Methods and systems for determining a temperature distribution of water stored in a water heater

Abstract

Methods and systems for determining a temperature distribution of water stored in a water heater are disclosed. The method comprises heating water in a tank of the water heater for at least a heating period, measuring a temperature of the water to obtain measurements of a first temperature of the water at the start of the heating period and a second temperature of the water at the end of the heating period, determining an amount of energy consumed for heating the water during the heating period, and determining a quantity of water at the second temperature based on the first temperature, the second temperature, and the amount of energy consumed. Methods and systems for operating a water heater are also disclosed.

Description

[0001] METHODS AND SYSTEMS FOR DETERMINING

[0002] A TEMPERATURE DISTRIBUTION OF WATER STORED IN A WATER HEATER

[0003] TECHNICAL FIELD

[0004] [1] The present invention relates to methods and systems for determining a temperature distribution of water stored in a water heater. The present invention further relates to methods and systems for operating a water heater.

[0005] BACKGROUND

[0006] [2] Water heaters that store hot water function as stores of thermal energy. They can be used for energy-storage purposes, such as for storing excess energy generated by renewable energy sources. The energy to be stored is converted to thermal energy by heating water in a tank of the water heater for later use. Since the amount of thermal energy that a water heater can store is finite, it is useful to know how much thermal energy a water heater is storing at a given time.

[0007] [3] The amount of thermal energy stored is related to the temperature of the water in the water heater. However, due to the tendency of water to stratify, with warm water rising above cold water, an accurate assessment of the thermal energy requires knowledge of the stored water’s temperature distribution. Determination of the temperature distribution in water heaters has conventionally been facilitated by using multiple temperature sensors distributed along the vertical dimension of the water heater’s tank.

[0008] [4] It is desired to address or ameliorate one or more disadvantages or limitations associated with the prior art, or to at least provide a useful alternative.

[0009] [5] Any reference in this specification to prior art or matter which is said to be known is not to be taken as an acknowledgement or admission that such prior art or matter forms part of the common general knowledge in the field of invention to which this specification relates.

[0010] SUMMARY

[0011] [6] According to an example aspect, there is provided a method for determining a temperature distribution of water stored in a water heater. The method comprises: heating water in a tank of the water heater for at least a heating period; measuring a temperature of the water to obtain measurements of a first temperature of the water at the start of the heating period and a second temperature of the water at the end of the heating period; determining an amount of energy consumed for heating the water during the heating period; and determining, based on the first temperature, the second temperature, and the amount of energy consumed, a quantity of water at the second temperature.

[0012] [7] In some examples, heating the water comprises activating a heating device of the water heater at the start of the heating period and deactivating the heating device at the end of the heating period. In some examples, the heating device comprises one of a heating element, a heat pump, a heat exchanger, and a heat transfer fluid. In some examples, the duration of the heating period is predetermined. In some examples, the duration of the heating period is the time required to measure a predetermined change in the temperature of the water.

[0013] [8] In some examples, the water in the tank is stratified into two or more layers, and the quantity of water at the second temperature corresponds to a size of a bottom layer of the two or more layers. In some examples, the method further comprises: assigning an estimated value to a size of a middle layer of the two or more layers; and determining a size of a top layer of the two or more layers based on the sizes of the bottom and middle layers. In some examples, the determination of the size of the top layer is further based on an estimated heat loss of the water since the determination of the size of the bottom layer. In some examples, the method further comprises determining a quantity of usable hot water in the tank based on the size and temperature of one or more of the layers, the usable hot water being water with a temperature greater than a minimum delivery temperature, the minimum delivery temperature being less than a maximum temperature of the water heater.

[0014] [9] In some examples, the method further comprises determining a thermal energy capacity of the water heater based on the size and temperature of one or more of the layers. In some examples, the method further comprises: verifying a present thermal energy capacity based on a past thermal energy capacity; and, if the present thermal energy capacity is invalid, repeating the foregoing method with an extended heating period to derive a revised thermal energy capacity. In some examples, the verification of the present thermal energy capacity is further based on an estimated heat loss of the water during a time elapsed between the determination of the past thermal energy capacity and the determination of the present thermal energy capacity.

[0015]

[0010] In some examples, before heating the water, the method further comprises: heating the water until all the water in the tank reaches a maximum temperature; and ceasing to heat the water temporarily.

