Patent Publication Number: US-10316833-B2

Title: Hydroelectric power optimization

Description:
BACKGROUND 
     Hydroelectric power generation generally involves harnessing the force of moving water to generate electricity. In most cases, an electric generator generates electricity from the potential energy of dammed water that drives a water turbine. Often, a hydroelectric power station may generate electricity for an entire area; however, some hydroelectric stations are controlled by and for a single entity, such as a factory. There are many factors involved in the operation of hydroelectric power stations. For example, constraints such as reservoir volume, the difference in height (i.e., the head) between the reservoir (forebay) and the water&#39;s outflow (tailrace), turbine efficiency, water flow rates, and even water rights can each have effects on the amount of power generated at any given time. 
     Managers and operators of hydroelectric power stations are often confronted with difficult operational and planning decisions. For example, determining appropriate flow rates through each turbine or combinations of turbines, pumped-storage times and volumes, and turbine replacement options are all decisions that may face each hydroelectric power station manager or operator. Additionally, these operators may need to evaluate operational policy, optimize the system, administer water rights and accounting, and prepare long-term resource plans. Unfortunately, current products do not provide accurate or efficient solutions for handling today&#39;s highly competitive water resources needs. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The detailed description is set forth with reference to the accompanying figures. In the figures, the left-most digit(s) of a reference number identifies the figure in which the reference number first appears. The use of the same reference numbers in different figures indicates similar or identical items. 
         FIG. 1  illustrates an example architecture for providing optimized hydroelectric solutions based at least in part on hydroelectric power system data received from local data or from a remote server. 
         FIG. 2  illustrates an example of hydroelectric system data, which, in one aspect, may be displayed by a spreadsheet application. 
         FIG. 3  is a flow diagram illustrating a method of providing the optimized hydroelectric solutions of  FIG. 1 . 
         FIG. 4  is a flow diagram illustrating an alternative method of providing the optimized hydroelectric solutions of  FIG. 1 . 
         FIG. 5  is a flow diagram illustrating an additional alternative method of providing the optimized hydroelectric solutions of  FIG. 1 . 
     
    
    
     DETAILED DESCRIPTION 
     Overview 
     Embodiments of the present disclosure are directed to, among other things, providing optimized hydroelectric solutions for managing and/or operating hydroelectric power stations or other types of water management systems. As an overview, hydroelectric power may be generated by harnessing the potential energy contained in dammed water that drives a turbine or water wheel, with the aid of an electric generator for converting the mechanical energy of the turbine into electricity. Mechanical gates or sluices may control the flow rate of the dammed water through the turbine. In some instances, pumps may channel the water back to the reservoir to store energy for peak hours. Station operators and managers generally face a myriad of challenges when controlling the flow and storage of water while attempting to optimize power production. This is due to the fact that many factors affect power output, such as turbine efficiency, head, and flow. Additionally, each of these factors may affect the other, such that the equation for calculating power,
 
Power=(1/11.82)·η· h·Q   (Equation 1)
 
where η=efficiency, h=head, and Q=flow rate, is a non-linear, multi-variable equation. For example, an increase in flow may directly affect efficiency and/or head; however, the relationships may not be linear. Additionally, other factors, such as water rights (e.g., tribal fishing rights, conservation and environmental regulations, etc.), private licenses, public grants, reservoir size, and rainfall can indirectly affect the power output by directly affecting the equation variables. For example, rainfall may affect head while licenses and grants may require changes in flow rate.
 
     In some instances, a system of the present disclosure may receive hydroelectric power station data from a local data store, or from a remote server, for calculating an optimized power solution. Additionally, or in the alternative, the system may form optimization models for optimizing power over an extended period of time. The system may use an iterative process to calculate the optimized power solution linearly. As such, a variable of the power equation (Equation 1) may be locked with an estimated value to create a linear estimation. In some instances, the locked variable may be the head variable, while in other cases, the flow or the efficiency variables may be locked. Locking a variable entails setting a particular variable to a predetermined or estimated value so that it is no longer an unknown. As such, a solution to a single non-linear equation may be computed linearly. In some examples, based on locking a variable and solving linearly, a solution that historically would have taken hours, may now be returned in less than 60 seconds, or sometimes less than 10 seconds, depending on the sample size of data, the accuracy of the desired solution, and the speed of the computing system used to compute the solution. Multi-year studies that historically were impossible to solve may now be completed in hours or a few days. 
