the effect of disturbances in the electrical power...

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THE EFFECT OF DISTURBANCES IN THE ELECTRICAL POWER SYSTEM ON TORQUE MOMENTS OF THE HIGH-POWER TURBINE SET SHAFT

Józef Wiśniewski / Technical University of Łódź

The results presented in this paper have been obtained through research co-financed by the National Cen-tre for Research and Development (NCBiR) as a part of the contract SP/E/1/67484/10, The Strategic Research Program – Advanced Technologies of Power Acquisition: Development of technologies for high-performance, zero-emission coal power units integrated with flue gas CO2 capture.

1. INTRODUCTION

There are plans to introduce power units of approx. 1000 MW into the National Power System in the near future. These power units will operate at super-critical mean-temperature parameters and with the following steam parameters: temperature – 560-580°C, pressure – 25.8 MPa. The switch from the traditional parameters of 535°C and 18 MPa leads to an increase in the efficiency of electrical power generation by approx. 1.5-1.7 percentage points. The nearest goal seems to be the power unit efficiency of 50% (the 50+ Program). The new power unit designs carry new problems regarding the cooperation of power units with the electrical power sys-tem [1].

This paper presents the problem of modelling a rotating system of masses of turbines and of a generator. The purpose of this modelling is to calculate the torque moments in the shafts which couple individual system components during disturbances in the electrical power system. The calculations are performed with the EMTP/ATP software [2].

The turbine set components are coupled by shafts with a determined mechanical strength which can be exceeded upon specific failures.

The rotating system of the turbine set is characterised by intrinsic vibration frequencies. Calculation of these frequencies and preventing the system from working upon their presence is a critical condition of proper operation of the turbine set.

This paper presents the model of a 1000 MW turbine set mechanical rotating system and the results of modal calculations of intrinsic vibration frequencies for the components of this system. The work considers the cases of disturbances in the electrical power system which increase the torque moments of the shaft. These are symmetrical and asymmetrical faults within the grid, action of the single-phase automatic reclosing system, im-proper synchronisation and the effect of grid harmonics in the generator current on the rotor, which may result in resonance vibrations.

The threat to the shaft strength depends on the torque moment value upon a failure and also on the number and frequency of oscillation, as well as on the shaft overload history. For reasons of simplification, the paper adopts the value of the torque moment amplitude in the shaft of 3 p.u. as the permissible momentary limit value under the conditions of disturbance.

The Effect of Disturbances in the Electrical Power System on Torque Momentsof The High-power Turbine Set Shaft

Abstract

Mechanical parameters are determined for a set of turbines and power generator of 1000 MW of the refer-ence power unit operated at super-critical parameters. The modal method is used to calculate the frequencies of intrinsic vibrations of the vibrating systems. The paper in-vestigates the values of torqu moments which may occur

in the sections of shafts upon disturbances in the electri-cal power system, e.g. near faults, action of automatic reclosing systems, synchronisation or interaction of elec-tromagnetic moments from the grid side which introduce the system into resonance vibration.

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2. DEVELOPMENT OF THE REFERENCE POWER UNIT MODEL

The turbines. The design of the turbine system in high-power units is diverse. High and intermediate pressure turbines are usually designed as single-flow turbines, while intermediate-pressure turbines for theelectrical power of more than 500 MW and low-pressure turbines are double-flow units. The number and ar-rangement of turbines, as well as their share in the total driving power are explained in the references [1].

This article assumes a turbine set system with five turbines and one generator (see Fig. 1).

Power output Due to the limits of transport, the power unit output system precludes the use of a single three-phase transformer rated at more than 1000 MVA. The manufacturers of large transformers consider the use of a system with two transformers operating in parallel or a system which ensures higher reliability of the system, equipped in three single-phase transformers (plus one backup transformer) with the total power cor-responding to that of the power unit (see Fig. 2).

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Reference power unit data. The planned power unit of super-critical parameters will be rated at 1000 MW of power at least. No such power unit currently exists in Poland. The reference literature on this subject has been reviewed to obtain the predicted mechanical data for a power unit of similar magnitude. There are consid-erable amounts of such data in the publications from the 1980s, when units of similar magnitudes were commis-sioned – usually at nuclear power plants. The list of turbine set mechanical parameters is based on several pub-lications [e.g. 3 to 7]. Fig. 3 shows the constants of generator inertia Hgen for the unit power range of 500-1100 MVA, in the units [p.u.*s], the mean value Hgen_mean of these constants (ca. 0.82 p.u.*s), as well as the totals of the inertia constants for all turbines, Hturb_sum, which power the generator, and finally the mean value Hturb_sum_mean of these totals (ca 2.96 p.u.*s). The constants of inertia H allow the calculation of moments of inertia J.

