Patent Publication Number: US-2017351234-A1

Title: Methods and systems for reducing a peak energy purchase

Description:
BACKGROUND 
     In energy distribution networks, such as electric power grids, utility companies charge end users for the amount of energy that they consume during a given billing period. For some types of end users, such as larger power consumers, utilities also charge based on the peak power consumed during the billing period. Thus, for such a user, a given amount of energy consumption evenly drawn from the utility over the billing period will result in lower overall charge than the same amount drawn from the utility in power spikes during the billing period. End users facing a peak demand charge will therefore likely be motivated to reduce the peak energy rate that they demand from the utility. 
     Previous efforts to reduce the peak energy rate include the use of a battery at the end user&#39;s facility to selectively store and release energy drawn from the utility. During periods of low energy consumption by the user, the user may draw more energy than needed from the utility to charge the battery, and then during periods of high energy consumption by the user, the user may use the stored energy from the battery to at least partially lower energy that must be purchased from the utility. The peak energy rate may thereby be reduced if decisions as to when to charge and discharge the battery are properly made. 
     SUMMARY 
     However, there are problems with such systems. As the peak demand reduction approach discussed above relies upon the user timely drawing more energy than needed from the utility during periods of high energy consumption, uncertainty in the location of such periods may greatly decrease the effectiveness of such reduction efforts. For example, if the user experiences an unexpectedly high energy need while the battery is empty or low, the reduction technique may fail altogether. Additionally, batteries typically store energy at less than perfect efficiency. This may further reduce the margin of error available for charging decisions, as every charging event may involve its own energy cost. 
     Embodiments of the present invention provide methods and systems to utilize energy storage systems in a manner that reduces peak energy demand while effectively accommodating uncertainty in energy consumption needs of the user. 
     According to an example embodiment of the present invention, a method of operating an energy consumption and storage system to reduce a peak energy purchase by the system includes obtaining a load forecast for an energy consumption system; observing a charge state of an energy storage component and a load presented by the energy consumption system; determining an energy action for the energy storage component as a function of the load forecast, observed load and observed charge state; and executing the determined energy action. For example, in an example embodiment, the determined energy action includes charging the energy storage component at a determined charging rate from an energy generation and supply system, or discharging the energy storage component at a determined discharge rate to power the energy consumption system. 
     In an example embodiment, selected steps of the method are performed iteratively over a predetermined time period corresponding to a planning horizon, so as to continually adapt to changing conditions. For example, in an example embodiment, the method observes the energy storage component and load, determines the energy action, and executes the determined action at each of a plurality of predetermined time intervals during the predetermined time period. In example embodiments, the method also iteratively obtains the load forecast to further increase the responsiveness of the peak energy purchase reduction. 
     In an example embodiment, the method iteratively executes selected steps over a plurality of the predetermined time periods, or planning horizons, collectively forming an energy purchase billing period. In such embodiments, the method, for example, tracks a peak energy purchase for the billing period over the plurality of the predetermined time periods. 
     In an example embodiment, the energy action is determined by composing and optimizing a sample average approximation of a cost function for the energy storage and consumption system, so as to transform what may be an indeterminate cost function into a determinate problem. Composing the sample average approximation can include generating a predetermined number of random load trajectories for the energy consumption system, each including a load at each of the predetermined time intervals based on a corresponding mean and variance of the obtained forecast, and forming the sample average approximation as an average, over the plurality of trajectories, of a maximum difference between the trajectory and a respective energy action for the plurality of time intervals. In an example, the sample average approximation of the cost function is constrained by a maximum charging rate, maximum discharging rate, and maximum capacity of the energy storage component. 
     In an example, optimizing the sample average approximation of the cost function is performed by converting the sample average approximation to a system of linear inequalities, and providing the system of linear inequalities to an optimization engine for optimizing. 
     These and other features, aspects, and advantages of the present invention are described in the following detailed description in connection with certain exemplary embodiments and in view of the accompanying drawings, throughout which like characters represent like parts. However, the detailed description and the appended drawings describe and illustrate only particular example embodiments of the invention and are therefore not to be considered limiting of its scope, for the invention may encompass other equally effective embodiments. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic diagram depicting an energy generation and consumption system, according to an example embodiment of the present invention. 
         FIG. 2  is a schematic diagram depicting an energy storage system, according to an example embodiment of the present invention. 
         FIG. 3  is a schematic diagram depicting an energy consumption system, according to an example embodiment of the present invention. 
         FIG. 4  is a schematic diagram depicting an energy monitoring and control system, according to an example embodiment of the present invention. 
         FIG. 5  is a schematic diagram depicting an energy action determination component, according to an example embodiment of the present invention. 
         FIG. 6  is a flowchart depicting a method of operating the energy consumption and storage system, according to an example embodiment of the present invention. 
         FIG. 7  is a flowchart depicting a method of operating the energy consumption and storage system, according to another example embodiment of the present invention. 
         FIGS. 8A and 8B  are graphs depicting timelines of selected quantities associated with an exemplary simulated performance of the method of  FIG. 7 . 
         FIG. 9  is a flowchart depicting a method of operating the energy consumption and storage system, according to another example embodiment of the present invention. 
         FIGS. 10A-10E  are graphs depicting timelines of selected quantities associated with an exemplary simulated performance of the method of  FIG. 9 . 
     
