This method performs calculations to compute the power generated at each timestep.

If Turbine Release is already set from the dispatch method solveMB_givenInflowRelease, the following checks are performed:

If the Turbine Release was input by the user, a RiverWare error is posted and the run is terminated. If neither the Energy nor the Turbine Release were input and the Energy was not set by a rules, the Turbine Release is set equal to the lesser of the Maximum Power Release or the value of the Outflow minus the Spill.

Using the calculated value of Operating Head, QmaxTemp and QbestTemp are obtained from the Max Turbine Q Table and the Best Turbine Q Table, respectively. Both values are then multiplied by the Power Plant Cap Fraction to obtain Qmax and Qbest. The Operating Head is also used to determine both the best power coefficient and the max power coefficient through interpolation of the Best Power Coefficient and Max Power Coefficient tables, respectively.

The following calculations are not performed if Energy is Input, set by a Rule, or flagged BEST EFFICIENCY or MAX CAPACITY. In these cases the Power, Energy, and Power Coefficient have already been calculated in Plant Power Coefficient Release.

If the Power Coefficient is not input by the user, the following steps are performed.

Power is then calculated using the following equation:

If the user has input the Plant Power Limit, the following steps are taken.

If the Power Coefficient is not equal to the best power coefficient, Turbine Release, Power, and the Power Coefficient need to be recalculated. This is done through the following steps.

If the Spilled Energy Power Coefficient is visible on the reservoir and it is not input, it is set equal to the Power Coefficient.

Energy is calculated as Power multiplied by the timestep (in hours).

The following calculations always take place, regardless of the flag on Energy.

If either the Turbine Release is equal to the maximum power release or the Energy is at the maximum capacity, Hydro Capacity is set equal to Power and the Best Hydro Capacity is obtained from the getHydroCap function. If the energy is at the Best Efficiency, the Best Hydro Capacity is set equal to the Power and the Hydro Capacity is obtained from the getHydroCapacity function. If neither the Turbine Release is equal to the maximum power release, the Energy is at the maximum capacity, nor the Energy is at the Best Efficiency, both Hydro Capacity and Best Hydro capacity are obtained with the getHydroCap function.

At the start of an optimization run, the Plant Power Table is checked for concavity. The slope of each segment for each block is calculated as follows:

The table is considered concave if:

The table is required to be concave for optimization runs, but not for simulation or rulebased simulation runs.

This method performs calculations to compute the power generated at each timestep.

Operating Head is used to determine the maximum power release through interpolation on the Plant Power Table. The maximum power release value is multiplied by the Power Plant Cap Fraction to account for the state of the turbine units.

The method first checks whether Energy is either user input or set by rules. If it is, the method finishes successfully and exits; all power calculations were already performed in the Plant Power Equation Release method.

Otherwise, Tailwater Elevation and Operating Head are determined based on the user method selected in the Tailwater category.

Next, the selected method in the Power Plant Failure category is executed. This method sets the Power Plant Cap Fraction (the default is 1.0) and checks for plant shutoff/failure.

Then, the method checks if the Minimum Power Elevation was input by the user. If no value was input, a RiverWare error is posted and the simulation run is terminated. If the previous Pool Elevation is less than the Minimum Power Elevation or the plant has shut off failed (from the call to the selected Power Plant Failure category method), the following steps are taken.

Once the initial checks are performed, the method calculates Net Head and Turbine Release as follows:

Next, the Max Turbine Release for the current Net Head is interpolated from the Net Head vs. Max Turb Release table.

If there is a valid value in the Plant Efficiency Value slot, that is used for the efficiency. Otherwise, given the net head from the previous timestep (Operating Head at previous timestep minus Head Loss), the efficiency is interpolated from the Net Head vs Efficiency table. The previous Operating Head is used as an approximation so as not to introduce an additional variable in the iteration. As a result, the Tailwater Elevation at the initial timestep must be input. The net head for the initial timestep is the initial Pool Elevation minus the initial Tailwater Elevation minus Head Loss.

