AU2017202731B2 - Improvements in Water Heating Elements - Google Patents

Abstract

P4825AU02 21 ABSTRACT A resistive heating element for a water heater 3.048, having at least one resistive member 3.050 with a negative thermal characteristic (NTC) matched to a photovoltaic (PV) source 3.042. The PV source has a solar input current/voltage characteristic exhibiting a maximum power point (MPP) 2.021 ... 2.025 corresponding to each level of solar input, the NTC resistance having an NTC characteristic which varies the operating point towards the MPP as the temperature of the NTC heating resistance varies. Fig 3 3/11 LO CJ 000 0 Ii uJ i i I i i e (5e i C\Ji 0

Description

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Improvements in Water Heating Elements

Field of the invention

[001] This invention relates a method, a device, and an apparatus using a negative temperature heating element.

[002] The invention will be described in the context of a negative temperature coefficient (NTC) heating element. The NTC heating element can be adapted for use with a photovoltaic (PV) electricity generator. In particular, the invention will be described in the context of a solar panel supplying an NTC resistive heating element for a water heating system. The invention can be utilized to improve the performance of a solar cell array under variable irradiance conditions in which the array is deployed.

Background of the invention

[003] Mains powered electric water waters have traditionally employed fixed resistance heating elements, and fixed resistance heating elements have also been used with solar-electric water heaters. However, the power from a photovoltaic electricity generator such as a solar panel is subject to variation due to changes in the incident solar energy. If the load resistance is "R", the output voltage from the PV array solar panel is "V" then according to Ohm's Law V= IR or R=V/1, with the current being "I". The ratio of V to I is fixed by V=IR, but the ratio of V to I at which the PV panels can deliver maximum power (optimal power transfer) varies with varying irradiance. When a constant value resistive load ("R" in the example given) is supplied by a photovoltaic panel, the operating load point moves away from the maximum possible power which can be delivered by the PV panel for the available incident solar radiation.

[004] Figure 1 illustrates the variability of the power output of a solar panel with variation in available sunlight when the panel feeds a constant resistive load, each curve 1.001, 1.002, 1.003, 1.004, 1.005 representing the current/voltage for a corresponding level of solar input or irradiance. Where solar input is given in W/m 2 for each curve.

[005] Each power curve of the solar panels exhibits an almost constant current over a range of voltages until the "saturation" knee, where the current drops off steeply. The maximum power point for a solar input curve is the point on the knee where product of current and voltage is at a maximum. The load line 1.010 for a constant resistive load intersects the power curves at corresponding operating points as shown in Figure 1. In the arrangement shown in Figure 1, the resistive load is shown as intersecting the 1000 W/m2 curve at its maximum power point (MPP) 1.015, 1.025. As can be seen, the intersection 1.011 of the load line with the 200 W/m2 curve is far below the corresponding MPP 1.021.

[006] One technique which is used to address this problem is maximum power point tracking (MPPT). These devices use DC/DC converters to match the current and voltage to the MPP for the corresponding solar power input. MPPT tracking requires sensors and a processor to adjust the performance to the input power. MPPT systems use an active monitoring and adjustment system to calculate required changes to adjust the output voltage to match the MPP.

[007] The complexity and cost of such systems can be seen as a disadvantage.

[008] It is desirable to provide a means of reducing the power loss of solar panels with varying power input while reducing one or more of the disadvantages of known MPPT systems.

[009] It is thus desirable to provide a system which reduces the loss of power resulting from the movement of the operating point of the system away from the maximum power point with changing incoming solar energy or irradiance.

Summary of the invention

[010] An underlying concept of the invention proposes the use of a resistive load including NTC (Negative Temperature Coefficient) material to add heat to an object or material via a resistive load.

[011] In one embodiment, an NTC heating element can be used in conjunction with a photovoltaic (PV) power source such as a solar panel or array.

[012] The characteristics of the NTC heating element can be tuned to the characteristics of the PV power source to enhance the energy output and / or power transfer from the system.

[013] According to an embodiment of the invention, there is provided a resistive heating element for a water heater, wherein the resistive load includes at least one resistive element having a negative thermal characteristic.

[014] The invention is a more efficient way to enable a PV power source to maximise (or more closely approach maximum) power output over a wide range of solar irradiance when coupled to a resistive load, without the complexity of the contemporary method (MPPT). Said resistive load to be used for heating.

[015] The innovation here is for the load to be a resistance device whose resistance increases in response to decreasing temperature, and for that resistance device to be used as a heating element for water, air or other fluids.

[016] According to a further embodiment of the invention, there is provided a photovoltaic (PV) powered electrical heating element, wherein the heating element includes a first NTC heating resistance, the resistance of the NTC heating resistance being chosen to cause the operating point to coincide approximately with at least one maximum power point (MPP) of an associated PV source.

