Patent Publication Number: US-2018046160-A1

Title: Methods and systems for providing photovoltaic plant power feed-in

Description:
BACKGROUND INFORMATION 
     Photovoltaic power plants generate electric energy from solar energy, and feed the generated electric energy to an electric energy transmission system, often to generate revenue. Photovoltaic power plants and electric energy transmission systems are typically operated by different entities, and the electric energy transmission system is likely to place requirements on the form of the electric energy it receives from the photovoltaic power plant. Such requirements originate from limits of the electric energy transmission system&#39;s ability to receive electric energy, energy regulations, market considerations, etc., as well as other factors, and power levels required by the electric energy transmission system may differ substantially from power levels naturally generated by the photovoltaic power plant. Failure of the photovoltaic power plant to fulfil these requirements results in a penalty in the form of a reduction in payment from the electric energy transmission system for the energy feed-in. 
     Previous efforts to provide greater control over the electric energy fed from energy generation sources to energy transmission systems have include the use of a battery to selectively store energy generated by the energy generation source and then release the stored energy to the energy transmission system. For example, during periods of high energy generation, a portion of the energy generated may be used to charge the battery, and then during periods of low energy generation, the battery may provide stored energy to supplement newly generated energy fed into the energy transmission system. 
     SUMMARY 
     However, problems have arisen in attempting to realize such systems. Prior approaches have relied upon systems using complex, non-linear equations, which have proven to be time consuming and expensive to operate. Moreover, uncertainty in the power level generated by the energy generation source may greatly decrease the effectiveness of such systems, potentially resulting in penalties and revenue reduction. Additionally, inefficiencies in energy storage may further reduce the margin of error available, as every charging and discharging event may involve its own energy cost. 
     Therefore, a need exists for improved methods and systems for utilizing energy storage systems to provide photovoltaic and other renewable power plant energy feed-in to energy transmission systems, to reduce complexity and cost while effectively accommodating uncertainties in power generation. 
     Example embodiments of a method of controlling a photovoltaic energy generation and supply system maximize revenue generated for feeding energy from the photovoltaic system to an energy transmission system in an improved manner by utilizing a revenue generation model that reduces complexity and cost. For example, in an example embodiment, the method composes a revenue generation model having a linear revenue generation objective function and linear constraints based on an energy generation forecast and requirements for electrical energy feed-in to the electrical energy transmission system, and optimizes the revenue generation model using a mixed-integer linear programming approach. 
     An example embodiment of the method includes: obtaining a forecast of energy generation by a photovoltaic energy generation system for a predetermined time period; determining a linear revenue generation objective function describing revenue generated by feeding electrical energy from the photovoltaic energy generation and supply system into an energy transmission system; determining a plurality of linear constraints on the feeding of electrical energy into the energy transmission system, at least some of the constraints being a function of the forecast; optimizing the revenue generation function under the constraints to determine an energy feed-in action and an energy storage action; and executing the determined energy actions. 
     The formulation of the revenue generation model, including the revenue generation objective function and the plurality of constraints as linear functions, can enable the revenue generation objective function to be optimized using a mixed integer linear programming approach. In an example, the revenue generation objective function and plurality of constraints are provided to an optimization engine configured to implement a mixed integer linear programming approach, and an optimized solution of the revenue generation objective function in view of the plurality of constraints is received from the optimization engine. 
     In example embodiments, selected steps of the method are performed iteratively over a predetermined time period, so as to continually adapt to changing conditions. For example, in an example, the method performs, at each of a plurality of time intervals during the predetermined time period, one or more of: observing a current energy generation by the photovoltaic energy generation system, obtaining the energy generation forecast, determining the revenue generation objective function and the plurality of constraints, optimizing the revenue generation function, and executing the energy actions determined as a result of the optimization. 
     In example embodiments, the plurality of constraints include constraints power fed to the electrical energy transmission system during ramp-up, quasi-stationary, and ramp-down phases of the predetermined time period, such as one or more of: a limit on a rate of increase of power feed-in during the ramp-up phase, a limit on a variation of a power feed-in during the quasi-stationary phase, and a limit on a rate of decrease of power feed-in during the ramp-down phase. In example embodiments, the constraints also limit the order, length and/or frequency, etc., of these phases. The constraints can further enable the revenue generation model to implement physical characteristics and limitations of the photovoltaic energy generation and supply system. 
     Example embodiments of a non-transitory machine-readable storage medium include program instructions that, when executed by a processor, perform embodiments of the method of controlling the photovoltaic energy generation and supply system. 
     Example embodiments of a photovoltaic energy generation and supply system include a processor and a non-transitory machine-readable storage medium on which are stored program instructions that, when executed by a processor, cause the processor to perform example embodiments of the method of controlling the photovoltaic energy generation and supply system. 
     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 transmission system according to an example embodiment of the present invention. 
         FIG. 2  is a schematic diagram depicting a photovoltaic energy generation and supply system according to an example embodiment of the present invention. 
         FIG. 3  is a schematic diagram depicting a photovoltaic energy generation system according to an example embodiment of the present invention. 
         FIG. 4  is a schematic diagram depicting an energy storage system according to an example embodiment of the present invention. 
         FIG. 5  is a schematic diagram depicting a monitoring and control system according to an example embodiment of the present invention. 
         FIG. 6  is a schematic diagram depicting an energy action determination module according to an example embodiment of the present invention. 
         FIG. 7  is a flowchart depicting a method of providing electrical energy from the photovoltaic energy and supply system to an electrical energy transmission system according to an example embodiment of the present invention. 
         FIG. 8  is a graph depicting electrical energy generated by the photovoltaic energy and supply system and electrical power fed into the electrical energy transmission system over a predetermined time period according to example embodiments of the present invention. 
         FIG. 9  is a flowchart depicting another embodiment f a method of providing electrical energy from the photovoltaic energy and supply system to an electrical energy transmission system according to an example embodiment of the present invention. 
         FIGS. 10A-10B  are graphs depicting an electrical energy generation forecast for the photovoltaic energy and supply system, electrical power fed into the electrical energy transmission system, and an energy state of the energy storage module for an exemplary performance of the method of  FIG. 7  according to example embodiments of the present invention. 
         FIGS. 11A-11B  are graphs depicting an electrical energy generation forecast for the photovoltaic energy and supply system, electrical power fed into the electrical energy transmission system, and an energy state of the energy storage module for another exemplary performance of the method of  FIG. 7  according to example embodiments of the present invention. 
         FIGS. 12A-12B  are graphs depicting embodiments of an electrical energy generation forecast for the photovoltaic energy and supply system, electrical power fed into the electrical energy transmission system, and an energy state of the energy storage module for yet another exemplary performance of the method of  FIG. 7  according to example embodiments of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF EXAMPLE EMBODIMENTS 
       FIG. 1  depicts an example embodiment of an energy generation and transmission system  20 . The illustrated energy generation and transmission system  20  includes a photovoltaic energy generation and supply system  24  and an electrical energy transmission system  28 , where the photovoltaic energy generation and supply system  24  generates electrical energy from solar energy, and supplies electrical energy to the electrical energy transmission system  28 . The electrical energy transmission system  28  receives electrical energy from the photovoltaic energy generation and supply system  24 , and transmits the electrical energy to end users for consumption. 
     The photovoltaic energy generation and supply system  24  and the electrical energy transmission system  28  can each be owned, operated and/or located on the premises of different entities, such as corporations, public utilities, governmental bodies, etc. For example, the photovoltaic energy generation and supply system  24  can be owned, operated and/or located on the premises of a first entity, and the electrical energy transmission system  28  can be owned, operated and/or located on the premises of a second entity. The second entity can provide payments to the first entity for electrical energy supplied by the photovoltaic energy generation and supply system  24  to the electrical energy transmission system  28  that meets requirements for such transfer, but may provide only a reduced or no payment for electrical energy supplied that does not meet such requirements. 
       FIG. 2  depicts an example embodiment of the photovoltaic energy generation and supply system  24 , including a photovoltaic energy generation system  32 , an energy storage system  36 , and a monitoring and control system  40 . The photovoltaic energy generation system  32  receives solar energy from which it generates electrical energy. The photovoltaic energy generation system  32  is connected to, and is configured to supply electrical energy to, the energy storage system  36  and the electrical energy transmission system  28 . The energy storage system  36  is configured to receive, store and provide electrical energy. The energy storage system  36  is connected to and receives energy from the photovoltaic energy generation system  32 , and is connected to and provides energy to the electrical energy transmission system  28 . The monitoring and control system  40  monitors components of the photovoltaic energy generation system  32  and energy storage system  36 , and provides control signals to control these systems. For example, in an example, the monitoring and control system  40  is connected to the photovoltaic energy generation system  32  and energy storage system  36  to receive monitoring information from, and provide control signals to, these systems. 
       FIG. 3  depicts an example embodiment of the photovoltaic energy generation system  32 . The example photovoltaic energy generation system  32  includes a photovoltaic energy generation module  44  and a switching and/or conversion module  48 . The photovoltaic energy generation module  44  includes one or more components configured to receive solar energy power and convert the received solar energy power to electrical energy power, such as a direct current (DC) power in the form of one or more voltage or current output signals. The photovoltaic module  44  should be arranged in a location having favorable solar conditions. 
