Methodology for tests in hydroelectric power plant using RT-LAB BERTA Test Bench

Transcription

1 Methodology for tests in hydroelectric power plant using RT-LAB BERTA Test Bench Presented to... OPAL-RT TECHNOLOGIES Montréal, Québec July 2014 By: Marc Langevin, ing., PhD

2 Marc Langevin, Eng., PhD Page 2

3 Table of contents 1 INTRODUCTION 6 2 VALIDATING MODELS 6 3 PREPARATION BEFORE TESTS 6 4 HYDRAULIC TURBINE MODEL Block diagram of the hydraulic turbine non-linear model Equations for the modeling of hydraulic pressurized conduits Definitions One single penstock or pressurized tunnel Francis Turbine SPEED GOVERNOR MODEL 13 6 TESTS Starting procedure Controller panel Monitoring of steady-state values Open loop tests Test # Test # Test # Closed loop tests Test # Closed loop tests with PSS emulation Tests # 5 and # RECOMMENDATIONS Speed governor model and settings Turbine model CONCLUSION 33 Marc Langevin, Eng., PhD Page 3

4 Table of illustrations Figure 1: Block diagram of hydraulic turbine non-linear model... 7 Figure 2: Water flow versus servomotor stroke Figure 3: Power versus water flow Figure 4: Power versus servomotor stroke Figure 5: Example of a PID speed governor model block diagram Figure 6 : Typical gate servomotor model Figure 7: Gate servomotor characteristic curve Figure 8: Example: Test #1. PID output and gate servomotor stroke Figure 9: Example: Test #1. Power Figure 10: Example: Test #2. Injected frequency deviation signal Figure 11: Oscillation frequency from the frequency sweep; Logarithmic scale Figure 12: Example: Test #3. Frequency deviation Figure 13: Example: Test #3. PID output and gate servomotor Figure 14: Example: Test #3. Measured electric and estimated mechanical power from polynomial; Filtered signals Figure 15: Example; Test #4. Frequency deviation Figure 16: Example: Test #4. Gate servomotor stroke Figure 17: Example: Test #4. Electric power transmitted to the grid and mechanical power estimated from polynomial 27 Figure 18: Example: Test #4. Closed loop test and simulations. Frequency deviation signals Figure 19: Example: Test #4. Closed loop test and simulations. Gate servomotor signals Figure 20 : Example: Test #4. Closed loop test and simulations. Mechanical power and load signals Figure 21: PSS and excitation system model in closed loop (islanded mode) test Figure 22: Example: Test #5. Impact of the low frequency band setting of a multi-band PSS; Simulated electric power. 32 Figure 23: Example: Test #5. Impact of the low frequency band setting of a multi-band PSS; Frequency deviation Marc Langevin, Eng., PhD Page 4

5 List of tables Table 1: Example of Francis turbine steady-state characteristics... 9 Table 2: Example of PSS emulator settings Marc Langevin, Eng., PhD Page 5

6 1 Introduction This report presents a recommended methodology for conducting speed governor tests on a synchronous hydro-generator. Besides some specific tests conducted in order to appreciate the impact of the water hammer effect on the mechanical power, tests on hydraulic units are not significantly different from tests on other kinds of units. However, you may have to make more tests, mostly closed loop tests, in order to determine if the speed governor is correctly tuned for allowing the tested unit to contribute to the whole power system frequency stability. Remind that synchronized units that appear to be very stable do not automatically contribute to the frequency stability. They often contribute to its deterioration. Because it transiently pushes the mechanical power in a direction opposite to the load variation, the water hammer effect is a significant source of instability for a hydraulic unit. This procedure is written in the form of a report on test results analysis, validation of speed governor and prime mover models for power system dynamic stability program, and recommendations of speed governor settings. 2 Validating Models Before testing, preliminary models are loaded on a Matlab Simulink platform. The initial setup and parameters are adjusted according to the available data. When available, use data from previous on-site tests, e.g. commissioning tests. During the test session, once sufficient data have been collected, off-line simulations are performed the results of which are compared to those of the real tests. The preliminary models can therefore be modified on site. If there are differences in behaviors between the real tests and the Matlab simulations, additional tests are performed to improve the models. Speed governor and turbine models validation is achieved by comparing the results of real, open and closed loop tests against identical simulated test results. 3 Preparation before tests Before conducting the tests, prepare a test procedure. Make a daily planning. It is important to collect all the available data that will eventually help in validating the turbine and speed governor models. Prepare the turbine model: o o Rated values: Generator rated MVA Rated net head (m) Rated water flow (m 3 /s) Rated turbine power (MW) Steady-state data at rated head for: Water flow VS gate servomotor position; Power VS water flow; Power VS gate servomotor position Marc Langevin, Eng., PhD Page 6