     In one aspect, the head variable may be locked with an estimated head value. The system may then solve the equation for power using the estimated head value and known efficiency and flow data. Additionally, the known efficiency and flow data may be accessible, or extrapolated, from an efficiency curve for a particular turbine. Alternatively, the efficiency and flow data may be calculated based on historical data from a known power station, or it may be received from the remote server that provided the power station data. 
     When the head value is locked with an estimated head value, the system may then calculate an actual head value based at least in part on other information known about the power station. In one aspect, this other information may be flow and efficiency data from an efficiency curve, data from a historical spreadsheet, or measured data for a particular point in time. The calculated head value may then be compared to the estimated head value used in calculating the optimized power solution. In one aspect, if the difference is outside a predetermined tolerance threshold, and/or an iteration threshold has not been reached, the system may re-solve the equation for power using the calculated head value. Additionally, the system may iteratively repeat these calculations and comparisons until the head value difference (between the previously locked head value and the next calculated head value) is within the predetermined tolerance threshold or until the iteration threshold is reached. 
     In some aspects, the optimized power solution may be made up of each calculated power solution and/or data from each iteration. For example, the optimized power solution may include one power solution for a given time, a combination of power solutions for different respective times, or a combination including one or more power solutions and the associated variable inputs that formed each respective power solution for one or more respective times. The system may then populate a spreadsheet or database with the data, provide the data to a local user of the system, or provide the data to a remote server. 
     Additionally, the described techniques may also be used on water management systems that are not designed to generate power such as water storage reservoirs for flood control. Alternatively, or in addition, the described techniques may also be used for providing solutions to systems that both provide power generation and water storage. 
     The discussion begins with a section entitled “Illustrative Architecture,” which describes a non-limiting environment in which optimized power solutions may be iteratively calculated and provided. Next, a section entitled “Illustrative Data” follows and describes example data for implementing the described calculations. Finally, the discussion concludes with a section entitled “Illustrative Processes” and a brief conclusion. 
     This brief introduction, including section titles and corresponding summaries, is provided for the reader&#39;s convenience and is not intended to limit the scope of the claims, nor the proceeding sections. Furthermore, the techniques described above and below may be implemented in a number of ways and in a number of contexts. Several example implementations and contexts are provided with reference to the following figures, as described below in more detail. However, the following implementations and contexts are but a few of many. 
     Illustrative Architecture 
       FIG. 1  depicts an illustrative architecture  100  in which techniques for iteratively calculating and providing optimized hydroelectric power solutions may be implemented. In architecture  100 , one or more users  102  may utilize local server  104  to access a system (or website)  106  for iteratively calculating and providing optimized hydroelectric power solutions. Additionally, or alternatively, one or more users  108  may utilize a remote server  110  to access the system  106  via a network  112 . Network  112  may include any one or a combination of multiple different types of wired or wireless networks, such as cable networks, the Internet, local area networks (LANs), and other private and/or public networks. While the illustrated example represents users  108  accessing system  106  over network  112 , the described techniques may equally apply in instances where users  108 , or users  102 , interact with the system  106  over the phone, via a kiosk, or in any other manner. It is also noted that the described techniques may apply in other client/server arrangements (e.g., via a dedicated terminal, etc.), as well as in non-client/server arrangements (e.g., locally-stored software applications, etc.) such as when users  102  access the system  106  via the local server  104 . 
     As described briefly above, system  106  may allow users  102  or  108  to provide hydroelectric power station data  114  (“hydro data”) to system  106 . In some aspects, the users  102  may provide the hydro data  114  directly to the system via a data receiving module  116  to be stored in memory  118  of the local server  104 . In other aspects, however, users  108  may provide the hydro data  114  to the remote server  110 . Here, the remote server  110  may provide the hydro data  114  to system  106  via the network  112 . As noted above, system  106  may be implemented as a website  106  for interacting with users  108  over the network  112 . System  106  may additionally, or alternatively, be implemented as a Web service, or other application programming interface (API) that allows communication between the system  106  and users of computing devices other than local server  104 . In yet other examples, users  108  may provide hydro data  114  in any digital manner known, such that system  106  may receive it at the local server  104 . For example, users  108  may provide the hydro data  114  to system  106  via email, text message, compressed file, Hypertext Markup Language (“HTML”) file, Extensible Markup Language (“XML”) file, data stream or feed, etc. Additionally, in one example, the hydro data may be collected by a sensor network and received by system  106  in real-time or substantially real-time. 