[0011] In some examples, the water is heated and the temperature is measured at about the same level of the tank.

[0016]

[0012] In some examples, the water is heated and the temperature is measured at a first level of the tank, the amount of energy consumed is a first amount of energy consumed, the quantity of water at the second temperature is a first quantity of water, and the method further comprises: heating water in the tank at a second level of the tank for at least a second heating period; measuring a temperature of the water at the second level of the tank to obtain measurements of a third temperature of the water at the start of the second heating period and a fourth temperature of the water at the end of the second heating period; determining a second amount of energy consumed for heating the water at the second level of the tank during the second heating period; and determining, based on the third temperature, the fourth temperature, and the second amount of energy consumed, a second quantity of water at the fourth temperature.

[0017]

[0013] According to another example aspect, there is provided a system for determining a temperature distribution of water stored in a water heater. The system comprises at least one processing system configured to: control a heating device of the water heater to heat water in a tank of the water heater for at least a heating period; receive temperature data representing a first temperature of the water at the start of the heating period and a second temperature of the water at the end of the heating period; receive energy consumption data representing an amount of energy consumed by the heating device for the heating the water during the heating period; and determine, based on the temperature data and the energy consumption data, a quantity of water at the second temperature.

[0018]

[0014] In some examples, the at least one processing system is further configured to: determine a thermal energy capacity of the water heater based on the quantity of water at the second temperature and on the second temperature; and, based on the thermal energy capacity, and in response to detecting a predetermined event, control the operation of the water heater. In some examples, the predetermined event is one of a receipt of a control signal indicative of a state of an electrical grid connected to the water heater, and a generation of excess energy by a renewable energy source connected to the water heater.

[0019]

[0015] According to another example aspect, there is provided a method for operating a water heater, the method comprising: determining a quantity of water stored in the water heater and a temperature of the quantity of water in accordance with the method of claim 1; determining a thermal energy capacity of the water heater based on the quantity of water and the temperature of the quantity of water; and based on the thermal energy capacity, and in response to detecting a predetermined event, controlling the operation of the water heater. In some examples, the predetermined event is one of a receipt of a control signal indicative of a state of an electrical grid connected to the water heater, and a generation of excess energy by a renewable energy source connected to the water heater.

[0020] BRIEF DESCRIPTION OF THE DRAWINGS

[0021]

[0016] Examples of the present invention are described next with reference to the accompanying drawings, in which:

[0022]

[0017] Figure 1 shows an example water heating system including a system for determining a temperature distribution of water stored in a water heater;

[0023]

[0018] Figure 2 shows a flowchart of an example method for determining a temperature distribution of water stored in a water heater; and

[0024]

[0019] Figure 3 shows a flowchart of an example method for operating a water heater.

[0025] DETAILED DESCRIPTION

[0026]

[0020] Examples of the invention provide methods and systems for determining, or estimating, a temperature distribution or temperature profile of water stored in a water heater. On account of stratification, at any given time the water heater generally stores one or more quantities of water with different temperatures. Temperature distribution here refers to one or more of the quantities of water stored in the water heater and their respective temperatures. In some examples, a quantity of water determined by the invention is a stratification layer in a tank of the water heater having substantially the same temperature, i.e. an isothermal quantity of water. Therefore, in some examples, methods and systems of the invention determine a quantity of water stored in a water heater at a particular temperature.

[0027]

[0021] The water heater may be any water heater configured to store and heat water in a tank, such as a storage water heater, a tank-type water heater, or a hot water system. The tank may be any kind of container, of any shape and size, configured to hold water.

[0028]

[0022] The temperature distribution may be used to determine, or estimate, the thermal energy capacity, or state of charge, of the water heater, here defined as a measure of the water heater’s ability to either store additional thermal energy or deliver thermal energy. In the description that follows, “thermal energy capacity” has the sense of energy-delivery potential, so that it is maximum when all the water in the tank of the water heater has a temperature equal to or greater than a first threshold temperature, and minimum when all the water in the tank has a temperature equal to or less than a second threshold temperature, lower than the first threshold temperature. However, it is to be understood that the alternative sense of energy- storage potential can be used to the same effect, since one is the inverse of the other. The thermal energy capacity could be represented by an absolute quantity (e.g. with units of joules) or by a relative quantity (e.g. from 0 to 100%).

