Deriving Machine Parameters for Simulation

For use in power system stability simulations, utilities and system operators may desire to derive accurate model parameters of generators, excitation systems, governor controls and other control equipment. The utility may have found that actual events have not been accurately simulated by computer models or that individual equipment characteristics do not seem to match the manufacturer data. Further, adjustments may have been made by field or operating personnel that have altered the response of the equipment. In these situations, there is a need to obtain more accurate models for simulation. This Techblog provides an overview of the methodology for obtaining more accurate model response from measurements of the actual equipment and appropriate derivation of parameters for the model.

Approach

There are three essential stages to the methodology for obtaining more accurate machine models:

  • Machine and equipment measurements. In this stage, actual tests and measurements are made of the study machines and equipment. In this memo, we focus on low impact methodologies, or methodologies that do not impose unusual stresses on the machine or equipment.
  • Parameter derivation. Based on the measurements, the function diagram of the equipment or machine is developed, and the applicable parameters derived. This process has been largely conducted heuristically although some approaches have attempted development of computer automation.
  • Model development. Based on the function diagrams, the model may or may not fit into standard model libraries available from the simulation software (PSS/E or PSLF). If a standard model does not exist, an attempt may be made to fit the model into a standard model by adjusting parameters. Alternatively, a user-specified model may be developed.

Each of the above is discussed further in the following sections.

Machine and Equipment Measurements

Several methodologies for conducting actual site measurements are in use. The most common methods are the small perturbation, continuous monitoring and standstill frequency response methods.  All methods require direct access to the equipment and machine to be modeled, and to hook up measurement equipment.  For article, we will only discuss the small perturbation method.  The other methods are described in further detail in the reference articles. In the small perturbation method, small test signals are injected into the equipment. Alternatively, the test may be performed with small amounts of load being rejected. Load rejection methods are preferable to signal injection as they are usually much easier to implement while providing the required data. Depending on the equipment, signal injection can be complex to accomplish physically or perhaps not possible at all. Depending on the type of control equipment being measured, these tests may include:

  1. Generator open-circuit saturation curve. The open circuit saturation curve is measured with the unit operating off-line at rated speed. The generator field excitation is varied and measurements of terminal voltage, field voltage and field current are taken.
  2. Steady state on-load measurements at various MW/MVAr dispatches. The on-load measurements have the unit connected to the electrical network and placed at a given load. At that load level, the generator field excitation is varied to change the reactive power output. Usually five points at a load are taken: two points with the generator absorbing vars, one point at unity power factor, and the last two points with the generator producing vars. The maximum and minimum reactive power output depends on the generator capability curve, limits in the excitation system, and voltage constraints.
  3. With the automatic voltage regulator (AVR) in manual position, rejection of small MW and MVAr to record generator terminal voltage response. The purpose of the dynamic tests is to provide a simple and safe disturbance to excite the unit in order to provide its dynamic response.
  4. AVR performance through injection of test signals or MVAr rejections (AVR in manual control). Measuring generator field voltage provides information on the dynamic response for the excitation system.
  5. Governor performance through injection of test signals or MW rejections. Measuring governor signals provides information on the dynamic response for the turbine/governor.

The signals to be measured vary depending on the equipment and machine to be modeled. Typical signals measured for generators include:

  • Phase to Phase Voltages – obtained off the station’s PTs; primary side of the PTs should be connected between the generator terminals and the main breaker
  • Line Currents – obtained from station CTs
  • Generator Field Voltage (exciter field voltage if a brushless unit) – obtained from the excitation source
  • Generator Field Current (exciter field current if brushless) – obtained from the excitation source
  • Turbine Speed – derived directly from the terminal voltage
  • Control signal out of governor
  • Power Angle – The machine measurement procedure requires an accurate measurement of power angle, the angle difference between the field axis and the phase “A” voltage This is typically accomplished by acquiring a sinusoidal signal whose phase is “locked” to the position of the generator’s rotor. The phase of this signal is compared to the phase of the generator terminal voltage to obtain a relative value of the power angle.

