Overview

The purpose of this TechNote is to discuss the how to model turbines in Bentley HAMMER. Additional information can be found in the Help documentation for the product. 

Background

Turbines are used in hydropower generation plants. Given the importance of turbines in these systems, it is essential for a modeler to predict the transient pressures that might occur and to implement an adequate surge control strategy to ensure the safety and reliability of the turbine.

Bentley HAMMER can be used to model transient simulations where turbines are involved and analyze potential protective measures that can be used to mitigate the effects of transient events.

Turbines in HAMMER 

Hydropower turbines are located at the downstream end of a conduit, or penstock, to absorb the moving water's energy and convert it to electrical current. Conceptually, a turbine is the inverse of a pump, but very few pumps or turbines can operate in both directions without damage. If the electrical load generated by a turbine is rejected, a wicket gate must rapidly stop flow, resulting in a large increase in pressure, which propagates upstream (in the penstock).

The primary purpose of transient simulations with turbines is to look at ways to protect the system against rapid changes in the electrical and/or hydraulic components of the hydroelectric system. In each case, hydraulic transients result from changes in the variables controlled by the governor.

Electrical Load or Torque on the turbine-generator system varies with the electrical load in the distribution grid. In steady-state operation, the electrical torque and the hydraulic torque are in dynamic equilibrium. From a hydraulic perspective, electrical torque is an external load on the turbine.

The moment of inertia comes into play here as it can ifluences the rate at which a turbine speeds up or slows down. Moment of inertia is HAMMER is defined by the equation WR^2, where W is the weight on the turbine and R is the radius of gyration.

Moment of inertia is related by torque by way of the following equation:

I*d/dt = M

where:

I is the moment of inertia, which is a constant
 is the rate at which the turbine is spinning (measured in radians per second)
d/dt is the rate of change in (omega) over time (radians per second per second)
M is the net torque applied to the turbine (i.e., the difference between the torque from the water that is spinning the turbine and the torque from the generator that the turbine is attached to).

So if M = 0, then the hydraulic and electrical torque is balanced, and the turbine speed doesn't change (d/dt = 0)

But if the electrical torque drops to zero, such as in a load rejection operating case, then M becomes greater than zero and the turbine starts to speed up. It will speed up quickly if it has a small moment of inertia, and it will speed up less quickly if it has a large moment of inertia.

Speed is another possible control variable for numerical simulations. For turbines, however, the governor strives to keep the turbine at synchronous speed by varying the wicket gate position during load variation and acceptance (assuming a 'perfect' governor). If field data were available, the speed could be used to determine whether the model simulates the correct flow and pressures.

Once the time-varying electrical torque and wicket gate positions are known, HAMMER solves flow, Q, and rotational speed, N, in conjunction with the characteristic curves for the turbine. This yields the transient pressures for the load rejection, load acceptance, emergency shutdown, operator error or equipment failure. The possible emergency or transient conditions are discussed separately in the sections that follow.

Note: The turbine element in HAMMER is not used to represent impulse turbines. Transients caused by impulse turbines can be approximated in HAMMER by using a Throttle Control Valve (TCV) or Discharge to Atmosphere element to represent the turbine nozzle.

Turbine Properties

Time (Delay until Valve Operates):  The period of time that must elapse before the spherical valve of the turbine activates. This should be set to a large value if it will not impact the operation of the turbine.

Time for Valve to Operate: The time required to operate the spherical valve. By default, it is set equal to one time step. This should be set to a large value if it will not impact the operation of the turbine.

Pattern (Gate Opening): The percentage of wicket gate opening with time. This is set up in the Patterns dialog, found in the Components pulldown.

Operating Case: Allows you to choose among the four possible cases: Instantaneous Load Rejection, Load Rejection (requires torque/load vs. time table), Load Acceptance, and Load Variation.

Diameter (Spherical Valve): The diameter of the spherical valve.

Efficiency: The efficiency of the turbine as a percentage. This is typically shown in the curves provided by the manufacturer. A typical range is 85% to 95%, but values outside this range are possible.

Moment of Inertia: This value will account for the turbine, generator, and entrained water. This is also typically provided by the manufacturer. As mentioned in the previous section, Moment of inertia is HAMMER is defined by the equation WR^2, where W is the weight on the turbine and R is the radius of gyration.

Speed (Rotational): The rotation of the turbine blades per unit time, typically as rotations per minute or rpm. The power generated by the turbine depends on this value.

Specific Speed: Enables you to select from four-quadrant characteristic curves to represent typical turbines for three common types: 30, 45, or 60 (U.S. customary units) and 115, 170, or 230 (SI metric units). You can enter your own four-quadrant data in the XML library. See the Help documentation for more information.