     In some examples, users  108  may provide data to system  106  and receive power solutions in exchange for fees. The fees may be one-time fees, fees based on a subscription basis, fees based at least in part on the granularity of the optimal power data, an amount of exchange of the optimal power data, fees based on a frequency of exchange of the optimal power data, fees based on a speed with which the optimal power data is provided, fees based on a number of clock cycles to determine the optimal power data, fees based on a number of computations to determine the optimal power data, and/or fees based on a power savings achievable using the optimal power data. Additionally, in some examples, optimal power data may be provided to remote server  110  in the form of potential profit estimates for a hydroelectric power station, results of a potential turbine comparison, results of a power savings analysis, and/or in the form of peak shaving data. Hydro data may also include a recommendation to make a change, perform an act (e.g., maintenance or replacement of turbines, open or close sluice gates), etc. 
     Further, as noted briefly above, hydro data  114  may comprise hydroelectric power station data from a hydroelectric power station (or system) such as hydro-system  120 . In one aspect, hydro-system  120  represents a hydroelectric power station with one or more dams, reservoirs, turbines, generators, and/or transformers. The hydro data  114  may be data corresponding to an entire hydro-system made up one or more of each of the elements listed above, may be data corresponding to a hydro-system such as the one shown in  FIG. 1  (i.e., hydro-system  120 ) made up of a single reservoir, dam, turbine, generator, and transformer, or may be data corresponding to a hydro-system of any configuration. 
     As noted above, local server  104 , or multiple local servers perhaps arranged in a cluster or as a server farm, may host system (or website)  106 . Other server architectures may also be used to host the system  106 . System  106  is capable of handling requests from many users and serving, in response, various user interfaces that can be rendered locally by a display device of the local server  104  or at user computing devices, such as remote server  110 . System  106  can be any type of software system or website that supports user interaction, including interaction with operators, managers, contractors, or other types of users, and so forth. However, as discussed above, the described techniques can similarly be implemented without a website altogether. 
     Taken together,  FIG. 1  allows users  102  and/or users  108  to request that optimized power solutions be calculated based on provided hydro data  114 . To illustrate, envision that user  108  accesses system  106  via network  112  and provides hydro data  114  corresponding to at least flow data, head data, and efficiency data for hydro-system  120  over the previous six months. In this example, the hydro data  114  may be provided in a spreadsheet file, database file, or other type of file for organizing data, with each respective value corresponding to a particular time of day for the six month period. In other examples, however, the system  106  may provide a graphical user interface (GUI) to user  108  (including text fields for entering data), displayed by the remote server  110 , which provides a method for manually entering the hydro data  114  or a method for uploading a file containing the hydro data  114 . 
     While  FIG. 1  illustrates local server  104  and remote server  110  as personal computing devices, other types of computing devices may include laptop computers, portable digital assistants (“PDAs”), mobile phones, set-top boxes, game consoles, mainframe computers, super computers, data centers, and so forth. In each instance and as illustrated, each server is equipped with one or more processors  122  and memory  118  to store applications and data, such as the data receiving module  116  that enables hydro data  114  to be provided to system  106 . 
     Once the data is received by system  106  via the Internet or other network connection, such as network  112 , the system  106  may iteratively calculate optimized power solutions based on the hydro data  114  and provide the optimized power solutions to the users  108  via the network  112 . In some instances the power solutions may be provided based on iteratively calculating, at a predetermined time interval granularity (e.g., one week, one day, or even one minute), until a tolerance percentage is reached, until an iteration threshold is reached, and/or until a predetermined time period has elapsed. In one some examples, the tolerance percentage may be 1%, 0.05%, or any other percentage based on the intended use of the solution. 
       FIG. 1  further illustrates local server  104  having processing capabilities and memory suitable to store and execute computer-executable instructions. In this example, local server  104  includes one or more processor(s)  122 , communications interface(s)  124 , and memory  118 . Depending on the configuration of local server  104 , memory  118  is an example of computer storage media and may include volatile and nonvolatile memory. Thus, memory  118  may include, but is not limited to, random-access memory (“RAM”), read-only memory (“ROM”), electrically erasable probramable read-only memory (“EEPROM”), flash memory, or other memory technology, or any other non-transmission medium which can be used to store digital items or applications and data which can be accessed by local server  104 . Computer storage media, however, does not include any data in a modulated data signal, such as a carrier wave or other propagated transmission medium. 