The method checks whether Turbine Release is user input or set by a link or a rule. If Turbine Release is known at the dispatch level, the method will check that it is not greater than Outflow minus Spill or the Max Turbine Release given the current Net Head. If either of these are true, an error will be posted and the run will terminate. Otherwise, the known Turbine Release value will be used in the Power calculations. If Turbine Release is not user input or solved for in the dispatch methods, it is calculated as the minimum of the Max Turbine Release (given the current Net Head) and Outflow minus Spill (either unregulated spill or user specified regulated spill):

Once efficiency, Net Head, and Turbine Release are all known, Power is solved for using the Power Equation:

The unit compatibility factor comes from balancing units and is 102.01697767 in internal RiverWare units.

If the computed Power is greater than the Plant Power Limit, the Power is reset to the Plan Power Limit and Turbine Release is recomputed by solving this equation for Turbine Release.

Lastly, Energy is computed as Power multiplied by the time length of the timestep.

The Unit Generator Power method begins by computing the availability and power limits of each unit type. Availability and power limit values are computed as the sum of the values from the availability and power limit columns, respectively, in the Generators Available and Limit slot. A value for availability and power limit is computed for each unit type.

First, Tailwater Elevation and Operating Head are determined based on the user method selected in the Tailwater category.

Next, the selected method in the Power Plant Failure category is executed. This method sets the Power Plant Cap Fraction if necessary (the default is 1.0) and checks for plant shutoff/failure.

If the plant has shut off or failed (from the call to the selected Power Plant Failure category method), the following steps are taken.

Then the efficiency of each unit type is calculated by the following equation:

PowerTemp and flowTemp, both local variables, are computed from the Best Generator Power and Best Generator Flow tables, respectively, using the current Operating Head. Each unit type is then sorted in descending order based on the computed efficiency.

Turbine Release has already been computed by the dispatch method and the power produced from the known Turbine Release must be calculated. The method begins to add entire unit types (operating according to the best flow and power tables and beginning with the most efficient type) until the Turbine Release is exceed or all the unit types have been added. If the power generated by a particular unit type exceeds the power limit for that unit type, the power produced from that type is set to the power limit. The power limit has no effect on the flow going through the turbines. If the Turbine Release is exceeded, the last generator type is interpolated to compute the Power exactly (see equation below). However, if all the unit types have been added and the Turbine Release cannot be met, the method assumes all unit types are operating at full capacity (according to the Full Generator Flow and Full Generator Power tables). Then if the Turbine Release is exceeded, the last generator type added is interpolated to compute the Power exactly (see equation below). However, if the Turbine Release still cannot be met, all unit types are run at full capacity. Turbine Release is reset to the maximum flow through the turbines and Power is set as the maximum power produced by the turbines (at the given operating head). The spill must be recalculated to handle the excess Turbine Release that could not be met.

The interpolation equation used to calculate Power is given below:

The Power Coefficient is then calculated by the following equation:

If all the unit types were added, the Spilled Energy Power Coefficient is equal to the Power Coefficient. However, if all the types were not added, the Spilled Energy Power Coefficient is set equal to the efficiency of the last type added.

Energy is calculated as the product of the Power and the timestep length. Hydro Capacity is set as the power produced from all units operating at full capacity.

First, the selected method in the Power Plant Failure category is executed. This method sets the Power Plant Cap Fraction if necessary (the default is 1.0) and checks for plant shutoff/failure.

If the plant has shut off or failed (from the call to the selected Power Plant Failure category method), the following steps are taken.

If either the Energy or Turbine Release is input by the user, a RiverWare error is posted and the simulation run is terminated. These are not valid input slots for the Peak and Base method. Peak Flow and Peak Power are then calculated as follows.

Once Peak Power and Peak Flow (called flow in the calculations above) are calculated, Base Power and Base Flow can be determined. Base Power is set equal to Off Peak Capacity and Base Flow is determined from Outflow and the Base Flow Table.

If Outflow minus Unregulated Spill is greater than the product of Peak Flow, Number of Units, and Power Plant Cap Fraction; the following steps are taken.

The Peak Flow slot represents the flow through the entire power plant. Therefore, the value in this slot is calculated as Peak Flow times Number of Units times Power Plant Cap Fraction. In the calculations that follow, Peak Flow represents the slot value just calculated. Plant Peak Power is calculated as Peak Power times Number of Units times Power Plant Cap Fraction.

The number of hours required to operate at base and peak flows are computed next using the following equations:

If Peak Hours is greater than the length of the timestep; Peak Hours is set equal to the timestep, Base Hours are set to zero, Turbine Release is set to Peak Flow, and Total Controlled Release is calculated as Outflow minus Unregulated Spill. If Peak Hours is less than or equal to the length of the timestep, Peak Hours and Base Hours remain as calculated by these formulas, Turbine Release is Outflow minus Spill, and Total Controlled Release is set equal to the Peak Flow.

