Proceedings of the 14 th International Middle East Power Systems Conference (MEPCON 1), Cairo University, Egypt, December 19-21, 21, Paper ID 192. Mitigating Subsynchronous resonance torques using dynamic braking resistor S. Helmy and Amged S. El-Wakeel M. Abdel Rahman and M. A. L. Badr Armed forces Department of electric power and machines Egypt Faculty of engineering, Ain-Shams university Sherif_mtc@yahoo.com Cairo, Egypt m_abdel_rahmanca@yahoo.com Abstract Series compensation has proven to increase stability in transmission of electric power. On the other hand insertion of series capacitor results in severe subsynchronous torques. The subsynchronous torque leads to generator-turbine shaft damage. Mitigation of subsynchronous transient torques is achieved through resistor bank connected to generator terminals. The insertion of resistor bank is controlled by fuzzy logic controller. The proposed controller has been tested on IEEE First Benchmark Model and it proved to have good damping for the torsional torques. Index Terms - Dynamic braking resistor, First Benchmark Model, fuzzy logic control, subsynchronous resonance. I. INTRODUCTION Since the two shaft failures at Mohave station at 197 and 1971, subsynchronous resonance has become topic of interest by utility industry. By definition, subsynchronous resonance is a case where the electric network exchanges significant amount of power with the mechanical network [1]. Intensive studies showed that insertion of series capacitor may result to SSR. When dealing with SSR, the main danger is the possibility of shaft damage. Several countermeasures have been reported to counteract SSR. The published countermeasures include excitation control, static VAR compensators as well as many other countermeasures [2-4]. Moreover, dynamic braking resistor is used as a powerful countermeasure for SSR [5, 6]. This countermeasure is used to control the power consumed by a resistor bank for the purpose of damping the torsional modes of turbo-generators. The proposed control technique for controlling the dynamic braking resistor is the fuzzy logic controller (FLC) [7]. The proposed fuzzy logic controller (FLC) is used to control the insertion of resistor bank to sustain the transient stability of the combined turbine-generator system under different SSR effects. The advantage of applying dynamic braking resistor as a countermeasure is its effectiveness in damping self-excitation SSR as well as transient torque SSR. However, ref. [7] showed only the application of FLC to control dynamic braking resistor to overcome self-excitation SSR. The severity of transient torques on turbine-generator shaft is much greater than that of self-excitation SSR. Hence, it is important to test the proposed controller behaviour on the case of transient torque. Therefore, this paper examines the application of FLC-driven dynamic braking resistor in mitigating transient torque SSR. The system under study is the well-known IEEE First Benchmark Model (IEEE FBM) [8]. The results show that the proposed controller is adequate for damping SSR. II. DYNAMIC BRAKING RESISTOR Dynamic braking resistor has previously been considered for augmenting system stability as well as for improving the transient response of power systems following major system disturbances [9]. The resistor bank is connected to the machine terminals. Fig. 1 shows a schematic of dynamically controlled resistor bank. Fig. 1 Dynamically controlled three-phase resistor bank During normal system operation, the resistor bank is disabled and no power is dissipated. Following a system disturbance, the power consumed by the resistor bank is controlled so as to damp the torsional oscillations of the turbogenerator. After the torsional oscillations decay to a small level, the resistor bank is again disabled from service. Bonneville Power Administration (BPA) has implemented dynamic braking resistor for enhancing transient stability[9]. The resistor is 14 MW, 24 KV. It consists of 45, ft of ½ inch stainless steel wire on three towers. Dynamic braking resistor has been reported to be used in different countries like: Japan, China, Russia and australia[1]. III. CASE STUDY The system under study is the IEEE First Benchmark Model (IEEE FBM) which is shown in Fig. 2. 416
The synchronous machine model is developed with threephase ac armature windings on the stator, one field winding on the rotor, and three damper windings on the rotor[11]. The parameters of the equivalent circuit of synchronous generator are calculated using Canay s conversion[12]. The parameters of the synchronous generator are stated in Reference [8]. These parameters are in the form of IEEE and IEC standards[13, 14]. Hence, Canay s conversion[12] is used to transform these parameters into equivalent circuit parameters. Fig. 2. IEEE First Benchmark Model with dynamic braking resistor The voltage equation is given by[15, 16]: V R i ψ d a d d V q Ra i q ψ q V Ra i ψ d Vf = - Rf if - ψf dt V g Rg i g ψ g VD RD id ψ D V Q R Q i Q ψ Q U d U q + (1) Where: V d, V q and V d-axis, q-axis, -axis voltages V f, V g, V D and V Q field and damper bars voltages R a armature resistance R f, R g, R D and R Q field and damper bars resistances I d, I q and I d-axis, q-axis, -axis currents I f, I g, I D and I Q field and damper bars currents Ψ d, Ψ q and Ψ d-axis, q-axis, -axis flux linkages Ψ f, Ψ g, Ψ D and Ψ Q field and damper bars flux linkages U d, U q d-axis and q-axis speed voltages The mechanical part of the system is described by the rotational form of Newton's second law: d d [ T ] = [ J] [ θ ] + 2 [ D] [ θ ] + [ K][ θ] (2) dt dt Where: [θ] [J] [D] [K] [T] Vector of angular positions Diagonal matrix of moments of inertia Tridiagonal matrix of damping coefficients Tridiagonal matrix of stiffness coefficients Vector of turbine and electromagnetic torques III. SIMULATION ALGORITHM The algorithm for the simulation is outlined as follows[11]: 1) The parameters of the synchronous machine are computed from the IEEE standard parameters using Canay s conversion[12]. This conversion is used to retrieve the generator parameters from standard IEEE tests. 