    
    
     DETAILED DESCRIPTION 
       FIG. 1  depicts an example embodiment of an energy generation and consumption system  20 , including an energy generation and supply system  24  and an energy consumption and storage system  28 . 
     The energy generation and supply system  24  is configured to generate and supply electrical energy to end users. For example, the energy generation and supply system  24  can include an energy generation component, such as an electrical power plant, to generate energy, and an energy transmission component, such as an electrical transmission grid, to supply the generated energy to end users. The energy generation and supply system  24  can connect to the energy consumption and storage system  28  via the energy transmission component. Components of the energy generation and supply system  24  can be provided by a utility company, such as an electrical utility, and may be located at the utility company&#39;s premises and/or the end user&#39;s premises. 
     In an example, the energy consumption and storage system  28  includes an energy consumption system  32 , an energy storage system  36 , and an energy monitoring and control system  40 . The energy consumption system  32  can include one or more components that require a supply of energy, such as electrical power, to operate. The energy consumption system  32  can be connected to and selectively receive energy from both the energy generation and supply system  24  and the energy storage system  36 . The energy storage system  36  can include one or more components that store energy, such as electrical energy, for later consumption. The energy storage system  36  can be connected to, and receive energy from, the energy generation and supply system  24 , and can provide energy to the energy consumption system  32 . The energy monitoring and control system  40  is configured to monitor the state of components of the energy consumption and energy storage systems  32 ,  36 , and provide control signals to control energy actions of those systems. For example, in an example embodiment, the energy monitoring and control system  40  is connected to the energy consumption system  32  and energy storage system  36  to receive and provide signals including monitoring and control information. Components of the energy consumption and storage system  28  can be operated by an end user, such as a business or consumer, and may be located at the end user&#39;s premises. 
       FIG. 2  depicts an example embodiment of the energy storage system  36 , including an energy storage component  44 , a first energy switching and/or conversion component  48 - 1 , and a second energy switching and/or conversion component  48 - 2 . The energy storage component  44  can include one or more components, such as a battery, etc., that stores energy, such as electrical energy, for later consumption. The energy switching and/or conversion components  48 - 1 ,  48 - 2  (also referred to herein as energy switching and/or conversion component(s)  48 ) can include a component for energy switching component and/or a component for energy conversion. The component for energy switching can, in response to a control signal from the energy monitoring and control system  40 , control whether energy is delivered from the energy power generation and supply system  24  to the energy storage component  44  for storage, in the case of the first switching component  48 - 1 , or from the energy storage system  36  to the energy consumption system  32 , in the case of the second switching component  48 - 2 . In an example, the component for energy conversion can provide conversion of energy from one form to another, such as from AC electrical energy to DC electrical energy, or vice versa, as required by the energy storage component  44  and energy consumption system  32 , in response to a control signal from the energy monitoring and control system  40 . 
       FIG. 3  depicts an example embodiment of the energy consumption system  32 , including one or more energy consumption components  52 - 1  . . .  52 -N, and an energy switching and/or conversion component  56 . The energy consumption components  52 - 1  . . .  52 -N (also referred to herein as energy consumption components(s)  52 ) can include one more components, such as manufacturing equipment, consumer equipment, etc., that require a supply of energy, such as electrical power, to operate. The switching and/or conversion component  56  can include an energy switching component and/or an energy conversion component, that, for example, controls whether energy is delivered from the energy power generation and supply system  24  or the energy storage system  36  to the energy consumption system  32  in response to a control signal from the energy monitoring and control system  40 . In an example, the switching and/or conversion component  56  also provides conversion of energy from one form to another, such as from AC electrical energy to DC electrical energy, or vice versa, as required by the energy consumption system  32 , e.g., in response to a control signal from the energy monitoring and control system  40 . 
     In embodiments, the switching and/or conversion components  48 ,  52  of the energy storage system  36  and energy consumption system  32  are distributed across these systems, as depicted in  FIGS. 2 and 3 , or are wholly or partially consolidated into one of these systems and omitted from the other system. 
       FIG. 4  depicts an example embodiment of the energy monitoring and control system  40  including a sensor component  60 , an energy action determination component  64 , and a control component  68 . 
     In an example, the sensor component  60  includes one or more of a sensor to sense a state or receiver to receive a sensed state of components of the energy consumption and storage system  28 , such as a power level demanded by the energy consumption system  32 , a charge state of the energy storage system  36 , etc. As indicated, the sensor component  60  can include either sensors themselves or components to receive signals from sensors. The sensors can include voltage level sensors, current level sensor, power level sensors, etc. 
     The energy action determination component  64  can receive an output from the sensor component  60 , such as information representing the power level demanded by the energy consumption system  32 , the charge state of the energy storage system  36 , etc. The energy action determination component  64  can then determine, by performing operations discussed below, a corresponding energy action for one or more of the energy consumption system  32  and energy storage system  36 , such as selectively providing power to the energy consumption system  32  from the energy generation and supply system  24  or from the energy storage system  36 , based on output of the sensor component  60 . The energy action determination component  64  can provide an output signal to the control component  68  indicating the determined energy action. 
