equipment (e.g. transformers). To do this effectively, it is helpful to be able to understand household water usage patterns. Currently, however, capturing the water usage data needed to understand the household water usage patterns typically requires installing a water flow meter on the water heater in an individual residence. Unfortunately, this approach is time-consuming, costly per unit, and rarely implemented.

[0006] Accordingly, it would be desirable to have a more efficient and / or easier to implement system to estimate water usage for residential water heaters and / or other apparatus and reasons.BRIEF SUMMARY OF THE INVENTION

[0007] The intent of this section of the specification is to briefly indicate the nature and substance of the invention, as opposed to an exhaustive statement of all subject matter and aspects of the invention. Therefore, while this section identifies subject matter recited in the claims, additional subject matter and aspects relating to the invention are set forth in other sections of the specification, particularly the detailed description, as well as any drawings.

[0008] The present invention provides, but is not limited to, virtual water usage sensors, methods of estimating hot water usage in a tank water heater, and tank water heating systems.

[0009] According to one nonlimiting aspect, a virtual water usage sensor for estimating water usage in a tank water heater includes a first temperature sensor for measuring inlet water temperature of water flowing into a water tank of the tank water heater, at least one second temperature sensor for measuring tank water temperature of water being held within the water tank, and a water usage estimation module having a digital computer system configured with program instructions that, when executed, cause the digital computer system to derive an estimated water usage from the tank water heater from the inlet water temperature measurements and the tank water temperature measurements.

[0010] According to another nonlimiting aspect, a method of estimating hot water usage in a tank water heater includes measuring inlet water temperature of water flowing into a water tank of the tank water heater, measuring tank water temperature of water being held within the water tank, and deriving an estimated water usage from the tank water heater based on the inlet water temperature measurements and the tank water temperature measurements.

[0011] According to yet another nonlimiting aspect, a tank water heating system includes a water tank, a heat source to heat water held within the water tank, and a virtual water usage sensor as described herein.

[0012] Technical aspects of virtual water usage sensors, methods of estimating hot water usage in a tank water heater, and tank water heating systems as described above preferably include the ability to provide more efficient systems and methods of measuring and / or controlling functioning of tank water heaters relative to conventional water heaters.

[0013] These and other aspects, arrangements, features, and / or technical effects will become apparent upon detailed inspection of the figures and the following description.BRIEF DESCRIPTION OF THE DRAWINGS

[0014] FIG. 1 is schematic representation of a virtual water usage sensor implemented as part of a tank water heating system connected to a community water supply.

[0015] FIG. 2 is a schematic representation of the tank water heating system showing additional aspects of a model predictive controller for controlling heating of water in a tank water heater as implemented in a nonlimiting investigation setup.

[0016] FIG. 3 is an example thermal model that may be used by a model predictive controller to derive the mass flow rate in a tank water heating system.

[0017] FIG. 4 is an example estimation algorithm block diagram representing the flow of data and inputs to outputs that may be used by a model predictive controller to derive the mass flow rate in a tank water heating system.DETAILED DESCRIPTION OF THE INVENTION

[0018] The intended purpose of the following detailed description of the invention and the phraseology and terminology employed therein is to describe what is shown in the drawings, which include the depiction of and / or relate to one or more nonlimiting embodiments of the invention, and to describe certain but not all aspects of the embodiment(s) to which the drawings relate. The following detailed description also describes certain investigations relating to the embodiment(s), and identifies certain but not all alternatives of the embodiment(s). As nonlimiting examples, the invention encompasses additional or alternative embodiments in which one or more features or aspects shown and / or described as part of a particular embodiment could be eliminated, and also encompasses additional or alternative embodiments that combine two or more features or aspects shown and / or described as part of different embodiments. Therefore, the appended claims, and not the detailed description, are intended to particularly point out subject matter regarded to be aspects of the invention, including certain but not necessarily all of the aspects and alternatives described in the detailed description.

[0019] As used herein the terms “a” and “an” to introduce a feature are used as open-ended, inclusive terms to refer to at least one, or one or more of the features, and are not limited to only one such feature unless otherwise expressly indicated. Similarly, use of the term “the” in reference to a feature previously introduced using the term “a” or “an” does not thereafter limit the feature to only a single instance of such feature unless otherwise expressly indicated.