[0029]

[0023] In some examples, the first threshold temperature is a maximum or set point temperature of the water heater. In some examples, the second threshold temperature is an inlet water temperature or a temperature of water from a water source feeding the water heater, such as a municipal water source. In other examples, the first and second threshold temperatures have any other values, including values set by a user.

[0030]

[0024] The invention may allow for a determination of the thermal energy capacity of a water heater using a single, or no more than one, temperature sensor. Therefore, existing water heaters with a single temperature sensor for controlling a heating device may be retrofitted with the systems described here, or may be configured to operate according to the methods described herein. Moreover, by not requiring multiple temperature sensors, the invention may reduce the complexity or manufacturing costs of water heaters able to determine their own thermal energy capacities.

[0031]

[0025] An example water heating system 100 is shown in Figure 1. Water heating system 100 comprises a water heater 110 and a processing system 120.

[0032]

[0026] Water heater 110 comprises a tank 130 configured to hold water, and a heating device or heat source 140 comprising a heating element configured to heat the water in tank 130. In other examples, the heating device may comprise any means of supplying thermal energy to water, such as a heat pump, a heat exchanger, or a heat transfer fluid. Water heater 110 further comprises a temperature sensor or thermostat 150 configured to measure the temperature of the water in tank 130. Heating device 140 and temperature sensor 150 are secured to tank 130 at or near the bottom of tank 130, such as in a bottom half, a bottom third, or a bottom quarter of tank 130, at substantially the same level, or vertical position. In other examples, they may be located at different levels of tank 130.

[0027] Heating device 140 and temperature sensor 150 are communicatively coupled to processing system 120, which is configured to receive temperature data from temperature sensor 150, and to control the operation of heating device 140 based on the temperature data and, in some examples, based on one or more other control parameters or signals, such as user-set parameters (e.g. a temperature set-point), data representing local renewable energy consumption, and control signals from an electrical grid operator or intermediary (e.g. a utility aggregator). Heating device 140 is also operatively connected to one or more energy sources 160, such as renewable energy sources or an electrical grid.

[0033]

[0028] Water heater 110 further comprises a water inlet comprising an inlet or dip tube 132, through which unheated water, or water to be heated, is supplied to tank 130, normally at or near the bottom of tank 130, and a water outlet comprising an outlet tube 134 through which heated water is drawn from tank 130, normally at or near the top of tank 130. In other examples, water heater 110 comprises any other kind of water inlet or outlet arranged in any way. For example, the water inlet may comprise a tube connected to a side of tank 130 instead of a dip tube entering tank 130 from the top.

[0034]

[0029] If the water in tank 130 does not all have the same temperature, it stratifies naturally, forming distinct layers or regions, including a first or bottom layer 170, a second or middle layer 172, also known as a thermocline or a transition layer, and a third or top layer 174. (Layer 172 may be subdivided into two or more transition layers or sub-layers, but it is treated as a single layer here for the sake of simplicity.) Layer 170 has the lowest or minimum temperature in tank 130, layer 174 has the highest or maximum temperature in tank 130, and layer 172 has a temperature that varies between the temperatures of layers 170 and 174. Unlike the temperature of layer 172, which varies spatially, approximately uniformly, between layers 170 and 174, the temperatures of layers 170 and 174 are approximately spatially uniform, so that there is negligible temperature variation within layer 170 or 174.

[0035]

[0030] While the total quantity of water in tank 130 during normal operation is approximately constant, the quantities of water in, or the sizes of, layers 170, 172, and 174, and their temperatures, change over time through, for example, heating by heating device 140, outflow of heated water, inflow of unheated water, and natural heat losses. For example, before heating begins, when tank 130 is full of unheated water, layer 170 spans the whole tank, whereas layers 170 and 172 are non-existent or negligible. During heating, provided water is heated at a higher rate than it is drawn from tank 130, layer 170 contracts as layers 172 and 174 form and expand. Eventually, all water in tank 130 reaches a maximum temperature, so that layer 174 spans the whole tank and layers 170 and 172 are non-existent or negligible. The temperature distribution and the thermal energy capacity of water heater 110 at any given time depend on the size and temperature of one or more of layers 170, 172, and 174.

[0036]

[0031] An example method 200 for determining a temperature distribution of water stored in water heater 110 is shown in the flowchart of Figure 2. Method 200 may be a computer- implemented method performed by a processing system, such as processing system 120.