     The switching and/or conversion module  48  includes one or more switching and/or conversion components. For example, in an example, the one or more switching components control whether generated electrical energy is delivered from the photovoltaic energy generation module  44  to electrical energy transmission system  28 , and whether generated electrical energy is delivered from the photovoltaic energy generation module  44  to the energy storage system  36 , the control being in response to one or more control signals from the monitoring and control system  40 . The switching component(s) include, for example, transistor-based switches, electromagnetic switches, mechanical switches, etc. In an example, the one or more conversion components provide conversion of energy from one form to another, such as from DC electrical energy to alternating current (AC) electrical energy, or vice versa, and/or from one voltage or current level to another, as may be required by the electrical energy transmission system  28  or the energy storage system  36 , the conversion being in response to, e.g., one or more control signals from the monitoring and control system. In one example, the switching and/or conversion module  48  includes one or more inverters to convert a DC signal produced by the photovoltaic energy generation module to an AC signal, and one or more transformers to convert the AC signal to a higher voltage level, for delivery to the electrical energy transmission system  28 . In another example, the switching and/or conversion module  48  includes one or more DC to DC converters to convert a DC signal produced by the photovoltaic energy generation module  44  to a second DC signal having a different voltage level for delivery to the energy storage system  36 . 
       FIG. 4  depicts an example embodiment of the energy storage system  36  including an energy storage module  52  and a switching and/or conversion module  56 , where the energy storage module  52  includes one or more components, such as one or more batteries, etc., that store electrical energy for later access, and the switching and/or conversion module  56  includes one or more switching and/or conversion components, similar to those described above with respect to the switching and/or conversion module  48 . In an example, one or more switching components control whether electrical energy stored in the energy storage module  52  is delivered to the electrical energy transmission system  28  in response to one or more control signals from the monitoring and control system  40 . In an example, one or more conversion components provide conversion of energy from one form to another, such as from DC electrical energy to alternating current (AC) electrical energy, or vice versa, and/or from one voltage or current level to another, as may be required by the electrical energy transmission system  28  or energy storage system  36 , in response to, e.g., one or more control signals from the monitoring and control system  40 . For example, in an example, the switching and/or conversion module  56  includes one or more inverters to convert a DC signal produced by the energy storage module  52  to an AC signal, and one or more transformers to convert the AC signal to a higher voltage level, for delivery to the electrical energy transmission system  28 . 
     In example embodiments, the switching and/or conversion components  48 ,  56  of the photovoltaic energy generation system  32  and the energy storage system  36  may be are variously distributed across these systems, such as depicted in  FIGS. 3 and 4 , or wholly or partially consolidated into one of these systems and correspondingly omitted from the other system. 
       FIG. 5  depicts an example embodiment of the monitoring and control system  40 , including an interface and/or sensor module  60 , an energy action determination module  64 , and a control module  68 . 
     In an example, the interface and/or sensor module  60  includes one or more components to receive and/or sense a state of components of the photovoltaic energy generation system  32  and the energy storage system  36 , such as an electrical energy power level generated by the photovoltaic energy generation module  44 , a charge state of the energy storage module  52 , etc. The interface and/or sensor module  60  can include either components to receive signals from sensors or the sensors themselves. Examples of the sensors include voltage level sensors, current level sensors, power level sensors, etc. 
     In an example, the energy action determination module  64  includes one or more components to receive sensed information outputs from the interface and/or sensor module  60  and determine a corresponding energy action for the photovoltaic energy generation system  32  and/or the energy storage system  36 , such as selectively providing electrical power from the energy generation system  32  to the electrical energy transmission system  28  and/or to the energy storage system  36 , and/or from the energy storage system  36  to the electrical energy transmission system  28 , based on the received sensed information and other factors and functionality as discussed herein. In an example, the energy action determination module  64  provides an output signal to the control module indicating the determined energy actions. 
     In an example, the control module  68  provides control signals to components of the photovoltaic energy generation system  32  and/or energy storage system  36  to implement determined energy actions for these systems, such as to selectively control delivery of electrical energy from the photovoltaic energy generation system  32  to the electrical energy transmission system  28  and/or energy storage system  36 , and/or from the energy storage system  36  to the electrical energy transmission system  28 . 
       FIG. 6  depicts an example embodiment of the energy action determination module  64 , including an energy feed-in revenue generation maximization module  72 , a photovoltaic energy generation forecast module  76 , a component model module  80 , and an optimization engine module  84 . For example, in example embodiments, the energy feed-in revenue generation maximization module  72  receives one more of sensed information from the interface and/or sensor module  60 , forecast information from the photovoltaic energy generation forecast module  76 , and model information from the component model module  80 , and determines energy actions for the photovoltaic energy generation system  32  and energy storage system  36  to optimize revenue generated by providing electrical energy from the photovoltaic energy generation and supply system  24  to the electrical energy transmission system  28  for a predetermined planning horizon based on the received information. For example, in an example, the energy feed-in revenue generation maximization module  72  is configured to compose a revenue generation model including a linear revenue generation objective function and associated linear constraints, and optimize the composed revenue generation model using, e.g., a mixed integer linear programming approach, such as by providing the revenue generation model to the optimization engine module  84  and receiving an optimized solution from the optimization engine module  84  determining energy actions and associated system parameters. The energy feed-in revenue generation maximization module  72  is, for example, configured to output an indication of the determined energy actions to the control module  68 . 
     In example embodiments, the photovoltaic energy generation forecast module  76  is configured to receive sensed information from the interface and/or sensor module  60  and provide a forecast of the photovoltaic energy generation for the predetermined planning horizon to the energy feed-in revenue generation maximization module  72  based on one or more of the received sensed information, stored historical energy generation forecast data, etc. 
     In example embodiments, the component model module  80  provides parameters characterizing components of the photovoltaic energy generation and supply system  24  to the energy feed-in revenue generation maximization module  72 , such as charging and discharging efficiencies of the energy storage module  52 , etc. 
     In example embodiments, the optimization engine module  84  is configured to receive the composed revenue generation model from the energy feed-in revenue maximization module  72 , such as the revenue generation objective function and associated constraints, optimize the revenue generation model to maximize the revenue generation objection function in view of the associated constraints, and provide an optimized solution of the revenue generation model to the energy feed-in revenue maximization module  72 , to determine corresponding energy actions and associated system control parameters of the optimized solution. 
     Components of the monitoring and control system  40  can be implemented as hardware, software, or a mixture of hardware and software. For example, components of the monitoring and control system  40 , such as any individual one, subset, or all of the energy action determination module  64 , interface and/or sensor module  60 , and control module  68  can include a processor and a non-transitory storage medium, where the non-transitory storage medium includes program instructions, which when executed by the processor, cause the processor to perform embodiments of the functions of such components discussed herein, such as example embodiments of methods of feeding electrical energy from the photovoltaic energy generation and supply system  24  to the electrical energy transmission system  28  depicted in  FIGS. 7 and 9  and discussed below. 
     Although  FIGS. 1-6  depict embodiments of systems, modules and components of a photovoltaic energy generation and supply system  24 , these systems, modules and components can also be used in connection with other types of renewable energy generation and supply systems, such as wind-based energy generation and supply systems, by replacing the photovoltaic energy generation module  44  with other types of renewable energy generation modules, such as wind-based energy generation modules. 
       FIG. 7  is a flowchart that illustrates a method of feeding electrical energy from the photovoltaic energy generation and supply system  24  to the electrical energy transmission system  28  so as to maximize revenue generated by the feed-in in an improved manner, according to an example embodiment of the present invention. In example embodiments, the method utilizes a simplified revenue generation model, based on a photovoltaic energy generation forecast for a predetermined planning horizon and requirements for the electrical energy feed-in, to provide improved revenue generation in a less complex and reduced cost manner. For example, in an example, the method composes a simplified revenue generation model having a linear revenue generation objective function and plurality of linear constraints, and optimizes the composed simplified revenue generation model using a mixed-integer linear programming approach. 
     The illustrated example method begins at step  702 . At step  704 , a forecast of energy generation by the photovoltaic energy generation system  32  for a predetermined time period is be obtained. The predetermined time period is, for example, a planning horizon for planning energy actions of the photovoltaic energy generation and supply system  24 , such as, e.g., a one day period. The forecast of photovoltaic energy generation is obtained, for example, by the energy feed-in revenue maximization module  72  from the photovoltaic energy generation forecast module  76 . 
     The method of  FIG. 7  is implemented either statically or dynamically, the latter of which is also discussed further below in regard to  FIG. 9 , the forecast being obtained either at a selected time during the predetermined time period, such as at a beginning of the predetermined time period, in embodiments of a static implementation, or at a plurality of selected time intervals during the predetermined time period, in embodiments of a dynamic implementation. 
       FIG. 8  is a graph depicting exemplary embodiments of a forecast of energy generation  88  by the photovoltaic energy generation system  32  and an electrical power feed-in  92  by the photovoltaic energy generation and supply system  24  to the electrical energy transmission system  28 . In  FIG. 8 , the forecast includes a predicted electrical energy generation at each of a plurality of time intervals during the predetermined time period. The predicted electrical energy generation can have a form aligned to solar energy conditions, such as minimum energy generation during the evening, e.g., at the beginning and ending of the predetermined time period, and a maximum during the day, e.g., in the middle of the predetermined time period. 
     Returning to  FIG. 7 , at step  706  of the illustrated example method, a revenue generation objective function representing revenue generated by feeding energy from the photovoltaic energy generation and supply system  24  to the electrical energy transmission system  28  over the predetermined time period is determined. To compose a simplified revenue generation model, the revenue generation objective function is, in an example embodiment, a linear function, which can enable the revenue generation model to be optimized using a mixed integer linear programming approach. In example embodiments, the revenue generation objective function can be represented as follows: 
       maximize Σ t=1   T   q   t   Δt/ 60  (1)
 