[0020] The following disclosure describes a virtual water usage sensor that is preferably capable of being more efficient than previously known water usage sensors, and in some applications can replace the need for a conventional water flow meter. The water usage sensor may be implemented as part of a system that estimates water usage in an area using a single additional temperature measurement on a water inlet line. Since inlet water temperatures are typically consistent within local regions (e.g., a city), this measurement can be taken only once per area and shared with individual water heaters, for example by an internet or other data connection. By deriving the hot water demand, historical water usage profiles can be stored per household, and a forecast water draw profile can be developed. Water heaters can then be intelligently controlled to shift loads while maintaining user comfort, all at a fraction of the cost and effort of traditional methods. This can save residents money on their energy bills, provide for more efficient water heating and water transmission, and has the potential to save utility companies money by protecting local power transmission equipment.

[0021] The virtual water usage sensor is capable of being used in a model predictive control (MPC) architecture so as to require only a single additional temperature sensor on the water inlet line. The model estimates water use from temperature changes without requiring addition of a water flow meter on the tank water heater and forecasts demand with a hybrid machine learning model. By estimating water draws (usage) through temperature measurements and forecasting demand using a hybrid machine learning model, the controller can dynamically adjust heating schedules to maintain comfort while shifting the load and improving efficiency.

[0022] The MPC system of the present disclosure is preferably capable of being adapted to household water draw patterns to optimize energy use. For instance, if a utility needs to shift loads in the evening, the water heater may preheat the tank only if evening water usage is typical for that household. If not, preheating is avoided to prevent unnecessary energy consumption. This can help ensure that each home remains comfortable during load-shifting periods while optimizing energy use based on individualized water usage forecasts.

[0023] A demand response control algorithm may also be integrated into the system with advanced rate structures, such as day-ahead pricing, where electricity costs vary hourly. Additionally, the demand response algorithm may be configured to work with local panel protection controllers to prevent or reduce total home power consumption from exceeding the panel's rated limits.

[0024] The water usage sensor and / or system described herein are preferably capable of offering broader benefits, such as protecting local electrical infrastructure, reducing unnecessary water heating to lower energy bills, improving energy efficiency and reducing environmental impact, and / or maximizing savings through dynamic utility rate structures like time-of-use and day-ahead pricing. By accurately predicting household water usage, consumers may achieve significant energy cost reductions while supporting a more resilient electrical grid.

[0025] Further areas of applicability will become apparent from the description provided herein. The description and specific examples in this summary are intended for purposes of illustration only and are not intended to limit the scope of the present disclosure.

[0026] Turning now to the drawings, in FIG. 1 a tank water heating system according to some embodiments may include a virtual water usage sensor 10 that is operatively coupled with a tank water heater 12 to estimate water usage of the tank water heater. The tank water heater 12 includes a water tank 14 that holds water therein and a heat source 16 for heating the water in the water tank 14. The heat source 16 may include any one or more heat sources suitable for heating the water, such as a heat pump, an electric resistance heating element, an open flame (e.g., from burning natural gas, oil, kerosene, coal, wood, etc.), an induction heating element, and / or any other heat source suited for heating the water inside the water tank 14. In some embodiments, the tank water heater 12 may be heat pump water heater or a hybrid heat pump water heater including both a heat pump and another heating source, such as an electric resistance heating element or induction heating element.

[0027] The virtual water usage sensor 10 includes an inlet temperature sensor 18 for measuring inlet water temperature of water flowing into the water tank 14 and one or more tank temperature sensors 20 for measuring tank water temperature of the water inside the water tank 14 (“tank water temperature”). In some embodiments, the inlet temperature sensor 18 may be disposed on or about the water inlet 22 of the water tank 14 to measure the temperature of the water as it enters the water tank 14. In other embodiments, the inlet temperature sensor 18 may also or alternatively be located remote from the tank water heater 12, such as on a community water supply line 24 (e.g., a city water main, branch line, residential supply connection line into a property, etc.) and / or in a water treatment plant 26. In this example, two tank temperature sensors 20, an upper temperature sensor and a lower temperature sensor, are provided for measuring the water temperature at upper and lower vertical regions in the water tank 14, respectively. However, additional temperature sensors 20 could be used to measure water at additional vertical regions and / or other volumes of water within the water tank 14, or only a single temperature sensor 20 may be used to measure the water temperature inside the tank 14.