[0037]

[0032] Step 210 of method 200 comprises heating the water in tank 130 for at least a heating period, or between a first time and a second time. The water may be heated by activating or turning on heating device 140 for at least the heating period. In some examples, heating device 140 is deactivated or turned off at the end of the heating period, so that heating device 140 may perform a procedure known as “burst heating”.

[0038]

[0033] In some examples, a duration of the heating period is predetermined or fixed, such as a duration greater than one minute, a duration less than 10 minutes, a duration less than 5 minutes, or any other duration. In other examples, the duration of the heating period is undetermined or variable, and the heating period may last as long as necessary to detect a predetermined or fixed change in the temperature of the water, such as 5°C, 10°C, or any other temperature change. The duration of the heating period may be chosen to allow heating device 140 to produce an observable change in the temperature of water in tank 130 — the duration of the heating period may therefore depend on factors such as the capacity of tank 130, the temperature of the water, the power rating of heating device 140, and the sensitivity of temperature sensor 150. In some examples, the duration of the heating period is set or changed automatically depending on these and / or other factors.

[0039]

[0034] Step 220 of method 200 comprises measuring a temperature of the water to obtain measurements of a first, or initial, temperature of the water at the start of the heating period and a second, or final, temperature of the water at the end of the heating period. The measurements may be obtained using temperature sensor 150.

[0040]

[0035] Step 230 of method 200 comprises determining an amount of energy consumed for heating the water during the heating period.

[0041]

[0036] In some examples, the amount of energy consumed is determined by measuring or monitoring an energy usage of heating device 140 during the heating period using an electricity meter or any other energy or power measurement device. In other examples, the amount of energy consumed is determined by calculating or inferring an energy usage of heating device 140 during the heating period based on operational characteristics of heating device 140. For example, if heating device 140 operates at a known fixed power or rate of energy consumption, the amount of energy consumed may be determined based on the power or rate of energy consumption and the duration of the heating period.

[0042]

[0037] The energy consumed may be electrical energy or any other kind of energy, depending on the principle of heat generation employed by heating device 140.

[0043]

[0038] Step 240 of method 200 comprises determining a quantity of water in tank 130 at the second temperature (or, equivalently, a quantity of water that exhibited the first temperature, or a quantity of water that was heated from the first temperature to the second temperature). The quantity of water is determined based on the first temperature, the second temperature, and the amount of energy consumed. In some examples, the quantity of water is determined based on a change in the temperature of the water during the heating period (i.e. the difference between the second and first temperatures).

[0044]

[0039] For example, when the quantity of water is a volume, V , it can be determined using Equation 1 : where E is the energy consumed to heat the water, p is the density of water, c is the specific heat capacity of water, and AT is the temperature change of the water. The density and the specific heat capacity of water may be assumed to be constants. In other examples, the determined quantity of water is a mass or any other measure, absolute or relative, of an amount of water.

[0045]

[0040] Since heating device 140 and temperature sensor 150 are positioned at or near the bottom of tank 130, the temperature measured in step 220 generally corresponds to the temperature of layer 170, and the energy usage determined in step 230 generally corresponds to the energy consumed for heating layer 170, so that the quantity of water determined in step 240 is approximately equal to the quantity of water in layer 170. In other examples, any other isothermal quantity of water in tank 130 may be determined by performing the steps of method 200 at other levels of tank 130. For example, if heating device 140 and temperature sensor 150 were positioned at or near the top of tank 130, method 200 would determine the size of layer 174. Alternatively, if heating device 140 and temperature sensor 150 were positioned at or near the middle of tank 130, method 200 would determine a size of a sublayer of layer 172 with substantially the same temperature.

[0046]

[0041] In other examples, water heater 110 comprises multiple heating devices and / or multiple temperature sensors positioned at multiple levels of tank 130, each heating device being positioned near to or at the same level as one of the temperature sensors. Method 200 may then comprise heating water and measuring temperature at multiple levels of tank 130 to determine multiple water quantities, each water quantity representing water with substantially the same temperature at or near the level of one of the heating devices and / or of the temperature sensors.

[0047]

[0042] The temperature distribution of the water stored in tank 130 may further be determined by determining one or more other quantities of water in tank 130 at one or more other temperatures.