     where q t  is an electric power feed-in by the photovoltaic energy generation and supply system  24  to the electrical energy transmission system  28  for which an entity associated with the photovoltaic energy generation and supply system  24  is reimbursed by an entity associated with the electrical energy transmission system  28 ; Δt is a time interval between times t−1 and t, such as between energy actions, during the predetermined time period, where Δt can be expressed in units of time, e.g., minutes; T is a number of such time intervals in the predetermined time period, and 60 is a conversion factor to convert a unit of time of Δt, such as minutes, into a unit of time on which q t  is based, such as, e.g., hours, although in other embodiments different conversion factors can be selected depending on the units of time on which Δt and q t  are based. That is, the revenue generation can be represented by a sum of an amount of reimbursed electrical power fed by the photovoltaic energy generation and supply system  24  into the electrical energy transmission system  28  for each of the time intervals making up the predetermined time period. 
     At step  708 , a plurality of constraints on the revenue generation function are determined. To compose a simplified revenue generation model, the constraints can be linear constraints, again which can enable the revenue generation model to be optimized using a mixed integer linear programming approach. 
     In example embodiments, the plurality of constraints include at least some constraints based on requirements for the feeding of electrical energy from the photovoltaic energy generation and supply system  24  to the electrical energy transmission system  28  that must be satisfied in order for the operator of the photovoltaic energy generation and supply system  24  to receive payment for the energy feed-in. 
     In example embodiments, there can be three phases of the electrical energy feed-in during the predetermined time period, including a ramp-up phase, which is a period in which the electrical power feed-in can increase or stay the same; a quasi-stationary phase, which is a period during which the electrical power feed-in can vary only within predetermined limits; and a ramp-down phase, which is a period during which the electrical power feed-in can decrease or stay the same. In an example embodiment, a transition time is at which the ramp-up phase transitions to the quasi-stationary phase and a transition time tf at which the quasi-stationary phase transitions to the ramp-down phase are announced by the photovoltaic energy generation and supply system  24  to the electrical energy transmission system  28  at a predetermined amount of time before they occur. 
     Returning to  FIG. 8 , the depicted electrical power feed-in has a ramp-up phase between the beginning of the predetermined time period and a first transition time ts 1 , a quasi-stationary phase between the first transition time ts 1  and a second transition time tf 1 , and a ramp-down phase between the second transition time tf 1  and the end of the predetermined time period. 
     In an example embodiment, each of these phases are required to satisfy rate or level limits. For example, in an example embodiment, during the ramp-up phase, the rate of increase of the level of the electrical power feed-in is limited to be below a predetermined rate of increase, such as a below a predetermined percentage of an allowed maximum electrical power feed-in level. A constraint based on this requirement can be represented as follows: 
       − M   1 (1− x   t−1 )≦ P   t   −P   t−1 ≦0.006 P max+ M   1 (1− x   t−1 ),∀ t= 2 . . .  T   (2),
 
