Patent Publication Number: US-2007101989-A1

Title: Apparatus and method for the conversion of thermal energy sources including solar energy

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS  
      This application claims the benefit of U.S. provisional patent Application No. 60/735,056, filed Nov. 8, 2005, and U.S. provisional patent Application No. 60/737,682, filed Nov. 17, 2005, the disclosures of which are hereby incorporated by reference herein. 
    
    
     TECHNICAL FIELD  
      The invention relates generally to energy conversion systems and methods, and more particularly to the conversion of solar and similar forms of heat energy to other forms of energy.  
     BACKGROUND  
      There are several sources of relatively abundant, relatively inexpensive low density thermal energy, such as solar energy, geothermal energy, waste-heat energy, and equivalent types of low energy density heat energy. Conversion of this thermal energy to other forms of more useful energy, while desirable to meet today&#39;s increasing energy demands and costs and because of environmental reasons, has not been widely used because it has been relatively expensive and inefficient. Solar energy has a relatively low power density, typically providing an average of 4-6 kilowatts per square meter per day for a given flat surface collector area in the continental USA, and conventional approaches to increase energy production have focused on the use of very large arrays of mirrors or lens systems to concentrate the photon energy of solar radiation, which are problematic.  
      The problems with very large arrays include the installation and land cost, vulnerability to high winds, dust and sand damage to mirrors and lenses, and the traditional maintenance costs for both tracking systems and the lens/mirror systems. Mirror and/or lens systems are also susceptible to degradation over time, and the tracking equipment to keep the mirror and/or lens properly positioned in correspondence with the movement of the sun is complex and costly to maintain.  
      Conventional generation of electricity from solar energy has also had several serious problems. One common method to generate electricity from solar energy is the use of photovoltaic cells (“PV”). However, conventional PV systems typically use less than 30% of the solar light frequency spectrum, that is photons having a wavelength above that needed to create hole-electron pairs in a PV cell. Therefore only a fraction of the total solar energy is converted to electricity, and the efficiency of converting solar energy into usable power from photovoltaic cells is fairly low, requiring either very large surface areas or solar energy concentrators. The photovoltaic cells also degrade over time and lose most of their DC electricity production efficiency, typically there is a significant decrease in output after 20 years or less. Since most electrical power is AC, inverters are required to convert the DC electricity from the photovoltaic cells to AC electricity, and these electrical inverters have relatively short mean times between failures, typically requiring repair within five years or less. In a current study of energy usage in California, for example, only about 0.5% of the useable energy comes from solar energy, as the cost of a solar PV KWH of electricity is on the order of 10 times greater than that from fossil fuel.  
      An alternative to photovoltaic systems is to utilize thermally powered heat engines operating on various thermodynamic cycles (e.g., an organic Rankine or other similar cycle). Thermally powered engines can generally use fluids to both absorb the heat from a heat source (e.g., solar energy, geothermal energy, waste-heat energy, bio-mass combustion, and other such types of energy) to create a gas, and use high pressure gas to drive some sort of mechanical device or expander. The fluids can be a single fluid, or a mixture of two or more fluids such as a binary solution of ammonia and water, or the like. However, such systems have not been found to be cost effective for large scale use. Because of the generally low temperature differential between the hot side of an engine and a condenser, conventional thermal power engines suffer from low efficiency in energy conversion, expensive equipment and materials, unreliability for long-term operation, and costly maintenance.  
      There are three main types of passive thermal energy collector systems used for collecting thermal energy (e.g., solar energy, or an equivalent). Low-temperature collectors (unglazed) normally operate at up to approximately 18 F° (10 C°) above ambient temperature, and are most often used for heating swimming pools. Often, the pool water is colder than the air, and insulating the collector would be counter-productive. Low-temperature collectors are typically extruded from polypropylene or other polymers with UV stabilizers. Flow passages for the pool water are molded directly into the absorber plate, and pool water is circulated through the collectors with the pool filter circulation pump. Swimming pool heaters typically cost from $10 to $40/ft 2  (based on 2004 prices).  
      Mid-temperature collectors are usually flat plates insulated by a low-iron cover glass and fiberglass or poly-isocyanurate insulation. Reflection and absorption of sunlight in the cover glass reduces the efficiency at low temperature differences, but the glass is required to retain heat at higher temperatures. A copper absorber plate with copper tubes welded to the fins is typically used. In order to reduce radiant losses from the collector, the absorber plate is often treated with a black nickel selective surface, which has a relatively high absorptivity in the short-wave solar spectrum, but a relatively low-emissivity in the long-wave thermal spectrum. Mid-temperature collectors typically range in cost from $90 to $120/ft 2  of collector area (based on 2004 prices).  
      High-temperature collectors utilize evacuated tubes around a receiver tube to provide high levels of insulation and often use focusing curved mirrors to concentrate sunlight. High temperature collectors are normally used for absorption cooling or electricity generation, but are also sometimes used for mid-temperature applications, such as commercial or institutional water heating as well. Evacuated tube collectors themselves typically cost about $75/ft 2 , but use of curved mirrors and economies of scale get this cost down for large system sizes to a relatively low cost of $40-70/ft 2  of collector area (based on 2004 prices).  
      A need exists for a higher efficiency, lower cost systems for thermal energy conversion and utilization, in general, and especially for the utilization of solar energy that avoid the foregoing and other problems of known approaches. There is a need for systems that do not require expensive equipment, materials, or maintenance, are relatively stable and non-degradable in long-term operation, and have good efficiency. It is to these ends that the present invention is directed.  
     SUMMARY OF THE INVENTION  
      The invention affords a system and method which use the phase transformation of a working expansion medium (e.g., a liquid, or a solid such as dry ice) into a gas during heat absorption. During expansion, the enthalpy of the system is the physical work done plus the work of the latent heat of fusion which is used to change the liquid to a gas. This increases the internal energy of the system, which may be recovered during a cooling period, such as night time, when the gas is cooled and returned to the liquid state and the heat evolved is emitted into deep space on the dark side of the planet which is not facing the sun. This cycle creates a change in the solar cross section of the planet, as all energy that is captured by phase transformation from liquid to gas over a given absorption area is released into space by black body radiation during the night time operations. Energy systems in accordance with the invention, if utilized on a large scale, can efficiently produce energy such as electricity or other forms of useful power and power storage, as well as help to reduce global warming.  
      Advantageously, the invention may provide a heat energy conversion system that is coupled to the normal varying, more or less sinusoidal, energy field that characterizes the daily solar heat cycle due to the daytime exposure to the sun and the subsequent nighttime exposure to a cold heat sink (e.g., deep space). This cycle comprises a heat energy source (or photons which can be converted to heat) and an energy sink. The energy source may be the sun (in the case of the planet earth) and the energy sink may comprise interstellar space (deep space on the side of the earth not facing the sun). A portion of heat energy absorbed during daylight may go directly into generating external work via a prime mover, and the rest of the absorbed heat may be used to raise the enthalpy (or internal energy) of the system. The energy that goes into driving an expansion medium, i.e., a working fluid or working liquid, to the gas phase raises the internal energy of the system. This energy can be stored in the system and can be emitted via black body radiation to deep space on during nighttime operations. Heat is not absorbed by the system, rather it passes through the system, is absorbed in the liquid-to-gas phase transformation, and then is emitted in the transformation of the expansion medium from gas to liquid.  