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500 600 700 800 900 1000 1100 1200

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Fig. 2. The solu-tions for the high power generator power output: a) traditional, b) the system with two three-phase transformers; c) the system with three single-phase transformers

Fig. 1. The structure of the turbine set in the 1000 MW adopted reference power unit

Fig. 3. The constants of inertia Hgen of genera-tors, the totals of inertia constants Hturb_sum of turbines and the means of these values, Hgen_mean and Hturb_sum_mean for power units of various power magnitudes


a) b) c)

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Fig. 4 shows – depending on the power of the unit – the averaged values of the coefficients of flexibilityKmean for the shafts which couple the turbines and the generator, expressed in the units [p.u./rad] and the aver-age of these values, Kmean_average (approx. 83.5 p.u./rad).

Reference power unit parameters Based on the assessment of parameters of high-power units avail-able in the reference literature or in the processing characteristics of power plant, the power unit with the fol-lowing parameters is adopted in further calculations:

• Generator: n = 2, f = 50 Hz, Pn_gen =1000 MW, Sn_gen = 1176 MVxA, Un_gen = 27 kV• Impedances (p.u.): Xd = 2.5, Xd’ = 0.3, Xd” = 0.26, XL = 0.23, Ra = 0.003, Xq = 2.2, Xq’= 0.5, Xq” = 0.25• Time constants (s): Tdo’ =6, Tdo “= 0.04, Tqo’ = 0.6, Tqo “= 0.03• The share of the turbines in the driving moment (%): HP = 30, IP = 22, LP1 = 16, LP2 = 16,

LP3 = 16• Constants of inertia (p.u.*s): HP = 0.17, IP = 0.4, LP1 = 0.6, LP2 = 0.6, LP3 = 0.6, GEN = 0.8• Attenuation rates (p.u.*s/rad): HP = 0.0002, IP = 0.0002, LP1 = 0.0002, LP2 = 0.0002, LP3 =

0.0002, GEN = 0.0001• Coefficients of flexibility (p.u./rad): HP-IP = 150, IP-LP1 = 200, LP1-LP2 = 250, LP2-LP3 = 300,

LP3-GEN = 350.

3. MODEL PARAMETERS

The EMTP/ATP software [2] allows simulating the dynamics of turbine systems with any number of sepa-rate rotating masses on a single shaft. Each mass is rigid and flexibly connected to the adjacent masses.

Each mass is assigned with the driving power which can be constant or change due to the action of regu-lating systems.

The electrical part of the turbine generator model The three-phase synchronous generator model applied in the EMTP/ATP software is shown in Fig. 5. The model consists of the following: three phase windings of the stator, connected to the grid; the excitation winding producing a flux in axis d, the substitute winding attenuating in axis d, the substitute winding which represents the effect of eddy currents and the substitute winding attenuating in axis q.

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500 600 700 800 900 1000 1100 1200

K mean

K mean_average

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��Fig. 4. The average values of the coefficients of flexibility,Kmean, of the shafts which couple the turbines and the gen-erator, and the average of these values, Kmean_average

Fig. 5. The substitute electrical diagram of the generator

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The Effect of Disturbances in the Electrical Power System on Torque Moments of The High-power Turbine Set Shaft

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The generator model is described by two sets of equations: • the voltage equations:

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dtd

(1)

• the flux-current equations:

iL� (2)

where: u, R, L, i, λ are, respectively, the vectors of the following: voltages on the windings, resistances of the windings, inductances of the windings, currents of the windings and fluxes in the windings.

The input data for the generator modelling can be the resistances and inductances of the windings, or the data obtained through standard measurements from the generator manufacturer, which is more convenient.

