Abstract:
The present invention relates to methods and apparatuses for allocating amounts of energy for prosumers, wherein the prosumers provide minimum and maximum amounts of energy for a future interval of time and the respective amounts of energy from the prosumers are generated in such a manner that, on the one hand, a relative position of the amount of energy within an interval for the particular prosumer, as defined by the minimum amount of energy and the maximum amount of energy, assumes an identical value for all prosumers and, on the other hand, a sum of the amounts of energy from all prosumers produces a value of zero. The invention can be used in the distribution of amounts of energy in a power supply system having conventional energy producers and energy consumers as well as in novel participants in the power supply system which can both consume and provide energy, for example an electric vehicle.

Description:
[0001]    The present application is a §371 nationalization of PCT Application No. PCT/EP2012/060141, filed May 30, 2012, and designating the United States, which, in turn, claims the benefit of DE 102011078045.9, filed on Jun. 24, 2011, the entire disclosures of which are incorporated by reference herein. 
     
    
     BACKGROUND 
       [0002]    The present embodiments relate to methods and devices for allocating amounts of energy for prosumers in an electric grid. 
         [0003]    The progressive expansion of renewable energies is leading to an increasing decentralization of power generation. In addition, it is becoming increasingly more difficult to forecast an amount of energy to be expected or to be generated because of potentially larger fluctuations in energy in the case of renewable energies (e.g., because of weather dependence). 
         [0004]    This change may be taken into account by introducing smart electric grids that have in addition to the actual electric grid a communication network for exchanging information and for controlling decentral units. Power generation and power consumption may thus be regulated within certain limits by appropriately smart generators and consumers connected to the communication network. This is accompanied by an increasing complexity in the balancing of power generation and power consumption in the electric grids. The control of this complexity, and the suitable balancing of power generation and power consumption are a precondition for meeting the energy requirements of the consumers in the grid, and for providing grid stability. 
         [0005]    In addition to the traditional power generators and power consumers, there are also new types of participants in the electric grid that may store the energy and also output the energy such as, for example, electric cars. These traditional power generators and consumers and new types of participants are referred to as prosumers. The new types of participants may absorb energy into their batteries at night when there is mostly an excess of energy, and output the energy again at peak times (e.g., in the morning between 6:00 and 9:00). 
       SUMMARY AND DESCRIPTION 
       [0006]    The scope of the present invention is defined solely by the appended claims and is not affected to any degree by the statements within this summary. 
         [0007]    The present embodiments may obviate one or more of the drawbacks or limitations in the related art. For example, methods and devices for allocating amounts of energy that facilitate adaptation of power consumption and power generation in an electric grid and enable the allocation of the amounts of energy per prosumer are provided. 
         [0008]    In one embodiment, a method for allocating an amount of energy per prosumer includes determining a maximum amount of energy and a minimum amount of energy for each prosumer. The method also includes generating the respective amount of energy such that a relative position of the amount of energy is produced within an interval, defined by the minimum amount of energy and the maximum amount of energy, of the respective prosumer such that the relative positions of the prosumers assume an identical value. The respective amount of energy is also generated such that a sum of the amounts of energy yields a value of zero. 
         [0009]    “Prosumer”—may be a power generator that provides only energy in an electric grid, a power consumer that consumes only energy from an electric grid, and a new type of participant that may both store energy and output energy. 
         [0010]    One or more of the present embodiments are advantageous because amounts of energy are considered instead of power values. This permits an inherent imaging with an account of storage capacities at the prosumers. In addition to controllable generators and consumers, it is the responsibility of storage capacities that the minimum amounts of energy to be drawn do indeed turn out to be lower than the maximum amounts of energy that may be drawn. 
         [0011]    This provides that when energy is being allocated, each prosumer has a margin that the prosumer may utilize in the context of allocating the amounts of energy to the prosumers. The consideration of minimum and maximum amounts of energy per prosumer dictates for each prosumer the definition of a band of amounts of energy. The amount of energy actually allocated to the respective prosumer is to fall within this band of amounts of energy. 
         [0012]    In order to provide that the amounts of energy are adjusted between consumption and generation, the sum of the amounts of energy is to yield a value of zero over all prosumers after allocation. The electric grid is balanced in this state, and there is no oversupply or undersupply of energy. 
         [0013]    Generating the respective amount of energy such that a relative position of the amount of energy within an interval, defined by the minimum amount of energy and the maximum amount of energy, of the respective prosumer assumes an identical value for all prosumers provides that each prosumer is treated identically by comparison with other prosumers. The result of this is that none of the prosumers respectively receives an amount of energy that corresponds either to a maximum or to a minimum amount of energy of the prosumer. Consequently, capacities that the prosumers may equalize by absorbing or outputting energy are available for short-term fluctuations in the electric grid. However, this conclusion is valid only for prosumers having minimum and maximum amounts of energy that are unequal. 
         [0014]    The following acts are carried out in a first embodiment of the method. A maximum total amount of energy is generated by summing the maximum amounts of energy, and a minimum total amount of energy is generated by summing the minimum amounts of energy. A first amount of energy is generated by forming the difference between the maximum total amount of energy and the minimum total amount of energy. A respective second amount of energy is generated per prosumer by forming the difference between the respective maximum amount of energy and the respective minimum amount of energy. An energy factor is generated per prosumer by multiplying the respective second amount of energy by the reciprocal of the first amount of energy, and the respective amount of energy is generated by adding the respective minimum amount of energy and the product of an absolute value of the minimum total amount of energy and the respective energy factor. 