[017] The NTC heating resistance can be adapted for use with an associated PV source having a solar input current/voltage chart exhibiting a maximum power point (MPP) corresponding to each level of solar input, the NTC heating resistance having an NTC characteristic which varies the operating point towards the MPP as the temperature of the NTC heating resistance varies.

[018] The NTC heating resistance can have an operating temperature range between a first temperature and a second temperature, the first temperature being higher than the second temperature, the value of the NTC resistive heating resistance being chosen such that the operating point approximately coincides with an MPP at at least one temperature within the operating temperature range.

[019] The photovoltaic (PV) powered electrical heating element can include a second resistive heating element connected electrically in series with the first NTC heating resistance.

[020] The second heating resistance may also be an NTC heating resistance.

[021] The photovoltaic (PV) powered electrical heating element can include a third resistive heating element in parallel with the first NTC heating resistance.

[022] The first NTC heating resistance can include a substantially planar NTC layer located between and in contact with first and second electrical contacts.

[023] In an alternate embodiment of the invention, there is provided a photovoltaic (PV) powered electrical heating element for use with a PV electricity supply, wherein the PV electricity supply a voltage/current characteristic which varies according to the solar input to the PV electricity supply, there being a maximum power point (MPP) corresponding to each level of solar input, the heating element including a first resistive member made of negative temperature coefficient (NTC) material and having negative temperature coefficient characteristics, wherein the first resistive member is adapted to have a range of resistance values between a first temperature and a second temperature, the first temperature being lower than the second temperature, a first resistance value of the first resistive member being chosen such that the operating point of the heating element corresponds approximately with a first MPP at the first temperature, the NTC characteristic of the first resistive member resulting in a decrease in the resistance of the first resistive member at the second, temperature. For example, for a cold start as described further in the Detailed Description.

[024] According to another embodiment of the invention, there is provided a solar electric water heating system including a PV source and a first NTC heating resistance load connected to the output of the PV source, the first NTC heating resistance being arranged to deliver heat to a water heater tank, the first NTC heating resistance having a resistance chosen to cause the operating point to coincide approximately with at least one maximum power point (MPP) of the PV source for maximum power transfer from the PV source.

[025] The solar electric water heating system can include a bobbin forming an enclosed space within the tank, the interior of the bobbin being isolated from the water in the tank, and wherein the first NTC heating resistance is located within the bobbin.

[026] According to yet another embodiment, the first NTC heating resistance is an elongate member wound around the tank.

[027] The characteristics of the NTC resistive load and/or the PV panel source can be tuned to enhance the power output from the system, approaching or approximating MPPT as much as possible with varying solar input.

[028] In the case of a storage electric water heater, the NTC resistance load heating element or elements can be submerged in the storage tank or can deliver heat to the tank via a heat exchange arrangement.

[029] According to another embodiment of the invention, there is provided a water heater resistive heating element. The resistive heating element comprises a resistive member with a negative temperature coefficient.

[030] According to another embodiment of the invention, there is provided a photovoltaics-powered electrical heating element. The heating element comprises a first resistive member with a negative temperature coefficient. The resistance of the first resistive member is variable between two or more resistance values at two or more respective temperatures, wherein at least one of the two or more resistance values is such as to cause the operating point of the heating element to approximately coincide with a maximum power point of a photovoltaic source electrically connected to the heating element, wherein the maximum power point is the maximum power point of the photovoltaic source for a solar irradiance value associated with the respective temperature corresponding to the at least one resistance value.

[031] According to another embodiment of the invention, there is provided a method of configuring a negative temperature coefficient heating element for operation with a photovoltaic source. The method comprises: identifying at least one maximum power point of the photovoltaic source; selecting one or more negative temperature coefficients for the heating element; and dimensioning the heating element to at least approximately coincide with the at least one maximum power point.

[032] According to another embodiment of the invention, there is provided a method of dimensioning a negative temperature coefficient heating element for operation with a photovoltaic source. The method comprises: determining at least one relevant solar-input-dependent characteristic of the photovoltaic source, the relevant characteristic identifying at least one maximum power point of the photovoltaic source; and dimensioning the heating element to at least approximately coincide with the at least one maximum power point.

Brief description of the drawings

[033] An embodiment or embodiments of the present invention will now be described, by way of example only, with reference to the accompanying drawings, in which:

[034] Figure 1 is graph showing the change of operating point with variation in the available output power of a solar panel according to an arrangement of the prior art.

[035] Figure 2 shows the idealized effect of providing solar panel with a negative temperature coefficient resistive load in accordance with an embodiment of the invention.