     where M 1  is a predetermined constant; x t  is a binary variable at time t having a value of 1 if t is during the ramp-up phase and 0 otherwise; Pt is a pseudo power feed-in at time t, for which the constraints on power levels during the ramp-up, quasi-stationary and ramp-down phases are stated, and representing the actual power feed-in if these constraints are also satisfied by the actual-power feed in (as discussed further below, to enable an optimization of the revenue generation objective function even in circumstances where penalties are unavoidable, such as due to unfavorable weather conditions, so that actual power levels cannot satisfy these constraints, the power level requirements can instead be stated in terms of the pseudo power feed-in Pt, and the difference between this pseudo power feed-in and the actual-power feed-in can be tracked, and thus minimized, by performing a balancing of the pseudo power feed-in with the utilized generated photovoltaic power, the electrical power flowing into and out of the energy storage module, and a slack variable); Pmax is the maximum allowed power feed-in; and 0.006, i.e., 6%, is an exemplary predetermined percentage of the maximum allowed power feed-in, although in other embodiments different predetermined percentages can be selected. The M1 factor and xt can be utilized to effectively implement “if” and “or” functions, whereby constraint (2) can equate to a first equivalent constraint of 0≦Pt−Pt−1≦0.006Pmax during the ramp-up phase, to implement the limit on the electrical power feed-in rate of increase during this phase, and a second equivalent constraint of −M1≦Pt−Pt−1≦M1 during the other phases, where M1 is chosen to have a relatively large value, such as much greater than 0.006Pmax, to effectively impose no meaningful constraint during these other phases. 
     During the quasi-stationary phase, the electrical power feed-in can be limited to be within a predetermined range, such as between a predetermined percentage of the maximum electrical power feed-in above a predetermined reference electrical power feed-in and a predetermined percentage of the maximum electrical power feed-in below the predetermined reference electrical power feed-in. A constraint based on this requirement cab be represented as follows: 
       −0.025 P max− M   2 (1− y   t )≦ P   t   −P ref≦0.025 P max+ M   2 (1− y   t ),∀ t− 1 . . .  T   (3)
 