     In an example embodiment, the control component  68  is configured to provide control signals to the energy consumption system  32  and energy storage system  36  to implement determined energy actions for these systems, such as to selectively control delivery of energy from the energy generation and supply system  24  to the energy storage system  36  and the energy consumption system  32 , and from the energy storage system  36  to the energy consumption system  32 . 
       FIG. 5  depicts an example embodiment of the energy action determination component  64 , including an energy cost reduction module  72 , a load predictor module  76 , a component model module  80  and an optimization engine module  84 . The energy cost reduction module  72  is configured to receive one more of observed information from the sensor component  60 , such as a power level demanded by the energy consumption system  32 , a charge state of the energy storage system  36 , etc.; prediction information from the load predictor module  76 , such as a predicted mean and variance of a power level to be demanded by the energy consumption system  32  at specified time intervals and time periods in the future; and model information from the component model module  80 , such as a storage component efficiency, etc. The energy cost reduction module  72  is configured to optimize a peak energy cost function for an identified billing period based on the received information, such as by composing a sample average approximation of the peak energy cost function and optimizing the sample average approximation, to determine a minimum cost solution to the peak energy cost function and an associated energy action to implement the minimum cost solution. In an example, to perform the optimization, the energy cost reduction module  72  transforms a composed sample average approximation of the cost function to a format required by the optimization engine  84 , sends the formatted sample average approximation to the optimization engine  84 , and receives the optimized solution from the optimization engine  84 . The energy cost reduction module  72  can then output an indication of the determined energy action to the control component  68 . 
     In an example, the load predictor module  76  is configured to receive observed information from the sensor component  60 , such as a power level demanded by the energy consumption system  32 , and provide a load forecast to the energy cost reduction module  72 , such as a predicted mean and variance of a power level to be drawn by the energy consumption system  32  at specified time intervals for time periods in the future. The forecast can be based on, for example, a load of a most recent period or corresponding period (e.g., a period of the prior year corresponding to the current period), or an average of loads for a plurality of prior periods, etc. Any suitably appropriate forecasting method and bases for forecasting can be used. 
     In an example, the component model module  80  is configured to provide parameters characterizing other components of the energy consumption and storage system  28  to the energy cost reduction module  72 , such as an energy storage efficiency of an energy storage component  44  of the energy storage system  36 . 
     The energy action monitoring and control system  40  can be implemented to selected degrees in hardware or software. In an example embodiment, energy action monitoring and control system  40  includes a processor and a non-transitory storage medium on which are stored program instructions that are executable by the processor, and that, when executed by the processor, cause the processor to perform embodiments of methods of operating the energy consumption storage system, such as embodiments of methods depicted in  FIGS. 6, 7 and 9  discussed below. 
       FIG. 6  is a flowchart that illustrates a method  600  of operating the energy consumption and storage system  28  so as to reduce a peak energy rate purchased by the system  28  in an improved manner, according to an example embodiment of the present invention. At step  602 , the example method  600  begins, for determining energy actions for components of the energy consumption and storage system  28 , such as selectively purchasing energy to charge the energy storage component  44  from the energy generation and supply system  24  or discharging the energy storage component  44  to power the energy consumption components  52 , that minimize an energy cost function based on an observed state of the energy consumption system  32  and energy storage system  36 , such as a charge state of the energy storage component  44  and a load presented by the energy consumption components  52 , and a load forecast, such as forecast mean and variance of the load. Such determined energy actions can accurately and consistently identify or approach maximum peak energy rate reduction. 
     At step  604 , energy states of the energy storage component  44  and the energy consumption components  52  are observed. For example, a charge state of the energy storage component  44 , such as a voltage or percentage charge, and load presented, i.e., a power demanded, by the energy consumption components  52 , such as an electrical power, can be observed, e.g., using the sensor component  60  of the energy action monitoring and control system  40 . For example, a voltage sensor or chemical potential sensor can be used to sense a voltage or percentage charge of a battery. A current and/or voltage sensor can be used to sense an electrical power drawn by the energy consumption components  52 . 
     At step  606 , a forecast of the load to be presented, i.e., the power demanded, in the future by the energy consumption components  52  is obtained. For example, in an example, as forecast mean and variance of the load are obtained. The load forecast can be obtained for specified time points for a specified time period into the future. For example, the load forecast can be obtained for time points separated by a specified time interval, such as a predetermined number of minutes or hours, e.g., 15 minutes, 1 hour, etc., starting at the present time and for a predetermined period of time into the future, such as a remaining period of time in a current utility billing period, e.g., a remaining number of days in the current billing period. The load forecast can be obtained from the load predictor  76 . The load predictor  76  can predict the load based on a present load, a load history, and/or component models for the energy consumption components  52 . 
     At step  608 , an energy action is determined for the energy storage component  44  as a function of the observed state of the energy storage component  44  and energy consumption components  52  and the obtained load forecast. 
     For example, an energy action can be determined at step  608  for charging or discharging the energy storage component  44  so as to minimize a maximum power purchased from the energy generation and supply system  24  for the current billing period. An ideal energy action can be determined as a charge or discharge action that minimizes a cost function of the energy consumption and storage system  28 . In an example embodiment, the energy action is constrained to lie within operational limits of the energy storage component  44 , which, in an example, is represented as follows: 
     