[0028] The virtual water usage sensor 10 also includes a water usage estimation module 28 that is configured to derive estimated water usage from the tank water heater 12 based on the inlet water temperature measurements obtained by the inlet temperature sensor 18 and the tank water temperature measurements obtained by the tank temperature sensors 20. The water usage estimation module 28 includes a digital computer system with various hardware and / or software components configured with program instructions that, when executed, derive the estimated water usage from the inlet and tank temperature data without having to use any direct mass flow measurements of water flow into or out of the water tank 14 to derive the estimated water usage. The digital computer system may be any combination of digital processors, memory, electrical power, data communications modules, input / output devices, etc. and / or other computer processing equipment suitable for receiving and manipulating the sensor data as described herein. The digital computer system may also include and / or be loaded with software and / or hardware instructions suitable for executing various programs as described herein for receiving the sensor data and / or other types of data relative to the tank water heater 12, estimating water usage, predicting water usage, controlling the heat source 16, and any other data manipulation to be completed by the computer system.

[0029] The water usage estimation module 28 is configured to estimate the water usage based on the inlet water temperatures and the tank water temperatures taken over a given time period. The water usage estimation module 28 may also use other data and / or information relative to various characteristics of the tank water heater 12, the environment surrounding the tank water heater 12, a signal 34 indicating whether the heating source 16 of the water heater 12 is on or off with the heating source's capacity, and / or other factors. For example, the water usage estimation module 28 may also base the estimate on historical water usage data, heat transfer rates into and / or out of the water tank 14 and / or the heating source 16, temperature(s) of the surrounding environment inside and / or outside of the building, and / or other factors. In any case, the water usage estimation may be calculated by any suitable algorithm capable of estimating the (hot) water usage / mass flow of water exiting the water tank 14 over time without having to include directly sensed / measured water output mass flow data, such as the type of mass flow data that would be obtained by a water flow meter. This way, the water usage estimation module 28, and by extension the virtual water usage sensor 10, obtain (hot) water usage estimates without having to install a water meter, which can reduce costs and / or complexity of obtaining the water usage data. In some embodiments, the water usage estimation module 28 includes a program that estimates the hot water usage in the tank water heater 12 by measuring the inlet water temperature of water flowing into the water tank 14, measuring the tank water temperature of water being held within the water tank 14 in at least one, and preferably at two different water levels, and then deriving the estimated water usage based on the inlet water temperature measurements and the tank water temperature measurements. The inlet water temperatures are measured by the inlet temperature sensor 18 located in any location suitable for obtaining a suitably accurate reading of the water temperature as it enters the tank 14 from the inlet 22. The tank water temperatures are measured by one or more of the tank temperature sensors 20. In this example, the estimation is made using two tank temperature sensors 20, and measuring tank water temperatures of water being held within different vertical regions of the water tank 14, including at least an upper region and a lower region of the water tank 14. This allows the tank water measurements to estimate a temperature gradient and / or different temperatures at different water strata within the water tank 14. The program can then derive the estimated water usage using the inlet water temperature measurements and the tank water measurements from the upper and lower regions within the water tank 14.

[0030] In other embodiments, the water usage estimation module 28 includes a program that estimates the hot water usage in the tank water heater 12 by receiving a signal 34 if the heat source 16 is on or off, measuring the inlet water temperature of water flowing into the water tank 14, measuring the tank water temperature of water being held within the water tank 14 at least one water level, and then deriving the estimated water usage based on the inlet water temperature measurements and the tank water temperature measurements. The inlet water temperatures are measured by the inlet temperature sensor 18 located in any location suitable for obtaining a suitably accurate reading of the water temperature as it enters the tank 14 from the inlet 22. The tank water temperatures may be measured by one or more of the tank temperature sensors 20. The signal 34 of the heating source 16 being on or off can be monitored by the tank water heater 12 and sent to the virtual water usage sensor 10. The program can then derive the estimated water usage using the signal 34 that the heating source 16 is on or off, the inlet water temperature measurements, and the tank water measurements within the water tank 14.