7 o Water starting time including all the adduction components under pressure (s) o Head loss at rated water flow and rated head (m) o Gross head (m) o Inertia constant o Quadrature axis reactance X q o Armature resistance R a Prepare the speed governor model: o Recognize the model according to the manufacturer's documentation; o Determine the calibration of all the input/output signals; o Determine with great accuracy the 0% and 100% calibration values of the gate servomotor stroke; o Identify the source of the frequency/speed signal. 4 Hydraulic Turbine Model 4.1 Block diagram of the hydraulic turbine non-linear model Figure 1: Block diagram of hydraulic turbine non-linear model 4.2 Equations for the modeling of hydraulic pressurized conduits Definitions Q = Water flow in cubic m/s; H = Water head in meters; H r = Rated head value; Q r = Rated water flow. For convenience, it should correspond to the water flow at full wicket gate opening and rated head. Hence, could be different from official rated value. q = Q/Q r = per unit value of water flow; Marc Langevin, Eng., PhD Page 7

8 h = H/H r = per unit value of water head; s = Laplace operator; h in = per unit value of available water head; Equals gross head when there is no surge chamber; h = per unit value of H considering transient and steady-state losses due to water flow; T w = water starting time in seconds; T w = Q r L Equation 1) g H r S L = length of a segment of pressurized conduit; S = section area of a segment of pressurized conduit; g = constant of gravity; φ = friction losses coefficient; Friction losses = J Q 2 Equation 2) φ = J Q r 2 H r Equation 3) One single penstock or pressurized tunnel h = h in s T w q φ q 2 Equation 4) Solving technique: Compute q using integration Francis Turbine The water flow is related to the net head and small deviation of speed by equation 5 following: q = q g (1 + a 12 ω) h Equation 5) Where: q g = per unit value of water flow as a function of gate servomotor position at rated head condition; Δω = speed deviation in p.u.; a 12 = coefficient of variation of water flow as a function of speed deviation. Solving technique: h = 2 q q g (1+a 12 ω) Equation 6) And the mechanical power is defined by equation 7 following: p = h q η (1 + ab 22 ω) Equation 7) Marc Langevin, Eng., PhD Page 8

9 Where: η = turbine efficiency in p.u. The reference value is the efficiency at 100% gate opening and rated head; ab 22 = coefficient of variation of power as a function of speed deviation (only). In the model of Figure 1, the expression "q η" is replaced by the power that would result, at rated head, from the water flow value. Example: Rated head: 60 m Rated flow: 170 m 3 /s Rated efficiency: 95% Rated power: 95 MW Table 1 depicts possible characteristic values of water flow and power related to the gate servomotor stroke (position). Table 1: Example of Francis turbine steady-state characteristics Servomotor Stroke (G) Water flow (Q) Power mm % m 3 /s p.u. MW p.u Marc Langevin, Eng., PhD Page 9

10 Servomotor Stroke (G) Water flow (Q) Power mm % m 3 /s p.u. MW p.u Instead of using correspondence tables, such as an "Outlook Table" in Matlab Simulink, to model water flow and power according to wicket gate opening (defined by the servomotor stroke value), we can use polynomials. In the example above, the polynomial relating the water flow to the servomotor stroke in per unit values is described by equation 8 following: Where: Q = 0, 0069 G 3 0, 5890 G 2 + 1, 8507 G 0, 2686 Equation 8) G is gate servomotor stroke in p.u. Q is water flow in p.u. Figure 2 shows comparisons between fictitious measured values of water flow versus servomotor stroke and results from models based on third polynomial of equation 8 or classical theory. Marc Langevin, Eng., PhD Page 10

11 Figure 2: Water flow versus servomotor stroke The polynomial relating the power to the water flow in per unit values is described by equation 9 following: P = 1, 0311 Q 3 + 1, 5282 Q 2 + 0, 5692 Q 0, 0662 Equation 9) Where: Q is water flow in p.u. P is power in p.u. And the power can also be related to the servomotor stroke using the following polynomial: P = 1, 3534 G 3 + 1, 5013 G 2 + 1, 1345 G 0, 2927 Equation 10) Figure 3 shows comparisons between fictitious measured values of power versus water flow and results from models based on third polynomial of equation 9 or classical theory. Figure 4 shows comparisons between fictitious measured values of power versus servomotor stroke and results from models based on third polynomial of equation 10 or classical theory. Marc Langevin, Eng., PhD Page 11