     where M2 is a predetermined constant; yt is a binary variable at time t having a value of 1 if t is during the quasi-stationary phase and 0 otherwise; Pt is the pseudo power feed-in at time t; Pref is the predetermined power feed-in reference value; and 0.025, i.e., 2.5%, is an exemplary predetermined percentage of the maximum allowable power feed-in above and below the predetermined power feed-in reference value, although in other embodiments different predetermined percentages can be selected. Similar to as with constraint (2), the M2 factor and yt can be utilized to effectively implement “if” and “or” functions, whereby constraint (3) equates to a first equivalent constraint of −0.025Pmax≦Pt−Pref≦0.025Pmax during the quasi-stationary phase, to implement the limit on the electrical power feed-in level variability during this phase, and a second equivalent constraint of −M2≦Pt−Pref≦M2 during the other phases, where M2 is chosen to have a relatively large value, such as much greater than 0.025Pmax, to effectively impose no meaningful constraint during these other phases. 
     During the ramp-down phase, the electrical power feed-in rate of decrease can be limited to be below a predetermined rate of decrease, such as a below a predetermined percentage of an allowed maximum electrical power feed-in. A constraint based on this requirement can be represented as follows: 
       −0.006 P max− M   3 (1− z   t+1 )≦ P   t   −P   t−1   ≦M   3 (1− z   t+1 ),∀ t= 2 . . .  T   (4)
 
     where M3 is a predetermined constant; zt is a binary variable at time t having a value of 1 if t is during the ramp-down phase and 0 otherwise; 0.006 is an exemplary predetermined percentage of the maximum allowable power feed-in, although in other embodiments different predetermined percentages can be selected; and Pt is the pseudo power feed-in at time t. Similar to as with constraints (2) and (3), the M3 factor and zt can be utilized to effectively implement “if” and “or” functions, whereby constraint (4) can equate to a first equivalent constraint of −0.006Pmax≦Pt−Pt−1≦0 during the ramp-down phase, to implement the limit on the electrical power feed-in rate of decrease during this phase, and a second equivalent constraint of −M3≦Pt−Pt−1≦M3 during the other phases, where M3 is chosen to have a relatively large value, such as much greater than 0.006Pmax, to effectively impose no meaningful constraint during these other phases. 
     In an example embodiment, the ramp-up, quasi-stationary, and ramp-down phases are required to appear in a predetermined order. For example, in an example, the ramp-up phase is required to occur first during the predetermined time period, the quasi-stationary phase is required to occur second during the predetermined time period, following the ramp-up period, and the ramp-down phase is required to occur third during the predetermined time period, following the quasi-stationary phase. In an example embodiment, the quasi stationary phase is also required to be of at least a predetermined length. Constraints based on these requirements can be represented as follows: 
         x   1 =1  (5)
 
         z   T =1  (6)
 
         x   t   ≧x   t+1 ,∀ t =1, . . . , T− 1  (7)
 
         z   T   ≦z   t+1 ,∀ t =1, . . . , T− 1  (8)
 
         x   t   +y   t   +z   t =1  (9)
 
       Σ t=1   T   y   t   ≧L,∀   t =1, . . . , T   (10)
 
     where L is a predetermined time index length. That is, constraint (5) requires xt to be 1 at time  1 , and thus the ramp-up phase to be first. Constraint (6) requires zt to be 1 at time T, and thus the ramp-down phase to be last. Constraint (7) requires xt to be decreasing as a function oft, and thus once the ramp-up phase has ended, i.e., xt has gone to 0, the ramp-up phase may not occur again. Constraint (8) requires zt to be increasing as a function of t, and thus once the ramp-down phase has begun, i.e., zt gone to 1, it may not end for the remainder of the predetermined time period. Constraint (9) limits the occurrence of only one of the ramp-up, quasi-stationary, and ramp-down phases at any given time t. Constraint (10) limits the quasi-stationary phase to have a length greater than the predetermined time index length L. 
     The transition times ts, tf at which the photovoltaic energy generation and supply system transitions from the ramp-up phase to the quasi-stationary phase, and from the quasi-stationary phase to the ramp-down phase, can be limited to occur only at predetermined times or time intervals. For example, transition times ts, tf can be limited to occur only at half hour or hour increments from the beginning of the predetermined time period or another selected starting time. Constraints based on this limitation can be represented as follows: 
         ts=Σ   t=1   T   x   t   Δt/ 30,∀ t =1, . . . , T   (11)
 
         tf=Σ   t=1   T ( x   t   +y   t )Δ t/ 30,∀ t =1, . . . , T   (12)
 
     where ts and tf are limited to be integers, and 30 is a conversion factor to convert a unit of time of time of Δt, such as minutes, into integers representing half hour increments, although in other embodiments different conversion factors can be selected to produce other predetermined time intervals. 
     In example embodiments, the electrical power feed-in from the photovoltaic energy generation and supply system  24  to the electrical energy transmission system  28  at any given time is limited to be below the maximum power feed-in in the quasi-stationary phase, such as below the predetermined percentage of the maximum electrical power feed-in above the predetermined reference electrical power feed-in. A constraint based on this limitation can be represented as follows: 
         P   t   ≦P ref+0.025 P max,∀ t =1, . . . , T.   (13)
 