         [0015]    These acts describe a first embodiment of the method considering intervals of the prosumers defined by the respective minimum and maximum amounts of energy. These acts are characterized by a simple and cost-effective ability to be executed. 
         [0016]    The following acts are carried out in a second alternative variant embodiment. A maximum total amount of energy is generated by summing the maximum amounts of energy. A minimum total amount of energy is generated by summing the minimum amounts of energy. An energy ratio is generated by multiplying the maximum total amount of energy by the reciprocal of the minimum total amount of energy. An intermediate value per prosumer is generated by subtracting a product of the energy ratio and the respective minimum amount of energy from the respective maximum amount of energy. The respective amount of energy per prosumer is generated by multiplying the respective intermediate value by the reciprocal of a subtraction of the energy ratio from a value of one. 
         [0017]    These acts describe a second alternative exemplary embodiment of the method. In this case, the respective amounts of energy are determined with the aid of the energy ratio by multiplying the maximum total amount of energy by the reciprocal of the minimum total amount of energy. This second alternative exemplary embodiment is also distinguished by a simple ability to be implemented and executed. 
         [0018]    In a development of the method, the allocation of the amounts of energy is respectively carried out for a future time interval. It is thereby provided that changes in the behavior of the prosumer may be taken account of, and thus an optimization of a provision of amounts of energy may be taken account of. In addition, the stability of the entire grid is thereby improved, since fluctuations in the power generation and power consumption may be reacted to. 
         [0019]    In a development, a length of the future time interval is set equidistantly. A simple applicability of the method is thereby provided for future time intervals. 
         [0020]    As an alternative to this, the length of the future time interval may be set such that in the case of an increase in a difference between maximum and minimum total amounts of energy of a current time interval and a difference between maximum and minimum total amounts of energy of a time interval earlier than the current time interval, the length of the future time interval is dynamically adapted (e.g., shortened) by a comparison of the length of the current time interval. 
         [0021]    As a result, in the event of a drifting apart from one another of the minimum and maximum total amounts of energy, which indicates, for example, a relatively high uncertainty in a prediction of the power consumption to be expected, the future time interval for which the amounts of energy of the prosumer are to be fixed is changed (e.g., shortened). The result of this is an improved balancing of the allocation of the amounts of energy, and thus also an improved stability of the electric grid. 
         [0022]    The following acts are carried out in a development. A cost function is assigned per prosumer. The respective cost function specifies costs for values of the amounts of energy within the minimum amount of energy and the maximum amount of energy of the respective prosumer. A first and second agent are selected from the set of the prosumers such that the cost function of the first agent has a slope of maximum absolute value, and the cost function of the second agent has a slope of minimum absolute value. The maximum and the minimum slope refer respectively to a slope of the respective cost functions in the amount of energy associated with the agent. New amounts of energy of the first and second agents are generated such that a differential value between the respective amount of energy and the respective new amount of energy of the first agent becomes identical to a differential value between the respective new amount of energy and the respective amount of energy of the second agent. The new amounts of energy of the first and second agents are respectively selected within the minimum amount of energy associated with the first and second agents and the associated maximum amount of energy. A sum of the respective costs of the new amounts of energy is smaller than a sum of the respective costs of the amounts of energy of the first and second agents. 
         [0023]    A cost reduction in the allocation of amounts of energy of the prosumers under consideration is achieved by this development. The allocated amount of energy of a prosumer who registers a high cost increase in the event of a rise in an amount of energy is reduced in this case. In order to keep the power consumption balanced out in relation to power generation in the electric grid (i.e., the sum of the amounts of energy over all prosumers is zero), the reduced amount of energy is made available to another prosumer. The increase in the amount of energy causes a slight cost increase for the other prosumer. A local displacement of the allocated amounts of energy thereby takes place, but the consumption of the amount of energy is still balanced out against the generation of the amount of energy. In addition, the costs in the overall electric grid may be reduced. 
         [0024]    This development may be supplemented by replacing the amounts of energy of the prosumers represented by the first and second agents by the new amounts of energy (E1W, E2W) and repeating the acts of the previous development. Cost optimization in the allocation of amounts of energy may thus be provided in a heuristic way. 
         [0025]    One or more of the present embodiments relate to a device for allocating an amount of energy per prosumer. The device includes a first unit for determining a maximum amount of energy and a minimum amount of energy for each prosumer. The device also includes a second unit for generating the respective amount of energy such that a relative position of the amount of energy is produced within an interval, defined by the minimum amount of energy and the maximum amount of energy, of the respective prosumer such that the relative positions of the prosumers assume an identical value, and a sum of the amounts of energy yields a value of zero. 
         [0026]    The method may thus be implemented and executed in accordance with the previously described advantages. Further units may implement and execute developments. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0027]      FIG. 1  shows a flowchart and the structure of a device for carrying out the method in a first variant; 
           [0028]      FIG. 2  shows an overview of various amounts of energy for an exemplary embodiment; 
           [0029]      FIG. 3  shows a flowchart and the structure of a device for carrying out the method in a second variant; 
           [0030]      FIG. 4  shows cost functions for illustrating the costs per respective value of the amount of energy; and 
           [0031]      FIG. 5  shows a flowchart and the structure of a device for carrying out the method in a third variant. 
       