     Memory  118  may be used to store any number of functional components that are executable on processor(s)  112 , as well as data and content items that are rendered by local server  104 . Thus, memory  118  may store an operating system and several modules containing logic. 
     As noted above, a data receiving module  116  located in memory  118  and executable on processor(s)  122  may facilitate receiving hydroelectric power station data, such as hydro data  114 . 
     Memory  118  may further store variable locking module  126  to lock a variable of the non-linear, multi-variable power equation  128  (Equation 1). In one aspect, variable locking module  126  may be configured to lock the head variable by setting the “h” variable of the power equation  128  to an estimated head value. In some examples, the estimated head value may be selected from the hydro data  114 , from historical data of another power station, randomly, or in a pseudo-random fashion. In another aspect, however, variable locking module  126  may be configured to lock the efficiency variable or the flow variable by setting the “η” or “Q” variables to estimated values, respectively. 
     Memory  118  may also store linear estimation module  130  and iteration module  132 . Linear estimation module  130  may be configured to calculate a linear estimation of the non-linear power equation  128 . In other words, by locking a single variable, the non-linear power equation  128  becomes a linear equation and may be solved much faster and much less computationally demanding. While the solution is an estimate, the iteration module  132  described will generally converge on a solution that is more accurate than the original estimated solution. In one example, once the variable locking module  126  locks the head variable, and flow and efficiency data for a given time period are received from the hydro data  114  spreadsheet, the linear estimation module  130  may calculate an estimated power solution linearly. 
     Memory  118  may also store variable calculation module  134 , which may be configured to calculate an actual value for the variable that was previously locked by the variable locking module  126 . That is, in the example, where the head value is locked prior to the linear estimation, the variable calculating module  134  will calculate an actual head value. In some aspects, variable calculation module  134  may calculate the actual value based on an efficiency curve  136  for a particular turbine. In other examples, the actual value may be calculated based on other data from the hydro data  114  spreadsheet or other data known about the hydro-system  120 . Additionally, in some examples, the efficiency curve  136  may chart turbine efficiency against flow. This data may be provided by the manufacturer of the turbine, may be known from trials, or may be determined from historical data. 
     Iteration module  132  may be configured to iterate to within a tolerance and/or until an iteration threshold is reached. Iteration module  132  may also be configured to operate the linear estimation module  130  and the variable calculation module  134  repeatedly until such tolerance or threshold is reached. For example, until the tolerance or threshold are reached, the iteration module  132  may continue to instantiate the linear estimation followed by the variable calculation. 
     Additionally, memory  118  may further store a tolerance checking module  136  configured to check whether the linear estimation module  130  has estimated the power solution to within the tolerance or whether the iteration threshold has been reached. In one example, an iteration threshold of 5 iterations may be pre-selected by users  102  or  108 . In this case, the tolerance checking module  136  will determine after the fifth iteration, that the condition has been met. The tolerance checking module  136  will then instruct the iteration module  132  to stop iterating. In another example, a tolerance of 1% may be pre-selected by users  102 ,  108 , or by another user of system  106 . In this example, the tolerance checking module  136  will determine if the difference between the calculated actual value for the locked variable is within 1% of the value used for that variable in the last estimation iteration. If so, the tolerance check module  136  will instruct the iteration module  132  to stop iterating. In the alternative, the iteration module  132  will continue iterating until either the tolerance or the iteration threshold is reached. 
     In some instances, memory  118  may also store a solution providing module  138  configured to provide the optimized power solutions to users  102 , users  108 , or some other users who have requested the data. In some examples, providing optimized power solutions involves, storing the solutions in memory  118  or some other memory, displaying them to users  102  of the local server  104 , transmitting them over network  112  to remote server  110 , or preparing them for display to users  108 . Additionally, in some aspects, the optimized power solutions may be formatted such that they accurately may be represented or displayed within a spreadsheet application. 
     In one general, non-limiting example, the following calculations may be performed by several of the afore-mentioned modules:
         An estimated head value of 20 meters is selected from a table of historical data and a tolerance of 1% is selected.   Based on an appropriate efficiency curve, efficiency and flow values of 50% and 2 cubic feet per minute (“CFM”) (for example) are calculated and entered into to the power equation (Equation 1) along with the estimated head.   An estimated power of 20 kW may be solved for based on the above values.   Based on calculated forebay and tailrace changes that occurred in response to the flow of 2 CFM, an actual head may be calculated.   In this example, the actual head is calculated to be 19.5 meters; thus, the percent difference is (20−19.5)/20=0.025 or 2.5%.   When 2.5% is compared against the selected 1% tolerance, the system determines that the estimated value is not within the tolerance and another iteration may be performed.   During the next iteration, the calculated head value of 19.5 meters will be used as the head value.   This process may continue until the head value converges to within the selected tolerance or until an iteration threshold is reached.       