[0048]

[0043] In some examples, method 200 further comprises estimating, inferring, or guessing a size of layer 172. Computer simulations carried out by the inventors using TRNSYS have shown that an estimate of about 30% of the volume of tank 130 for the volume of layer 172 provides sufficient accuracy for determining the thermal energy capacity of water heater 110 under typical working conditions, when only part of the water in tank 130 is at the maximum temperature, assuming a constant quantity of water is heated. In other examples, any other estimate may be used for the size of layer 172. Once the sizes of layers 170 and 172 are determined, since the capacity of tank 130 is known, the size of layer 174 may also be determined. The temperature of layer 174, if it is not measured, may be assumed to be the maximum or set point temperature of water heater 110.

[0049]

[0044] In some examples, method 200 further comprises determining a quantity of usable hot water in tank 130. Usable hot water is water with a temperature greater than a minimum delivery (e.g. 45°C), which is less than the maximum temperature of the water heater (e.g. 60°C). The quantity of usable hot water may be determined based on the size and temperature of one or more of the layers, such as layer 174 and, in some examples, at least part of layer 172 and / or layer 170.

[0050]

[0045] In some examples, method 200 further comprises determining the thermal energy capacity of water heater 110 based on the size and temperature of one or more of layers 170, 172, and 174. Different expressions for the thermal energy capacity may be formed from these parameters. In some examples, the thermal energy capacity (in the sense of energy- delivery potential) increases with the size and temperature of layer 174 and, in some examples, with the size and temperature of layer 172.

[0051]

[0046] One example expression for the thermal energy capacity, Ethermab of water heater 110 at a specific time is given by Equation 2:

[0052] T - T ■

[0053] ^ ctherma ,l - 1 rp^. _ _ 2 rp22Ea? max min where Tavgis the average temperature of the water in tank 130 at that time, Tminis the minimum delivery temperature, and Tmaxis the maximum temperature for water heater 110. Tmaxand Tminare known constants for water heater 110, while Tavgmay be estimated from the sizes of layers 170, 172, and 174, and from the temperatures of these layers — the temperature of layer 170 may be measured using temperature sensor 150, the temperature of layer 174 may be assumed to equal the maximum temperature Tmaxfor water heater 110, and the (average) temperature of layer 172 may be estimated to be halfway between, or the average of, the temperatures of layers 170 and 174.

[0054]

[0047] Another example expression for the thermal energy capacity of water heater 110 at a specific time is given by Equation 3: p > ^170 ■ ^ 170 + ^174 ■ ^ 174—^min ’ ^ 130 thermal 717 _ r , tiq. J

[0055] U max ' mini ' ^130 where T170and k170are the temperature and size, respectively, of layer 170, T174and k174are the temperature and size, respectively, of layer 174, and 713o is the total volume of water stored in tank 130.

[0056]

[0048] A current value or indication of the thermal energy capacity may be checked or verified using a past or previous value or indication of the thermal energy capacity of water heater 110. For example, the thermal energy capacity (in the sense of energy-delivery potential) generally decreases over time unless the water in tank 130 is heated. Therefore, if the water has not been heated in the time between the determination of the previous and current indications (other than during the heating period), and if the current indication of the thermal energy capacity exceeds the previous indication of the thermal energy capacity by a threshold amount (to account for changes in the thermal energy capacity caused by heating during the heating period), then it can be inferred that the current indication is invalid. In some examples, an estimate of heat losses in the water during a time elapsed between the determination of the past thermal energy capacity and the determination of the present thermal energy capacity may also be considered in the verification of the present thermal energy capacity. If the current indication is found to be invalid, method 200 may be repeated to obtain a revised or updated value or indication of the thermal energy capacity. When step 210 is repeated, the duration of the heating period may be extended to induce a greater temperature change, less affected by measurement errors or random perturbations. Once the current indication of the thermal energy capacity is verified, the previous indication is replaced by the current indication for the verification of future indications of the thermal energy capacity.

[0057]

[0049] Since the thermal energy capacity of water heater 110 depends on time-varying factors and may be influenced by thermal draw-off events, a determination of the thermal energy capacity is reliable only for a limited time, after which the thermal energy capacity may need to be redetermined.