[036] Figure 3 illustrates the features of a solar water heater system using a photovoltaic panel supplying a heating element with a negative thermal characteristic according to an embodiment of the invention.

[037] Figure 4 illustrates the features of a solar water heater system using a photovoltaic panel supplying a heating element with a negative thermal characteristic according to a second embodiment of the invention.

[038] Figure 5 illustrates the features of a water heater system using a photovoltaic panel supplying a heating element with a negative thermal characteristic according to a further embodiment of the invention.

[039] Figure 6 illustrates the features of a water heater system using a photovoltaic panel supplying heating elements with a negative thermal characteristic according to another embodiment of the invention.

[040] Figure 7 shows a section of an NTC resistor element according to an embodiment of the invention.

[041] Figure 8 illustrates a sectional view of an NTC resistor element according to an embodiment of the invention.

[042] Figure 9 illustrates a section of an NTC resistor element according to an embodiment of the invention.

[043] Figure 10 illustrates a section of an NTC resistor element according to an embodiment of the invention.

[044] Figure 11 illustrates a section of an NTC resistor element according to an embodiment of the invention.

[045] Figure 12 illustrates a segment of an NTC resistor element according to an embodiment of the invention.

[046] Figure 13 illustrates a frusto-conical NTC resistive heating element according to an embodiment of the invention.

[047] Figure 14 illustrates an equivalent circuit of a photovoltaic cell.

[048] Figure 15 illustrates a plan view of a segment of the conductor pattern of an NTC heater element according to an embodiment of the invention.

[049] Figure 16 illustrates an elevation view of Figure 15.

[050] Figure 17 illustrates a section of an NTC resistor element according to an embodiment of the invention.

[051] Figure 18 illustrates a section of an NTC resistor element according to a further embodiment of the invention.

[052] Figure 19 is an hypothetical graph illustrating the relationship between insolation (solar in-out) and power for a P power source.

[053] Figure 20 is an hypothetical graph illustrating the relationship between power and the temperature of a heating element.

[054] Figure 21 is an hypothetical graph illustrating the relationship between temperature and resistance of an NTC heating element.

[055] Figure 22 is an hypothetical graph illustrating the variation in power against resistance for different levels of insolation.

[056] In the drawings showing a solar panel, it is understood that an array of solar panels could be used. The array of solar panels can be connected in series, in parallel, or in a series/parallel combination to provide the required electrical current and voltage output.

[057] The numbering convention used in the drawings is that the digits in front of the full stop indicate the drawing number, and the digits after the full stop are the element reference numbers. Where possible, the same element reference number is used in different drawings to indicate corresponding elements.

[058] The drawings are intended to illustrate the inventive features of the embodiments illustrated and are not necessarily to scale. The orientation of the drawings is chosen to illustrate the inventive features and is not necessarily indicative of the orientation of the device in use.

Detailed description of the embodiments

[059] The invention will be described with reference to the embodiments illustrated in the accompanying drawings.

[060] The graph of Figure 1 shows the effect of varying illumination of a typical solar panel with a fixed resistive load. By way of example, line 1.005 shows an illumination level of 1000 W/m 2, while line 1.001 shows an illumination of 200 W/m 2

The load line 1.010 indicates the current and voltage which the PV panel can deliver to a fixed resistance load. The operating point is the intersection of the load line 1.010 with the corresponding solar input line (1.001, 1.002, 1.003, 1.004, 1.005). In the example shown in Figure 1, the operating point 1.015 at the highest irradiance (line 1.005) coincides with the MPP 1.025. As the irradiance decreases, the operating point progressively moves away from the MPP until, at line 1.001, the operating point has fallen to the point 1.011, while the MPP is at 1.021.

[061] On line 1.001, the voltage at the operating point 1.011 is substantially below the voltage at MPP 1.021.

[062] As shown in Figure 1, the voltage at which the MPP occurs varies over a narrow range, while the current varies over a larger range over the range of solar irradiance. That is, the locus of the MPP is approximately vertical.

[063] In all embodiments, the present invention seeks to reduce the difference between the operating point and the MPP over the operating range of the PV panel by providing a load with one or more negative temperature coefficient/s.

[064] Ideally the operating point should track the locus of the MPP.

[065] Figure 2 illustrates an idealized application of the present invention in which the load resistance changes with temperature so that the operating point coincides with the MPP at all operating solar energy input levels. It will be understood that, in practice, the operating point may not be exactly coincident with the MPP, but that adjusting the operating point substantially towards the MPP will increase the efficiency / power transfer of the system.