[0031] Typically, the temperature of the water at the inlet 22 does not vary much from the temperature of the water as it flows through the community water pipe supply system 24 and / or in the water treatment plant 26. Therefore, inlet water temperature can typically be assumed to be substantially the same regardless of where along the water route from the water treatment plant to the water tank inlet 22 the temperature is measured. Thus, the inlet water temperature can likewise be measured directly at the water tank inlet 22 and / or at almost other suitable location on a water supply line remote from the tank water heater 12 that supplies water to the tank water heater 12. This makes it possible, for example, to have an inlet temperature sensor 18 located almost anywhere along the community water supply system that can provide the inlet water temperature measurement data to water usage estimation modules 28 associated with tank water heaters located in many different houses, buildings, or other locations. The measured inlet water temperature data can then be supplied to the water usage estimation modules 28 by any suitable data communication link, such as via the internet, LAN, WLAN, Wi-Fi, wireless data transmission, and / or Bluetooth. The local water usage estimation modules 28 associated with the individual tank water heater 12 can then estimate the water usage based on the remotely acquired inlet water temperature measurement without having to install / provide the inlet temperature sensor 18 on each water tank 14, thereby further reducing costs and / or complexity of the system.

[0032] The virtual water usage sensor 10 has many potential use cases and applications, such as tracking hot water usage within a household or other location to provide insights into how to reduce water and / or energy usage to reduce environmental and / or financial impact. Other use cases may include deriving diagnostic information regarding the tank water heater 12 based on the estimated water usage. For example, the estimated water usage information may be used to detect and / or identify potential faults in and / or around the tank water heater 12, such as water leaks from the water heater 12 and / or the various outlet lines (e.g., sink, shower, tub, etc.) coupled to the outlet 30 of the water tank 14.

[0033] In some embodiments, the virtual water usage sensor 10 may be combined in a tank water heating system that also includes a model predictive controller (MPC) 32 for predicting future water usage rates at various future time intervals and controlling the amount of heating provided to the water inside the water tank 14 based on the hot water use predictions. In such an embodiment, the model predictive controller 32 may include a digital computer system operatively coupled with the virtual water usage sensor 10 to receive the estimated water usage and also operatively coupled with the heat source 16 to provide control signals to control a temperature set-point of the water tank 14 and / or the heating source 16. The digital computer system of the model predictive controller 32 may be separate from or combined with the digital computer system of the water usage estimation module 28. For example, the model predictive controller 32 and the virtual water usage sensor 10 may be separate software and / or other program configurations implemented on a common digital processing system, such as dedicated processor / controller computer circuit, a computer server, etc., or may be programs implemented on separate, individual ASICs for each module or other computer processors. In either case, the model predictive controller 32 includes program instructions that, when executed, cause the digital computer system to estimate hot water draws from the water tank 14 based on the inlet water temperature data and the tank water temperature data, forecast water demand by a variety of methods, such as, but not limited to, using a hybrid machine learning model, and dynamically adjust heating schedules via the temperature set-point or heating source based on the forecast water demand. In one nonlimiting embodiment, the estimated water draws (usage) can be derived by estimating the heat loss or gain in the water tank 14 attributed by the inlet water and dividing by the specific heat change per unit mass of that inlet water to estimate the mass flow rate of the inlet water; thereby also estimating the mass flow rate of the outlet water of the water tank. The step of estimating the hot water draws may be accomplished using the virtual water usage sensor 10 either as a separate program module or as an integrated part of a single model predictive controller module. The hybrid machine learning model may include a combination of a short-term time horizon model (e.g., from the current time until the next 15-30 minutes), a mid-term time horizon model (e.g., from 15-30 minutes from the current time until 8-10 hours from the current time), and a long-term time horizon model (e.g. from 8-10 hours from the current time until 20-24 hours from the current time). The short-term time horizon model may be a random forest model. The mid-term time horizon model may be a Prophet model. The long-term time horizon model may be based on the water usage profile of the tank water heating system from the previous day, for example, by simply using the previous day's water usage information as a prediction for the same time in the next 24 hours. Of course, other types of predictive models may be implemented for calculating the predicted water usage.

[0034] FIG. 2 illustrates one example configuration of internet-of-things (“IoT”) infrastructure in a test house 102 used to test a tank water heating system 100 that implements the virtual water usage sensor 10 with the model predictive controller 32, and the following description provides descriptions of certain nonlimiting examples and investigations conducted in the process of the development of the systems and methods disclosed herein. In this test setup, a Yokogawa data acquisition system 104 reads sensor data obtained from the temperature sensors 18 and 20 in a heat pump water heater (HPWH)-type tank water heater 12 and feeds the temperature data to a cloud storage 106. A computer 108 in the home 102 runs the MPC 32 and Python scripts that push set points to the water heater 12 via an application program interface. The MPC 32 generates hot water usage forecasts, which are supplied to an optimizer. The optimizer then computes set points to be sent back to the water heater 12 to control the heat source 16. The set-points are dynamic in that they change with time based on the ongoing water temperature data received from the sensors 18 and 20 as well as the continuously updating hot water usage prediction / forecast provided by the MPC 32 based on continuously updated water usage estimates.