      The invention may utilize, in part, the fact that when an expansion fluid makes the transformation from a liquid to a gas, the volume occupied by the expansion fluid may increase by several, typically about three; orders of magnitude (1000 times larger). The liquid-to-gas transformation is done with the liquid at a high pressure, as will be shown later on the pressure vapor curve for the expansion fluid. Heat is supplied by the sun to drive the temperature of the expansion fluid to the boiling point and then into the liquid-to-gas transformation. As the volume of gas increases, this volume change can be used to displace another working medium, referred to as a storage medium, to a higher potential energy. Once the storage medium is at the higher potential energy it can either be used directly being returned to a lower potential through a prime mover which extracts energy from the storage medium, or it can be stored at the higher potential energy level for use at some later time.  
      The invention can be used to pump a working medium, such as water, to a higher potential energy and transport it over a hill such as the California aqueduct passing over the Grapevine area of California, where it can be available for different uses. In this case the working medium (water) can be replaced on the pumping side by water flowing in the California aqueduct from Northern California to Southern California  
      The invention also affords a pixelized collection system to allow for more efficient use of the absorbed heat energy, and enables use of cells that have been fully expunged of the working medium by the gaseous expansion medium to heat the liquid expansion medium for subsequent cells in the pixelization collector, thus increasing the overall efficiency of the system. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       FIG. 1  illustrates a block diagram of a conventional Rankine cycle engine, as used in conventional solar energy applications;  
       FIG. 2  illustrates a block diagram of a modified Rankine cycle in accordance with one embodiment of the invention;  
       FIG. 3  illustrates a vapor pressure curve of an expansion medium, such as ammonia, that may be used in the invention;  
       FIG. 4  is a block diagram of a thermal energy system in accordance with a first embodiment of the invention;  
       FIG. 5  is a more detailed block diagram of the system shown in  FIG. 4 ;  
       FIG. 6  is a diagrammatic view of an implementation of a thermal energy system in accordance with the invention;  
       FIG. 6A  is a diagrammatic view of a thermal energy system in accordance with an alternative embodiment of the invention where energy production is only required during day light hours and high potential energy storage is not used;  
       FIG. 7  is a flowchart of a method in accordance with the embodiment of FIGS.  4 -6, 6A for converting thermal energy to another useful form of energy;  
       FIG. 8  is a flowchart of another method in accordance with the invention for converting thermal energy to another form of energy in a pixilation system of the type illustrated in FIGS.  15 A-C;  
       FIG. 9  illustrates a flowchart of a method of generating energy, in accordance with another embodiment of the invention;  
       FIG. 10  illustrates a flowchart of a method of generating electricity, in accordance with a further embodiment of the invention;  
       FIG. 11  is a diagrammatic view of the solar energy generation system shown in  FIG. 6 ;  
       FIG. 12  is a diagrammatic view of a solar pumping system in accordance with the invention;  
       FIG. 13  is a cross-sectional view of a containment assembly that may be used in the systems of the invention;  
       FIG. 14  is a diagrammatic view of another embodiment of a containment assembly, partially broken away, that may be used in the systems of the invention;  
       FIG. 15A  is a block diagram of a pixelized energy collection system in accordance with another embodiment of the invention.  
       FIG. 15B  is a more detailed diagrammatic view of a pixelized energy generation system in accordance with another embodiment of the invention having two or more interconnected energy generator assemblies;  
       FIG. 15C  illustrates a diagrammatic view of an alternative embodiment of the system of  FIG. 15B ;  
       FIG. 16  is a flowchart of a method of converting thermal energy to another useful form of energy from a plurality of interconnected energy generator assemblies; and  
       FIG. 17  illustrates a fractal solar energy collector array that may be employed for the pixelized collection of energy in accordance with the invention. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS  
      Embodiments of the invention can be constructed from commercially available components. In all of the embodiments disclosed below, various different materials may be used for the chambers, reservoirs, and piping, including but not limited to various plastics, rubbers, resins, ceramics, cements, and metals, or other equivalent man-made materials. The collector may be a low-temperature collector, a mid-temperature collector, a high-temperature collector, or a combination of different types of collectors.  
      The invention employs a working medium, also referred to as an expansion medium, and a storage medium. The expansion medium and storage medium of the invention preferably comprise fluids, as will be explained. These two fluids may be the same, or one fluid may be used as the expansion medium and a second different fluid may be used as the storage medium. Materials that may be utilized for the working (expansion) fluid and storage fluid include, but are not limited to, acetone, alcohol, water, various water solutions, ammonia and water solutions (e.g., such as an 80% ammonia and 20% water solution, or equivalents), liquefied natural gas (LNG), chloro-fluorocarbon (CFC) refrigerants (e.g., R-410A, R-22, R-32, R-125, R-407C, R-134A), the equivalent hydrogenated CFC (HCFC) refrigerants, ammonia, carbon dioxide, or other non-aqueous fluids having similar vapor pressure curves. Preferred criteria for selecting the expansion and storage media will be explained in connection with  FIG. 3 . Additionally, as will also be explained, the storage medium may also comprise a slurry, a powder, or a solid mass that can be transformed to a higher potential energy.  
      The invention affords a system for generating useful mechanical power, for generating chemical energy or for supplying chemical fuels (e.g. chemical fuels generated from electrolysis, e.g., hydrogen and oxygen, or equivalents), or connected to one or more electrical generators for producing either AC or DC electricity. The invention may also be used to generate cryogenic fluids such as liquid nitrogen. Some embodiments of the invention can accommodate variations in the heights available for utilizing a storage medium, if necessary.  
      The invention has some similarities to a Rankine cycle engine and to a Sterling engine, but differs in several significant ways. First, the invention may utilize a substantially constant pressure and a changing volume of a working medium, e.g., a fluid, the volume increasing during an expansion phase and decreasing during a contraction phase, to produce useful work. Work may be extracted by a corresponding increase in the volume of a displacement chamber, for example, caused by the conversion of a liquid expansion medium to a gas. This expansion ratio of gas to liquid may be on the order of 1000 times the volume in the gas phase verses the liquid phase.  
       FIG. 1  illustrates a block diagram of a conventional Rankine cycle engine. As shown, there is a boiler  102  connected with a pipe  169  to a turbine  112 , which is connected with an output pipe  167  to a condenser  124 . The condenser is connected with an output pipe  165  to a feed pump  106  that supplies boiler  102  by an output pipe  104 . The expansion medium in a conventional Rankine cycle engine is typically water.  
      The turbine  112  (e.g., a steam turbine, water turbine, or generator) utilizes a substantially isentropic expansion; the condenser  124  utilizes a substantially isobaric heat rejection; the feed pump  106  utilizes a substantially isentropic compression; and the boiler  102  utilizes a substantially isobaric heat supply. Heat  103  is supplied to the boiler  102  and heat  105  is rejected by the condenser  124 . The work output  107  is from the turbine and the work input  108  is to the feed pump  106 . The net work produced by this engine is the difference of the work output  107  and the work input  108 .  