[066] As shown in Figure 2, the load line 2.035 intersects the upper solar input level of line 2.005 so that the operating point coincides with the MPP 2.025. In the example illustrated in Figure 2, the load line is adjusted to cause the operating point to coincide with the MPP at each level of solar input / irradiance. Thus the load line 2.035 intersects the solar input line 2.005 at MPP 2.035, load line 2.034 intersects the solar input line 2.004 at the MPP 2.024, load line 2.033 intersects the solar input line 2.003 at the MPP 2.023, load line 2.032 intersects the solar input line 2.002 at the MPP 2.022, and load line 2.031 intersects the solar input line 2.001 at the MPP 2.021.

[067] As shown in Figure 2, the resistance of the load increases in response to the reduction in irradiance seen by the PV panel. The change in resistance is a consequence of the power output of the PV panel falling, which results in a lowering of the temperature of the resistance load, which uses an NTC heating element.

[068] Figure 3 illustrates a solar water heater including:

* water tank 3.048;

* solar panel 3.042;

* negative thermal coefficient (NTC) resistive heating element 3.050;

* cold water inlet 3.026;

* hot water outlet 3.028;

* temperature sensor 3.030; and

* thermal cutout switch 3.029.

[069] Optionally an auxiliary heating element 3.060, and auxiliary heater control switch 3.064 can be included. Power for the auxiliary heating element can be provided from the mains electricity supply 3.062 or other source of electric power.

[070] Alternatively, an auxiliary gas heating can be used.

[071] Optionally, a mixer 3.027 can be attached to the outlet of the cold water inlet pipe 3.026. The mixer can assist in reducing temperature fluctuations in the water surrounding the NTC heating element 3.050 as replacement water enters the tank 3.048.

[072] The solar panel or solar panel array 3.042 is connected to the NTC heating element 3.050 via electrical wires 3.044, 3.046. These wires enter the tank 3.048 via an electrically insulating seal 3.094 to connect with the NTC heating element 3.050.

[073] The negative thermal coefficient of the resistance of the NTC resistive heating element 3.050 can be selected to maintain the operating point at or near the MPP over most or all of the operating solar input range. It will be readily appreciated also that the negative temperature coefficient of resistance of the heating element may also designed and / or selected to vary over the operating range and still continuously operate as one or more negative temperature coefficient/s.

[074] The circuit of the auxiliary heating element 3.060 in this embodiment is electrically separate from the NTC resistive heating element circuit. The temperature sensor 3.030 is used to control switch 3.064. The auxiliary heating element can be operated when the temperature of the water sensed by the temperature sensor falls below a threshold value.

[075] Thermal cutout switch 3.029 can be inserted in the electrical lines 3.044, 3.046 between the solar panel output and the heating element 3.050. The thermal cutout switch 3.029 can be controlled by a temperature sensor 3.030. Because solar input is unregulated, a thermal cutout switch may shut off the current from the solar panel to the heating element 3.050 when the temperature of the water reaches a predetermined threshold temperature.

[076] Because the NTC resistive heating element 3.050 is inserted in the water in the tank 3.048, the heating element can be encased in a suitable jacket which can prevent contact between the water and the NTC material. The jacket can be thermally conductive to transfer heat from the NTC resistive heating element to the water.

[077] The temperature fluctuations due to contact with the water affect the heat transfer rate from the heating element which influences the temperature of the heating element which in turn alters the resistance of the heating element to move the operating point away from the MPP.

[078] In addition, the pressure inside a mains fed water heater tank can be quite high, eg, 1Obar gauge. Boiling point can thus be as high as about 180°C. When boiling occurs at the surface of the heating element, the laminar boundary layer can be stripped from the surface of the heating element. This can result in a substantially increased convection coefficient which in turn reduces the temperature of the heating element. Thus the resistance of the NTC heating element increases, resulting in a decrease in power delivered by the heating element as the operating point moves beyond the MPP on the knee of the solar panel output curve.

[079] Figure 4 shows a water heating system according to an alternative embodiment of the invention. In this example, a negative thermal coefficient resistor heating element 4.052 is wound around at least part of the external surface of the water tank 4.048. In practice, the tank would have insulation (not shown) applied over its external surface, the heating element being located between the tank surface and the insulation. This arrangement has the advantage that the NTC resistive heating element is not in contact with the water in the tank. The NTC heating element 4.050 can be flexible to permit it to be formed around the exterior of tank 4.048.

[080] Auxiliary heating can be added to the system of Figure 4, as discussed in relation to Figure 3.

[081] Figure 5 shows a water heating system using a solar electric panel in which the NTC heating element 5.050 is contained inside an airtight bobbin chamber pipe 5.090 which passes through the wall of the tank 5.048. The heating element 5.050 can be mounted within the bobbin chamber pipe (BCP) 5.090 as illustrated schematically by mounting block 5.092.

