GovCT2 / GGOV2
Reviewers: Mathilde Bongrain (CRESYM)
Context
In a power plant, a governor regulates the mechanical power (\(P_m\)) or torque (\(T_m\)) delivered from the turbine to the electrical generator. This governor model includes the turbine dynamics, i.e. it takes a reference power and generator speed and outputs the mechanical torque.
This GovCT2 is a modification of the GovCT1 in order to represent the frequency-dependent fuel flow limit of a specific gas turbine manufacturer. Both are based on Rowen’s model from 1983 [1].
When comparing to older standards: GovCT2 is identical to GGOV2 and GovCT1 is identical to GGOV1.
GovCT2 is part of the CIM/CGMES standard, see [2] and [3]. CIM is developed by ENTSO-E and aims at ensuring the reliability of grid models and market information exchanges. ENTSO-E developed CGMES as a superset of the IEC CIM standards (belonging to IEC CIM16) in 2013 to fulfill the requirements of transmission system operators and their data exchanges.
The following information has been gathered from [2], [4] and [3].
Model use, assumptions, validity domain and limitations
General model for any prime mover with a PID governor.
For example used for:
Can be used to represent a variety of prime movers controlled by PID governors, such as:
- Single shaft combined cycle turbines and Gas turbines
- Diesel engines (with modern digital or electronic governors)
- Steam turbines with
- steam supplied from a large boiler drum
- or steam supplied from a large header with approximately constant pressure (over the time period of the simulation)
- Simple hydro turbines in dam configurations with
- short water column length
- and minimal water inertia effects
The model is a positive-sequence RMS model, hence it assumes symmetrical operating conditions and neglects high-frequency dynamics. This type of model is often used in large-scale stability studies, for which it reflects the relevant phenomena. It is not a detailed physical model of the unit. Also for some stability phenomena (e.g. resonance stability) this model is not sufficient and EMT models or other approaches may be necessary.
Model description
Model schema
Major control paths
The following section is based on [1] (p. 517f).
The model has three major control paths (speed/load, acceleration, temperature) associated with the dynamic response during disturbances. Outputs of these control functions are all inputs into a minimum value selector determining the least fuel request. This is then given to the actuator.
Speed/load (fsrn)
This can be considered the main control path. It corresponds directly to the governor. The inputs are load demand \(P_\mathrm{ref}\), rotor speed \(\omega\) and automatic generation control power \(P_\mathrm{MWSet}\).
The resulting signal is then passed through a deadband, limits and a PID-controller. To represent a specific governor, some elements can be deactivated by setting parameters to zero (examples in [1]).
Supervisory load controller
In [3] the \(P_\mathrm{MWSet}\) path is described as an optional additional outer loop associated with a power plant control (supervisory load controller). This is active when \(K_\mathrm{I\,MW}\) is not equal to zero. It is a slow acting reset control and it adjusts the speed/load reference of the turbine governor to maintain the electrical power of the unit at the value which it has been initialized with. That value is stored in \(P_\mathrm{MW\,set}\) when the model is initialized, and can be changed during simulation. The load controller is expected to have a slow reaction compared to the speed governor. [3]
A value \(K_\mathrm{I\,MW}\) = to 0.01 corresponds to a time constant of 100 s; 0.001 corresponds to 1000 s (relatively slow acting) [3].
Acceleration (fsra)
[…] for studies of large power systems, [the acceleration control loop] can be ignored. It is important for islanding studies and smaller power systems with large frequency variations. If the generating unit begins to accelerate at a rate over [\(a_\mathrm{set}\)] (pu/s^2) then this control loop acts to limit fuel flow. [1]
It can be disabled by setting \(a_\mathrm{set}\) to a large value, such as 1. [3]
Temperature (fsrt) / load limit
The load limiter module allows to set a maximum output limit \(P_\mathrm{ldref}\). This can also model an exhaust temperature limit, in which case \(P_\mathrm{ldref}\) is not to be interpreted as a power value. The time constant \(T_\mathrm{f\,load}\) should match the measurement time constant for temperature (or power or which ever signal is being modelled). Additionally, the gains of the limiter, \(K_\mathrm{P\,load}\) and \(K_\mathrm{I\,load}\), should be set to achieve fast and stable control when the limit \(P_\mathrm{ldref}\) is reached. To deactivate the load limit, set the parameter \(P_\mathrm{ldref}\) to a high value [3].