      In a conventional Rankine cycle engine, work is extracted by expanding a high pressure gas (and volume) and reducing the gas pressure during this expansion cycle. Unlike a Rankine cycle, as will be explained, the invention does not have to expand the gas to a lower pressure to extract work. It may reduce the gas temperature and volume, and heat a liquid expansion medium to near its boiling point. The expansion of the gas may be used to displace a storage medium from a low potential energy (“LE”) to a high potential energy (“HE”). As the storage medium is returned to the lower potential energy, it may pass through a prime mover (e.g., a turbine, generator, pump, mechanical power take off) or other system that uses the energy change to produce work. Thus, while the work extracted is from the expansion of the working medium from liquid to gas, the invention does not expand the gas to a lower pressure as is done in a conventional Rankine cycle.  
      In addition, as mentioned above, the invention may utilize the fact that work is required for the transformation of a liquid to a gas, (the latent heat of fusion or internal energy of the system), and physical work may be extracted as the liquid expands, typically about 1000 times, as it goes through the phase transformation at a high pressure. This expansion of volume may be used to generate physical work, as in a collector/expansion system. If the collector/expansion system is composed of a plurality of small chambers, then when a given chamber has all of its storage medium (the “storage medium” may be a fluid such as water, a slurry or powder, or a physical mass that can be lifted to a higher potential energy) displaced by the expansion medium, that chamber can be isolated from the main system&#39;s storage media, and the heat trapped in that smaller chamber can be used to raise an expansion fluid temperature to just below the liquid-to-gas transformation temperature. The invention may employ several fully displaced chambers so that all of the heat energy that was used to raise the first chamber liquid to the boiling point can be recovered from the hot working medium gas.  
      As the temperature of the gas is lowered, the chamber can then be partially refilled with the storage media and then reheated to force more storage media to a higher potential. This is similar to the reheat cycle in an advanced reheat Rankine cycle engine or somewhat like that of a Sterling engine.  
      Thus, the invention differs substantially from a conventional Rankine cycle in the fact that the gas that is evolved from the expansion medium is not expanded in an increased volume and the temperature is not lowered. Rather, the pressure can be retained at a constant value and the volume may be expanded to contain the increased gas volume due to the liquid-to-gas transformation of the expansion media. The increased volume may be used to move the working medium to a higher potential energy, from which it may be run through a prime mover (turbine, expander, pressurizer, etc. ) to produce work as it moves to a lower potential energy. The working medium may then be returned to its lowest potential energy as it is used to pressurize the gaseous expansion medium and help (with cooling) to drive the phase transformation of the expansion media from the gas phase to the liquid phase. The invention may comprise a binary system that includes an expansion medium which is separate from the working media, and the expansion medium drives the working media to a higher potential energy. In addition the invention does not require a conventional feed water pump as does a conventional Rankine cycle engine.  
       FIG. 2  illustrates a block diagram of a thermodynamic cycle of a modified Rankine cycle engine in accordance with the invention. Referring to  FIG. 2  there is a reservoir  110 , connected with an output pipe  169 , to a turbine (e.g., steam turbine, water turbine, generator, or equivalent)  112  with an output pipe  167  witch is connected to a condenser  124 , connected with an output pipe  165  to the containment assembly  130 , may be connected by a pipe  163  to the reservoir  110 . There is no feed pump  106  and no output pipe  104 , as in a conventional Rankine cycle engine. Heat  103  may be supplied to the containment assembly  130 , and heat  105  is rejected by the condenser  124 . The work output  107  from this engine is from the prime mover  112 .  
      The prime mover  112  (e.g., a steam turbine, water turbine, generator, or equivalent) may utilize a substantially isentropic process, the condenser  124  may utilize a substantially isobaric heat rejection, and the reservoir  110  in one embodiment may be filled with a storage medium (not shown) moved by pressure provided by an expansion medium (not shown). Several possible materials could be utilized for the expansion medium and storage medium, including acetone, alcohol, water, various water solutions, ammonia and water solutions (e.g., such as an 80% ammonia and 20% water solution, or equivalents), liquefied natural gas (LNG), chloro-fluorocarbon (CFC) refrigerants (e.g., R-410A, R-22, R-32, R-125, R-407C, R-134A), the equivalent HCFC refrigerants, ammonia, carbon dioxide, or other non-aqueous fluids having substantially similar vapor pressure curves. Substantially the same fluid may be used for both the expansion medium and the storage medium. The expansion medium in the modified Rankine cycle engine can be any fluid having a suitable vapor pressure curve, for example, as shown in  FIG. 3  (and described below).  
       FIG. 3  illustrates a vapor pressure curve of an exemplary expansion medium, ammonia, that may be used in the invention. The vertical axis  302  indicates the vapor pressure of the expansion medium, and the vapor pressure curve  304  of the expansion medium is shown plotted, between the vertical axis  302  and the horizontal axis  306  indicating the temperature in degrees Kelvin and the horizontal axis  308  indicating the temperature in degrees Celsius.  
      Suitable expansion medium for the invention is preferably selected to have a high pressure at the high temperature side of the thermodynamic cycle, and a fairly low pressure in the condensation side of the cycle. Two suitable fluids are ammonia and carbon dioxide which have pressures of about 40-50 bar at a working temperature of about 30-40° C. above ambient, and also have a good pressure, on the order of 10 bar, for the condensation of gas back to liquid. Also important is the latent heat of fusion vs. the expansion factor. CO 2  may have a slight advantage in efficiency as compared to ammonia in this regard.  
      The process of evaporation in a closed chamber will proceed until there are as many molecules returning to the liquid as there are escaping. At this point the vapor is said to be saturated, and the pressure of that vapor is called the saturated vapor pressure. Since the molecular kinetic energy is greater at higher temperature, more molecules can escape the surface and the saturated vapor pressure is correspondingly higher. If the liquid is open to the air, then the vapor pressure is seen as a partial pressure along with the other constituents of the air. The temperature at which the vapor pressure is equal to the atmospheric pressure is called the boiling point. The phase change of a fluid from a liquid to a vapor (and the reverse process) can be utilized in multiple ways by the invention, as described below.  
       FIG. 4  illustrates a block diagram of a system in accordance with a first embodiment of the invention to utilize thermal energy. The system includes a high potential energy reservoir  110 , a turbine  112 , a low potential energy reservoir  114 , and a containment assembly  130  containing the storage media  129 . The system also includes a thermal energy collector  120  connected to an expansion medium reservoir  126 , which receives the expansion medium  127  from a condenser  124 , which is connected to the containment assembly  130 . The expansion medium  127  is capable of undergoing a phase change from a liquid to a vapor upon the application of thermal energy, and disposed to circulate through the thermal energy collector  120 , the containment assembly  130  and the condenser  124 . The storage media  129  circulates through the high potential energy reservoir  110 , the turbine  112 , the low potential energy reservoir  114 , and the containment assembly  130  as a result of displacement in the containment assembly  130  caused by the vaporization of the expansion medium  129 . The thermal energy collector  120  can collect heat from one or more sources (e.g., solar energy, geothermal energy, waste-heat energy, bio-mass combustion, and other equivalent types of energy).  