The mechanical part of the model. The mechanical system presented in Fig. 1 is adopted as a linear system, so the flexibly coupled rotating masses can be described with Newton’s second law, according to thisequation:

genturbdt

d2dt

2d TT�K�D�J (3)

where the matrices are designated as follows: δ are the angular positions of the rotating masses; J are the moments of inertia of the rotating masses; D are the attenuation rates; K are the coefficients of flexibility of thecouplings between the rotating masses; Tturb are the driving moments of the turbine, Tgen is the electromagnetic moment of the generator.

The modal analysis [2, 3, 5]. By assuming a matrix of modal transformation Q, where its columns are the intrinsic vectors of the product J x K, the equation (3) is converted into the modal form. Its solution allows finding the modal frequencies of the system vibrations. In the case of the system being considered, these fre-quencies are: f = [1.44 13.37 23.77 32.98 38.17 44.9] Hz.

Fig. 6 presents the shape of the specific moduli (the normalised values of the intrinsic vector componentsof the transformation matrix Q). The shape of the modes represents the reciprocal shifts of individual rotating masses upon a resonance at the given modal frequency.

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Fig. 6. The shape of the specific moduli (the normalisedvalues of the intrinsic vector components of the transforma-tion matrix Q


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Fig. 7 shows the dependence of the maximum torque moments Ti (referenced to the rated moments of the shafts) at the specific sections of the shafts as the function of the external sinusoidal input function frequencyfrom the grid side, at the amplitude of 1% of the rated moment Tn_gen acting on the generator rotor. The chart displays a strong amplification of the input function signal at the frequencies of the system intrinsic vibrations;the amplification manifests in the values of the torque moments, which exceed the ratings.

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0 10 20 30 40 50

T1T2T3T4T5

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Fig. 7. The dependence of the maximum torque moments at the specific sections of the shafts asthe function of the external sinusoidal input function frequency, at the amplitude of 1% of Tn_gen acting on the generator rotor

f [Hz]

Note that even at such small excitation of the rotor with the disturbing moment, the torque moments exceed the ratings of these shafts at certain resonance frequencies.

4. CALCULATING THE TORQUE MOMENTS ACTING ON THE TURBINE SET SHAFTS

The impact of the grid on the rotor. The rotating system is tested for the susceptibility to the action of a disturbance signal at the frequency close to the frequency of intrinsic vibrations. This disturbance may origi-nate from the electrical power system as the generator loading current which contains a component with the suitable frequency. The increasing numbers of electronic power devices in the grid favours this situation. The calculations assume the presence of a disturbing sinusoidal moment at the frequency equal to the resonance frequency and at the amplitude equal to 1% of the rated moment. The EMTP/ATP software is used for simulation calculations of torque moments for the generator in two states: at the rated load and synchronised and operated without any load. The shaft sections exhibited significant values of torque moments; their values were higher forthe generator at the rated load. The modelled generator power output system is presented in Fig. 8.

Fig. 9 shows the amplitudes of the torque moments expressed in relative units (p.u.) and referenced to the rated moments of all shaft sections when the disturbing moment is applied to the generator rotor. The gen-erator is loaded with full power.

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Fig. 8. The modelled generator power output system

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13.4 23.8 33.0 38.2 44.9

T1maxT2maxT3maxT4maxT5max

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Fig. 9. The amplitudes of torque moments for the disturbing moment acting on the generator rotor at the amplitude equal to 1% of the rated moment Tn_gen

fres[Hz]

The Effect of Disturbances in the Electrical Power System on Torque Moments of The High-power Turbine Set Shaft

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Faults in the electrical power system Fig. 10 shows the values of the maximum torque moments in the rotating system shafts during the following disturbances (A to E):

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fault A fault B fault C fault D fault E


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A – Three-phase fault at the generator voltage buses. The generator cut-off switch Q1 breaks after 100 ms. After the following 500 ms the steam cut-off valves are actuated. The generator is loaded with full power.

B – The fault is the same as in the scenario A. The generator is not loaded.C – Three-phase fault at the HV terminals of the transformer TB. The generator cut-off switch Q1 breaks after 100

ms. After the following 500 ms the steam cut-off valves are actuated. The generator is loaded with full power.D – The fault is the same as in the scenario C. The generator is not loaded.E – Single-phase fault at the power unit 400 kV line. The automatic control of the successful single-phase auto-

matic reclosing is triggered in 0. 4 s.The generator is loaded with full power. The calculations indicate that the torque moments significantly

exceed the permissible value.Fig. 11 shows the courses of the torque moments in the shaft sections with the rotational speeds of the

turbines and of the generator during a three-phase fault at the generator voltage buses, isolated after 100 ms, when the generator is running at full load.