     Various instructions, methods and techniques described herein may be considered in the general context of computer-executable instructions, such as program modules, executed by one or more computers or other devices. Generally, program modules include routines, programs, objects, components, data structures, etc. for performing particular tasks or implementing particular abstract data types. These program modules and the like may be executed as native code or may be downloaded and executed, such as in a virtual machine or other just-in-time compilation execution environment. Typically, the functionality of the program modules may be combined or distributed as desired in various embodiments. An implementation of these modules and techniques may be stored on some form of computer-readable storage media. 
     Illustrative Data 
       FIG. 2  depicts an illustrative spreadsheet document of hydro-system data  200  for use by the system  106  of  FIG. 1 . In one aspect, the hydro-system data  200  includes data collected over a period of time at a hydroelectric power station. In another aspect, the hydro-system data  200  includes iteratively created estimations of power solutions for a given turbine or a system of turbines. In yet another aspect, the hydro-system data  200  may be a combination of historical data and iterative calculations. 
     In one example, column A of the hydro-system data  200  may represent theoretical turbine efficiency for a given turbine for each flow. Additionally, column of the hydro-system data  200  may represent each potential flow rate for the power station from 0 to 9,000 cubic feet per minute (CFM). In one example, column may represent a benchmarked efficiency which is calculated by dividing the power curve efficiency (column A) by some historical data regarding the actual turbine or the actual efficiency at each given flow. 
     In one aspect, column D of the hydro-system data  200  may represent the calculated power solution based on an estimated head value. Columns E, F, G, H, and J may then represent the calculated head value for each of five iterations while columns K, L, M, N, and P represent the percent error between each calculated head value and the estimate. Where the percent error was within the pre-selected tolerance (in this case 1%, or 0.01), the calculated head values are shaded grey in columns E-J. At these instances, the power calculation has been optimized. 
     As seen here, hydro-system data  200  may be represented in spreadsheet form. However, the data may be stored, displayed, rendered, provided, or represented in any other form known. Additionally, this spreadsheet may serve as the underlying data to perform the iterations discussed above and/or it may be used as a GUI for the user to interact with the system  106  and to present the resulting power solutions to users  102  or  108 . 
     Illustrative Processes 
       FIGS. 3-5  are flow diagrams showing respective processes  300 ,  400 , and  500  for iteratively calculating and providing optimized power solutions for hydroelectric power stations. These processes are illustrated as logical flow graphs, each operation of which represents a sequence of operations that can be implemented in hardware, software, or a combination thereof. In the context of software, the operations represent computer-executable instructions stored on one or more computer-readable storage media that, when executed by one or more processors, perform the recited operations. Generally, computer-executable instructions include routines, programs, objects, components, data structures, and the like that perform particular functions or implement particular abstract data types. The order in which the operations are described is not intended to be construed as a limitation, and any number of the described operations can be combined in any order and/or in parallel to implement the process. 
       FIG. 3  illustrates an example flow diagram of process  300  for iteratively estimating optimized power solutions, and may, but need not, be implemented using the systems, architecture, and data of  FIGS. 1 and 2 . 
     Process  300  includes receiving a tolerance threshold and data as inputs for making a power calculation at  302 . In one aspect, a user of a local computing device may provide the data. In other aspects, the data may be provided by a user of a remote computing device accessing process  300  over a network such as the Internet. Further, the tolerance threshold may be selected by a user through a GUI, pre-selected based on operational criteria, or set to a standard value. At  304 , process  300  may set one of the variables of the power calculation to an estimated value. In one aspect, process  300  may set the head variable to an estimated head value; however, other variables may be locked. At  306 , process  300  may solve for an optimal power solution linearly using the estimated value and the data received at  302 . For example, when the head variable is locked with an estimated head value, values for flow and efficiency may be selected from the received data for calculating the estimated power. 