       FIG. 5  illustrates in more detail the system shown in  FIG. 4 .  FIG. 5  shows, for example, more details of the containment assembly, and includes a plurality of valves that may be used to control the system. As shown, containment assembly  130  may have a containment assembly interior  116  containing the storage medium (fluid)  129 , and a displacement chamber  122  containing the working vapor  128 .  
      Valve  143  may control the flow in the pipe between the high potential energy reservoir  110  and the containment assembly interior  116  in the containment assembly  130 . Valve  142  may control the flow in the pipe between the low potential energy reservoir  114  and the containment assembly interior  116  in the containment assembly  130 . Valve  149  may control the flow in the pipe between the low potential energy reservoir  114  and the containment assembly interior  116  in the containment assembly  130 . Valve  141  may control the flow in the pipe between the turbine  112  and the low potential energy reservoir  114 . Valves  146  and  148  may control the flow of expansion medium (working fluid)  127  between the thermal energy collector  120  and the expansion medium (working fluid) reservoir  126 . Valve  147  may control the flow of working fluid  127  between the condenser  124  and the working fluid reservoir  126 ; and valve  145  may control the flow of working fluid vapor  128  between the condenser  124  and the displacement chamber  122  in the containment assembly  130 .  
       FIG. 6  illustrates diagrammatically an implementation of the system of  FIGS. 4 and 5  in accordance with a preferred embodiment of the invention. As will be described, the invention may be implemented as a solar energy system using natural or man-made geographical features, such as lakes, as reservoirs.  FIG. 6  illustrates lakes as reservoirs. However, it may be appreciated that the reservoirs may take other forms, and that the invention may be implemented in other contexts.  
      As shown in  FIG. 6 , the system may include a high potential energy reservoir  110  (such as lake  1 ), a turbine  112 , a low potential energy reservoir  114  (lake  2 ), and a containment assembly  130  (pump chamber) containing the storage medium  129  (e.g., water) in the containment assembly interior  116 . The system also includes a thermal energy collector  120  (e.g., an evaporator) connected to an expansion medium reservoir  126  (fluid tank), which receives expansion medium  127  from a condenser  124 , which is connected to the containment assembly  130 . The expansion medium, preferably a fluid, is capable of undergoing a phase change from a liquid to a vapor  128  (gas) in displacement chamber  122  upon the application of thermal energy (e.g., from the sun  600 ) and disposed to circulate through the thermal energy collector  120 , the containment assembly  130  and the condenser  124 . The storage medium (water)  129  circulates through the high potential energy reservoir  110 , the turbine or prime mover  112 , the low potential energy reservoir  114 , and the containment assembly  130  as a result of displacement caused by the vaporization of the expansion medium  129  in the displacement chamber  122 . Valves v 1 , v 2 , v 3 , v 4 , v 5 , v 6 , v 7 , and v 8 , which are analogous to various ones of the valves shown in  FIG. 5 , control the system and will be described in detail in connection with  FIGS. 11 and 12 . The sun may be the thermal energy source in this embodiment, but in other embodiments other heat sources may be used alone or in combination to supply the thermal energy.  
      Generating electrical energy in large quantities for an electrical power grid is not trivial, especially for AC electricity power grids. Large amounts of electricity needed by an electrical power grid cannot be stored as electricity in conventional systems, although it may be stored in another form. Therefore, the energy taken from an electrical power supply grid must always be equal to the energy being delivered by the electrical power plants. If this were not the case, the frequency and voltage of the supply grid would deviate from standard values.  
      Pumped storage plants address this problem by storing electrical energy as potential energy. They pump water to an upper reservoir at times of surplus energy on an electrical supply grid-typically, at night. This potential energy is then released through a hydro-electrical generator at times of high demand. Use of hydroelectric turbines allows direct energy conversion to AC electrical power. Electrical DC to AC conversion (used in many conventional solar energy systems) is not required, thereby significantly reducing the complexity, reliability problems, and cost of construction and maintenance, as compared to conventional DC electricity supply systems.  
       FIG. 6A  illustrates a modification of the system of  FIG. 6  which is used for power generation during daylight operations only. In this system, the flow of the working medium (water) is not supplied to a high potential energy reservoir, such as lake  1 , but is directly input into the inlet of the prime mover or turbine  112  to generate power, such as electricity.  
       FIG. 7  is a flowchart of a method of converting thermal energy to another useful form of energy, in accordance with the embodiment of the invention shown in  FIGS. 4-5 . Referring to  FIG. 7 , the method begins at  702 . At  704 , thermal energy is absorbed into an expansion medium, such as a working fluid. At  706 , at least a portion of the expansion medium is vaporized to exert pressure on a storage medium, such as a storage fluid, to displace at least a portion of the storage fluid from a lower potential energy state to a higher potential energy state. This corresponds, for example, to transporting the storage fluid from chamber  116  of containment assembly  130  of the system of  FIG. 6  to the reservoir  110 . At  708 , the portion of the expansion fluid that was vaporized is substantially condensed, corresponding, for example, to condensing a portion of the expansion gas  128  from chamber  122  back to a liquid in condenser  124 . At  710 , a portion of the storage fluid displaced to a higher potential energy state (to reservoir  110 ,  FIG. 6 ) is supplied to at least one turbine to produce a second form of energy. At  712 , substantially the portion of storage fluid from the at least one turbine is supplied to at least one lower potential energy state. The method ends at operation  714 .  
       FIG. 8  illustrates a flowchart of another method in accordance with the invention for converting thermal energy to another form of energy in a pixelized system (such as will be described in more detail in connection with FIGS.  15 A-C) which combines the contributions of multiple energy collector/generator assemblies. The method contemplates a system that uses of one or more expansion and storage media, e.g., fluids, as well as multiple separate components for some system components, such as thermal energy collectors, containment assemblies, condensers, prime movers, etc. The method begins in operation  802 . At  804 , at least one expansion medium (working fluid) is stored in a working fluid reservoir. At  806 , the at least one working fluid is communicated to at least one thermal energy collector to vaporize a portion of the at least one working fluid. At  808 , the vaporized portion of at least one working fluid is communicated into at least one containment assembly, where the portion of the vaporized working fluid exerts pressure on at least one storage medium (fluid) in the at least one containment assembly to transport the at least one storage fluid to at least one higher potential energy reservoir. At  810 , the portion of vaporized at least one expansion fluid from the at least one containment assembly is communicated to at least one condenser, where the vaporized portion of the expansion fluid is condensed and communicated to at least one expansion medium reservoir. At  812 , at least one storage fluid from the least one higher potential energy reservoir is communicated to at least one turbine generator, where another form of energy, e.g., electricity, is generated, and at  814  the at least one storage fluid is communicated from the at least one generator to at least one lower potential energy reservoir. At  816 , the at least one storage media is communicated from the at least one lower potential energy reservoir to the at least one containment assembly, and the method ends at  818 .  