     where P t  is the pseudo power feed-in at time t; Pref is the predetermined power feed-in reference value; and 0.025 is the exemplary predetermined percentage of the maximum allowable power feed-in above and below the predetermined power feed-in reference value, although in other embodiments different predetermined percentages can be selected. 
     In example embodiments, the predetermined reference value of the electrical power feed-in from the photovoltaic energy generation and supply system  24  to the electrical energy transmission system  28  is limited to be below a predetermined percentage of the maximum allowable power feed-in. A constraint based on this limitation may be represented as follows: 
         P ref≦0.4 P max;  (14)
 
     where Pref is the predetermined power feed-in reference value; 0.4, i.e., 40%, is an exemplary predetermined percentage, although in other embodiments different predetermined percentage can be selected; and Pmax is the maximum allowable power feed-in. 
     Penalties in the form of withheld payment for electrical energy feed-in can be imposed by an operator of the electrical energy transmission system  28  if requirements, such as those related to feed-in power levels during the ramp-up, quasi-stationary and ramp-down phases, are not met for any given time interval. To enable an optimization of the revenue generation objective function even in circumstances where penalties are unavoidable, such as due to unfavorable weather conditions, these requirements can be stated in terms of the pseudo power feed-in, and the difference between this pseudo power feed-in and the actual-power feed in can be tracked, and thus minimized, by performing a balancing of the pseudo power feed-in with the utilized generated photovoltaic power, the electrical power flowing into and out of the energy storage module, and a slack variable. A constraint that performs such a balancing may be expressed as follows: 
         P   t   =E   t +PV t   +a   t ,∀ t =1, . . . , T   (15)
 
     where P t  is the pseudo power feed-in at time t; E t  is a power flow at time t into or out of the terminals of the energy storage module  52 ; PV t  is a utilized portion of the forecast power of the photovoltaic energy generation system  32  at time t; and a t  is a slack variable to implement flow balance. The slack variable a t  thus tracks the difference between the pseudo power feed-in and the actual electrical power feed-in, the actual electrical power feed-in being equal to P t −a t . 
     The electrical power feed-in for which the operator of the photovoltaic energy generation and supply system  24  is paid can be limited to be less than or equal to the electrical power actually fed into the electrical energy transmission system  28  (for example, payment can be less than that corresponding to the actually fed-in power due to penalties incurred due to power level constraints not being satisfied). A constraint based on this limitation can be represented as follows: 
         q   t   ≦P   t   −a   t ,∀ t =1, . . . , T   (16)
 
     However, minor differences between the pseudo power feed-in and the actual electrical power feed-in can be ignored and not result in penalties. For example, differences between the pseudo power feed-in and the actual electrical power feed-in below a predetermined error level can be ignored. A set of constraints to implement this feature can be represented as follows: 
         a   t   ≦ε+M   4 (1− k   t )∀ t =1, . . . , T   (17)
 
       − a   t   ≦ε−M   4 (1− k   t )∀ t =1, . . . , T   (18)
 
         a   t   ≦ε−M   4 (1− l   t   +k   t )∀ t =1, . . . , T   (19)
 
       − a   t   ≦ε−M   4 ( l   t   +k   t )∀ t =1, . . . , T   (20)
 
         l   t   +k   t ≦1 ∀ t =1, . . . , T   (21)
 
     where a t  is the slack variable representing the difference between the pseudo power Pt satisfying the constraints on the power levels during the ramp-up, quasi-stationary and ramp-down phases at time t; E is a predetermined error power level; M 4  is a predetermined constant; k t  is a binary variable having a value of 1 at time t if −ε≦a t ≦ε and 0 otherwise; l t  is a binary variable having a value of 1 if a t ≧ε and 0 if a t ≦−ε. That is, if M4 is chosen to be large, constraints (17)-(21) require k t  to have a value of 1 at time t if −ε≦a t ≦ε and 0 otherwise, and l t  to have a value of 1 if a t ≧ε and 0 if a t ≦−ε. 
     The penalty for not satisfying the constraints on the power levels during the ramp-up, quasi-stationary and ramp-down phases at time t can include forfeiture of payment for electrical energy feed-in for a predetermined number of time intervals. A constraint that implements this limitation can be represented as follows: 
       Σ j=t   j=t+D−1   q   j   ≦M   5   k   t ∀ t =1, . . . , T   (22)
 
     where j is a time index; D is the predetermined number of time intervals for which payment is forfeited; q j  is an electrical power feed-in at time j for which reimbursement is received; M 5  is a predetermined constant; and kt is the binary variable having a value of 1 at time t if −ε≦a t ≦ε and 0 otherwise. That is, when kt=1, the power level requirements have been met and no penalties have been incurred as a result of the power feed-in at time t, and constraint (22) effectively disappears if M 5  is chosen to be a large number. When k t =0, penalties have been incurred as a result of the power feed-in at time t, and constraint (22) effectively requires the reimbursed power feed-in q j , which can take on a positive value or the value of zero, starting at the present time t and lasting for the predetermined number D of time intervals, to be set to zero. 
     The forecast generated power of the photovoltaic energy generation system  32  that is utilized at any given time can be limited to be less than the total forecast generated power of the photovoltaic energy generation system  32 . A constraint based on this limitation can be represented as follows: 
       PV t ≦ PV t   ,∀ t =1, . . . , T   (23)
 
     where PVt is the utilized forecast generated power of the photovoltaic energy generation system  32  at time t, and  PV t    is the total forecast generated power of the photovoltaic energy generation system  32  at time t. 
     In example embodiments, the plurality of constraints also include at least some constraints to ensure that an optimization of the revenue generation function corresponds to physical and other limitations of the photovoltaic energy generation and supply system  24 . 
     It can occur that energy storage module  52  charges and discharges at less than perfect efficiency. Power flowing into terminals of the energy storage module  52  can be reduced by an efficiency factor as it is stored in the energy storage module  52 . Similarly, power flowing out of terminals of the energy storage module  52  can be reduced from that withdrawn from the energy stored in the energy storage module  52  by another efficiency factor. A constraint based on these limitations can be represented as follows: 
         E   t   =u   t   + η d   −u   t   − /η c ,∀ t =1, . . . , T.   (24)
 