    
    
     DETAILED DESCRIPTION 
       [0032]    Elements having the same function and mode of operation are provided with the same reference symbols in the figures. 
         [0033]      FIG. 1  shows a flowchart for carrying out one embodiment of a method for allocating amounts of energy. 
         [0034]    By way of example, in act S 1 , prosumers P1, . . . , P5 use a central unit to request respective minimum amounts of energy EN1, . . . , EN5 and maximum amounts of energy EX1, . . . , EX5 (see arrow PFL). The respective minimum and maximum amounts of energy per prosumer in an example are shown in  FIG. 2 . 
         [0035]    In general, the maximum amount of energy defines an amount of energy that a prosumer may consume the most in a time interval or may minimally produce. In a way similar thereto, the minimum amount of energy defines an amount of energy that a prosumer may consume the least in a time interval or may maximally produce. Negative values of amounts of energy are available in  FIG. 2  for providing amounts of energy, and positive values of amounts of energy are available for consuming amounts of energy. In general, negative values may also be used for consumption together with positive values for production. 
         [0036]    In act S 2 , the respective amounts of energy E 1 , . . . , E 5  are generated such that a relative position R 1 , . . . , R 5  of the amount of energy within a time interval, defined by the minimum amount of energy and the maximum amount of energy, of the respective prosumer assumes an identical value for all prosumers, and a sum of the amounts of energy yields a value of 0. Special embodiments of the act S 2  are illustrated below with the aid of two variant embodiments. 
         [0037]    After provision of the respective amounts of energy, the state diagram is terminated in the END state. 
         [0038]    The method is explained in more detail below with the aid of a first exemplary embodiment. For example, in this case, there is an examination of processing acts S 21 , S 22  that, in  FIG. 1 , are sub-acts of the act S 2 .  FIG. 3  shows these processing acts. 
         [0039]      FIG. 2  shows the minimum amounts of energy and maximum amounts of energy per prosumer. The amounts of energy are specified, for example, in kilowatt hours (kWh). Positive values correspond, for example, to an energy consumption, while negative values correspond to provision of energy (i.e., power production). 
         [0040]    For example, the fifth prosumer P5 with i=5 specifies EN5=10 as minimum amount of energy, and EX5=20 as maximum amount of energy. The fifth prosumer is a pure power consumer. 
         [0041]    The second prosumer P2 is a pure power generator that may provide amounts of energy in the interval EN5=−80 to EX5=−70. 
         [0042]    Particular reference is made to the first prosumer P1, which specifies EN1=−10 as minimum amount of energy, and EX5=10 as maximum amount of energy. This provides that the first prosumer may supply energy as well as to consume energy. 
         [0043]    The prosumer is, for example, an electric car that stores energy via a battery, or may output the energy. 
         [0044]    The maximum total amount of energy EXG is calculated by summing the respective maximum amounts of energy EXi to be 
         [0000]    
       