       FIG. 9  is a flowchart of a method of generating energy that is somewhat similar to that shown in  FIG. 7 , except that the method is more precisely focused on  FIG. 6 . The method begins at  902 . At  904 , at least one expansion medium (working fluid) is stored in an expansion medium reservoir. At  906 , the at least one working fluid is communicated to an energy collector. At  908 , the working fluid in the energy collector is vaporized and communicated into a containment assembly at  912 , where the vaporized working fluid exerts pressure on a storage fluid in the containment assembly to transport the storage fluid to a high potential reservoir. At  912 , the vaporized working fluid from the containment assembly is communicated to a condenser where it is condensed. At  914 , the expansion medium from the condenser is communicated to the expansion medium reservoir. Operation  916  is next and includes supplying the storage fluid from the high potential reservoir to a generator where energy is generated. At  918 , the storage fluid from the generator is communicated to a low potential reservoir, and at  920  is communicated to the containment assembly. The method ends at  922 .  
       FIG. 10  illustrates a method of generating electricity, in accordance with the invention. The method begins at  1002 . At  1006 , working fluid stored in a reservoir is transported using gravity to a solar collector where it is vaporized by solar energy. At  1008 , the vaporized working fluid is communicated into a containment assembly, where the vaporized working fluid exerts pressure on a storage fluid in the containment assembly which transports the storage fluid to a high potential reservoir. At  1010 , the vaporized working fluid is communicated from the containment assembly to a condenser where it is condensed by heat transfer to the ambient environment. Operation  1012  is next and includes using gravity to transport the working fluid from the condenser to the working fluid reservoir. At  1014 , the storage fluid supplied from the high potential reservoir to an electrical generator, whereby electricity is generated. At  1016 , the storage fluid is exhausted from the electrical generator to a low potential reservoir, and transported using gravity to the containment assembly at  1016 . The method ends at  1020 .  
       FIG. 11  is diagrammatic view of an embodiment of an energy generation system  100  corresponding to that shown in  FIGS. 4-6 . A reservoir  126  holds an expansion medium, i.e., a working fluid,  127  and may be connected by a pipe  166  to a collector  120 . A valve  146  may control the flow of expansion medium  127  between reservoir  126  and collector  120 . Flow of expansion medium  127  from reservoir  126  to collector  120  may be induced by gravity or pumping. Collector  120  is configured to increase the temperature of the expansion medium flowing through it when exposed a source of energy, such as the sun. Once the temperature of the expansion medium  127  in collector  120  reaches a critical temperature, it undergoes a phase change from a liquid to a vapor. The gaseous expansion medium vapor  128  occupies a larger volume than the liquid expansion medium  127 , and it may be communicated through pipe  164  into a displacement chamber  122  contained in the interior  116  of a containment assembly  130 . A valve  144  may control the communication of vapor  128  from collector  120  to displacement chamber  122 . Significantly, the displacement chamber  122  may be constructed, as with bellows or the like, to increase its volume in response to increasing pressure within the displacement chamber so as to maintain the pressure in the chamber substantially constant. Accordingly, as the vapor  128  expands into displacement chamber  122 , the displacement chamber  122  increases in volume. Pressure exerted by liquid working fluid in chamber  116  on the vapor in expandable displacement chamber  122  causes the vapor to flow through a pressure equalization line  1 . 68  to maintain approximately equal pressure between collector  120  and reservoir  126 . A valve  148  may control the communication between reservoir  126  and collector  120 .  
      When displacement chamber  122  has increased by a predetermined volume, ΔV 1 , expansion medium vapor  128  may be conducted through a pipe  165  to a condenser  124 . A valve  146  may control flow of the vapor  128  between the displacement chamber and the condenser. In condenser  124 , the expansion medium vapor  128  undergoes a phase change from a vapor  128  to a liquid  127 . In undergoing this phase change from vapor to liquid, the expansion medium vapor  128  decreases by a predetermined volume ΔV 2  in the condenser, and displacement chamber  122  also decreases by about the same predetermined volume ΔV 2 . The expansion liquid  127  may flow to reservoir  126  through a pipe  167  between condenser  124  and reservoir  126  may be controlled by a valve  147 . The flow of condensed expansion liquid  127  from condenser  124  to reservoir  126  may be induced by gravity or pumping.  
      Containment assembly  130  also contains a storage medium, e.g., a fluid,  129  in the containment assembly interior  116 . As displacement chamber  122  expands inside of containment assembly interior  116 , pressure on storage medium  129  causes it to be displaced and communicated by a pipe  163  to a high potential energy reservoir  110 . A valve  143  may control the communication of storage medium  129  between the containment assembly interior  116  and the reservoir  110 . Subsequently, the storage medium  129  may then be communicated from the high potential energy reservoir  110  through a pipe  169  to a prime mover  112 , such as a generator, a turbine, or other power producing device. A valve  149  may control the communication of storage medium between the high potential reservoir  110  and prime mover  112 . Storage medium  129  may then be communicated through a pipe  161  from the prime mover to a low potential reservoir  114 . A valve  141  may control the communication of the storage medium between the prime mover and the low potential reservoir. Storage medium  129  may then be communicated through a pipe  162  from the low potential reservoir  114  to the interior  116  of containment assembly  130 . A valve  142  may control this flow.  
      As discussed above, the flow of expansion medium  127  from reservoir  126  to collector  120  may be induced by gravity or pumping. Placing the reservoir  126  at a higher gravitational potential than the collector  120 , i.e., at a higher height than the collector, enables the expansion medium  127  to flow down under the influence of gravity from the reservoir  126  to the collector  120 . Pressure equalization line  168  prevents a vacuum from disrupting the flow of expansion medium between reservoir  126  and collector  120  by equalizing the pressure between reservoir  126  and collector  120 .  
      High potential reservoir  110  is preferably placed at an elevation or height Hi above the containment assembly  130  so that the work required to move the storage medium  129  from containment assembly  130  to the high potential reservoir  110  is imparted to the storage medium as potential energy. At such elevation H 1 , the storage medium in the high potential reservoir exerts a pressure P 1  through pipe  163  at containment assembly  130 . The pressure P 1  is determined by the height H 1  of high potential reservoir  110  above containment assembly  130 . For example, when the storage medium  129  is water, the pressure P 1  is about 0.43 pounds per square inch for each foot of height H 1 . For a height H 1  of about 1300 feet, the pressure at the containment assembly  130  will be about 560 pounds per square inch (560 psi).  
      The minimum amount of work, W, required to raise a predetermined mass M 1  of storage medium  129  from the containment assembly  130  to the high potential reservoir  110  is simply the mass M 1 , times the height H 1 , times gravitational acceleration g, or: 
 
 W=M 1* g*H 1   (1) 
 
      The storage media  129  in high potential reservoir has a potential energy equal to the work W. This potential energy is available for conversion to some other form of energy, for example electricity. For example, a portion of this potential energy may be used to operate the prime mover  112 . The prime mover  112  may be placed a distance H 2  below the high potential reservoir  110 , so that the amount of potential energy E available to operate generator  112  may be calculated as the predetermined mass M 2  of the storage medium released to the prime mover  112 , times the distance H 2 , times g or: 
 
 E=M 2* g*H 2   (2) 
 
      While a generator is an example of a prime mover that may be used, other forms of energy conversion apparatus may also be utilized to advantage. For example, mechanical energy may be extracted from the potential energy E in a variety of ways well known in the mechanical and hydraulic arts.  