[082] In this embodiment, the NTC heating element 5.050 heats the air in the BCP 5.090, and the air heats the walls of the BCP. The BCP acts as a heat exchanger in which the walls of the BCP provide a heat transfer surface to transfer the heat to the water in the tank 5.048. Locating the NTC heating element within the BCP ensures that the NTC heating element does not come into direct contact with the water in the tank 5.048. The BCP provides a larger heat transfer surface than the surface of the NTC heating element.

[083] Figure 6 illustrates a further embodiment of the invention in which a second resistive heating element 6.054 is connected in series with the NTC heating element 6.050. The solar panel 6.042 is connected to the first heating element 6.050 via switch 6.056. The switch can be a temperature controlled switch in contact with the outer wall of the tank 6.048.

[084] The second heating element can be either a standard resistive heating element or another NTC resistive heating element as indicated by the dashes NTC symbol lines. If the second heating element 6.054 is also an NTC resistive heating element, it can be made of material having the same or different temperature/resistance characteristic as those of NTC resistive heating element 6.050 to provide flexibility in designing the overall temperature/resistance characteristics of the combined elements 6.050, 6.054. An embodiment of such a combined resistance is described below with reference to Figure 9.

[085] Figure 7 illustrates a longitudinal cross section 7.100 of an NTC resistive heating element according to an embodiment of the invention. The NTC resistive heating element can be a planar device made up of a layer of NTC material 7.080 between a first conductive electrode layer 7.102 and a second conductive electrode layer 7.104. The NTC material and the conductive electrodes can be encased in a thermally conductive electrically insulating material 7.081. The casing material can be immersed in water and hermetically seals the NTC resistance material 7.080.

[086] It will be readily appreciated that the thermal transfer characteristic of the NTC resistive heating element can also be selected and designed so as to aid in the performance of the invention. The thermal transfer characteristic may also be termed the energy flux at the heating element surface. For example a selection and/ or design may be to allow the NTC resistive heating element to heat sufficiently in cold start conditions, operate appropriately across the operating range for the fluid to be heated as well as maximise power transfer by providing an appropriate load resistance with respect to the PV array source and to the particular fluid temperature, for example water in the tank.

[087] It will also be readily appreciated that the thermal transfer characteristic selection and / or design for the NTC resistive heating element can include a heating element material selection, for example a thermal conductivity of the material, a geometry of the heating element and an intensity and a type of mixing of the water in the tank about the heating element.

[088] The NTC resistive heating element can have any required shape. It can be rectangular, circular, ribbon shaped etc.

[089] Electrical connections to the two electrodes 7.102, 7.104 can project through the casing 7.081 to enable the heating element to be connected to an electrical supply.

[090] Figure 8 illustrates a section of an NTC resistive heating element according to another embodiment of the invention. In this embodiment the heating element includes an NTC resistive heating layer 8.080, and a second resistive layer 8.084. Depending on the design criteria, the second resistive layer can be an NTC layer or a normal resistive layer. An electrode layer 8.087 is interposed between the two NTC materials 8.080, 8.084 providing electrical contact with both resistive layers 8.080, 8.084. Electrical contact layer 8.082 is in contact with the other side of NTC layer 8.080, and electrical contact layer 8.083 is in contact with the other side of resistive layer 8.084. Layers 8.080, 8.082, 8.087, 8.084, and 8.083 can be encased in an outer covering 8.081.

[091] Electrical contact 8.095 is in contact with conductive layer 8.087 and projects through the casing 8.081. Similarly, electrical contacts 8.096, 8.097 are in contact with conductive layers 8.082, 8.083 respectively, and project through the outer casing 8.081. The common electrical contact makes it possible to connect the resistive layer 8.084 in parallel with the NTC layer 8.080.

[092] Where both layers 8.08, 8.084 are NTC materials, the NTC characteristics of the NTC materials 8.080, 8.084 can be chosen to be the same or different. Different materials can be chosen to tune the combined NTC performance of the heating element to the MPP solar input locus.

[093] Figure 9 illustrates a heating element arrangement similar to that of Figure 8, with the omission of projecting contact 8.095. In this arrangement, the NTC layer 9.080 can be connected in series with the resistive layer 9.084.

[094] Figure 10 shows a cross-section of an NTC heating element according to an embodiment of the invention. The heating element can have an elongate shape. A pair of parallel conductor wires 10.102, 10.104 is embedded in NTC material 10.080, and a jacket 10.081 encloses the NTC material.