       
         
           
             
               
                 
                   
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     where s t  is the charge state of the energy storage component  44  at time t (s 1  in the above equation referring to the charge state at a first moment in time t), ranging from 0% C, i.e., empty, to 100% C, i.e., full; C is the energy storage component capacity; Pmax is the maximum discharge power of the energy storage component; −Pmax is the maximum charge power of the energy storage component. Constraint (2) limits the charge state of the energy storage component  44  to be between zero and the charge capacity of the energy storage component  44 . Constraint (3) limits the energy action to be between maximum charging and discharging powers for the energy storage component  44 . In an example, the optimization of the cost function is represented as follows: 
     
       
         
           
             
               
                 
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     where J is the minimized cost function; u(of u   min ) is (u 1 , . . . , u T ), a vector of energy actions from time 1 to time T; E is a cost function for the energy consumption and storage system  28 ; d is a peak energy rate cost; tε1, . . . , T is a time index of the problem; T is a planning horizon; Δt is the predetermined time interval, e.g., between t and t+1; L t  is a random load at time t; u t  is an energy action power at time t, where u t &lt;0 represents charging and u t &gt;0 represents discharging; and L t −u t  is an energy purchase at time t, which may also be referred to as g t  (referenced below by the term gmax). The optimization of the cost function essentially looks for an energy purchase g t  at each time t that minimizes the expected cost function. 
     A direct minimization of the above cost function to determine a corresponding energy action may be indeterminate because the load at any given time in the future may be unknown. However, in an example embodiment, a forecast of the mean and variance of the load is made, and a minimization of the cost function to determine a corresponding energy action is performed based on such a forecast load mean and variance. For example, the above cost function can be converted to a deterministic function based on such a forecast load mean and variance, and a solution then obtained. A sample average approximation method can be used to create a stochastic model approximating the underlying cost function by sampling the possible load vectors based on the forecast load mean and variance, and then an equivalent deterministic function based on the model can be optimized. The cost function alternatively can be converted to a deterministic function based on the forecast load mean and variance in other ways. 
     In an example embodiment, composing the sample average approximation proceeds as follows. A predetermined number N of random load trajectories {ξ 1 , ξ 2 , . . . , ξ N } is generated according to the forecast load mean and variance. Each trajectory can be expressed as ξ i ={ξ 1   i , ξ 2   i , . . . , ξ T   i }, where ξ t   i  is a random realization of the load Lt according to the forecast mean and variance, expressed as L t ˜N(μ t , σ t   2 ). The optimization of the cost function can then be restated as follows: 
     