The lead-lag block with \(T_\mathrm{sa}\) and \(T_\mathrm{sb}\) can be used to model the exhaust gas temperature measurement system in gas turbines. A “radiation shield” component of larger gas turbines can be modeled by setting \(T_\mathrm{sa}=4\,\mathrm{s}\) and \(T_\mathrm{sb}=5\,\mathrm{s}\), for example [3].
The temperature limit [tlim] in pu corresponds to the fuel flow required for 1 pu turbine power. [1]
Turbine/engine model
The output from the low value select block is given to the first order lag element representing the fuel or gate system (Valve). [1]
\(V_\mathrm{max}\) and \(V_\mathrm{min}\) represent the maximum and minimum fuel valve opening. \(W_\mathrm{fspd}\) is the fuel flow multiplyer.
\(W_\mathrm{fnl}\) is the fuel required to run the compensator [1].
The range of fuel valve travel and of fuel flow is unity, so the limits lie between 0 pu and 1 pu. \(V_\mathrm{max}\) can be reduced below 1, for example to model a load limit defined by the operator or supervisory controller [3]. Additionally there is a dynamic frequency dependent limit reduction, see Section 3.2.3.
For a gas turbine, in the presence of a minimum firing limit, \(V_\mathrm{min}\) normally is set greater than zero and less than \(W_\mathrm{fnl}\) [3].
The value of the fuel flow at maximum power shall be \(\leq 1\), depending on the value of \(K_\mathrm{turb}\) [3]. It translates the fuel consumption (or water flow) to mechanical power output [1].
The time delay \(e^{-sT_\mathrm{eng}}\) is used in representing diesel engines where there is a small but measurable transport delay between a change in fuel flow setting and the development of torque. \(T_\mathrm{eng}\) should be zero in all but special cases where this transport delay is of particular concern [3].
The switch \(W_\mathrm{fspd}\) is responsible for recognizing whether fuel flow, for a given fuel valve stroke, is be proportional to engine speed [3]. If True, fuel flow is proportional to speed. This is applicable for some gas turbines and diesel engines with positive displacement fuel injectors. If false, the fuel control system keeps fuel flow independent of engine speed.
Speed sensitivity / Damping
If \(D_\mathrm{m}=0\), the speed sensitivity paths are not active. [3]
If \(D_\mathrm{m}>0\), it models friction losses (variation of the engine power with the shaft speed; slightly increasing losses with increasing speed are characteristic for reciprocating engines and some aeroderivative turbines [3]).
If \(D_\mathrm{m}=<0\), it can model an influence of rotation speed on exhaust temperature using an exponential characteristic determined by \(D_\mathrm{m}\). The maximum permissible fuel flow falls with falling speed (typical for single-shaft industrial turbines due to exhaust temperature limits) [3]. The authors suspect that this could represent fan cooling.
Frequency dependent (valve) limit
The frequency-dependent limit block outputs the upper limit for valve position / the fuel flow signal fsr. It is shown in Figure 2.
In normal operation, the limit is \(V_\mathrm{max\,\omega} = V_\mathrm{max}\) and the there is no frequency dependent reduction.
When the frequency \(f\) in Hz drops below \(f_\mathrm{lim\,1}\), the value for \(P_\mathrm{lim}\), the power limit, is calculated by linear interpolation between the values \(f_\mathrm{lim\,1}, f_\mathrm{lim\,2}, \dots\) and \(P_\mathrm{lim\,1}, P_\mathrm{lim\,2}, \dots\) of a lookup table. The table consists of 10 data points which monotonically decrease in both power and frequency, point 1 being the hightest. The lowest data point does act as a lower limit, i.e. is not extrapolated to lower values.