[095] Figure 11 illustrates a cross-section of an NTC heating element in accordance with a further embodiment of the invention. A first heating element consists of first NTC material 11.080 with a pair of imbedded parallel conductors 11.102, 11.104. A second heating element consists of a second pair of parallel conductors 11.106, 11.108 embedded in second resistive material 11.084. As discussed with reference to Figure 8, the second resistive material may be an NTC material. Ajacket 11.081 encloses both heating elements.

[096] Figure 12 illustrates a segment of an NTC layer according to an embodiment of the invention. In the embodiment shown in Figure 12, alternate strips of NTC material 12.080 and insulating material 12.110. A layer of an NTC heating element formed in a similar pattern can be sandwiched between a pair of electrically conductive layers as shown for example in Figure 7. Such an arrangement enables the circuit designer to increase the surface area of the NTC resistive heating element relative to the surface area of the NTC material.

[097] Figure 13 illustrates an NTC resistive heating element according to an embodiment of the invention. The heating element has a frusto-conical shape and is formed of an NTC layer 13.080 between a pair of conductive elements 13.102, 13.104. Such a heating element will generate a concentrated internal column of heated water and a more diffuse external column of water which is somewhat cooler than the internal column. Such a heating element can be dimensioned to deliver heated water towards the top of the tank more rapidly than a flat horizontal heating element with comparable surface area and equal power input.

[098] Figure 14 shows an equivalent circuit 14.120 for a PV cell with a load resistance 14.134 connected to the output of the PV cell / array / panel via switch 14.132.

[099] The equivalent circuit includes a current generator 14.122, a shunt resistor 14.124, a shunt diode 14.126, and a series resistor 14.128. The values of the components of the equivalent circuit can be determined empirically by measuring the open circuit voltage Vo when switch 14.132 is open, and by measuring the output voltage when the switch is closed, connecting the load resistance 14.134 in series with the series resistor 14.128. By taking such measurements at various levels of solar irradiance, the optimal electrical and / or thermal transfer characteristic/s for the NTC resistive heating element can be calculated in-situ within the water tank or with an equivalent bench test thermal load. It will be readily appreciated that where a data sheet for the PV panel includes the performance curves, the characteristics of the NTC resistive heating element can be determined from the performance curves as appropriate.

[0100] Figures 15 & 16 illustrate a partial plan view and a partial elevation view of a segment of an NTC heating element according to an embodiment of the invention. Conductive contacts 16.102, 16.104 are applied on either side layer of NTC material, 16.080. The conductive contacts have a zig-zag or sinusoidal pattern as shown at 15.102.1, 15.102.2 in Figure 15. The individual conductive tracks can be electrically connected to assist in providing even distribution of the supply power. This pattern may be applied to assist in reducing differential thermal expansion between the conductive material and the NTC material.

[0101] Figure 17 illustrates a section of an NTC heating element according to an embodiment of the invention. The heating element includes a central conductor 17.102 enclosed by a layer of NTC material 17.080. A second conductive member 17.104 encloses the layer of NTC material.

[0102] Figure 18 is an illustration of a section view of a cylindrical NTC heating element. The heating element includes an inner cylindrical conductor 18.102, a layer of NTC material 18.080, and an external cylindrical conductor 18.104. The inner cylindrical conductor 18.102 can be hollow, or its core 18.112 can be filled with conductive or non-conductive material.

[0103] The resistance of a resistor can be determined from the formula:

R = p*L/A,

where R = resistance, p = resistivity, L = length, and A = area.

[0104] With NTC material, p varies inversely with temperature. The Steinhart Hart equation:

1/TK = ao + a1*n r + a3 *(ln r) 3

, where TK = Kelvin temperature, ao, ai, a3 are NTC material constants which may be provided in the manufacturer's data sheets, r = resistance (http://thermistor.sourceforge.net/),

can be used to calculate the resistance/temperature curve for the NTC material. This information may also be included in the data sheets for the material.

[0105] Figures 19 to 22 are hypothetical graphs illustrating relationships between various parameters which can be used in designing an NTC heating element. These graphs are for illustrative purposes only and do not represent actual data plots.

[0106] Figure 19 shows how the maximum available power (MPP) of a PV power source is dependent on the solar input. The available power increases with solar input until it levels off at a saturation level. This characteristic can be determined empirically or may be available from the PV manufacturer's data sheet.

[0107] Figure 20 shows variation of temperature of a heating element against power input. This characteristic can be determined empirically or calculated using heat flows.

[0108] Figure 21 shows how the resistance of an NTC heating element varies with the temperature of the NTC heating element. This characteristic can be determined empirically, calculated from the NTC material temperature - resistance coefficient, or may be available from the NTC heating element manufacturer's data sheets.