         
           
             EXG 
             = 
             
               
                 ∑ 
                 i 
               
                
               
                 EXi 
                 . 
               
             
           
         
       
     
         [0045]    EXG=80 in the example in accordance with  FIG. 2 . 
         [0046]    The minimum total amount of energy ENG is calculated by summation of the minimum amounts of energy as 
         [0000]    
       
         
           
             ENG 
             = 
             
               
                 ∑ 
                 i 
               
                
               
                 ENi 
                 . 
               
             
           
         
       
     
         [0047]    ENG=−20 for the example in accordance with  FIG. 2 . 
         [0048]    The formation of the minimum and maximum amounts of energy is carried out by the sub-act S 21 . Further acts of the first or second exemplary embodiment may be accomplished by the sub-act S 22 . 
         [0049]    A first amount of energy ED1 is formed by forming the difference between the maximum total amount of energy EXG and the minimum total amount of energy ENG (i.e., by ED1=EXG−ENG=100). 
         [0050]    In what follows, a second amount of energy ED21, . . . , ED25 is produced for each prosumer by forming the difference between the respective maximum amount of energy EX1, . . . , EX5 and the respective minimum amount of energy EN1, . . . , EN5 (e.g., ED21=EX1−EN1). The respective second amounts of energy are plotted in  FIG. 2  for the computational example. 
         [0051]    An energy factor EF1, . . . EF5 is formed per prosumer by multiplying the respective second amount of energy ED2i by the reciprocal of the first amounts of energy ED1. By way of example, this provides for the third prosumer P3 that EF3=ED23/ED1=40/100=0.40. A further row in  FIG. 2  reproduces the values for the respective energy factor. 
         [0052]    In a further processing act, the respective amounts of energy E 1 , . . . , E 5  are formed by adding the respective minimum amount of energy and the product of an absolute value of the minimum total amount of energy and the respective energy factor. 
         [0053]    The computational formula for this act is therefore: 
         [0000]    
       
      
       Ei=ENi+|ENG|·EFi=ENi−ENG·EFi  
      
     
         [0054]    The resolution of the absolute value results from the fact that the minimum total amount of energy is always negative or zero, since otherwise, equilibrium would not be possible between power consumption and power generation. 
         [0055]    The sum of the determined energy values E 1 , . . . , E 5  is zero. The supply and demand for amounts of energy are therefore balanced out. 
         [0056]    In an alternative second exemplary embodiment, the following subacts are run through in this regard (see  FIG. 3 ). 
         [0057]    An energy ratio EV is generated by multiplying the maximum total amount of energy EXG by the reciprocal of the minimum amount of energy ENG. In other words 
         [0000]    
       
         
           
             EV 
             = 
             
               
                 EXG 
                 ENG 
               
               . 
             
           
         
       
     
         [0058]    EV=80/(−20)=−4 in the present example. 
         [0059]    Intermediate values Z1, . . . , Z5 per prosumer are generated by subtracting a product of the energy ratio EV and the respective minimum amount of energy from the respective maximum amount of energy per prosumer. In other words, 
         [0000]    
       
         
           
             Zi 
             = 
             
               
                 EXi 
                 - 
                 
                   EV 
                   · 
                   ENi 
                 
               
               = 
               
                 EXi 
                 - 
                 
                   
                     EXG 
                     · 
                     ENi 
                   
                   ENG 
                 
               
             
           
         
       
     