A Permanent Magnet Generator (PMG) located on the generator shaft can often provide a signal which can be used for power angle measurement. When an appropriate PMG signal is not available, additional instrumentation is required to measure power angle. The measurements using any of the aforementioned method require a data recorder which can record the steady state and dynamic response of a number of typical electrical signals. The following provides more detail about the recording equipment in the areas of signal interface, data acquisition, event capture, and user operation.

Parameter Derivation

Once the measurements are completed, the next stage is (a) to identify the transfer functions that represent the equipment and (b) to specify the parameters applicable to the transfer function. The transfer functions and parameters must provide a reasonable fit to the test data. Control equipment may be represented in transfer functions or block diagrams. These functions define the algebraic and differential equation relationship of input and output variables and various parameters and time-domain states for internal variables. Various equipments may have standard block diagrams. For example, synchronous machines are typically represented as round-rotor or salient pole equivalents. The IEEE regularly issues standard block diagrams for excitation systems and turbine-governor controls. Alternatively, the manufacturer may suggest the block diagram for their equipment, which may or may not be one of the industry standard models. As a last resort, one may need to synthesize the block diagram from knowledge of the internal processes of the control equipment or from the test results. Once the model structure is known, the parameters are derived in a manner that most closely fits the test results. Certain parameters are obtained directly from the measurements, while others need to be derived. Curve-fitting techniques that minimize error versus the test results have been applied for deriving parameters. However, frequently, the machine tests and measurements may include some noise or lower frequency response that is not of interest to the simulation model. For example, stability simulations typically focus on response in the 0.1 to 10 Hz range; higher frequency characteristics do not impact system stability. Hence, there is some leeway in filtering the model parameters so as not to exactly match the test results but capture as much of the essential response for simulation. To illustrate this process for synchronous machines, following are the steps for deriving model parameters:

  • Identify whether the machine is salient pole or round rotor. Typically, salient pole machines are for slower rotating machines such as hydro turbines. Once the type is identified, obtain the block diagram for that machine that is provided by simulation software.
  • Fill in parameters for the model as follows:
    • Base values for field current and field voltage and saturation values from the plot of the open circuit test results. Typically, the saturation function can be estimated with an exponential function of the terminal voltage.
    • Machine Xd and Xq from the V-curve test results.
    • Load rejection tests provide information on time constants.

Derive the other parameters through curve-fitting techniques. Much of this process is intuitive and requires familiarity with the specific equipment. Some approaches have used iteration, least-squares and binary search methods. It should be noted from observations made earlier that a perfect fit may not be possible, and a close fit may be sufficient for the purposes of stability simulations.

Model Development

From time to time it is necessary to develop user models for equipment which do not have representation in commercial software standard libraries for stability assessments. Emerging technologies and new equipment are typical bases for user models. Sometimes an approximate model is applied comprised of a simple “blackbox” with current/voltage input and output. In a pinch, a forced fit to an existing model may be attempted. But in most cases, developing a new user model is a necessity if the objective is to accurately assess the interaction of equipment on the power network for stability.  (For further discussion on Model development, please refer to Techblog: “Developing My Dynamic Model,” M. Gutierrez, March, 2006.)

Conclusion

Once the user model is developed, the model is linked in with the standard model library of the simulation software. This completes the process of developing a more accurate model of equipment for simulation.

References:

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  3. “Maximum Likelihood Estimation of Solid-Rotor Synchronous Machine Parameters from SSFR Test Data,” Keyhani, A.; Hao, S.; Dayal, G.; Power Engineering Review, IEEE, Volume 9, Issue 9, Sept. 1989 Page(s):56 – 56
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  8. Identification of synchronous machine parameters using load rejection test data,” da Costa Bortoni, E.; Jardini, J.A.; Energy Conversion, IEEE Transaction on, Volume 17, Issue 2, June 2002 Page(s):242 – 247
  9. “Determination of Synchronous Machine Parameters Using Standstill Frequency Response Tests at Different Excitation Levels,” Sellschopp, F.S.; Arjona, M.A.; Electric Machines & Drives Conference, 2007. IEMDC ’07. IEEE International, Volume 2, 3-5 May 2007 Page(s):1014 – 1019
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