       
         
           
             
               
                 
                   
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     where {circumflex over (f)} N (u) is a sample average approximation of the cost function for the energy consumption and storage system  28 , and U is a region of feasible energy actions defined by the constraints (1) and (2). 
     A solution to the optimization of the sample average approximation of the cost function can be deterministic. Optimizing of the sample average approximation of the cost function can be performed using an optimization tool. The restated cost function can be converted into a format required by an optimization tool. For example, an existing linear optimization tool, such as the linprog function of the MatLab software tool provided by MathWorks, Inc., can optimize a stated function f T x for x, where f T x is the multiplication of a row vector of constants f and a column vector of variables x, constrained by linear inequalities A x≦b; where A is a matrix of constants and b is a vector of constants, linear equalities Aeq x=beq, where Aeq is a matrix of constants and beq is a vector of constants; and bounds lb≦x≦ub, where lb is a lower bound for x and ub is an upper bound for x. The above sample average approximation of the cost function can be converted into such a format by introducing a set of auxiliary variables q1, q2, . . . qN, where qi=max t ε {1, . . . , T}  (ξ t   i −ut}, and composing the function f as 1/N (q1+q2+ . . . qN) and linear inequalities as qi≧ξ t   i −ut for t=1, . . . , T, for input to the linprog function to solve for an optimal energy action u. Other optimization tools can also be used to optimize the sample average approximation of the cost function. 
     Returning to  FIG. 6 , at step  610 , the energy action determined to minimize the cost function for the energy consumption and storage system  28  is implemented. For example, the energy storage component  44  can be charged by connecting the energy storage component  44  to the energy generation and supply system  24 , or discharged to power the energy consumption system  32  by connecting the energy storage component  44  to the energy consumption system  32 , according to the determined energy action under control of the control component  68 . The method ends at step  612 . 
     Embodiments of the method of  FIG. 6  may include steps or sub-steps executed in an iterative fashion at each of a plurality of predetermined time intervals during a predetermined time period. For example, the method can perform one or more of observing the storage component  44  and load, determining an optimized energy action, and executing the determined energy action at each of a plurality of predetermined time intervals over a predetermined time period. The predetermined time intervals and predetermined time period can be selected to provide a desired peak energy reduction performance, such as by providing sufficient time resolution to suitably track a varying load, and an acceptable computational requirement, such as by limiting the time resolution or time period. For example, in one example, the method performs iterative steps every 15 minutes for a planning horizon of one day. 
       FIG. 7  depicts an example embodiment  700  of the method of operating the energy consumption and storage system of  FIG. 6 , showing further details of an iterative execution of the method in which an optimized energy action is determined and executed at each of a plurality of predetermined time intervals over a predetermined time period. The method begin sat step  702 . 
     At step  704 , parameters related to the iterative execution of the method are set. For example, one or more of a starting time, a predetermined time interval, and a predetermined time period can be set. For example, to begin execution of the method at the start of a one day period, with iterations every 15 minutes, a current time t can be set to 1, a time interval Δt can be set to 0.25 hours, and a predetermined time period T can be set to 24 hours. 
     At step  706  a forecast load, such as a forecast mean and variance of the load, is obtained. The load forecast can be obtained for each of the predetermined time intervals over the predetermined time period. Continuing the example mentioned with respect to step  704 , the load forecast can include a forecast load mean and variance, such as a predicted mean power demand in kW and a variance of the power demand in kW, at intervals of 15 minutes for a time period of 24 hours. As discussed above, the load forecast can be obtained from the load predictor module  76 , which can forecast the load based on one or more of a current load, a load history, component models, etc. 