[0035] In the test setup of FIG. 2, minimal additional sensing was introduced to keep the control solution scalable. The system interacts with the HPWH 12 via an application program interface connection to adjust set-point temperatures and operational modes. The only external sensors added were a thermocouple on the inlet water line to monitor entering water temperature and a flow meter. The flow meter for this study was only used to analyze the performance of the virtual sensor, forecasting algorithm and the control performance and was not used in the control loop or virtual sensor itself. The only sensors used in the control loop and virtual sensor are the three thermocouples for the upper, lower, and inlet tank temperatures.

[0036] A thermal model of the water heater 12 was developed to enable MPC for the water heater 12, a nonlimiting example of which is represented in FIG. 3. FIG. 4 is a high level block diagram of an example estimation algorithm and represents the flow of data and inputs to outputs that may be used by the model predictive controller 32 to derive the mass flow rate ({dot over (m)}) in a tank water heating system. In this nonlimiting example, the estimation algorithm could either be a static energy balance (such as presented in FIG. 3) or a state-estimator such as a Kalman Filter. While there is a range of modeling techniques available to model typical hot water storage tanks, from single node to multi-node models and linear to non-linear formulations, non-linear formulations are computationally expensive to solve and are therefore not as ideal for optimization algorithms embedded in the MPC 32. In this example, a linear formulation was used. Further, because most HPWHs have two temperature readings for the upper and lower portion of the tank 14, a two-node model was used. In the two-node model, because the control parameter for a water heater is the set-point temperature, the height of the stratification layer is maintained constant for tractability and to capture stratification of the water within the tank 14. There are then two energy balance equations to describe the two-node model with a stratification layer resembling a resistance layer. These equations represent the change in thermal capacitance for their respective portions of the tank 14. The resistance value to the ambient temperature surrounding the tank 14 (Tamb) is used to calculate the heat loss through the tank wall. The heat transfer due to the flow across the boundaries is a function of the mass flow rate of water ({dot over (m)}) , the specific heat capacity of the water (cp), and the temperature difference between the inlet and outlet water. The heat input into the tank 14 from a heat source (e.g., a condenser) is split between the two nodes. The upper and lower tank water temperatures TH and TL are obtained from the manufacturer's sensors (e.g., sensors 20), environmental temperature Tamb can be estimated as close to the indoor temperature if it is inside, or outdoor temperature if it is outside, and the inlet water temperature Tinlet can be measured from an additional thermocouple (e.g., sensor 18). Additional data are known from the manufacturer's specification sheets. From these, an energy balance formulation can be derived for a heat disturbance term, which is the aggregation of the heat loss from colder inlet water temperatures and heat input from the heat source. However, the mass flow rate ({dot over (m)}) and heat input from the heat source are unknown, and, therefore, neither term can be solved directly. The heat disturbance term can be split into two portions, positive and negative. When the heat disturbance term is negative, heat is entering the bottom node and is the resultant of heat from the heat source in the bottom node's respective portion. When the heat disturbance term is positive, heat is lost as it is leaving the node and is therefore dominated by heat loss from entering cold water.

[0037] The goal of this formulation is to derive an estimated value of the mass flow rate to be able to estimate when large water draws occur (i.e., showers) as smaller water draws (i.e., washing hands or rinsing dishes) have little effect on the state of charge of the water heater and is therefore not crucial in predicting. Therefore, it is important that the heat disturbance term is positive when large showers occur to get a signal that water draws are occurring. In typical circumstances, the heat loss from cold inlet water is typically at least 9.49 kW (32,400 Btu / hr). In the case that the heat pump is on at the same time, the max heat transfer rate is typically 1.5 kW (5,120 Btu / hr) for medium-sized water tanks (0.189 m3 (50 gal)) and up to 3 kW (10,240 Btu / hr) for large water tanks (0.303 m3 (80 gal)). Therefore, the heat from the heat source into the bottom node is at a maximum of 1.07 kW (3,650 Btu / hr)-2.1 kW (7,170 Btu / hr), due to only a portion of the heat from the heat source entering the bottom node. For either the medium or large water tanks, the heat transfer rate from a large water draw is typically at least 4 times the heat from the heat source at the initial point of the draw. To derive the mass flow rate term, it is then assumed the heat from the heat source is negligible when the heat disturbance term is positive.