[0109] Figure 22 shows the variation of power output from a PV power source varies with load resistance for different levels of solar input. As shown in Figures 1, 2, and 22, the MPP varies with solar input, as shown by theMPP locus 22.144. For example, MPP1 occurs at the peak of the maximum solar input 22.140 when the load resistance is R1, while MPP2 occurs on the minimum solar input curve at R2, where R2 > R1.

[0110] Preferably, the locus of the NTC resistance is designed to track the MPP locus. However, in some cases the NTC may not coincide exactly with the MPP locus. By designing the NTC heating resistance and / or thermal transfer characteristic to coincide with at least one point on the MPP locus, the variation of the NTC resistance value will cause the operating point to shift towards the MPP at other levels of solar input even when the locus of the NTC heating element resistance does not coincide exactly with the MPP locus.

[0111] For example, if the NTC resistance is chosen to be RX so the load point coincides with MPPX, and if the NTC locus is as shown at 22.146, it can be seen that the intersection of the RX vertical with the maximum solar input curve 22.140 is below the intersection of the NTC locus 22.146 with the maximum solar input curve. Similarly, the intersection of the RX vertical with the minimum solar input curve 22.142 is below the intersection of the NTC locus 22.146 with the minimum solar input curve.

[0112] On one embodiment, MPPX can be chosen to coincide with MPP1.

[0113] The NTC material should exhibit useful NTC characteristics within the working temperature range of the heating element. To ensure an adequate heating rate, the temperature of the heating element when operating should be above 100°C, preferably above 200°C. The temperature of the heating element is a function of the input power and the rate of heat dissipation. The rate of heat dissipation, or otherwise termed heat transfer characteristic, from the heating element is a function of the surface area of the heating element, the temperature of the water and as described herein.

[0114] Several NTC materials exhibit useful NTC characteristics above 100C including, for example CaTiO 3, BaTiO 3, and MgAO-LaCrMnO composite ceramics. The article High temperature NTC ceramic resistors (ambient-10000 C) D Houivet, J Bernard, JM Haussonne - Journal of the European Ceramic Society, 2004 describes NTC resistor materials with a working range from ambient to 1000°C.

[0115] The NTC resistance can be designed to be approximately coincident with at least one MPP. Solar power supplies can be installed in differing conditions of solar input, so the NTC resistance can be adjusted to suit the particular solar input conditions. For example, where the predominant conditions provide strong solar input, the NTC resistance can be selected to cause the operating point to approximately coincide with the peak solar input MPP. On the other hand, where the prevailing solar input is weak, the operating point can be chosen to be approximately coincident with a lower MPP.

[0116] The NTC characteristics can be a compromise, balancing such factors as the electrical and thermal transfer characteristics of the NTC materials, the energy flux at the element surface, and the influence of the variable temperature of the water upon the element material.

[0117] Various relationships between the parameters of the NTC material can be used in designing the NTC resistance to match the MPP locus of a PV power source.

[0118] The initial resistance to match at least one MPP can be determined from the product data sheets, or it can be determined empirically.

[0119] The NTC material resistivity can be used to match the initial resistance.

[0120] The resistivity of the NTC material can be used to determine the dimensions of the NTC initial resistance.

[0121] The NTC temperature-resistance coefficient can be used to determine the variation in resistance to track the MPP locus.

[0122] The power-resistance relationship can be measured for at least one level of solar input to determine the optimum resistance for at least one level of solar input.

[0123] The power-resistance relationship can be measured for two or more different levels of solar input to determine the optimum resistance for each level of solar input. Figure 19 illustrates the resistance R1 to match the MPP for high level of solar input, and resistance R2 to match the MPP for low level of solar input. Ideally the resistance should track the MPP locus 22.144 for varying solar input levels. Because there is a steep fall off beyond the MPP, if the resistance is not able to track the MPP locus, it should be designed to fall on the lower resistance side of the MPP locus, as shown, by way of example, at 22.146.

[0124] One advantage of using an NTC heating resistance is that, if the operating point is chosen to coincide approximately with an MPP at one level of input at one temperature, when the temperature changes, the new operating point will be closer to the new MPP than if the heating resistance were a non-NTC heating resistance. Additional design of the NTC heating resistance, or the use of two or more different NTC heating resistors, can assist in moving the new operating point still closer to the new MPP.

[0125] In this specification, reference to a document, disclosure, or other publication or use is not an admission that the document, disclosure, publication or use forms part of the common general knowledge of the skilled worker in the field of this invention at the priority date of this specification, unless otherwise stated.

[0126] References to documents in the specification are not an admission that the documents are part of the common general knowledge in the field of the invention.

[0127] In this specification, terms indicating orientation or direction, such as "up", "down", "vertical", "horizontal", "left", "right" "upright", "transverse" etc. are not intended to be absolute terms unless the context requires or indicates otherwise.