     where E t  is the power flowing at the terminals of the energy storage module  52  at time t, u t   +  is a discharging power flowing out of energy storage of the energy storage module  52  at time t, u t   −  is a charging flowing into energy storage of the energy storage module  52  at time t, η d  is a discharging efficiency factor, and η c  is a charging efficiency factor. 
     The internal power of the energy storage module  52 , that is, the power flowing into and out of the stored energy of the energy storage module  52 , can be composed of a difference of the discharging internal power and the charging internal power. A constraint based on this limitation can be represented as follows: 
         u   t   =u   t   +   −u   t   − ,∀ t =1, . . . , T.   (25)
 
     where u t  is the internal power of the energy storage module at time t, u t   +  is the discharging internal power at time t, and u t   −  is the charging internal power at time t. Both the discharging and charging internal powers can be positive in such a formulation. 
     The energy stored in the energy storage module  52  can be limited to be within a predetermined range of energy values for which the energy storage module  52  is configured for sustainable operation. For example, the energy stored in the energy storage module  52  can be limited to be above a predetermined minimum energy and below a predetermined maximum energy. A constraint based on this limitation can be represented as follows: 
           B ≦S   0 −Σ j=1   t   u   j   Δt/ 60 ≦ B ,∀   t =1, . . . , T   (26)
 
     where  B  is a predetermined minimum stored energy; S 0  is a stored energy of the energy storage module  52  at time  0 ; u j  is the internal power of the energy storage module  52  at a time j; Δt is the time interval between energy actions during the predetermined time period; T is a number of such time intervals in the predetermined time period; 60 is an exemplary time unit conversion factor, although in other embodiments different time unit conversion factors may be selected; and  B  is a predetermined maximum stored energy. 
     The internal power of the energy storage module  52  can be limited to be within a predetermined range of power values. For example, the internal charging power can be limited to be below a predetermined maximum charging power and the internal discharging power may be limited to be below a predetermined maximum discharging power. A constraint based on this limitation can be represented as follows: 
           U ≦u   t   ≦Ū;∀   t =1, . . . , T.   (27)
 