The theoretical and actual energy production are computed next. The local variable, peakEnergy is calculated as Peak Hours times Plant Peak Power. The local variable, baseEnergy is calculated as Base Hours times Base Power.

The local variable, bestBaseTheor (representing the theoretical, most efficient base energy) is calculated using the following equation:

The local variable bestPeakTheor (representing the theoretical most efficient peak energy) is calculated using the following equation:

The value, 0.00980229, is a conversion factor necessary for energy to have units of megawatt-hours.

For Q in cms and Head in meters the final conversion is 0.00980229.

Finally, the following slots are set:

If a spill method is selected which utilizes the Spilled Energy Power Coefficient and this value is not input by the user, it is set as follows:

If Turbine Release is zero, the Spilled Energy Power Coefficient is also zero.

First, the selected method in the Power Plant Failure category is executed. This method sets the Power Plant Cap Fraction if necessary (the default is 1.0) and checks for plant shutoff/failure.

If the plant has shut off or failed (from the call to the selected Power Plant Failure category method), the following steps are taken.

If Energy or Turbine Release are input by the user, an error is posted. These are not valid input slots for the Peak Power method. Peak Flow and Peak Power are then calculated as follows.

Otherwise, flow is determined by interpolation using Operating Head and the Best Generator Flow table. This set of calculations is repeated until the iteration criteria are met.

Once flow and Peak Power are determined, the following computations are performed:

If the value of Peak Hours is greater than the length of the timestep, Peak Hours is set to the length of the timestep, Turbine Release is equal to Peak Flow, and Total Controlled Release is equal to Outflow minus Unregulated Spill. Otherwise, Peak Hours remains unchanged, Turbine Release equals Outflow minus spill, and Total Controlled Release equals Peak Flow.

Next, the theoretical and actual energy production is calculated.

The value, 0.00980229, is a conversion factor necessary for energy to have units of megawatt-hours.

For Q in cms and Head in meters the final conversion is 0.00980229.

Finally, the following slots are set:

If Best Peak Theoretical is equal to zero, Plant Efficiency is also equal to zero. Otherwise Plant Efficiency is calculated as follows:

If a spill method is selected which utilizes the Spilled Energy Power Coefficient and this value is not input by the user, it is set as follows:

If Turbine Release is zero, the Spilled Energy Power Coefficient is also zero.

The Peak Power Equation method first performs a series of checks.

The selected method in the Power Plant Failure category is executed. This method sets the Power Plant Cap Fraction (the default is 1.0) and checks for plant shutoff/failure.

Then, the method checks if the Minimum Power Elevation was input by the user. If no value was input, a RiverWare error is posted and the simulation run is terminated. If the previous Pool Elevation is less than the Minimum Power Elevation or the plant has shut off or failed (from the call to the selected Power Plant Failure category method), the following steps are taken.

The method checks whether Turbine Release (the average flow through the turbines over the whole timestep) is user input or set by rules; that is, the method checks if the dispatch type is solveMB_givenInflowRelease. If the given Turbine Release value is greater than Outflow minus Spill, an error is posted and the run is terminated.

If Turbine Release is not user input or set by rules, it is calculated as the minimum of MaxTurbine Release and Outflow minus Spill,

In order to calculate the time at peak production, the flow which passes through the turbines during this time period must be calculated. This Peak Release is the maximum possible flow through the turbines given the Net Head and will be solved for iteratively as described in the steps below.

Once Peak Release is calculated, the Peak Time will be solved for as the volume of flow that passes through the turbines in a timestep divided by the Peak Release:

RiverWare checks that the Peak Time is not greater than the timestep length. If it is, the run terminates and an error is posted.

Power is calculated with the standard water power equation. The Peak Power Equation method uses Peak Release as the flow value and Net Head at Peak Release as the head value.

The unit compatibility factor comes from balancing units and is 102.01697767 in internal RiverWare units.

Energy is finally computed as the product of Power and Peak Time:

This method is called from the dispatch method, typically after Outflow, Storage, and Pool Elevation have been calculated. If Energy is input, then this method is also called from an iterative loop used to determine the Turbine Release, Peak Release, and Peak Time and/or Spill that satisfies the Energy.