\(V_\mathrm{max\,\omega}\) then ramps with the rate \(P_\mathrm{rate}\) from the initial and maximum value to the new value \(V_\mathrm{max\,omega} = (P_\mathrm{lim} / K_\mathrm{turb} + W_\mathrm{fnl})\).
\(P_\mathrm{lim}\) will then change with frequency. If f rises above \(P_\mathrm{lim\,1}\) again, \(V_\mathrm{max\,\omega}\) ramps back to \(V_\mathrm{max}\) [3].
Parameters
Per-unit power parameters are based on \(P_\mathrm{base}\), which is normally the capability of the turbine in MW. Per-unit frequency or acceleration parameters are based on the nominal frequency of the grid (e.g. 50 Hz in Europe).
| name | type | unit e | IEC name | description | typical value |
|---|---|---|---|---|---|
| \(a_\mathrm{set}\) | float | pu/s | Aset | Acceleration limiter setpoint | 10 |
| \(\Delta\omega_\mathrm{db}\) | float | pu | db | Frequency error deadband. Recommended to be =0 in most applications [3] | 0 |
| \(\Delta\omega_\mathrm{max}\) | float | pu | Maxerr | Maximum value for frequency error | 1 |
| \(\Delta\omega_\mathrm{min}\) | float | pu | Minerr | Minimum value for frequency error | -1 |
| \(\Delta t\) | float | s | \(\Delta t\) | Correction factor to adapt the unit of \(K_\mathrm{a}\) from pu/s to pu | 1 |
| \(D_\mathrm{m}\) | float | pu | dm | Speed sensitivity coefficient, see Section 3.2.2.1 | 0 |
| \(f_\mathrm{lim\,1}\) | float | Hz | flim1 | Frequency threshold 1 | 59 |
| \(f_\mathrm{lim\,10}\) | float | Hz | flim10 | Frequency threshold 10 | 0 |
| \(f_\mathrm{lim\,2}\) | float | Hz | flim2 | Frequency threshold 2 | 0 |
| \(f_\mathrm{lim\,3}\) | float | Hz | flim3 | Frequency threshold 3 | 0 |
| \(f_\mathrm{lim\,4}\) | float | Hz | flim4 | Frequency threshold 4 | 0 |
| \(f_\mathrm{lim\,5}\) | float | Hz | flim5 | Frequency threshold 5 | 0 |
| \(f_\mathrm{lim\,6}\) | float | Hz | flim6 | Frequency threshold 6 | 0 |
| \(f_\mathrm{lim\,7}\) | float | Hz | flim7 | Frequency threshold 7 | 0 |
| \(f_\mathrm{lim\,8}\) | float | Hz | flim8 | Frequency threshold 8 | 0 |
| \(f_\mathrm{lim\,9}\) | float | Hz | flim9 | Frequency threshold 9 | 0 |
| \(K_\mathrm{a}\) | float | pu | Ka | Acceleration limiter gain | 10 |
| \(K_\mathrm{D\,gov}\) | float | pu | Kdgov | Governor derivative gain | 0 |
| \(K_\mathrm{I\,gov}\) | float | pu | Kigov | Governor integral gain | 0.45 |
| \(K_\mathrm{I\,load}\) | float | pu | Kiload | Load limiter integral gain | 1 |
| \(K_\mathrm{I\,MW}\) | float | pu | Kimw | Supervisory load controller integral gain | 0 |
| \(K_\mathrm{P\,gov}\) | float | pu | Kpgov | Governor proportional gain | 4 |
| \(K_\mathrm{P\,load}\) | float | pu | Kpload | Load limiter proportional | 1 |
| \(K_\mathrm{turb}\) | float | pu | Kturb | Turbine gain (translates from fuel flow to power) | 1.9168 |
| \(P_\mathrm{base}\) | float | MW | Mwbase | Base for power values (> 0) | |
| \(P_\mathrm{ldref}\) | float | pu | Ldref | Load limiter reference value | 1 |
| \(P_\mathrm{lim\,1}\) | float | pu | plim1 | Power limit 1 | 0.8325 |
| \(P_\mathrm{lim\,10}\) | float | pu | plim10 | Power limit 10 | 0 |
| \(P_\mathrm{lim\,2}\) | float | pu | plim2 | Power limit 2 | 0 |
| \(P_\mathrm{lim\,3}\) | float | pu | plim3 | Power limit 3 | 0 |