     Where  U  is a predetermined maximum charging power, ut is the internal power of the energy storage module  52  at a time t, and Ū predetermined maximum discharging power. 
     In examples of the above revenue generation function and constraints, the variables k t , l t , x t , y t , z t  are binary; the variables t s , t f  are integers; the variables q t , p t , PV t , Pref, u t   + , u t   −  are continuous and greater than zero; and other variables can be continuous. 
     In an example embodiment, the plurality constraints can include each of constraints (2)-(27). In other example embodiments, the plurality of constrains can include selected subsets of constraints (2)-(27). 
     Returning to  FIG. 7 , at step  710 , the revenue generation function is optimized in view of the plurality of constraints, and energy actions are determined for implementing the optimized function. The formulation of the simplified revenue generation model, including the revenue generation objective function and the plurality of constraints as linear functions, and the variables as a mixture of continuous, integer, and/or binary variables, can enable the revenue generation objective function and constraints to be optimized using a mixed integer linear programming approach. 
     In an example embodiment, the revenue generation objective function and the plurality of constraints are provided to the optimization engine module  84 , which then produces, e.g., using an optimization methodology, such as a mixed integer linear programming approach, an optimized solution of the revenue generation objective function in view of the plurality of constraints. 
     In example embodiments, the revenue generation function and plurality of constraints are provided to the optimization engine module in a format that the optimization engine module is configured to accept. For example, an existing mixed integer linear programming tool, such as the intlinprog function of MatLab software provided by MathWorks, Inc., can accept a linear objective function; one or more linear constraints in the form of linear equalities, linear inequalities, or bounds; and an identification of variables that are integers; and provide an optimization of the objective function in view of the constraints for integer values of the identified variables. 
     The optimized solution can include values of the variables of the revenue generation objective function and plurality of constraints corresponding to a maximization of the revenue generation objective function in view of the plurality of constraints, which can represent energy actions to implement the maximized revenue generation. For example, the optimized solution can include an actual electrical power to be fed into the electrical energy transmission system  28  at each time t, the electrical power that is to be supplied to or drawn from the energy storage module  52  at each time t, the transition time t s  to transition between the ramp-up and quasi-stationary phases, and the transition time t f  to transition between the quasi-stationary and ramp-down phases. 
     The optimized solution can also include values of other variables of interest of the maximized revenue generation objective function, such as the forecast electrical power generated by the photovoltaic energy generation system  32  that is to be utilized at each time t, the electrical energy feed-in for which reimbursement will be received at each time t, etc., which can be used in evaluating the effectiveness of the optimization, adjusting parameters of the optimization, etc. 
     At step  712 , one or more of the determined energy actions can be executed to implement the optimized revenue generation. For example, at each time t of the predetermined time period, the determined actual electrical power feed-in, which can be fed into the electrical energy transmission system  28 , can consist of a corresponding portion of the utilized forecast generated photovoltaic electrical energy at time t and a corresponding portion of electrical energy drawn from the electrical energy storage module  52  at time t, and any determined power to be supplied to the energy storage module  52  can be supplied. Additionally, if the transition time t s  to transition between the ramp-up and quasi-stationary phases, or the transition time t f  to transition between the quasi-stationary and ramp-down phases, is upcoming within a predetermined length of time at time t, the transition can be announced to the electrical energy transmission system. To implement the energy actions, the monitoring and control system  40  can issue corresponding control signals to components of the photovoltaic energy generation system  32  and energy storage system  36 . At step  714 , the method ends. 
     As indicated above, the method of  FIG. 7  can be implemented either statically or dynamically.  FIG. 9  depicts an example embodiment of the method of  FIG. 7  in which one or more of the steps of the method are implemented at each of a plurality of selected time intervals during the predetermined time period. 
     The method begins at step  902 . At step  904 , parameters for dynamic execution of the method are initially set, such as in a storage component of the energy feed-in revenue maximization module. For example, one or more of a current time t, a current energy state of the energy storage module  52 , etc. can be set. The current time t can be set to 0. The current energy state of the energy storage module  52  can be determined using the interface and/or sensor module  60  of the monitoring and control system  40  and set. 
     At step  906 , a current energy generation by the photovoltaic energy generation system  32  is obtained. The energy generation by the photovoltaic energy generation system  32  can be determined using the interface and/or sensor module  60 . 
     At step  908 , a forecast of energy generation by the photovoltaic energy generation system  32  from the outlook at time t for the remainder of the predetermined time period is obtained. Step  908  can be performed similarly to as discussed above for static implementations of step  704  of method  700  of  FIG. 7 , except the photovoltaic energy generation forecast module  76  can utilize one or more of the current energy generation by the photovoltaic energy generation system  32  and previously realized energy generation, in addition to a weather forecast for the predetermined time period, historical energy generation data to provide the forecast, etc. 
     At steps  910  and  912 , a revenue generation objective function and a plurality of constraints are determined, respectively, for time t. Steps  910  and  912  can performed in a same or similar way to as discussed above for steps  706  and  708 , respectively, of the method  700  of  FIG. 7 , except that the revenue generation objective function and plurality of constraints can be modified to account for currently observed and past realized variable values. For example, the forecast power generation  PV t    of the photovoltaic energy generation system used in, e.g., constraint (23) can be composed of the realized power generation at past times, the observed power generation at the current time, and the forecast of energy generation by the photovoltaic energy generation system  32  from the outlook at time t for the remainder of the predetermined time period. If the transition times t s  and t f  have already been determined, they can be set to the determined values in corresponding constraints rather than remain as variables. Similarly, past values of the state of the energy storage system  52  can be incorporated in respective constraints. 
     At steps  914  and  916 , the revenue generation objective function is optimized in view of the plurality of constraints to determine energy actions and the determined energy actions are executed, respectively, for time t. Steps  914  and  916  can performed in a same or similar way to as discussed above for steps  710  and  712 , respectively, of the method  700  of  FIG. 7 . 
     At step  918 , parameters for dynamic execution of the method are updated, such as in a storage component of the energy feed-in revenue maximization module  72 . For example, the time t can be incremented. 
     At step  920 , whether the end of the predetermined time period has been reached is determined. If the end of the predetermined time period has not yet been reached, the method proceeds back to step  906  for additional iteration(s) of the dynamic steps of the method, but if the end of the predetermined time period has been reached, the method proceeds to step  922 , where the method ends. 
     Although embodiments of the methods  700 ,  900  of  FIGS. 7 and 9  of feeding electrical energy from a photovoltaic energy generation and supply system to an electrical energy transmission system can be implemented using embodiments of the photovoltaic energy generation and supply system  24  depicted in  FIGS. 1-6 , such as discussed above, embodiments of these methods  700 ,  900  can also be used with energy generation systems and energy generation systems having configurations different from those of depicted in  FIGS. 1-6 . 
     Although  FIGS. 7 and 9  depict embodiments of methods of feeding electrical energy from a photovoltaic energy generation and supply system to an electrical energy transmission system, embodiments of these methods  700 ,  900  can also be used to feed electrical energy from other types of renewable energy generation and supply systems, such as wind-based energy generation and supply systems, to electrical energy transmission systems, by replacing photovoltaic energy generation with other types of renewable energy generation, such as wind-based energy generation, in the steps of the methods. 
       FIGS. 10A-10B, 11A-11B, and 12A-12B  are graphs depicting forecast electrical energy generation by the photovoltaic energy generation system  32 , actual electrical energy feed-in from the photovoltaic energy generation and supply system  24  to the electrical energy transmission system  28 , and electrical energy storage produced by exemplary performances of embodiments of the method  700  of  FIG. 7 .  FIGS. 10A-10B  depict a forecast electrical power generation  96 , an actual electrical power feed-in  100 , transition times ts 2 , tf 2 , and a corresponding energy state  104  of the energy storage module  52 , for a sunny day. The paid actual electrical energy feed-in can be calculated as 72.7% of the forecast generated power, significantly higher than in systems without an energy storage module or systems with other utilization of energy storage.  FIGS. 11A-11B  depicts a forecast electrical power generation  108 , an actual electrical power feed-in  112 , transition times ts 3 , tf 3 , and a corresponding energy state  116  of the energy storage module  52 , for a cloudy day. The paid actual electrical energy feed-in can be calculated as 98.5% of the generated power, again significantly higher than for other systems.  FIGS. 12A-12B  depicts a forecast electrical power generation  120 , an actual electrical power feed-in  124 , transition times ts 4 , tf 4 , and a corresponding energy state  128  of the energy storage module  52 , for a case where a penalty is unavoidably incurred due to varying weather conditions and energy storage module capacity, starting at hour 15.5 and ending at hour 17.5, but nonetheless again still resulting significantly higher paid feed-in percentage than for other systems. 
     An example embodiment of the present invention is directed to processing circuitry configured to perform the example methods described herein. In example embodiments, the processing circuitry, for example, includes one or more processors, which can 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 the methods. 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 method(s). 
     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 method(s). 
     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 may 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 the following claims. 
     For example, additional embodiments of the photovoltaic energy generation and supply system and methods of controlling the photovoltaic energy generation and supply system are possible. For example, any feature of any of the embodiments of the photovoltaic energy generation and supply system and methods of controlling the photovoltaic energy generation and supply system described herein can be used in any other embodiment of the photovoltaic energy generation and supply system and methods of controlling the photovoltaic energy generation and supply system. Also, embodiments of the photovoltaic energy generation and supply system and methods of controlling the photovoltaic energy generation and supply system can include only any subset of the components or features of the photovoltaic energy generation and supply system and methods of controlling the photovoltaic energy generation and supply system discussed herein.