Turbine Curve: This curve is used to define the flow and head for the turbine in the initial conditions computation. For a transient run, HAMMER uses a four-quadrant curve based on Specific Speed, Rated Head, and Rated Flow.

Flow (Rated): Denotes the flow under normal operating conditions. Only applies to the Load Acceptance operating case.

Head (Rated): Denotes the headloss through the turbine under normal operating conditions, corresponding to the rated flow. Only applies to the Load Acceptance operating case.

Electrical Torque Curve: defines the time vs. applied (electrical) torque response for the turbine. Only applies to the Load Rejection operating case.

Setting up the Turbine properties

This section gives a brief overview of the general setup for a turbine. The exact information entered will vary based on the turbine and the modeling case that is being used.

The properties fields “Operating Case” and “Pattern (Gate Opening)” go hand-in-hand, and are the primary modeling usage for a turbine. More details can be found in the next section. There are four operating cases to choose from: Load Rejection, Instant Load Rejection, Load Acceptance, and Load Variation. The pattern is created in the section “Operational (Transient, Turbine). It used in conjunction with this will represent the relative wicket gate opening at the time from the start of the simulation.

The property field “Turbine Curve” is used to determine the relation between flow and head during the steady state analysis used for the initial conditions. If you are modeling a Load Acceptance operating case, you will also need to enter a rated flow and rated head. This is so that the program has a starting point for the development of the four-quadrant curve. In the other modeling cases, the flow and head used are derived from the turbine curve in the initial conditions. Load Acceptance assumes that the initial status of the turbine is closed, meaning there is no rated flow and head results. Instead, the program will use the rated flow and head entered in the properties.

The flow and head relationship defined in the Turbine Curve is not used in the transient analysis. The transient analysis will use a four-quadrant curve derived from the rated flow and head, as well as the moment of inertia, rotational speed, and specific speed.

This information should be available from the turbine manufacturer. The specific speed can be estimated with the following equation:

In US units n is in rpm, P is in hp, and H is in ft.
In SI units n is in rpm, P is in kW, and H is in m.

There are three different specific speeds available to choose from: “SI=115, US=30,” “SI=170, US=45,” and “SI=230, US=60.”

Note: In a case where you need to have a specific four-quadrant curve not represented by the choices above, it is possible to create a custom four-quadrant curve. Please see the Help topic “Pump and Turbine Characteristics in Bentley HAMMER” for details.

Lastly, the property field “Report Period (Transient)” will allow the user to see the turbine results in the Transient Analysis Detailed Report. These results will include the time, the gate opening percentage, flow, speed, and head.

Note: While the four-quadrant curves for turbines have information for different gate openings, a result of 20% gate opening is as low as the report will go. That means it is not possible to compute or interpolate the turbine operating point when the wicket gates are less than 20% open, so what HAMMER does is linearly interpolate from the flow at 20% open down to zero flow (at the time when the operating rule says the wicket gates are 0% open). Without any four-quadrant turbine characteristic curves available for these gate openings, there is no way to compute the turbine behavior.

Modeling cases with Turbines

Like pumps, there are specific operating rules that can be assigned to a turbine in HAMMER. Below is a brief description of each case. There is a sample model which uses each case below. The sample model can be found at C:\Program Files (x86)\Bentley\HAMMER8\Samples\Turbine_Example.wtg.

Load Rejection

Load rejection occurs when the distribution grid fails to accept electrical load from the turbine-generator system. After the load is rejected by the grid, there is no external load on the turbine-generator unit and the speed of the runner increases rapidly. This can be catastrophic if immediate steps are not taken to slow and stop the system. To keep the speed rise within an acceptable limit, the wicket gates must close quickly and this may result in high (followed by low) hydraulic transient pressures in the penstock. Since load rejection usually results in the most severe transient pressures, it typically governs the design of surge control equipment.

During load rejection, the generation of electrical power by the turbine-generator unit should decrease to zero as quickly as possible to limit the speed rise of the unit. To accomplish this, the wicket gates close gradually in order to reduce flow. In a real turbine a governor would control the wicket gate closure rate, however the turbine governor is not modeled explicitly in HAMMER and the user controls the rate of wicket gate closure.

If the power generated by the water flowing through the turbine is greater than the electrical load, then the turbine will speed up; if the electrical load is greater, the turbine will slow down.

Note: Load and gate position are entered in different parameter tables in HAMMER because they may not use the same time interval. HAMMER interpolates automatically as required.

Instant Load Rejection

Instant Load Rejection is similar to the Load Rejection case, except the electrical load on the turbine drops instantaneously to zero (i.e. the turbine is disconnected from the generator).