Fig. 10. The maximum torque moment values in the shafts of the rotating system upon faults near the generator

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(f ile 1000MW.pl4; x-v ar t) t: T1 t: T2 t: T3 t: T4 t: T5 4.98 5.00 5.02 5.04 5.06 5.08 5.10 5.12 5.14[s]

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(f ile 1000MW.pl4; x-v ar t) t: VEL_1 t: VEL_2 t: VEL_3 t: VEL_4 t: VEL_5 t: VEL_6 4.98 5.00 5.02 5.04 5.06 5.08 5.10 5.12 5.14[s]

2970

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(f ile 1000MW.pl4; x-v ar t) t: DUD 0.0 0.2 0.4 0.6 0.8 1.0 1.2[s]

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(f ile 1000MW.pl4; x-v ar t) t: T1 t: T2 t: T3 t: T4 t: T5 0.95 1.00 1.05 1.10 1.15 1.20[s]

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Fig. 11. The courses of the torque moments and rotational speeds of the turbines and of the generator during a three-phase fault at the generator voltage buses

Synchronisation of the generator The courses of the torque moments in the turbine shafts are calculated for the synchronisation with the switch Q1 (see Fig. 8). The calculations were performed for the frequency difference be-tween the generator and the grid, Δf = 0.1 Hz and for the difference of phase angles ΔΦ at the interval of 0°-180°.

Fig. 12 shows the courses of the rumbling voltage and torque moments in the shaft sections during syn-chronisation, where the synchronisation exhibits a phase discordance ΔΦ = 5°.

Fig. 12. The courses of the rumbling voltage and torque moments synchronisation, where the synchronisation at the phase discordance ΔΦ = 5°


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REFERENCES

The dependence of the maximum magnitudes of torque moments Ti in the successive sections of the shaft during synchronisation on the difference of phase angles ΔΦ is shown in Fig. 13.

The calculations imply that in the case of the investigated turbine set, the maximum torque moment val-ues for different shaft sections occur when synchronisation is performed at the difference of phase angles ΔΦ within the interval of 110°-130°. The voltage phase upon voltage closing does not affect the magnitude of torque moments on the shaft.

5. SUMMARY

• Calculating the intrinsic vibration frequencies of the rotating system of the turbine and generator masses is an important part of programming the turbine set operation. It allows avoiding operation in states of hazard and occurrence of oscillation vibrations caused by an external input function.

• The calculations of the magnitudes of torque moments during external disturbances may be useful in the investigations into the causes of shaft damage, in the application of countermeasures and in the determination of operating rules for generators.

• The considered cases of faults, synchronisation and external effects on the generator rotor caused by an electromagnetic moment at the resonance frequency display considerable values of the torque mo-ments, which exceed the approved safe level.

1.Zagadnienia projektowania i eksploatacji kotłów i turbin do nadkrytycznych bloków węglowych, a collective work,Silesian University of Technology Publishing, Gliwice 2010.

2. EMTP Rule Book and Theory Book, Bonneville Power Administration, 1987.3. Machowski J., Białek J., Bumby J., Power System Dynamics and Stability, John Wiley & Sons Ltd., 1997.4. Jennings G., Harley R., New index parameter for rapid evaluation of turbo-generator subsynchronous resonance

susceptibility, Electric Power Systems Research, 37,1996.5. Jose A., Castillo J., Turbo-generator torsional behavior using the participation factors and considering the static loads

model. Transmission and Distribution Conference and Exposition: Latin America, IEEE/PES, 2008.6. Maljkovic Z., Stegic M., Kuterovac L, Torsional oscillations of the turbine-generator due to network faults, 14th Inter-

national Power Electronics and Motion Control Conference, EPE-PEMC, 2010.7. Tsai J., A new single-pole switching technique for suppressing turbine-generator torsional vibrations and enhancing

power stability and continuity, IET Gener. Transm. Distrib., 5, 2007.

Fig. 13. The dependence of the maximum torque moments during synchronisation on the difference of phase angles ΔΦ

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The Effect of Disturbances in the Electrical Power System on Torque Momentsof The High-power Turbine Set Shaft

the effect of disturbances in the electrical power...

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