     Process  300  may also include calculating an actual value for the locked variable at  308 . In the above example, when the head variable is locked (i.e., set to an estimated value), the process  300  may calculate an actual head value here. At  310 , process  300  may determine a difference between the estimated value and the calculated value. That is, by way of example only, process  300  may determine the percentage difference between estimated head value and the calculated head value. In other aspects, however, estimated and calculated head values may be used, along with the flow and efficiency data used to solve the optimal power solution, to determine estimated and actual power. The estimated and actual power may then be used, along with market rate information, to determine an estimated dollar value and an actual dollar value for electricity at each time period. In some aspects, at  310 , process  300  may determine a percentage difference between the estimated dollar value and the actual dollar value. 
     At  312 , process  300  may determine whether the percent difference is greater than the tolerance threshold received at  302 . If the percent difference is within the received tolerance threshold, process  300  may provide the optimal power solution at  314 . Optionally, at  316 , process  300  may store the optimal power solution as well. Alternatively, if the percent difference is less than the received tolerance threshold, process  300  may set the previously locked variable to the most recently calculated actual value for that variable at  318 . Following the same example as above, at  318 , process  300  may lock the head variable by setting it to the most recently calculated actual value. At  320 , process  300  may, once again, solve for optimal power linearly, this time using the most recently calculated actual value. 
     At  322 , process  300  may calculate a next actual value for the newly locked variable. Process  300  may then determine the difference between the calculated actual value from  320  and the next actual value calculated at  322  to determine a percent difference. Again, process  300  will determine whether the difference (this time between the calculated actual value from  320  and the next actual value from  322 ) is greater than the received tolerance threshold. As seen here, process  300  iterates from  318  to  324  and back to  312  until the desired tolerance is reached. In this way, both speed and accuracy can be controlled by selecting appropriate tolerance and iteration thresholds. 
       FIG. 4  illustrates an example flow diagram of process  400  for an alternative implementation for iteratively calculating an optimized power solution for a hydroelectric power station and may, but need not, be implemented using the systems, architecture, and data of  FIGS. 1 and 2 . 
     Process  400  includes receiving inputs to a non-linear equation for calculating power at  402 . At  404 , process  400  may set the head variable to an estimated head value. Process  400  may solve a linear equation to produce a power solution based on the estimated head value at  406 . At  408 , process  400  may calculate an actual head based, at least indirectly, on the estimated head. In one example, the actual head is calculated by determining a flow rate and turbine efficiency for the original estimated head. In another example, however, the actual head is calculated by using historical data from a hydro-system. At  410 , process  400  may compare the calculated head to a predetermined tolerance threshold. In one aspect, this comparison involves determining a percent difference between the estimated head and the actual head and comparing the difference against the tolerance threshold. 
     At  412 , process  400  may determine whether the calculated head is within the predetermined threshold. Generally, being within a threshold implies that the percent difference between the actual and estimated head values is less than the tolerance threshold when the tolerance threshold is represented as a percentage. If, at  412 , process  400  determines that the calculated head, or percent difference, is within the tolerance threshold, process  400  may provide the power solution at  414 . On the other hand, if the calculated head, or percent difference, is still greater than the tolerance threshold, process  400  may iteratively re-calculate the power solution using the previously calculated head value at  416  and return to  408  for calculating a next actual head value based at least in part on the most recently calculated head. Here, as in process  300 , the iterative process may continue until the tolerance threshold is satisfied. 
       FIG. 5  illustrates an example flow diagram of process  500  for an alternative implementation for iteratively calculating an optimized power solution for a hydroelectric power station and may, but need not, be implemented using the systems, architecture, and data of  FIGS. 1 and 2 . 
     Process  500  includes receiving a request to calculate an optimal power solution for a hydroelectric turbine at  502 . At  504 , process  500  may begin an iterative estimation process for calculating an optimal power solution. Iterative estimation, at  506 , may include determining a first estimated power based at least in part on a first estimated head value at  508  and determining subsequent estimated power solutions based at least in part on a calculated head value at  510 . 
     At  512 , process  500  may decide whether the percent difference between the estimated value and the calculated value is within a tolerance. If not, at  514 , process  500  may determine whether an iteration threshold has been reached. If the percent difference is not within the tolerance at  512  and the iteration threshold is not reached at  514 , process  400  may return to  506  to implement another iterative estimation. On the other hand, if either the percent difference is within the tolerance at  512  or the iteration threshold is reached at  514 , process  500  may end the iterative estimation at  516 . 
     CONCLUSION 
     Although embodiments have been described in language specific to structural features and/or methodological acts, it is to be understood that the disclosure is not necessarily limited to the specific features or acts described. Rather, the specific features and acts are disclosed as illustrative forms of implementing the embodiments.