The Peak Power Equation with Off Peak Spill method performs a series of checks. First, the method checks if maximum drawdown is exceeded for two cases. In the first case, if there is a valid Top of Conservation Pool slot—that is, this is a U.S. Army Corp of Engineers model—the method checks if the Pool Elevation is greater than the Top of Conservation Pool. If so, no error or warning is posted; the drawdown limitation only applies to the conservation pool. If the drawdown is exceeded and the Pool Elevation is less than the top of conservation pool, an error is posted and the run is terminated.

In the second case, if there is no Top of Conservation Pool slot—that is, a non U.S. Army Corp of Engineers model—if the calculated Pool Elevation results in exceeding the Maximum Power Pool Drawdown, a warning is posted.

If the calculated Pool Elevation is less than the value in the Minimum Elevation for Power Operations, a warning message is posted.

Next, the selected method in the Power Plant Failure category is executed. This method sets the Power Plant Cap Fraction (the default is 1.0) and checks for plant shutoff/failure.

Then, the method checks if the Minimum Power Elevation was input by the user. If no value was input, a RiverWare error is posted and the simulation run is terminated. If the previous Pool Elevation is less than the Minimum Power Elevation or the plant has shut off or failed (from the call to the selected Power Plant Failure category method), the following steps are taken.

The method checks whether Turbine Release (the average flow through the turbines over the whole timestep) is user input or set by rules; that is, the method checks if the dispatch type is solveMB_givenInflowRelease. If so, and if the given Turbine Release value is greater than Outflow minus Spill, an error is posted and the run is terminated.

In order to calculate the time at peak production, the flow which passes through the turbines during this time period must be calculated. This Peak Release is the maximum possible flow through the turbines given the Net Head and will be solved for iteratively as described in the steps below.

The new Peak Release value is compared with the previous value and the iteration, steps 3-7, continue until the value converges.

If Turbine Release is not user input or set by rules (not in the dispatch method solveMB_givenInflowRelease), TempTurbineRelease is calculated as the minimum of the Peak Release and Outflow minus Spill,

The Spill will be non-zero only if there is Unregulated Spill or a spill value is set by user input or rules. Once Peak Release is calculated, the Peak Time will be solved for as the volume of flow that passes through the turbines in a timestep divided by the Peak Release:

RiverWare checks that the Peak Time is not greater than the timestep length. If it is, the run terminates and an error is posted. Next power is set to be the Generator Capacity:

Turbine Release is the Peak Release averaged over the whole timestep:

Energy is computed as the product of Power and Peak Time:

Peak Spill and Off Peak Spill are then determined based on Peak Time, Spill, and Unregulated Spill. If Unregulated Spill is non-zero, then Peak Spill is assumed to be equal to Unregulated Spill. Unregulated spill is calculated based on the pool elevation and occurs over the entire timestep. Off Peak Spill is the sum of Unregulated Spill and the Regulated Spill plus Bypass apportioned over the off peak time. If there is no Unregulated Spill, the Peak Spill is zero, and the Off Peak Spill is the Regulated Spill plus Bypass apportioned over the off peak time. If the Peak Time is equal to the timestep length, then Peak Spill is equal to Spill and Off Peak Spill remains NaN.

Finally, if the Load slot is visible and valid, the Thermal Purchase, Dump Energy and Operation Factor are calculated. See “Load Calculation” for details on these slots.

The first step in the LCR Power method is to determine the Operating Head. This is accomplished by executing the Tailwater method specified by the user.

Next, the selected method in the Power Plant Failure category is executed. This method sets the Power Plant Cap Fraction (the default is 1.0) and checks for plant shutoff/failure.

Then, the method checks if plant has shut off or failed (from the call to the selected Power Plant Failure category method), the following steps are taken.

If Energy is input by the user or it has been flagged as Best Efficiency, the LCR Power Release method is called to calculate the Turbine Release. This method takes a power request, determines if it can be met given the maximum power that can be generated for the given head, and sets the Turbine Release required to generate the requested power. If the Turbine Release is not already calculated by the LCR Power Release method, it is set as Outflow minus Spill. The value of Turbine Release is checked against the maximum value set by the user (if it has been set). If Turbine Release is greater than the maximum value an error is posted, “Turbine Release required to meet Energy request is greater than the maximum Turbine Release.”