[0058]

[0050] Changes in the size of layer 172 may affect the accuracy of the thermal energy capacity if layer 172 is assumed to have a constant size in the determination of the thermal energy capacity. In fact, after heating stops, layer 172 will generally initially increase as warmer water from layer 174 cools, and eventually, as cooling continues, it will shrink. A baseline thermal energy capacity to compare against subsequent values may be obtained periodically by heating all the water in tank 130 to a known temperature, such as the maximum temperature of water heater 110, since in that state the thermal energy capacity of water heater 110 is known. For example, when the whole of tank 130 is at the maximum temperature, the thermal energy capacity (in the sense of energy-delivery potential) is maximum or 100%. Therefore, in some examples, before step 210, method 200 comprises heating the water until all the water in tank 130 reaches the maximum temperature. After all the water has reached the maximum temperature, heating may cease temporarily before step 210 is performed. In this way, the thermal energy capacity is effectively reset, and the measurement process is recalibrated. This reset process is convenient because it may already form part of the regular (e.g. weekly) operational cycle of certain water heaters, which may use it for the purpose of sanitation against Legionella bacteria.

[0059]

[0051] The determined thermal energy capacity, or other quantities derived from the size or temperatures of layers 170, 172, and 174, may be used to control the operation of water heater 110.

[0052] An example method 300 for operating a water heater, such as water heater 110, is shown in the flowchart in Figure 3. In some examples, method 300 is a computer- implemented method performed by processing system 120.

[0060]

[0053] Step 310 of method 300 comprises determining a quantity of water stored in the water heater and the temperature of the quantity of water. The water quantity and its temperature may be determined using method 200.

[0061]

[0054] Step 320 of method 300 comprises determining a thermal energy capacity of the water heater based on the water quantity and its temperature. In some examples, method 300 further comprises sending a signal indicative of the thermal energy capacity, for example, to a remote resource operatively coupled to the water heater, such as an electrical grid.

[0062]

[0055] Based on the thermal energy capacity, and in response to detecting a predetermined event, step 330 of method 300 comprises controlling the operation of the water heater. Examples of controlling the water heater include controlling the water heater to start or continue heating water, controlling the water heater to avoid or stop heating water, controlling the water heater to heat water until the thermal energy capacity reaches a threshold value, and controlling the water heater to not heat water for a specified time. Other examples of controlling the water heater, or a system operatively coupled to the water heater, are described in international application no. PCT / AU2022 / 050793, filed on 28 July 2022, incorporated by reference herein in its entirety.

[0063]

[0056] An example predetermined event is a receipt of a control signal, such as a demand response signal or a signal from a remote resource, indicative of a state of an electrical grid connected to water heater 110. Another example predetermined event is a generation of excess energy by a renewable energy source connected to water heater 110.

[0064]

[0057] Method 300 may allow water heater 110 to heat water at optimal or advantageous times based on the thermal energy state of water heater 110 and the availability of energy from energy source 160. For example, if the assessment of the thermal energy capacity indicates that water heater 110 at a given time has energy-storage potential above a certain threshold (e.g. because the quantity of water at the maximum temperature in tank 130 happens to be relatively low), then water heater 110 may be controlled to heat water upon detecting that a load on the electrical grid is low, or upon detecting that the renewable energy source is producing surplus energy.

[0058] The term “processing system” may refer to any electronic processing device or system, or computing device or system, or combination thereof (e.g. computers, web servers, smart phones, laptops, microcontrollers, etc.), and may include a distributed computing system, such as a cloud computing system. In general, processing or computing systems may include one or more processors (e.g. CPUs, GPUs), memory components, and input / output interfaces, connected by at least one bus. They may further include input / output devices (e.g. a keyboard, a display, a touchscreen, etc.). Processing or computing systems may be configured to execute instructions and process data, or perform operations on data, stored in memory. Processing or computing systems may be programmable through software.

[0065]

[0059] Throughout this specification and the claims which follow, unless the context requires otherwise, the words “about” and “substantially” will be understood to denote deviations from an exact value by ±10%, preferably by ±5%, and / or deviations that are insignificant for the function.

[0066]

[0060] Throughout this specification, unless the context requires otherwise, the word “comprise” and any variations thereof, such as “comprises” or “comprising”, are to be interpreted in a non-exhaustive sense.

Claims

CLAIMS1. A method for determining a temperature distribution of water stored in a water heater, the method comprising: heating water in a tank of the water heater for at least a heating period; measuring a temperature of the water to obtain measurements of a first temperature of the water at the start of the heating period and a second temperature of the water at the end of the heating period; determining an amount of energy consumed for heating the water during the heating period; and determining, based on the first temperature, the second temperature, and the amount of energy consumed, a quantity of water at the second temperature.