[0038] With these assumptions, the mass flow rate was estimated from the upper, lower, and inlet tank temperatures to derive historical water draw profiles. In this embodiment, the mass flow rate is approximated to be equal to the heat disturbance term for the lower vertical portion of the tank 14 divided by the heat energy transferred per unit mass of the inlet water. In other words, the estimated mass flow rate corresponds to the heat loss attributable to incoming water divided by the specific heat change per unit mass of that water. After filtering out noise from minor temperature fluctuations in the lower tank via a low-pass filter, the estimation method was applied to a month of data in January 2025. Relative to the directly measured water draw from the water flow meter, the estimation model achieved a mean squared error of 0.09 liters / min (0.024 gallons / min) and a total water draw error of −2.01%, underestimating water usage by only 3.9 liters (1.03 gallons) for the month. Comparisons of the estimated and measured water draws over a representative two-day period demonstrated strong alignment in timing and peak magnitudes, which are beneficial for obtaining effective predictive control. Minor discrepancies in the peak values arose from simplifications of the thermal model, including the exclusion of heat input from the heat source during active heat pump operation. However, by eliminating the heat pump operation from the modeling, there was no requirement for a power meter, which would otherwise add significant sensing equipment costs to the system.

[0039] A previously known forecasting methodology was applied for the prediction of the upcoming water draws over the next day in 5-minute time steps, yielding 288 forecasted values. The resulting forecast is a hybrid machine learning forecast model leveraging a combination of a Random Forest model, the Prophet model, and the previous day's water usage profile. The Random Forest model is an ensemble model of multiple decision trees, that can be used in tabular forecasting tasks. The Prophet model treats time-series forecasting problems as curve-fitting problems, with a consideration of seasonality and trends. The final forecast at any given time t given past measurements χt is dependent on the forecasting horizon and the respectively chosen models, a short-term model, a medium-term model, and a long-term model and the horizon thresholds. In the model, the short-term model was a Random Forest model for the first three time steps (equal to 15 minutes). The medium-term model is the Prophet model from the fourth time step to the 100th time step (15 minutes to 500 minutes). For the last segment of the prediction horizon, the previous day's water usage profile over same time span as the 100th time-step to the 288th was the most accurate and therefore is overplayed.

[0040] Using this modeling, investigations showed that The Prophet forecast predicts probable shower events in the morning with a rather smooth curve, which can be effectively used to schedule pre-heating. The Random Forest model then becomes active during a water draw event and more accurately predicts peak values. The long-term prediction horizon with the previous day's water draw profile provides the MPC algorithm with a sense of what will happen far out in time. This makes it possible, for example, to incorporate information about dynamic energy rate pricing structures, where it may be useful to have a 24-hour prediction horizon to determine the best times to preheat.

[0041] In design of the controller, a convex optimization problem was formulated for the MPC algorithm using known methodologies. The goal was to minimize the cost due to electricity consumption while ensuring the outlet temperature remains above a comfortable threshold of 38°C. (100° F.). This was achieved by formulating a multi-objective cost function that balances energy cost minimization and thermal comfort, while accounting for water draw forecasting errors.

[0042] A first objective function, Jcomf, ensures that the water heater maintains a comfortable outlet temperature. This function penalizes temperature deviations below the minimum temperature, ensuring that hot water remains available when needed. To prevent unnecessary energy use, the penalty may be adaptive. During periods of active water usage or recovery from a recent draw, the minimum temperature threshold is temporarily reduced from 43.3° C.—the water heater's set-point minimum—to 38° C.—the lowest acceptable comfort temperature—while the penalty weight is increased. A binary function determines when to adjust the threshold and to raise the weight of the objective, ensuring that temperature constraints are strictly enforced during periods of low or no water flow. To maintain comfort as a priority, the weight of Jcomf is set significantly higher than that of electricity costs. A second objective function, Jenergy, minimizes the power consumed for the water heater. The cost function accounts for the total electricity cost over the prediction horizon and can be expanded to incorporate both temporal variations in pricing. The third objective function, Jpreheat, incentives preheating the water. This cost function is added due to the lack in peak of the forecasted water draws and the possible error of the times at which water draws are forecasted. A state-space equation models the temperature evolution of the water heater. A set-point tracking constraint introduces a lag in the response of the high-temperature state TH relative to the set-point temperature TSP. This constraint prevents abrupt changes in temperature, ensuring a gradual adaptation toward the desired set-point. A weighting parameter a=0.8 determines the rate of adaptation, modeling the response delay of the heat-pump. This delay accounts for factors such as communication latency and the dead-band behavior in the manufacturer's built-in controller. A power consumption expression defines the relationship between the heating power P and the heating input q, scaled by the coefficient of performance (COP). A constraint limits the heating input within the system's capacity relative to the maximum allowable power. The COP is assumed constant to maintain linearity, and any deviations in real-world performance are compensated through the feedback mechanism in the MPC framework. No explicit constraints are imposed on the water heater temperature to avoid infeasibilities when the system cannot meet the minimum set point due to heating capacity limitations. Instead, the set points are post-processed to ensure a minimum of 43.3° C., allowing for a cost-efficient and adaptive control strategy that maintains user comfort while optimizing energy usage.