12 Figure 3: Power versus water flow Marc Langevin, Eng., PhD Page 12

13 Figure 4: Power versus servomotor stroke 5 Speed governor model Figure 5 shows the block diagram of a typical speed governor controller and Figure 6 shows a model of the wicket gate servomotor chain. Marc Langevin, Eng., PhD Page 13

14 Figure 5: Example of a PID speed governor model block diagram Figure 6 : Typical gate servomotor model A typical distribution valve curve is shown on Figure 7. Marc Langevin, Eng., PhD Page 14

15 Figure 7: Gate servomotor characteristic curve 6 Tests 6.1 Starting procedure Controller panel Open the "Controller" panel Refer to user's manual for parameter descriptions Make sure that: o Operating Mode = Opened loop o Closed loop disturbance = Step o Open loop disturbance = Step o Delta P0 = 0 MW o Delta F0 = 0 p.u. Marc Langevin, Eng., PhD Page 15

16 6.2 Monitoring of steady-state values Before starting any specific tests, monitor and record the steady-state values in all the operating range. Do not forget to record the gross head and net head values if available. Compare the servomotor and power data with those collected before: Table 1 in our example. Make sure that the voltage and current signals correspond to what you expected. 6.3 Open loop tests If the excitation system is equipped with a PSS, switch off the PSS in order to avoid interfering with the speed governor. Make many tests, at different operating points, using the variety of available open loop disturbance signals. Start with small amplitude frequency steps and increase amplitudes progressively. At least, perform the following tests: Negative and positive tests: ±0.001 p.u. and ±0.005 p.u. Positive and negative ramps using open loop disturbance signal; Positive and negative ramps using the gate control if possible. Reason for this is to generate a ramp in opening and power that will not be corrected by the feedback. This will allow to determine the delay between the gate movement and the power variation; Frequency sweep. Observe the resonance points; Sinus at approximately 0.05 Hz. Following are few examples of tests that could be conducted and how to analyze and report the results Test # Description Power at 75% of rated MVA Power feedback (Permanent droop to power) Negative frequency step: p.u. Reset Initial condition P0 = 75 MW Initial servomotor stroke = 73% Anticipated results Power will increase 10% in steady-state PID output immediate p.u. jump Fast gate opening: p.u Actual results Gate opening: Power increase: PID output behavior: Gate servomotor behavior: Rate of PID output increase: Marc Langevin, Eng., PhD Page 16

17 Discussion In this section, describe the behaviors of PID output, gate servomotor and power, identifying the effect of proportional, integral and derivative gains. Qualify and quantify the servomotor and power behaviors. Compare with anticipated results according to controller gains, and servomotor and power models based on the available data and/or classical modeling. Observe the water hammer effect on the power curve. Figure 8: Example: Test #1. PID output and gate servomotor stroke Marc Langevin, Eng., PhD Page 17

18 Water hammer effect Figure 9: Example: Test #1. Power Test # Description Power at 85% of rated MVA Gate feedback Frequency sweep from 0.01 Hz to 5 Hz Crest amplitude = 0,005 p.u Initial conditions P0 = 85 MW Initial servomotor stroke = 83% Anticipated results PID output will follow the frequency error according to the gain and phase determined by the frequency response of the PID controller; The gate servomotor will follow the PID output with good precision at the beginning, then with reduced gain, phase lag and possible distortion; Electric power will follow the gate variation and show a resonance close to its natural frequency of oscillation. Marc Langevin, Eng., PhD Page 18

19 Actual results Describe the actual results. Note the inversions of phase polarities if there are Discussion Compare actual and anticipated results. Try to explain the differences. Focus on possible dead times and distortions. Figure 10 shows the frequency deviation signal that is injected in the speed governor. Figure 10: Example: Test #2. Injected frequency deviation signal Figure 11 shows the oscillation frequency. Marc Langevin, Eng., PhD Page 19

20 Figure 11: Oscillation frequency from the frequency sweep; Logarithmic scale Test # Description Power at 85% of rated MVA Gate feedback 0.05 Hz frequency sinus Crest amplitude = p.u Initial conditions P0 = 85 MW Initial servomotor stroke = 83% Anticipated results PID output will follow the frequency error with a "Gain" gain and "degrees" phase delay, due to the PID controller frequency response; Etc Actual results Describe actual results Marc Langevin, Eng., PhD Page 20