     At step  708 , a predetermined number N of random load trajectories is determined according to the forecast load mean and variance. Each of the load trajectories can include a random load value at each of the predetermined time intervals, the randomization weighted according to the corresponding forecast mean and variance. Continuing the above example, each load trajectory can include a random load value in kW at intervals of 15 minutes for a time period of 24 hours. The randomized load values can be obtained from a random number generator configured to operate according to a selected mean and variance. 
     The predetermined number N can be selected to provide a result sufficiently close to an optimal peak energy reduction. In general, a larger number N can provide a result closer to an optimal result, but require greater computational power to execute the calculations of the method, while a smaller number N can provide a result less close to an optimal result, but require less computational power to execute the calculations of the method. To select the predetermined number N, the method can be performed at a range of values of the predetermined number N, and the results evaluated to determine the value of the number N for which the peak reduction is within a predetermined amount of an optimal result. For example, the method can be performed multiple times, beginning with a low N value and gradually increasing the N value for later iterations, until an N value is obtained that provides a result within an acceptable range of the ideal result, in order to avoid the computational intensity required for obtaining the most ideal result. 
     At step  710 , an energy state of the energy storage component  44  and the energy consumption components  52  is observed for the current time t. The energy state can include a charge state s t  of the energy storage component  44  and a current load l t  presented by the energy consumption components  52 . Continuing the above example, a current charge level as a certain percentage can be observed for the energy storage component  44 , and a power level in kW can be observed as being currently demanded by the power consumption components. As discussed above, the energy state of the energy storage component  44  and energy consumption components  52  can be observed using the sensor component  60 . Alternatively, the energy state of the energy storage component  44  can be observed from a previously calculated energy state, such as updated during step  718  discussed below. 
     At step  712 , a sample average approximation of the demand charge cost function is composed for the current time interval based on the generated random load trajectories and currently observed energy states of the energy storage and energy consumption components. The sample average approximation can take the form shown in equations (1), (2) and (4). 
     At step  714 , the generated sample average approximation of the demand charge cost function is optimized to determine a corresponding current energy action u t . The determined energy action can include a charging power to be delivered for the current time interval to the energy storage component  44  from the energy generation and supply system  24 , or a discharging power to be delivered for the current time interval from the energy storage component  44  to the energy consumption system  32 . Continuing the above example, a charging or discharging power in kW can be determined. As discussed above, the sample average approximation can be optimized by converting it into a form for input to the optimization engine  84 , and then input to the optimization engine  84  for optimization to determine a corresponding energy action. At any given time t during the predetermined time period T, a certain number of energy actions may have already been calculated for previous times during previous iterations of the method, and the form of the optimization problem can be restated to incorporate such energy actions at corresponding times in place of respective load trajectory values, by replacing the cost function as follows: 
     