[0043] Using this testing setup, a five-day field test was conducted during winter conditions in February to evaluate the performance of the MPC algorithm on the HPOWH. This field test is used to evaluate the thermal comfort performance of the MPC algorithm and its integration with the water heater. The temperature evolution of the water heater and the corresponding water usage profile over the testing period were tracked. The testing showed that the MPC algorithm adjusted the set-point temperature ahead of expected water draws, ensuring sufficient stored heat during peak demand periods, particularly in the mornings and evenings. The lower tank temperature exhibited sharp declines during high-usage events due to cold inlet water temperatures, while the upper tank temperature remained relatively stable, indicating that the system maintained temperature stratification within the water tank 14. This stratification underscores the benefit of using a two-node thermal model for the HPOWH to accurately predict whether the outlet water temperatures will meet the minimum comfort threshold. In one incidence, the investigation showed that the MPC algorithm did not preheat sufficiently for a low-probability event, which was caused by multiple showers being taken in immediate succession at an unusual time of day. As a result, given the limited heat transfer rate of the heat pump, tank temperatures dropped below the approximate comfort threshold. However, even in these limited, unusual usage scenarios, the water was still heated to a degree in which no discomfort was noticed by the occupants. If there was no pre-heating from the MPC, the water temperature would have likely dropped to a temperature where occupants would be uncomfortable.

[0044] This dynamic adjustment of set-point temperatures in anticipation of large water draw events improves the performance of the water heater compared to conventional constant set-point control. Typically, HPOWHs are maintained at or above 60° C. to ensure occupant comfort; however, this constant-set-point approach increases energy consumption as the heat pump must continuously sustain a high set-point throughout the year. Additionally, maintaining elevated water temperatures raises the condensing temperature, which in turn reduces the heat pump's efficiency. By dynamically adjusting heating based on expected inlet water temperatures and expected water usage, the MPC 32 can reduce unnecessary heating and further enhance the heating efficiency of the heat-pump.

[0045] This study demonstrated the feasibility of a low-cost MPC approach for HPOWHs using minimal sensing in accordance with systems and methods disclosed herein. By estimating water draws from temperature measurements and leveraging historical usage data, the model predictive controller 32 incorporating the virtual water usage sensor 10 optimized heating schedules to balance comfort, efficiency, and cost savings. Furthermore, although this example study used an inlet water thermocouple, widespread implementation may not require the addition of one inlet temperature sensor 18 per tank water heater 12. Rather, because inlet temperatures tend to be similar across homes in a given region, a utility-provided city-wide measurement could serve as a cost-effective alternative.

[0046] As previously noted above, though the foregoing detailed description describes certain aspects of one or more particular embodiments of the invention, alternatives could be adopted by one skilled in the art. For example, the virtual water usage sensor and tank water heating system, and their components, could differ in appearance and construction from the embodiments described herein and shown in the drawings, functions of certain components of the virtual water usage sensor and tank water heating system could be performed by components of different construction but capable of a similar (though not necessarily equivalent) function, and various materials could be used in the fabrication of the virtual water usage sensor and tank water heating system and / or their components. As such, and again as was previously noted, it should be understood that the invention is not necessarily limited to any particular embodiment described herein or illustrated in the drawings.