      Moreover, storage medium  129  could also be used to raise a mass other than the storage medium  129  to the high potential reservoir  110 . For example the storage medium could be employed to provide power other types of mechanical and hydraulic apparatus adapted to lifting a discrete object, or solid mass (such as rock or grain, for example) to the high potential reservoir.  
      As indicated above, the temperature of expansion medium  127  rises in collector  120  until the critical temperature of the expansion medium is reached. The critical temperature of a fluid is the temperature at which the fluid will undergo a phase change from fluid to vapor at the ambient pressure. For example, the critical temperature of a common refrigerant R-410A is about 150 degrees F. at an ambient pressure of 550-600 psi. The ambient pressure in the interior  116  of containment assembly  130  may be the pressure P 1 , as determined by the elevation H 1  of the high potential reservoir  110  above the containment assembly  130 . As indicated, when elevation H 1  is about 1300 feet the pressure P 1  at the containment assembly interior will be about 560 psi and the R-410A would undergo a phase change from fluid to vapor at about 150 degrees F. At the critical temperature, additional heat energy (for example heat energy from solar energy) applied to the collector  120 , causes additional molecules of the expansion medium to undergo the transition from fluid to vapor without increasing the temperature of the expansion medium above the critical temperature. R-410A is given by way of example as a suitable expansion medium, but many other types of expansion media may be used, as previously described.  
      As discussed above, when displacement chamber  122  has expanded to a predetermined volume, the expansion medium vapor  128  in displacement chamber  122  may be conducted through a pipe  165  to a condenser  124 . Condenser  124  may be maintained at a temperature substantially below the temperature of the collector  120  during the expansion of the expansion medium fluid into a vapor. At a lower temperature, the expansion medium will condense at a substantially lower pressure. Storage medium  129  in low potential reservoir  114  may be used to displace expansion medium vapor  128  from displacement chamber  122  through pipe  165  into condenser  124 . A pressure P 2  may be exerted through pipe  162  to compress displacement chamber  122  and exert a pressure P 2  on the expansion vapor therein. The pressure P 2  may be determined by the elevation H 3  of the low potential reservoir  114  above the containment assembly  130 . For example, when elevation H 3  is about 230 feet, pressure P 2  may be about 100 psi. At about 90-120 psi, R-410A vapor will condense at about 50 degrees F., for example.  
      The available work, Wa, from energy system  100  is the change in volume ΔV 1  times the pressure P 1  minus the change in volume ΔV 2  times the pressure P 2  or: 
 
 Wa=P 1*Δ V 1− P 2*Δ V 2   (3) 
 
 When ΔV 1 =ΔV 2 , the available work is: 
 
 Wa=ΔV 1( P 1− P 2)   (4) 
 
      As discussed above, the flow of expansion medium  127  from condenser  124  to reservoir  126  may be induced by gravity or pumping means. Placing the condenser  124  at a higher gravitational potential than reservoir  126 , that is above the reservoir  126 , enables the expansion medium  127  to flow down under the influence of gravity from the condenser to the reservoir  126 .  
      In an example of operation of the energy generator system  100 , solar energy may be used during the day to cause expansion of an expansion fluid  127  to an expansion vapor  128 . The expansion vapor may be used in the containment assembly  130  to pump water during a pumping step up to high potential reservoir  110 , for example a lake at a high level. The water may then generate electricity by running back down through a turbine during an energy generation step to low potential reservoir  114 , for example to a lake at a lower level. At night, when the condenser  124  has been cooled by giving off energy in the form of radiation to the sky, water in the low potential reservoir  114  may then be used to recompress the expansion vapor  128  into an expansion fluid  127  in the condenser  124 . In this case, energy may be input into the system  100  during the daytime from a high energy source, e.g., solar radiation. Energy may be output from the system  100  during the nighttime into a low energy sink, as by radiation to a black body (e.g., into space). The energy source is the sun, and the energy sink is space. The energy generator system  100  extracts useful work or electricity by moderating the flow of energy from the high-energy source to the low energy source.  
      Table 1 below illustrates examples of valve states for the system  100  of  FIG. 11  during a pumping phase, an energy generation phase and a recompression phase (either warm or cold). During conversion of heat energy to potential energy (the pumping phase), valves  142 ,  145 , and  147  may be closed while valves  143 ,  144 , 146 , and  148  may be open. During the day, solar energy heats the collector  120  and the expansion medium  127 , for example R-410, expands to an expansion vapor at about 150 degrees F. at a pressure of about 550-600 psi. Expanded vapor  128  flows through pipe  164  and open valve  144  into displacement chamber  122 . Valve  145  may be closed, thus forcing displacement chamber  122  to expand inside containment assembly  130 . As expansion medium  127  is used up by expansion into vapor  128 , the expansion medium  127  may be replaced from reservoir  126  through pipe  166  by opening valve  146 . Placing reservoir  126  above collector  120  enables gravitational flow of expansion medium  127  downhill from reservoir  126  to collector  120  through valve  146 . Valve  148  permits pressure equalization through pipe  168  between collector  120  and reservoir  126 , thus enabling flow from reservoir  126  to collector  120 . Expansion of the displacement chamber  122  displaces the storage medium  129 , for example water. The water is forced up hill to the high potential reservoir  110  through pipe  163  and valve  143  by the expansion of the working fluid to vapor. Valves  143  and  146  may be partially opened to control pressures in the containment assembly  130 , and may be adjusted to optimize the work extracted in lifting water to the high elevation lake  110 . Once in the lake (high potential reservoir  110 ), the water may be released through valves  141 ,  149 , as desired, to generate electricity. Thus the generation step may be independent of, or coincident with, either the pumping step or the recompression step. Valves  141  and  149  may be opened or closed as the generator may or may not be operated during the pumping step. The following Table  1  illustrates the valve states during different phases of operation of system  100 .  
                           TABLE 1                                      Expansion               medium/vapor   Storage Media           valves state                                                         144   145   146   147   148   141   142   143   149                                                                 Pumping step   1   0   1   0   1   X   0   1   X       Energy generation step   X   X   X   X   X   1   X   X   1       Recompression step (warm)   0   1   0   1   0   X   1   0   X       Recompression step (cold)   0   1   X   1   X   X   1   0   X                 state: 1 = open; 0 = closed; X = open or closed             
 
      During the energy generation phase, as illustrated in Table 1 the expansion medium, water for example, may be released through pipe  169  by opening valve  149  and valve  141 . Valve  149  may be redundant but it is desirable because it permits retaining the water in the lake with minimal pressure head on the generator  112 . Valves  142 ,  143 ,  144 ,  145 ,  146 ,  147 , and  148  may be open or closed during the energy generation step. The water may flow through generator  112 , for example, a turbine, to generate electricity. Alternatively, the water may be used to perform other forms of work. Open valve  141  permits water to flow through pipe  161  to low potential reservoir  114 , for example, a low level lake. The water may be stored in the low potential reservoir until time for recompression of the expansion medium vapor  128  back into the expansion medium  127  during the recompression step.  