Power and Energy are then calculated by the following equations:

If energy is zero, Plant Efficiency and the Power Coefficient are also zero. Otherwise they are calculated as follows:

When using the Unit Power Table method, you cannot specify (input or rules) the total Outflow, Energy, or Turbine Release slots. There are three approaches available for this method: specify Unit Turbine Release values, specify Unit Energy values, set the Max or Best flag on Energy. Each is described below.

With this approach, you must specify (input or rules) the Unit Turbine Release for every unit. Then you must set the “U” flag (Unit Values) on the Turbine Release slot. (See “Flags on the Timestep I/O Menu” in User Interface for details on setting the “U” flag interactively from a slot dialog. See “Buttons for Setting Flags on Slots” in RiverWare Policy Language (RPL) for details about using the RPL Palette to set the “U” flag from a slot assignment in a rule.)

The “U” flag on Turbine Release will trigger the reservoir object to dispatch given Turbine Release, and it will indicate to the object to get the sum of the Unit Turbine Release values in order to set Turbine Release. When the reservoir object solves, it will calculate Unit Energy, total Turbine Release and total Energy.

With this approach, you must specify (input or rules) the Unit Energy for every unit. Then you must set the “U” flag (Unit Values) on the Energy slot. (See “Flags on the Timestep I/O Menu” in User Interface for details on setting the “U” flag interactively from a slot dialog. See “Buttons for Setting Flags on Slots” in RiverWare Policy Language (RPL) for details about using the RPL Palette to set the “U” flag from a slot assignment in a rule.)

The “U” flag on Energy will trigger the reservoir object to dispatch given Energy, and it will indicate to the object to get the sum of the Unit Energy values in order to set Energy.When the reservoir object solves, it will calculate Unit Turbine Release, total Turbine Release and total Energy.

This method will use table interpolation to calculate Power and Energy at a known Operating Head based on the characteristics of each unit. This method, Unit Power Table, works in a similar manner to the current method, Plant Efficiency Curve.

At the beginning of the run, the method creates the Auto Unit Best and Auto Unit Max Turbine Q tables from the Unit Power Table. The Auto Unit Max Turbine Q table are the points from the Unit Power Table that correspond to the largest Turbine Release for a given Operating Head. The Auto Unit Best Turbine Q table is calculated from the Unit Power Table as follows: For each unit and each operating head, the method determines the point (flow, power) that corresponds to a line drawn from the origin and it tangent to the curve. This tangent point is determined by calculating the slope of the line from each point to the origin; the point with the largest slope is the tangent. Then the operating head and turbine flow for this point are added to the Auto Unit Best Turbine Q.

The description of the solution in this section assumes that mass balance has already occurred—that is, Inflow, Outflow, Storage, Pool Elevation have been calculated—and the method is trying to compute the Energy and Power produced by that Outflow. At the start of this method, there is also an estimate of the Turbine Release calculated as

In this description, “t” indicates the current timestep and “u” indicates that the method will do this for each unit.

The method calculates the tailwater and operating head using the selected method and current release and pool elevation.

For each unit, the previous pool elevation will be compared to the unit’s minimum power elevation.

Next, the selected method in the Power Plant Failure category is executed. This method sets the Power Plant Cap Fraction (the default is 1.0) and checks for plant shutoff/failure.

Then, the method checks if the plant has shut off or failed (from the call to the selected Power Plant Failure category method), the following steps are taken.

If any of these are non-zero, an error is issued No further computations are performed.

Next for each unit, an estimate of max flow through all the turbines is calculated as follows: estimate a temporary variable maxPowerRelease (flow) using the Auto Unit Max Turbine Q table. This table contains the columns Operating Head and Turbine Capacity. Because Operating Head is known at the current timestep, table interpolation is used to calculate maxPowerRelease for the given average Operating Head.

If Outflow is set to “Max Capacity” flag, set the Unit Turbine Release to the maximum calculated and compute the power produced by those flows.

Otherwise, if Unit Turbine Release is input/rules for any of the units:

Finally, the method computes the slot Unit is Generating based on the Unit Turbine Release and Unit Energy. For each unit, if these are non zero, the Unit is Generating is set to 1. If they are zero, Unit is Generating is set to 0. No inputs are overwritten. Then, the Number of Units Generating is computed as the sum over the columns of the Unit is Generating slot.