21 Discussion Figure 12 shows the frequency deviation sinusoidal signal injected in the speed governor. The aim of this test is to observe and quantify the gate and power in terms of gain and phase lag at the oscillation frequency of 0.05 Hz which is generally closed to the frequency of oscillation following disturbances that result in large frequency deviations in the power system. Note that a different value could be used if the system natural frequency is different. Figure 12: Example: Test #3. Frequency deviation Compare the PID output response to what you anticipated from the PID controller gains and time constants. Marc Langevin, Eng., PhD Page 21

22 Figure 13: Example: Test #3. PID output and gate servomotor Figure 14 shows actual and estimated from polynomial electric power signals. Note that filtering may be necessary for better appearance. In this example, a fifth order Butterworth filter tuned at 0.5 Hz was used. Marc Langevin, Eng., PhD Page 22

23 Water hammer effect Figure 14: Example: Test #3. Measured electric and estimated mechanical power from polynomial; Filtered signals 6.4 Closed loop tests The closed loop tests allow simulating the tested unit behavior in an islanded network. If the excitation system is equipped with a PSS, switch off the PSS in order to avoid interfering with the speed governor. In the control panel, set maximum and minimum values of frequency deviations according to the alarm settings. Default values are ±5%. Make many tests, at different operating points, using the variety of available close loop disturbance signals. Repeat similar tests varying the controller gains. Repeat some tests using the PSS emulation function, if a PSS actually exists. Start with small amplitude load steps and increase amplitudes progressively. At least, perform the following tests: Negative and positive tests: ±0.01 p.u. and ±0.05 p.u. It is important to understand well the meaning of the signals related to power. The electric power transmitted to the grid and the mechanical power, are almost equal when we do not consider the dynamic transition from mechanical to electric power. In BERTA, the electric power signal identified "TU_pelec" is computed as follows: The electric power output; Plus the estimated stator losses according to the armature resistance and the current; Marc Langevin, Eng., PhD Page 23

24 A first order filtering with a 0.02 second time constant The mechanical power signal identified "TU_pmec" is computed as follows: The electric power output; Plus the estimated stator losses according to the armature resistance and the current; Plus the accelerating power estimated from the rotational speed of the equivalent direct sequence voltage behind the quadrature axis reactance X q. Actually, the "TU_pmec" signal is an estimation valid in the frequency range from 0 to approximately 1 Hz. Above this threshold, the computation of the accelerating power is not reliable. In a multi-machine power system, if the electric power natural oscillations are adequately damped, signals "TU_pelec" and "TU_pmec" will significantly differ only if the whole power system is undergoing a generalized frequency disturbance. Remind that the closed loop simulated mechanical power signal, identified "Sim_pmec", is computed as follows: The "TU_pelec" signal; Plus a correction resulting from the variation of mechanical power versus the rotational speed, corresponding to the frequency in islanded operation mode. In other words, if the "dpm_dw" coefficient in the controller panel is set to zero, the signals "TU_pelec" and "Sim_pmec" are identical. The load signal, identified "Sim_pelec", is computed as follows: The "TU_pelec" signal at time T=0-, one time step before the disturbance; Plus the load disturbance signal. Following are few examples of tests that could be conducted and how to analyze and report the results Test # Description Power at 80% of rated MVA Gate feedback Load step = +5% Initial conditions P0 = 81 MW Initial gate servomotor = 79% Gross head : 61 m K p = ; K i =. Make sure to choose initially values that will ensure the system stability Anticipated results Simulated island frequency will decrease; Gate will open; Power will increase up to the value determined by the 5% step; The system should be stable. I you anticipate instability, be ready to stop the disturbance before reaching the maximum frequency deviations specified in the control panel; Marc Langevin, Eng., PhD Page 24

25 Because of gate feedback, the final steady-state frequency deviation will be determined by the final gate servomotor position corresponding to the new power Actual resuls As anticipated; (or not) System gets stable; (or not) Gate opening reaches 0.07 p.u. more; Steady-state frequency deviation is... It coincides (or does not) with the permanent droop setting; But we observe Discussion Figure 15 shows the island frequency behavior. Describe it. Figure 15: Example; Test #4. Frequency deviation Figure 16 shows the gate servomotor behavior. Describe it. Marc Langevin, Eng., PhD Page 25