      During the recompression phase, as illustrated in Table 1, valves  142 , 145 , and  147  may be open, and valves  143  and  144  may be closed. Valves  141  and  149  may be either open or closed. Valves  146  and  148  may be open or closed when the recompression step is performed under cold conditions, that is when the temperature of collector  120  is about the temperature of the condenser  124  or lower. When recompression is done under warm conditions, that is when the temperature of collector  120  is above the temperature of condenser  124 , then valve  146  and  148  are preferably closed. Recompression may take place when the condenser  124  reaches a substantially lower temperature than the pumping phase temperature, for example, about 50 degrees F. At about 50 degrees F R-410A may be recompressed at a pressure of about 90-120 psi. A pressure of about 90-120 psi may be exerted by a pressure head of about 200 feet. Therefore, the low level reservoir may be located about 200 feet above the containment assembly  130 . The recompression takes place as water from the low potential reservoir  114  flows down to the containment assembly  130  through pipe  162  and valve  142 . The water urges the expansion medium vapor  128  through pipe  165  and valve  145  to the condenser  124 . The condenser is preferably maintained at about 50 degrees F. In the condenser the expansion medium vapor  128  condenses to the expansion medium fluid  127 . Condensation of the expansion medium vapor  127  to the expansion medium fluid  128  creates a low-pressure region in the condenser  124  that draws more expansion medium vapor  128  into condenser  124  for condensation. Heat energy is released by the condensation process.  
      The condenser  124  may dissipate this heat energy through a number of methods. For example, the recompression may be conducted at night when the ambient temperatures are substantially lower than during the daylight hours. Such substantially lower temperature may be sustained by radiation from the condenser into a black body, such as a clear night sky, i.e., into space. The condenser may also be placed in a body of water, such as a lake, for example. Such bodies of water may be sized to afford a good sink and accept large quantities of heat energy from the condenser  124 , thus advantageously maintaining the condenser  124  at a substantially constant temperature. Moreover, bodies of water make excellent radiators into the clear night sky. In accepting heat energy from the condenser  124  and radiating it into a black body, such as space, bodies of water act as heat conductors to conduct heat from the condenser  124  to space. An example of a large body of water or lake may be the low potential reservoir  114 .  
       FIG. 12  is diagrammatic view of one embodiment of a solar pumping system  200 . The system of  FIG. 12  may be substantially similar to the system  100  of  FIG. 11 , except that instead of using a storage medium or fluid  129 , the system may be used to communicate a working pump fluid  229 , e.g., water, from a low position reservoir  214  to a high position reservoir  210 , where the pump fluid may be stored or use, e.g., for irrigation, and the system  200  does not have a return path through a prime mover  112  (and the associated components) for energy generation as does the system  100  of  FIG. 11 .  
      The operation of the system  200  of  FIG. 12  may be substantially the same as that described above for the system  100  of  FIG. 11 . As with system  100 , the pump fluid  229  may also provide power to a mechanical and hydraulic apparatus, for example, to lift a discrete object or a solid mass (such as rock or grain, for example) to the location of high position reservoir  210 .  
      Low position reservoir  214  may be any source of pump fluid  229  which it is desired to pump to a higher location. Preferably, since pump fluid is not returned to low position reservoir  214 , the low position reservoir  214  may be a source of pump fluid that is functionally unlimited, such as a lake, an aqueduct, or a river.  
      The valve states during operation of the system  200  may be the same as shown in Table 1, except that there are no valves  141  and  149  in system  200  since there is no return path from the high position reservoir.  
       FIG. 13  is a diagrammatic view of a first embodiment of a containment assembly  130  that may be employed in systems in accordance with the invention.  FIG. 13  illustrates the expansion medium vapor  128  in the displacement chamber  122  separated from the storage medium  129  by a piston  310 . Piston  310  may be a mechanical piston, as is well known in the mechanical arts, or a layer of fluid adapted to form a barrier between storage medium  129  and expansion medium vapor  128 , the fluid being non-miscible with the storage medium  129  and the expansion medium vapor  128 . A suitable fluid layer piston, where the storage medium  129  is water, is an oil that is non-miscible with water.  
      As illustrated in Table 1 above, during the pumping step of the cycle, valves  143  and  144  are open while  142  and  145  are closed. Expansion medium vapor  128  may be admitted to the interior  122  of the displacement chamber at a higher pressure than the pressure on the storage medium  129 , and the storage medium is displaced and exits through pipe  163  and valve  143 . During the recompression step, valves  143  and  144  may be closed while valves  142  and  145  may be open to control flow through pipes  162 ,  163 ,  164 , and  165 . Pressure from the low potential reservoir  114  drives piston  310  against the expansion medium vapor  127  in displacement chamber  122 . Displacement chamber  122  decreases in volume, and the expansion medium vapor  128  exits the displacement chamber through pipe  165  and valve  145 . As described above, the movable piston and the operation of the containment assembly advantageously insures that the expansion and recompression of the expansion medium is accomplished at substantially constant pressure.  
       FIG. 14  is a diagrammatic view of another embodiment of a containment assembly  130  that may be used in the invention.  FIG. 14  illustrates the expansion medium vapor  128  in the displacement chamber  122  which is separated from the storage medium  129  by a moveable piston  310 . As with  FIG. 13 , piston  310  may be a mechanical piston or a layer of non-miscible fluid adapted to form a barrier between storage medium and the expansion medium vapor. The piston  310  separates the expansion medium vapor  128  from the storage media  129  and preventing mixing of the fluid  129  with the vapor  128 . When piston  310  is a layer of fluid, such as oil, the piston has the added advantage of being capable of sealing complex or irregular interior surfaces of the containment assembly.  
      Tube  170  may communicate the storage medium  129  from the containment chamber  130  through a single orifice in the containment chamber wall to valves  142  and  143 , thus preserving the structural integrity of containment chamber  130 . Similarly, tube  171  may communicate the expansion medium vapor  128  to the containment assembly through pipes  164  and  165  controlled by valves  144  and  145 , respectively.  
      Pixelization of Energy Collection for Energy Concentration  
      Conventional thermal energy conversion systems typically concentrate the thermal energy in one location so that one central converter can transform the thermal energy into another useful form of energy such as electricity. The invention advantageously enables a different approach, referred to herein as “pixelization”, whereby multiple dispersed energy conversion systems (or portions thereof) such as previously described may be combined into a single system that effectively sums the individual contribution of each individual system. Pixelization in accordance with the invention may accomplished by moving storage media (e.g., water, or another storage media) from point to point rather than by moving the thermal energy to a central site. This movement of the storage medium from many dispersed collectors to a central collection site, for example, allows for the collected energy to be concentrated by adding the output of multiple fluid pumps of lower capacity, and reduces the need to transport heat over large distances to a central evaporator. Multiple evaporators can be positioned close to the solar collectors. Also, pixelization allows for the full displacement of a given chamber&#39;s working medium by hot gaseous expansion of the medium, and the use of the hot gaseous expansion to preheat liquid expansion medium that will be boiled off (converted to vapor, as described above) to evacuate other chambers of their working medium. Using several chambers in sequence will allow almost all of the heat energy that was used to raise expansion medium in a first chamber to the boiling point to be captured and reused, thus increasing system efficiency substantially. Also, because the chambers that have been used for heat exchange have a lower pressure, they can be partially refilled with working medium and reheated to drive even more working medium to a higher potential energy point.  