2. The method of claim 1, wherein heating the water comprises activating a heating device of the water heater at the start of the heating period and deactivating the heating device at the end of the heating period.

3. The method of claim 2, wherein the heating device comprises one of a heating element, a heat pump, a heat exchanger, and a heat transfer fluid.

4. The method of any one of claims 1 to 3, wherein the duration of the heating period is predetermined.

5. The method of any one of claims 1 to 3, wherein the duration of the heating period is the time required to measure a predetermined change in the temperature of the water.

6. The method of any one of claims 1 to 5, wherein the water in the tank is stratified into two or more layers, and wherein the quantity of water at the second temperature corresponds to a size of a bottom layer of the two or more layers.

7. The method of claim 6, further comprising: assigning an estimated value to a size of a middle layer of the two or more layers; and determining a size of a top layer of the two or more layers based on the sizes of the bottom and middle layers.

8. The method of claim 7, wherein the determination of the size of the top layer is further based on an estimated heat loss of the water since the determination of the size of the bottom layer.

9. The method of any one of claims 6 to 8, further comprising determining a quantity of usable hot water in the tank based on the size and temperature of one or more of the layers, the usable hot water being water with a temperature greater than a minimum delivery temperature, the minimum delivery temperature being less than a maximum temperature of the water heater.

10. The method of any one of claims 6 to 9, further comprising determining a thermal energy capacity of the water heater based on the size and temperature of one or more of the layers.

11. The method of claim 10, further comprising: verifying a present thermal energy capacity based on a past thermal energy capacity; and, if the present thermal energy capacity is invalid, repeating the method of claim 10 with an extended heating period to derive a revised thermal energy capacity.

12. The method of claim 11, wherein the verification of the present thermal energy capacity is further based on an estimated heat loss of the water during a time elapsed between the determination of the past thermal energy capacity and the determination of the present thermal energy capacity.

13. The method of any one of claims 1 to 12, wherein, before heating the water, the method further comprises: heating the water until all the water in the tank reaches a maximum temperature; and ceasing to heat the water temporarily.

14. The method of any one of claims 1 to 13, wherein the water is heated and the temperature is measured at about the same level of the tank.

15. The method of any one of claims 1 to 13, wherein the water is heated and the temperature is measured at a first level of the tank, the amount of energy consumed is a first amount of energy consumed, the quantity of water at the second temperature is a first quantity of water, and wherein the method further comprises: heating water in the tank at a second level of the tank for at least a second heating period; measuring a temperature of the water at the second level of the tank to obtain measurements of a third temperature of the water at the start of the second heating period and a fourth temperature of the water at the end of the second heating period; determining a second amount of energy consumed for heating the water at the second level of the tank during the second heating period; and determining, based on the third temperature, the fourth temperature, and the second amount of energy consumed, a second quantity of water at the fourth temperature.

16. A system for determining a temperature distribution of water stored in a water heater, the system comprising at least one processing system configured to: control a heating device of the water heater to heat water in a tank of the water heater for at least a heating period; receive temperature data representing a first temperature of the water at the start of the heating period and a second temperature of the water at the end of the heating period; receive energy consumption data representing an amount of energy consumed by the heating device for the heating the water during the heating period; and determine, based on the temperature data and the energy consumption data, a quantity of water at the second temperature.

17. The system of claim 16, wherein the at least one processing system is further configured to: determine a thermal energy capacity of the water heater based on the quantity of water at the second temperature and on the second temperature; and, based on the thermal energy capacity, and in response to detecting a predetermined event, control the operation of the water heater.

18. The system of claim 17, wherein the predetermined event is one of a receipt of a control signal indicative of a state of an electrical grid connected to the water heater, and a generation of excess energy by a renewable energy source connected to the water heater.

19. A method for operating a water heater, the method comprising: determining a quantity of water stored in the water heater and a temperature of the quantity of water in accordance with the method of claim 1 ; determining a thermal energy capacity of the water heater based on the quantity of water and the temperature of the quantity of water; and, based on the thermal energy capacity, and in response to detecting a predetermined event, controlling the operation of the water heater.

20. The method of claim 19, wherein the predetermined event is one of a receipt of a control signal indicative of a state of an electrical grid connected to the water heater, and a generation of excess energy by a renewable energy source connected to the water heater.

Images