         [0000]    For example, Z2=−70−(80*(−80))/(−20)=−70−640/20=−390 for the second prosumer. 
         [0060]    The respective amount of energy per prosumer is formed by multiplying the respective intermediate value by the reciprocal of the subtraction of the energy ratio EV from a value of 1. This provides that 
         [0000]    
       
         
           
             
               Ei 
               = 
               
                 Zi 
                 
                   ( 
                   
                     1 
                     - 
                     EV 
                   
                   ) 
                 
               
             
             , 
           
         
       
     
         [0000]    For example, E 2 =−390/(1−(−4))=−78 for the second prosumer. 
         [0061]    The generated amounts of energy E 1 , . . . , E 5  may be reported back to the prosumers so that the prosumers have, in a time interval to come, the amounts of energy to be consumed or to be provided. 
         [0062]    In a development of the method, a length of a future time interval TN may be set (see act S 3  in  FIG. 3 ). The length of the future time interval may be equidistant in this case. As an alternative thereto, in the case of an increase in a difference between the maximum and minimum total energy of a current time interval TN by comparison with a difference between a maximum and minimum total amount of energy of a time interval TN−1 earlier than the current time interval, the length of the future time interval may be dynamically adapted (e.g., shortened). 
         [0063]    The following illustration shows a minimum and maximum total amount of energy ENG, EXG in kWh for the earlier, current and future time interval, the respective difference EXG-ENG and the length of the respective time interval in ms: 
         [0000]    
       
         
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                   
                   
               
               
                   
                 ENG 
                 EXG 
                 Difference 
                 Length 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 TN-1 
                 −20 
                 100 
                 120 
                   
               
               
                   
                 TN 
                 −40 
                 100 
                 140 
                 55 
               
               
                   
                 TN1 
                   
                   
                   
                 50 
               
               
                   
                   
               
             
          
         
       
     
         [0064]    In this example, the difference increases such that the future time interval is shortened to 50 ms instead of the current 55 ms. 
         [0065]    As a result of this adaptivity of the time interval, the allocation of the respective amounts of energy per prosumer may be adapted to current conditions in the electric grid. In the case of a decrease in the difference between a maximum and minimum total amount of energy between two consecutive time intervals, the result is the closure of a relatively unstable electric grid of lesser flexibility at the individual prosumers with regard to the possibility that the individual prosumers may supply or absorb energy. The use of a relatively short future time interval may effect a stabilization of the electric grid. 
         [0066]    A development of the method using cost functions FC1, . . . , FC5 is illustrated with the aid of  FIG. 4 . This development is also shown in  FIG. 5 , which shows this development by comparison with  FIG. 3  in act S 4 . A cost function FCi (e.g., FC1 for the prosumer P1) specifies costs C (e.g., in euros) that arise in the event of the provision or consumption of amounts of energy. Since the individual prosumers prescribe bands of the amounts of energy that have a maximum and minimum amount of energy, the determination of the amounts of energy for a future time interval may also take account of the cost function. 
         [0067]      FIG. 4  shows, in partial figure (A), a cost function for the prosumer P1 that decreases linearly from (−10; 100) to (0; 50) and then continues to fall linearly from (0; 50) to (20; 45). In this description, the first number of the respective number pair EX thus represents a value of the amount of energy, and the second number of the respective number pair C thus represents the costs for a specific value of an amount of energy. The first prosumer P1 may both supply and absorb amounts of energy. However, the costs for supplying amounts of energy are very high because, for example, when amounts of energy are stored, more energy is to be absorbed than may later be supplied. Thus, a slope in the costs C between the values of the amounts of energy −10&lt;EX&lt;0 is greater in absolute value than in the range of the values of amounts of energy 0&lt;EX&lt;20. In accordance with the exemplary embodiment (see  FIG. 2 ), E 1 =−4 was assigned as the amount of energy to the first prosumer. This results in the costs C=70. 
         [0068]    In partial figure (B) of  FIG. 4 , a cost function is illustrated for the second prosumer P2. The prosumer P2 is a pure power generator that supplies amounts of energy in the band of amounts of energy from −80 to −70. Within this band, the cost function FC2 decreases linearly and runs from (−80; 10) to (−70; 5). By applying the exemplary embodiment in accordance with  FIG. 2 , the prosumer P2 has so far been assigned an amount of energy of E 3 =−78. This corresponds to the costs of C=9. 
         [0069]    From all the prosumers, the one prosumer having a cost function that has the steepest slope in absolute terms in the associated amount of energy is selected. This is the case for the first prosumer, which is therefore denoted below as first agent V1. In addition, the one prosumer having a cost function that has the shallowest slope in absolute terms in the associated amount of energy is selected from all the prosumer. This is the case for the second prosumer, which is therefore denoted below as second agent V2. 
         [0070]    The next act is to determine new amounts of energy E1W and E2W for the first and second agents V1, V2. For example, the new amounts of energy are E1W=−2 for the first agent V1, and the new amounts of energy are E2W=−80 for the second agent V2. The following conditions are to be simultaneously met when fixing the new amounts of energy. 
         [0071]    A first difference value, formed by subtracting the amount of energy E 1  from the new amount of energy E1W, with reference in each case to the first agent, is to be identical to a second difference value formed by subtracting the new amount of energy E2W from the amount of energy E 2 , with reference in each case to the second agent. In the above example, 
         [0000]        E 1 W−E 1=−2−(−4)=2 and  E 2− E 2 W=− 78−(−80)=2.
 