Claims

1. A virtual water usage sensor for estimating water usage in a tank water heater, the virtual sensor comprising:a first temperature sensor for measuring inlet water temperature of water flowing into a water tank of the tank water heater;at least one second temperature sensor for measuring tank water temperature of water being held within the water tank; anda water usage estimation module comprising a digital computer system configured with program instructions that, when executed, cause the digital computer system to derive an estimated water usage from the tank water heater from the inlet water temperature measurements and the tank water temperature measurements.

2. The virtual water usage sensor of claim 1, wherein the tank water heater comprises a heat pump water heater.

3. The virtual water usage sensor of claim 1, wherein a heat source for warming the water being held within the water tank comprises at least one of a heat pump, an electric resistance heating element, an open flame, and an induction heating element.

4. The virtual water usage sensor of claim 1, further comprising a plurality of the second temperature sensors for measuring tank water temperatures of water being held within different vertical regions of the water tank, including at least an upper temperature sensor and a lower temperature sensor, and the water usage estimation module derives the estimated water usage from the inlet water temperature measurements, the tank water measurements from each of the upper temperature sensor and the lower temperature sensor, and a signal that indicates whether the tank water heater is on or off.

5. The virtual water usage sensor of claim 1, wherein the first temperature sensor is disposed on a water supply line remote from the tank water heater that supplies water to the tank water heater.

6. The virtual water usage sensor of claim 5, wherein the first temperature sensor is disposed on a community water supply line from which a residential water supply line that supplies water to the water tank receives water.

7. The virtual water usage sensor of claim 6, wherein the first temperature sensor is located in a water treatment facility.

8. The virtual water usage sensor of claim 1, wherein the water usage estimation module does not use mass flow measurements of water flow into or out of the water tank to derive the estimated water usage.

9. A method of estimating hot water usage in a tank water heater, the method comprising:measuring inlet water temperature of inlet water flowing into a water tank of the tank water heater;measuring tank water temperature of water held within the water tank; andderiving an estimated water usage from the tank water heater based on measurements of the inlet water temperature and measurements of the tank water temperature.

10. The method of claim 9, wherein the deriving step comprises estimating heat loss or gain in the water tank attributed by the inlet water flowing into the water tank, and dividing by the specific heat change per unit mass of the inlet water to estimate mass flow rate of the inlet water; thereby also estimating mass flow rate of the outlet water of the water tank.

11. The method of claim 9, wherein the step of measuring tank water temperature comprises measuring tank water temperatures of water being held within different vertical regions of the water tank, including at least an upper region and a lower region, and wherein the step of deriving includes deriving the estimated water usage from the inlet water temperature measurements and the tank water measurements from each of the upper and lower regions.

12. The method of claim 9, wherein the step of deriving is completed without using mass flow measurements of water flow into or out of the water tank.

13. The method of claim 9, the inlet water temperature is measured at location on a water supply line remote from the tank water heater that supplies water to the tank water heater.

14. The method of claim 9, further comprising deriving diagnostic information regarding the tank water heater based on the estimated water usage.

15. The method of claim 14, wherein the diagnostic information comprises identifying a potential fault.

16. The method of claim 15, wherein the potential fault comprises a water leak from the tank water heater.

17. A tank water heating system comprising:a water tank and a heat source to heat water held within the water tank; andthe virtual water usage sensor of claim 1.

18. The tank water heating system of claim 17, further comprising:a model predictive controller comprising a digital computer system operatively coupled with the virtual water usage sensor to receive the estimated water usage and operatively coupled with the heat source to control a temperature set-point of the water tank and program instructions that, when executed, cause the digital computer system to:estimate hot water draws from the water tank based on the inlet water temperature data and the tank water temperature data;forecast water demand; anddynamically adjust heating schedules of the temperature set-point based on the forecast water demand.

19. The tank water heating system of claim 18, wherein the model predictive controller forecasts the water demand using a hybrid machine learning model.

20. The tank water heating system of claim 19, wherein the hybrid machine learning model includes a combination of a short-term model, a mid-term model, and a long-term model based on a water usage profile of the tank water heating system from the previous day.

21. The tank water heating system of claim 20, wherein the short-term model comprises a Forest model and the mid-term model comprises the Prophet model.

22. The tank water heating system of claim 17, wherein the heat source comprises at least one of a heat pump, an electric resistance heating element, an open flame, and an induction heating element.

23. The tank water heating system of claim 17, wherein the digital computer system of the model predictive controller and the digital computer system of the water usage estimation module comprise a common digital processing system.

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