| \(P_\mathrm{lim\,4}\) | float | pu | plim4 | Power limit 4 | 0 |
| \(P_\mathrm{lim\,5}\) | float | pu | plim5 | Power limit 5 | 0 |
| \(P_\mathrm{lim\,6}\) | float | pu | plim6 | Power limit 6 | 0 |
| \(P_\mathrm{lim\,7}\) | float | pu | plim7 | Power limit 7 | 0 |
| \(P_\mathrm{lim\,8}\) | float | pu | plim8 | Power limit 8 | 0 |
| \(P_\mathrm{lim\,9}\) | float | pu | plim9 | Power Limit 9 | 0 |
| \(P_\mathrm{rate}\) | float | pu | prate | Ramp rate for frequency-dependent power limit | 0.017 |
| \(R\) | float | pu | R | Droop (frequency/power) | 0.05 |
| \(R_\mathrm{close}\) | float | pu/s | Rclose | Minimum rate for valve closing | -99 |
| \(R_\mathrm{down}\) | float | pu | Rdown | temperature/load limit path output decrease rate limit | -99 |
| \(R_\mathrm{open}\) | float | pu/s | Ropen | Maximum rate for valve closing | 99 |
| \(R_\mathrm{select}\) | int | - | Rselect | governor controller feedback mode switch | |
| \(R_\mathrm{up}\) | float | pu | Rup | temperature/load limit path output increase rate limit | 99 |
| \(T_\mathrm{a}\) | float | s | Ta | Acceleration limiter time constant | 1 |
| \(T_\mathrm{act}\) | float | s | Tact | actuator (valve) reaction time constant | 0.4 |
| \(T_\mathrm{b}\) | float | s | Tb | Turbine lag time constant | 0.1 |
| \(T_\mathrm{c}\) | float | s | Tc | Turbine lead time constant | 0 |
| \(T_\mathrm{dgov}\) | float | s | Tdgov | Governor controller derivative time constant | 1 |
| \(T_\mathrm{D\,ratelim}\) | float | s | - | Ramp rate limter derivative time constant in s | 0.001 |
| \(T_\mathrm{eng}\) | float | s | Teng | Transport time delay for diesel engine | 0 |
| \(T_\mathrm{f\,load}\) | float | s | Tfload | Load limiter time constant | 3 |
| \(T_\mathrm{last\,value}\) | float | s | - | Time constant of very fast first order block to prevent algebraic loop | 1e-9 |
| \(T_\mathrm{p\,elec}\) | float | s | Tpelec | Electrical power measurement time constant | 2.5 |
| \(T_\mathrm{sa}\) | float | s | Tsa | lead time constant of temperature detection | 0 |
| \(T_\mathrm{sb}\) | float | s | Tsb | lag time constant of temperature detection | 50 |
| \(V_\mathrm{max}\) | float | pu | Vmax | Maximum valve position limit | 1 |
| \(V_\mathrm{min}\) | float | pu | Vmin | Minimum valve position limit | 0.175 |
| \(W_\mathrm{fnl}\) | float | pu | Wfnl | fuel flow with no load | 0.187 |
| \(W_\mathrm{fspd}\) | bool | - | Wfspd | Switch for fuel source characteristic | false |
Variables
Inputs
| name | type | unit | IEC name | description |
|---|---|---|---|---|
| \(\omega\) | float | pu | \(\omega\) | rotor speed |
| \(P_\mathrm{ref}\) | float | pu | Pref | load setpoint |
| \(P_\mathrm{MWSet}\) | float | pu | Pmwset | Supervisory power controller setpoint (automatic generation control) |
| \(P_\mathrm{e}\) | float | pu | Pe | measured electric power generation |
Outputs
| name | type | unit | IEC name | description |
|---|---|---|---|---|
| \(P_\mathrm{m}\) | float | pu | Pm | mechanical power |
Equations & algorithm
–
Initial equations / boundary conditions
The initial values for the system’s states are calculated from the initial mechanical power \(P_\mathrm{m\,0}\) and rotation speed \(\omega_\mathrm{0}\).