26 Figure 16: Example: Test #4. Gate servomotor stroke Figure 17 shows the comparison between the actual power and its estimated value according to the polynomial described in equation 4. A very small offset was added to the estimated value in order to match the initial condition. We can easily observe the quick power decrease following the gate opening and the subsequent time delay. The remaining power difference could result from an increase of the downstream level. (This is an assumption. There may be many other explanations due to the complexity of the actual behavior of a turbine) Marc Langevin, Eng., PhD Page 26

27 Figure 17: Example: Test #4. Electric power transmitted to the grid and mechanical power estimated from polynomial Off-line simulation of test #4 In order to validate adequately the dynamic model of the turbine and governor system, it is recommended to remake the test in off-line simulation. (e.g. with Matlab Simulink ) Compare the results from the actual test to those obtained in off-line simulation using assumed models and parameters, originating from manufacturer documentation, technical specifications, former tests, your own open loop tests, etc... Do not hesitate to make some adjustments in order to better fit curves resulting from simulation with those from the actual test. The analysis of many tests will reveal the validity of your assumptions. Also compare with results from simulations with classical models. Marc Langevin, Eng., PhD Page 27

28 Figure 18: Example: Test #4. Closed loop test and simulations. Frequency deviation signals Figure 18 shows the frequency deviation that would result from the load disturbance if the tested unit were supplying the load alone, i.e. if it were operating in islanded mode. Compare reality with simulation results from improved and classical models. Figure 19 shows gate servomotor signals and Figure 20 shows closed loop mechanical power and load signals. Marc Langevin, Eng., PhD Page 28

29 Figure 19: Example: Test #4. Closed loop test and simulations. Gate servomotor signals Marc Langevin, Eng., PhD Page 29

30 Figure 20 : Example: Test #4. Closed loop test and simulations. Mechanical power and load signals 6.5 Closed loop tests with PSS emulation These kinds of tests are realized in order to understand the impact of the power system stabilizer (PSS) on the frequency behavior in an islanded system. Although generally no PSS are enabled in islanded operation mode, it is worth examining its impact when the power system frequency varies following a generation/load rejection and/or trip. Figure 21 shows a functional diagram of the PSS emulator: A PSS model that generates a voltage set-point correction; A simplified static excitation system model with proportional gain and voltage transducer time constant, translating the voltage set point variation into the resulting simulated voltage deviation; The load characteristics defined by "Np", the coefficient of variation of electric power versus voltage deviation. Table 2 depicts an example of PSS emulator settings. Marc Langevin, Eng., PhD Page 30

31 Figure 21: PSS and excitation system model in closed loop (islanded mode) test Table 2: Example of PSS emulator settings Test # Frequency band T w K s 5 Low Tests # 5 and # Description Power at 80% of rated MVA Gate feedback Load step = +5% Emulation of multi-band PSS, low frequency band in test #5 PSS emulation off in test # Initial conditions P0 = 81 MW Initial gate servomotor = 76% Gross head : 66 m (Note the impact on the required gate opening) K p = ; K i = Anticipated results The simulated frequency will decrease The simulated electric power will be modulated by the PSS; The gate will open Power increase up to the value determined by the 5% step; System should stabilize; Due to gate feedback and permanent droop, the steady-state frequency deviation will be determined by the final gate servomotor position Actual results Final frequency deviation oscillates around the anticipated value; The minimum value reaches p.u Discussion Compare this test with its equivalent without PSS emulation. Marc Langevin, Eng., PhD Page 31

32 As an example, Figure 22 shows the simulated electric power signal with and without the PSS. The power step that would result from a sudden load increase or unit trip is compensated by the voltage modulation from the PSS reaction. Figure 22: Example: Test #5. Impact of the low frequency band setting of a multi-band PSS; Simulated electric power Figure 23 shows comparison of resulting frequency deviation. The PSS allowed to significantly reduce the frequency dip. The PSS also improved the damping. Note that PSS not always improve the frequency stability. Actually, it is generally the opposite because most of the existing PSS are not sophisticated enough for providing good damping in the whole frequency range of electric power and system frequency. Very often, a good tuning at the natural frequency of oscillation of electric power will result in stability deterioration at frequencies lower than 0.1 Hz. Marc Langevin, Eng., PhD Page 32

33 Figure 23: Example: Test #5. Impact of the low frequency band setting of a multi-band PSS; Frequency deviation 7 Recommendations 7.1 Speed governor model and settings Write your recommendations. 7.2 Turbine model Write your recommendation. 8 Conclusion Write your conclusion. Marc Langevin, Eng., PhD Page 33