       
         
           
             
               
                 
                   
                     
                       
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     Also, at each iteration, an energy action vector can be determined for each of the remaining times in the predetermined time period, although only the energy action for the current time t is typically executed, as the remaining energy actions can be redetermined using updated observations in subsequent iterations. 
     At step  716 , the determined energy action is executed for the energy storage component  44 . The determined energy action can include a charging power to be delivered for the current time interval to the energy storage component  44  from the energy generation and supply system  24 , or a discharging power to be delivered for the current time interval from the energy storage component  44  to the energy consumption system  32 . Continuing the above example, a charging or discharging power in kW may have been determined. As discussed above, the energy storage component  44  can be charged by connecting the energy storage component  44  to the energy generation and supply system  24 , or discharged by connecting the energy storage component  44  to the energy consumption system  32 . Although a certain charging or discharging power can be calculated for the current time interval, execution of the energy action also can implement a different but equivalent charging or discharging, such as charging or discharging at a related higher rate for a correspondingly shorter period, etc. 
     At step  718 , parameters related to the iterative execution of steps of the method are updated. For example, one or more of the current time and a current energy state of the energy storage component can be updated. The current time can be updated by adding the predetermined time interval to the previous current time, and the energy state of the energy storage component  44  can be updated by adding an amount based on a rate of the energy action multiplied by the time interval. Continuing the above example, the current time can be updated by adding 0.25 hours, and the energy state of can be updated by adding an amount based on the energy action rate multiplied by 0.25 hours. 
     At step  720 , whether the end of the predetermined time period, i.e., the planning horizon, has been reached is determined. If the end of the planning horizon has been reached, the method proceeds to step  722 , where the method ends. If the end of the planning horizon hasn&#39;t been reached, the method proceed to step  710 , for repeating the iterative portion of the method until the end of the planning horizon is reached. 
       FIG. 8A  is a graph depicting a timeline of selected quantities associated with an exemplary simulated performance of the method  700  of  FIG. 7 , including a forecast mean load  90 , an actual realized load  94 , and an energy purchase  98  for one hour time intervals over a 24 hour period.  FIG. 8B  is a graph depicting a timeline of a charge state  102  of the energy storage component  44  for the exemplary simulated performance of the method depicted in  FIG. 8A . As can be seen, energy purchases are used to effectively charge the energy storage component  44  during periods of low realized load, and reduce the maximum energy purchase from 163.70 kW without the described control of the energy storage system  36  to 127.05 kW with the described control of the energy storage system  36 . 
     Other example embodiments of the method of operating the energy consumption and storage system may allocate different combinations of steps or sub-steps for iterative execution at each of a plurality of time intervals over a predetermined time period. For example, the method described below with respect to  FIG. 9  includes additional steps not discussed with respect to the method illustrated in  FIG. 7 . 
     Additionally, example embodiments of the method, such as that described with respect to  FIG. 9 , enable minimizing the demand charge for a predetermined billing period different than the planning horizon over which the method iteratively optimizes the energy action. For example, the predetermined time period over which the method iteratively optimizes the energy action, i.e., the planning horizon, can be selected to be smaller than the billing period in order to reduce the computational cost of executing the method. In an example of such embodiments, the method tracks a peak energy purchase over the course of a billing period and determines energy actions to minimize the demand charge in view of both a current planning horizon and the peak energy purchase so far for the billing period. 
       FIG. 9  depicts another embodiment  900  of the method of operating the energy consumption and storage system of  FIG. 6 , showing further details of another allocation of steps to an iterative execution, in which the load forecast is iteratively determined, and which accommodates a planning horizon different that the billing period. Many aspects of the steps of the embodiment of  FIG. 9  are similar to corresponding steps of the embodiment of  FIG. 7 , and these will not be discussed in detail in the following, which will instead focus on the aspects of the embodiment of  FIG. 9  that differ from the embodiment of  FIG. 7 . The method begins at step  902 . 
     At step  904 , parameters related to the iterative execution of steps of the method are set, similar to as in step  704 . In addition to the parameters discussed in step  704 , the current planning horizon k within the billing period and an existing peak energy purchase gmax for the current billing period are set. For example, referring to equations (6)-(8) discussed below, to begin execution at the start of a one month billing period, with one day planning horizons and iterations every 15 minutes, a current time planning horizon k can be set to 1, t can be set to 1, a time interval Δt may be set to 0.25 hours, and a predetermined time period T can be set to 24 hours. 
     At step  906 , an energy state of the energy storage component  44  and the energy consumption components  52  are observed for the current time t, similar to as in step  710 . 
     At step  908 , a forecast load mean and variance is obtained, similar to as in step  706 . The load forecast can be obtained for each of the predetermined time intervals over the planning horizon. 
     At step  910 , a predetermined number N of random load trajectories is determined according to the forecast load mean and variance, similar to as in step  708 . 
     At step  912 , a sample average approximation of the demand charge cost function is composed for the current time interval based on the generated random load trajectories, currently observed energy states of the energy storage component  44  and the energy consumption components  52 , and present peak energy purchase for the billing period, similar to as in step  712 , although modified to accommodate a different planning horizon and billing period. To accommodate different a planning horizon and billing period, in an example embodiment, the optimization of equation (3) is modified as follows: 
     
       
         
           
             
               
                 
                   
                       
                   
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     and where k is the current planning horizon and gmax is the present peak energy purchase for the billing period. In an example embodiment, the sample average approximation of the cost function is correspondingly adapted as follows: 
       {circumflex over ( J )}=min{{circumflex over ( f )}( u ):= N   −1 Σ i=1   N   Q ( g max, u ))}  (8)
 