         [0072]    The new amounts of energy E1W, E2W is to respectively lie within the bands of the amounts of energy defined by the minimum and maximum amounts of energy of the respective agents. The term “within” may also be that the new amounts of energy may also be minimum or maximum amounts of energy. This is fulfilled for the new amounts of energy in accordance with the present example. 
         [0000]        E 1 W: − 10&lt;=−2&lt;=20
 
         [0000]        E 2 W: − 80&lt;=−80&lt;=−70.
 
         [0000]    (the symbol “&lt;=” means smaller than or equal to) 
         [0073]    A sum of the respective costs of the new amounts of energy is smaller than a sum of the respective costs of the amounts of energy of the first and second agents. 
         [0074]    Sum of the costs of the new amounts of energy: 
         [0000]        FC 1(−2)+ FC 2(−80)=60+10=70
 
         [0075]    Sum of the costs of the amounts of energy (costs to date): 
         [0000]        FC 1(−4)+ FC 2(−78)=70+8=78
 
         [0076]    This condition is therefore fulfilled. 
         [0077]    In a development in this regard, the amounts of energy are replaced by the new amounts of energy of the respective prosumers. The acts of selecting the agents, and the calculation of new amounts of energy for further prosumers are repeated iteratively until either there is a lasting improvement under prescribable savings in costs, or until no two prosumers that fulfill the conditions are found.  FIG. 5  shows this development by a dashed arrow around act S 4 . 
         [0078]    The methods presented and the associated developments may be executed by a device DEV, a first unit M 1  being capable of implementing and executing act  51 , a second unit M 2  likewise for the act S 2 , a third unit M 3  likewise for the act S 3 , and a fourth unit M 4  likewise for the act S 4 . The second unit M 2  is configured such that the specific method acts S 21 , S 22  of the two alternative variant embodiments may be implemented and executed. The units M 1 , . . . , M 4  may be implemented as software, hardware or in a combination of software and hardware. For example, a processor executes the acts S 1  to S 4  stored in a memory connected to the processor. The processor has an input and output interface with which the minimum and maximum amounts of energy may be requested by the prosumers, and the determined amounts of energy E 1 , . . . , E 5  may be made available to the prosumers for a future time interval. Intermediate results of the individual processing acts, such as a minimum and maximum total amount of energy or the cost functions FC1, . . . , FC5, may also be stored in the memory. In addition, the units M 1  to M 4  may also be implemented by permanently wiring electronic components to a memory module. 
         [0079]    The developments may be combined at will in the context of the methods or the devices. 
         [0080]    It is to be understood that the elements and features recited in the appended claims may be combined in different ways to produce new claims that likewise fall within the scope of the present invention. Thus, whereas the dependent claims appended below depend from only a single independent or dependent claim, it is to be understood that these dependent claims can, alternatively, be made to depend in the alternative from any preceding or following claim, whether independent or dependent, and that such new combinations are to be understood as forming a part of the present specification. 
         [0081]    While the present invention has been described above by reference to various embodiments, it should be understood that many changes and modifications can be made to the described embodiments. It is therefore intended that the foregoing description be regarded as illustrative rather than limiting, and that it be understood that all equivalents and/or combinations of embodiments are intended to be included in this description.