Helper variables
The following “helper variables” are defined to avoid repetition in the definitions of initial states below. They are the initial values of signals at certain points in Figure 1.
\(P_\mathrm{m\,noloss\,0} = \begin{cases} P_\mathrm{m\,0} + \omega_\mathrm{0} \cdot D_\mathrm{m},& \text{if } D_\mathrm{m}> 0\\ P_\mathrm{m\,0}, & \text{otherwise} \end{cases} \qquad(1)\)
\(C_\mathrm{fe\,0} = \begin{cases} W_\mathrm{fnl} + P_\mathrm{m\,noloss\,0} / K_\mathrm{turb},& \text{if } K_\mathrm{turb}>0\\ W_\mathrm{fnl}, & \text{otherwise} \end{cases} \qquad(2)\)
\(V_\mathrm{0} = \begin{cases} C_\mathrm{fe\,0} / \omega_\mathrm{0},& \text{if } W_\mathrm{fspd}\\ C_\mathrm{fe\,0}, & \text{otherwise} \end{cases} \qquad(3)\)
\(\vartheta_\mathrm{ex\,0} = \begin{cases} C_\mathrm{fe\,0} \cdot \omega_\mathrm{0}^{D_\mathrm{m}},& \text{if } D_\mathrm{m}<0\\ 1, & \text{otherwise} \end{cases} \qquad(4)\)
\(F_\mathrm{srt\,0} = (P_\mathrm{ldref}/K_\mathrm{turb} + W_\mathrm{fnl} - \vartheta_\mathrm{ex\,0}) \cdot K_\mathrm{P\,load} + x_\mathrm{I\,load} \qquad(5)\)
Initial states
\(x_\mathrm{I\,load\,0} = 1 \qquad(6)\)
\(x_\mathrm{turb\,0} = P_\mathrm{m\,noloss\,0} \qquad(7)\)
\(x_\mathrm{valve\,0} = V_\mathrm{0} \qquad(8)\)
\(x_\mathrm{fdl\,ratelimit\,0} = K_\mathrm{turb}(V_\mathrm{max}-W_\mathrm{fnl}) \qquad(9)\)
\(x_\mathrm{I\,gov\,0} = V_\mathrm{0} \qquad(10)\)
\(x_\mathrm{meas\,Pe\,0} = P_\mathrm{m\,0} \qquad(11)\)
\(x_\mathrm{fsrt\,ratelim\,0} = F_\mathrm{srt\,0} \qquad(12)\)
\(x_\mathrm{meas\,\vartheta\,ex\,0} = \vartheta_\mathrm{ex\,0} \qquad(13)\)
\(x_\mathrm{\vartheta\,ex\,0} = \vartheta_\mathrm{ex\,0} \qquad(14)\)
\(x_\mathrm{I\,MW} = 0 \qquad(15)\)
\(x_\mathrm{last\,value\,0} = V_\mathrm{0} \qquad(16)\)
\(x_\mathrm{fsra\,0} = 0 \qquad(17)\)
Initial power reference
\(P_\mathrm{ref\,0} = \begin{cases} 0, & \text{if } R_\mathrm{select}=0\\ R \cdot P_\mathrm{m\,0}, & \text{if } R_\mathrm{select}=1\\ R \cdot V_\mathrm{0}, & \text{otherwise} \end{cases} \qquad(18)\)
Open source implementations
This model has been successfully implemented in :
| Software | URL | Language | Open-Source License | Last consulted date | Comments |
|---|---|---|---|---|---|
| Open Modelica / Dynawo | Dynawo | modelica | MPL v2.0 | 15/05/2024 | For modeling assumptions and test results, see Dynawo repository. |