     That is, the optimziation iterating over the planning horizon now accounts for the present peak energy purchase during the billing period. 
     At step  914 , the generated sample average approximation of the demand charge cost function is optimized to determine a corresponding current energy action u kt , similar to as in step  714 , although, because the method of  FIG. 9  iteratively obtains the load forecast, in step  914  new remaining trajectory values can be used in equation (5) for each iteration, which can further improve the performance of the method by providing the ability to continuously improve the accuracy of the forecast. 
     At step  916 , the determined energy action is executed for the energy storage component  44 , similar to as in step  716 . 
     At step  918 , parameters related to the iterative execution of steps of the method are updated, similar to as in step  718 . In addition to the parameters discussed in step  718 , the peak energy purchase gmax for the current billing period can be updated and the current planning horizon k can be updated until the billing period length K is reached. The planning horizon is updated if the current time interval has concluded the current planning horizon. If the planning horizon is updated, the current time interval is reset to one to start the new planning horizon at the beginning. 
     At step  920 , it is determined both whether the end of the current planning horizon has been reached and whether the end of the billing period has been reached. If the end of the current planning horizon and the billing period have both been reached, the method proceed to step  922 , where the method ends. If the end of either the current planning horizon or the current billing period hasn&#39;t been reached, the method proceeds to step  906 , where the iterative portion of the method repeats until the end of both the planning horizon and billing period is reached. 
       FIGS. 10A-10E  are graphs depicting timelines of selected quantities associated with different times of an exemplary simulated performance over a single planning horizon of the method of  FIG. 9 .  FIG. 10A  shows a forecast mean load  104 - 1 , a present maximum energy purchase  108 , and an actual load  112  for the first of one hour time intervals over a 24 hour period.  FIG. 10B  shows previous and new forecast mean loads  104 - 1 ,  104 - 2 , the present maximum energy purchase  108 , and an actual load  112  by the second of the one hour time intervals over the 24 hour period.  FIG. 10C  shows the previous and new forecast mean loads  104 - 1  . . .  104 - 15 , the present maximum energy purchase  108 , and an actual load  112  by the 15th of the one hour time intervals over the 24 hour period.  FIG. 10D  shows all of the forecast mean loads  104 - 1  . . .  104 - 24 , the present maximum energy purchase  108 , and the actual load  112  at the end of the 24 hour period.  FIG. 10E  shows a charge state  116  of the energy storage component  44  for the exemplary simulated performance depicted in  FIGS. 10A-10D . As can be seen, the energy purchases are used to effectively charge the energy storage component  44  during periods of low realized load, and reduce the peak energy purchase during the planning horizon. 
     Additional embodiments of the energy consumption and storage system  28 , energy storage system  36 , energy action determination component  64  and methods  600 ,  700 ,  900  of operating the energy storage and consumption system  28  are possible. For example, any feature of any of the embodiments of the energy consumption and storage system  28 , energy storage system  36 , energy action determination component  64  and methods  600 ,  700 ,  900  of operating the energy storage and consumption system  28  described herein may be used in any other embodiment of the energy consumption and storage system  28 , energy storage system  36 , energy action determination component  64  and methods  600 ,  700 ,  900  of operating the energy storage and consumption system  28 . Also, embodiments of the energy consumption and storage system  28 , energy storage system  36 , energy action determination component  64  and methods  600 ,  700 ,  900  of operating the energy storage and consumption system  28  may include only any subset of the components or features of the energy consumption and storage system  28 , energy storage system  36 , energy action determination component  64  and methods  600 ,  700 ,  900  of operating the energy storage and consumption system  28  discussed herein. 
     An example embodiment of the present invention is directed to one or more processors, which may be implemented using any conventional processing circuit and device or combination thereof, e.g., a Central Processing Unit (CPU) of a Personal Computer (PC) or other workstation processor, to execute code provided, e.g., on a non-transitory computer-readable medium including any conventional memory device, to perform any of the methods described herein, alone or in combination. The one or more processors can be embodied in a server or user terminal or combination thereof. The user terminal can be embodied, for example, as a desktop, laptop, hand-held device, Personal Digital Assistant (PDA), television set-top Internet appliance, mobile telephone, smart phone, etc., or as a combination of one or more thereof. The memory device can include any conventional permanent and/or temporary memory circuits or combination thereof, a non-exhaustive list of which includes Random Access Memory (RAM), Read Only Memory (ROM), Compact Disks (CD), Digital Versatile Disk (DVD), and magnetic tape. 
     An example embodiment of the present invention is directed to one or more non-transitory computer-readable media, e.g., as described above, on which are stored instructions that are executable by a processor and that, when executed by the processor, perform the various methods described herein, each alone or in combination or sub-steps thereof in isolation or in other combinations. 
     An example embodiment of the present invention is directed to a method, e.g., of a hardware component or machine, of transmitting instructions executable by a processor to perform the various methods described herein, each alone or in combination or sub-steps thereof in isolation or in other combinations. 
     The above description is intended to be illustrative, and not restrictive. Those skilled in the art can appreciate from the foregoing description that the present invention can be implemented in a variety of forms, and that the various embodiments can be implemented alone or in combination. Therefore, while the embodiments of the present invention have been described in connection with particular examples thereof, the true scope of the embodiments and/or methods of the present invention should not be so limited since other modifications will become apparent to the skilled practitioner upon a study of the drawings, specification, and following claims.