During instant load rejection, the generation of electrical power by the turbine-generator unit should decrease to zero as quickly as possible to limit the speed rise of the unit. To accomplish this, the wicket gates close gradually in order to reduce flow. In a real turbine a governor would control the wicket gate closure rate, however the turbine governor is not modeled explicitly in HAMMER and the user controls the rate of wicket gate closure.

Load Acceptance

Full load acceptance occurs when the turbine-generator unit is connected to the electrical grid. Transient pressures generated during full load acceptance can be significant but they are usually less severe than those resulting from full load rejection.

HAMMER assumes the turbine initially operates at no-load speed (NLS), and the turbine generates no electrical power. When the transient simulation begins, HAMMER assumes the electrical grid is connected to the output terminal of the generator and wicket gates have to be open as quickly as possible to meet the power demand, all without causing excessive pressure in the penstock.

Note that in this case, HAMMER assumes the turbine governor is ‘perfect.’ In other words the power produced by the turbine always equals the electrical load. Therefore the user doesn't need to enter an electrical load, just a curve of wicket gate position versus time, and the turbine's rated flow and head. Under the Load Acceptance case the turbine will always operate at its rated (or synchronous) speed.

When using Load Acceptance, you must enter the Flow (Rated) and Head (Rated) for the turbine. The transient solver needs these values into order to use the four-quadrant curve. If the turbine was open, these values would be obtained by simply computing the initial conditions. Obviously, when the turbine is closed, the computed values will for the rated flow and rated head will be zero, which will not identify the appropriate four-quadrant curve.

To find the Flow (Rated) and Head (Rated), it is recommended to first set the status of the turbine to Open and compute the initial conditions. Note the Flow and Head results for the turbine and enter this for Flow (Rated) and Head (Rated). Set the turbine to Closed again and compute initial conditions and the transient analysis. The correct four-quadrant curve should now be used.

Load Variation

Load variation on the turbine-generator unit can occur due to the diurnal changes in electricity demand in the distribution grid. During load variation, the governor controls the wicket gate opening to adjust flow through the turbine so that the unit can match the electrical demand. The water column in the penstock and conduit system accelerates or decelerates, resulting in pressure fluctuations.

The transient pressures that occur during general load variation may not be significant from a hydraulic design perspective since they are often lower than the pressure generated during a full load rejection or emergency shutdown.

At steady-state, the turbine-generator system usually runs at full load with the wicket gates 100% open. The amount of electricity produced by the system depends on the flow through the wicket gates. A decrease in electrical load requires a reduction in the wicket gate opening to adjust the flow.

Note that in this case, like in the case of the Load Acceptance operating case, HAMMER assumes the turbine governor is ‘perfect.’ Under the Load Variation case the turbine will always operates at its rated (or synchronous) speed.

A Note on Impulse or Pelton Wheel Turbines

An impulse turbine has one or more fixed nozzles through which pressure is converted to kinetic energy as a liquid (typically water) jet. The jet impinges on the moving plates of the turbine runner that absorbs virtually all of the moving water's kinetic energy. In practice, the most common impulse turbine is the Pelton wheel shown in the figure below.

Its rotor consists of a circular disc with several "buckets" evenly spaced around its periphery. The splitter ridge in the center of each bucket divides the incoming jet(s) into two equal parts that flow around the inner surface of the bucket. Flow partly fills the buckets and water remains in contact with the air at ambient (or atmospheric) pressure.
 
It is important to note that the turbine element in HAMMER is not used to represent impulse turbines. Transients caused by impulse turbines can be approximated in HAMMER by using a Throttle Control Valve (TCV) or Discharge to Atmosphere element to represent the turbine nozzle.

An example of this setup would be to approximate the gate closure on the impulse turbine using a "Discharge to Atmosphere" (D2A) element. See the schematic below for one possible setup of the system:

If you want to model the impulse turbine gate closing in 10 seconds, you would set the D2A property field "Discharge Element Type" to Valve with an initial status of Open. Then you would set "Time to Fully Open or Close" to 10 seconds.

Note: remember to enter values for "Pressure Drop (Typical)" and "Flow (Typical)". The "Flow (Typical)" is simply the expected flow from the turbine. You can calculate the typical pressure drop using the orifice equation). More information on entering this information can be found in the Discharge to Atmosphere TechNote found here

If you want more control over the valve closure, you could use a Trottle Control Valve (TCV) element instead.

The TCV allows you to enter an Operating Rule that has curve of valve closure (or gate closure, for an impulse turbine) versus time. For example, you could have the gate close quickly until it 10% open, then close more slowly the rest of the way.

See Also

Product TechNotes and FAQs

Haestad Methods Product Tech Notes And FAQs

Protective Equipment FAQ

General HAMMER V8i FAQ

External Links

Water and Wastewater Forum

Bentley Technical Support KnowledgeBase

Bentley LEARN Server