       FIG. 15A  is a block diagram of a system for the pixelized collection of energy, in accordance with the invention. A plurality of energy generator assemblies  100 ′ a - n  may move a storage medium through a manifold  510  to a high potential energy reservoir  110 . Moreover, the transformation of thermal energy to another form of energy can be performed by multiple units at dispersed localized locations, and the transformed energy (e.g., the movement of a storage medium, such as water, to a higher elevation) from the dispersed units may be transported and added together at one or more other locations to take advantage of economies of scale in the transformation of potential energy into electrical energy, or in pumping or refrigeration applications.  
      A principal advantage with this system is that the losses associated with the transportation of low heat differential masses are minimized, and the savings are transformed into the increase in potential energy of the storage medium. Individual pixelization units can also be run using standard Rankine cycle pumps. Moreover, standard Rankine cycle pumps can be used in a first group of pixelization units, and modified Rankine cycle pumps of the invention, such as shown in  FIG. 2 , can be used in a second group of pixelization units and their energy contributions combined.  
       FIG. 15B  is a diagrammatic view of an embodiment of a pixelized energy generation system in accordance with the invention that comprises a plurality of two or more interconnected energy generator assemblies  100 ′ a - n  that have a common manifold  510  for receiving and combining the pump storage media from the individual generator assemblies  100 ′ a - n . The energy generator assemblies  100 ′ a - n  may be placed in dispersed locations or collocated in an array. Each of the energy generator assemblies  100 ′ a - n  produces a partial contribution to the total combined energy from the group of generator assemblies which is combined at the manifold  510  with the partial contributions from other generator assemblies. The partial energy generated by each of the energy generator assemblies  100 ′ a - n  may be proportional to the area of sunlight striking the energy generator assembly. The manifold  510  may communicate the combined energy to a high potential reservoir  110  through a pipe  163 , where the contribution of each energy generator assembly  100 ′ a - n  may be accumulated.  
       FIG. 15C  is a diagrammatic illustration of an alternative embodiment of an energy generation system similar to that shown in  FIG. 15B , except that instead of a common manifold, the partial contributions of the individual energy generator assemblies  100 ′ a - n  are separately communicated to the high position reservoir  110  by separate lines  163   a - n , each controlled by a corresponding valve  143   a - n . The system of  FIG. 15C  is more appropriate where the various energy generator assemblies  100 ′ a - n  are dispersed to different locations, and it is more efficient to separately provide storage media for the individual assemblies to the reservoir than to combine the storage media in a common manifold as in  FIG. 15B   
      As discussed above, in both of the embodiments of  FIGS. 15B  and C, storage media  129  may released through a generator  112  to flow to a low potential reservoir  114 , and the storage media from the low potential reservoir  114  through pipe  162  and distributed through manifold  514  through valves  142   a - n  to energy assemblies  100 ′ a - n . Thus, energy generator assemblies  100 ′ a - n  may advantageously be a large number of small generator systems distributed over a large area, and may be built on a small-scale with the economy of large-scale generators and reservoirs. This permits concentration of partial energy from many small energy generator assemblies  100 ′ composed of modest part sizes optimized to exploit economies of mass production, and that may not even be in line of sight of each other. For example, energy generator assemblies  100 ′ a - n  that are separated by buildings or terrain such as terrain including one or more hills or bluffs may still contribute energy to the system through plumbing connected to the reservoir  110 . Thus, energy generator assemblies  100 ′ a - n  are capable functioning in terrain where mirror systems for concentrating solar energy might be impractical because the line of sight is blocked. Moreover, energy generator assemblies  100 ′ a - n  that are spread over a large or irregular area, beyond the practical range of a lens concentrating system, may still contribute substantial energy to the system through plumbing connected to the reservoir  110 .  
       FIG. 16  is a flowchart of a method of converting thermal energy to another useful form of energy, in the systems of FIGS.  15 A-C. The method begins at  1602 . At  1604 , thermal energy may be absorbed into an expansion medium at a plurality of energy generator assemblies. At  1606 , at least a portion of the Expansion medium may be vaporized to exert pressure on a storage medium to displace at least a portion of the storage medium at the plurality of energy generator assemblies. Operation  1608  is next and includes condensing substantially the portion of the expansion medium that was vaporized. At  1610 , the displaced portion of the storage media from the plurality of energy generator assemblies may be collected. At  1612 , the displaced portion of the storage medium displaced to a higher potential energy state is supplied to power at least one turbine to produce a second form of energy. At  1614 , substantially the portion of storage media from the at least one turbine is supplied to a lower potential energy state. The method ends in operation  1616 .  
       FIG. 17  is a diagrammatic view of a fractal solar energy collector array that may be used in the above systems for the pixelized collection of energy. The fractal solar energy collector  1710  may comprise arrays of a plurality of solar energy collectors  1702 , arranged in a fractal pattern of, for example, sixteen collector groups  1704 , arranged in a fractal pattern of, for example, sixty-four collector groups  1706 , all connected to a fractal expansion medium transport system  1708 .  
      A fractal solar energy collector array as shown in  FIG. 17  may be advantageously dispersed across a landscape for the pixelized collection of energy, and connected to natural or man-made reservoirs or lakes for the storage and release of storage medium through one or more generators, or in the case of pumping systems, for the transport of water, for example, through aqueducts or the like.  
      Refrigeration and Generation of Cryogenic Fluids  
      As described in the foregoing, the invention may use a prime mover such as turbine or a generator to transform thermal energy to a second form of energy. The turbine may comprise a compressor in a refrigeration or air conditioning system, thus affording solar refrigeration and air conditioning systems, or may be used as part of a multiple stage refrigeration system to generate cryogenic fluids (e.g., liquid nitrogen, liquid air, liquid oxygen, etc.). The compressor can be a conventional closed-loop heat pump arrangement to compress a gas which is allowed to expand at another location and absorb thermal energy for the expansion to cool an object (e.g., the inside of a refrigerator, or an equivalent space). Cryogenic temperatures can be reached by a multiple stage implementation of heat pumps, and the cryogenic fluids (e.g., liquid nitrogen, liquid oxygen, etc.) may be used locally or transported to other locations for use in any of a variety of different applications (e.g., transportation, energy generation, various chemical processes, or equivalents).  
      As will be appreciated, while the invention has been described with reference to preferred embodiments, various changes in these embodiments may be made without departing from the spirit and principles of the invention, the scope of which is defined in the appended claims.