[0128] Where ever it is used, the word "comprising" is to be understood in its "open" sense, that is, in the sense of "including", and thus not limited to its "closed" sense, that is the sense of "consisting only of'. A corresponding meaning is to be attributed to the corresponding words "comprise", "comprised" and "comprises" where they appear.

[0129] It will be understood that the invention disclosed and defined herein extends to all alternative combinations of two or more of the individual features mentioned or evident from the text. All of these different combinations constitute various alternative aspects of the invention.

[0130] While particular embodiments of this invention have been described, it will be evident to those skilled in the art that the present invention may be embodied in other specific forms without departing from the essential characteristics thereof. The present embodiments and examples are therefore to be considered in all respects as illustrative and not restrictive, and all modifications which would be obvious to those skilled in the art are therefore intended to be embraced therein.

Claims (20)

The claims defining the invention are as follows:

1. A water heater resistive heating element, the resistive heating element comprising a resistive member with a negative temperature coefficient.

2. The water heater resistive heating element of claim 1, further comprising a first conductive layer and a second conductive layer, wherein the resistive member is located between the first and second conductive layers.

3. The water heater resistive heating element of claim 2, wherein the first conductive layer, the second conductive layer, and the resistive member are configured in a zig-zag or sinusoidal pattern.

4. The water heater resistive heating element of claim 2 or 3, wherein the resistive member is a first resistive layer, the resistive heating element further comprising a second resistive layer and a third conductive layer, wherein the second resistive layer is located between the second and third conductive layers.

5. The water heater resistive heating element of any one of claims 1 to 4, wherein the resistive member comprises alternating strips of a material with a negative temperature coefficient and an insulating material.

6. The water heater resistive heating element of any one of claims 1 to 5, wherein the resistive heating element has a frusto-conical shape.

7. The water heater resistive heating element of claim 1, further comprising a first conductive member and a second conductive member, wherein the first conductive member is enclosed by the resistive member, and wherein the resistive member is enclosed by the second conductive member.

8. The water heater resistive heating element of claim 7, wherein the first conductive member, the second conductive member, and the resistive member are cylindrical.

9. The water heater resistive heating element of any one of claims 1 to 8, wherein the resistive member has more than one negative temperature coefficient.

10. A photovoltaics-powered electrical heating element, the heating element comprising a first resistive member with a negative temperature coefficient, wherein the resistance of the first resistive member is variable between two or more resistance values at two or more respective temperatures, wherein at least one of the two or more resistance values is such as to cause the operating point of the heating element to approximately coincide with a maximum power point of a photovoltaic source electrically connected to the heating element, wherein the maximum power point is the maximum power point of the photovoltaic source for a solar irradiance value associated with the respective temperature corresponding to the at least one resistance value.

11. The photovoltaics-powered electrical heating element of claim 10, further comprising a second resistive member connected electrically in series with the first resistive member.

12. The photovoltaics-powered electrical heating element of claim 11, wherein the second resistive member has a negative temperature coefficient.

13. The photovoltaics-powered electrical heating element of claim 11 or 12, further comprising a third resistive member electrically connected in parallel with the first resistive member.

14. The photovoltaics-powered electrical heating element of any one of claims 10 to 13, wherein the first resistive member includes a substantially planar layer with a negative temperature coefficient, the layer being located between and in contact with first and second substantially planar electrical contacts.

15. A water heating system comprising: a water tank; a heating element as claimed in any one of claims 1 to 14, configured to heat water in the water tank; and a photovoltaic source electrically connected to the heating element and configured to power the heating element.

16. The water heating system of claim 15, further comprising a bobbin forming an enclosed space within the water tank, the interior of the bobbin being isolated from the water in the water tank, wherein the heating element is located within the bobbin.

17. The water heating system of claim 15, wherein the heating element is wound around at least part of an external surface of the water tank.

18. The water heating system of any one of claims 15 to 17, wherein the photovoltaic source is electrically connected to the resistive heating element through a temperature-controlled switch which is in contact with an exteral surface of the water tank.

19. A method of configuring a negative temperature coefficient heating element for operation with a photovoltaic source, the method comprising: identifying at least one maximum power point of the photovoltaic source; selecting one or more negative temperature coefficients for the heating element; and dimensioning the heating element to at least approximately coincide with the at least one maximum power point.

20. A method of dimensioning a negative temperature coefficient heating element for operation with a photovoltaic source, the method comprising: determining at least one relevant solar-input-dependent characteristic of the photovoltaic source, the relevant characteristic identifying at least one maximum power point of the photovoltaic source; and dimensioning the heating element to at least approximately coincide with the at least one maximum power point.