2) Calculate the initial values of the electrical part (load angle δ, initial d,q axis currents, initial field voltage and current) and, mechanical part (masses angles, initial masses speeds and initial masses torques). 3) The trapezoidal rule of integration is applied to equation(1) which converts each inductance to a resistance and current source in parallel. 4) d-axis equivalent circuit is reduced to one resistance in series with one voltage source and the same is done for the q-axis. 5) The three Thevenin equivalent circuits are converted from dq to phase quantities. 6) The complete network is solved and hence the generator voltage is calculated in phase quantities. 7) The generator phase quantities are converted again to dq quantities and these values are used to calculate the armature current and field current and electromagnetic torque. 8) The calculated torque is used to compute the speeds of the rotor masses and the torques of the turbine stages by solving equation(2). 9) The computed generator speed is used as an input to the FLC. 1) The output of the FLC is obtained according to the generator speed. 11) Steps from (3) to (1) are repeated till t = t max IV. PROPOSED FUZZY LOGIC CONTROLLER A. FLC linguistic variables and membership functions The FLC has two inputs which are the speed error of the generator (E) and the change of the error (CE). It has one output that is braking power (P b ). The FLC has four linguistic variables for the two inputs. In addition, it has four linguistic variables for the output. These variables are: (ZE, PS, PM, and PB) Where ZE stands for Zero, PS stands for Positive Small, PM stands for Positive Medium, and PB stands for Positive Big Fig. 3 shows the membership functions of the speed error (E). It has three triangular membership functions and one trapezoidal membership functions. 417
The universe of discourse is normalized to be in the range of (-1 to 1). Fig. 4 shows the membership functions of the change of error (CE). These membership functions are similar to those of speed error (E). Furthermore, the universe of discourse is normalized to be in the range of (-1 to 1). Fig. 5 shows the membership functions of the braking power (Pb). The membership functions of (Pb) are similar to those of (E) and (CE). The universe of discourse is in the range of ( to 3). IF (E) is PB AND (CE) is PB THEN (P b ) is PB This rule is explained as follows: if the generator speed is much greater than reference speed (E is PB) AND the speed of the generator is getting away from the reference speed (CE is PB), then the control action taken must be PB to stabilize the generator speed. The rest of the rules are formulated as the above rule. For the case of 4 linguistic variables for (E) and 4 linguistic variables for (CE) the resulting rule table would have 16 rules. Table I shows rule table of the proposed fuzzy logic control. TABLE I RULE TABLE OF PROPOSED FLC E CE PB PM PS ZE PB PB PB PB PB PM PB PB PB PM PS PB PB PM PS ZE PB PM PS ZE Fig. 3. Membership function for the error (E) The output of the FLC (P b ) is limited to 1 PU. Therefore, the maximum output power is 892.4 MW. This output power is feasible [9]. The dynamic braking resistor is connected if the generator speed exceeds predetermined value. For the given system the dynamic braking resistor is connected after the fault occurrence. As soon as the system is restabilised it will be disconnected. The proposed controller utilizes the dynamic braking resistor which is well-known of enhancing system stability. Therefore, the proposed controller is capable of suppression of different transients imposed on the system. Fig. 4. Membership function for the change of error (CE) Fig. 5. Membership function for the braking power (Pb) V. SIMULATION RESULTS The torsional interaction case is the IEEE FBM [8] with 3-phase short circuit located at point B at time and the fault is cleared at time.75 sec. The results of simulation are presented with and without controller. Fig. 6 shows the generator terminal voltage with and without control. The waveform of the voltage in case of no controller used is growing indicating unstable operation. In case of using FLC braking resistor the waveform of voltage indicates good damping of disturbance. Fig. 7 shows the generator terminal current in two cases (without and with control). Fig. 8 shows the capacitor voltage without control. Fig. 9 shows the capacitor voltage with control. Fig. 1 through Fig. 15 show the speed deviations for different masses. Fig. 16 through Fig. 2 show the torsional torques for different shaft sections. B. FLC rule table The rule table of fuzzy logic controller is a set of If-then statements. These statements are derived from experience about generator behavior and type of disturbance. To give an example for deriving rules: 418
Fig. 6. Generator terminal voltage deviation Fig. 9. Capacitor voltage with control Fig. 7. Generator terminal current Fig. 1. High Pressure turbine speed deviation Fig. 8. Capacitor voltage without control Fig. 11. Intermediate Pressure turbine speed deviation 419
Fig. 12. Low Pressure turbine stage A speed deviation Fig. 15.. Exciter speed deviation Fig. 13. Low Pressure turbine stage B speed deviation Fig. 16. HPT-IPT shaft torque deviation Fig. 14.. Generator speed deviation Fig. 17. IPT-LPTA shaft torque deviation 42
VI. CONCLUSIONS Application of fuzzy logic to control dynamic braking resistor for damping transient SSR has been tested in this paper. The proposed controller has proved to be effective in mitigating torsional torques in turbine-generator set. The studied system is the IEEE first benchmark model. The disturbance is 3-phase short circuit for 75 msec. Different waveforms show the suppression of torsional oscillations in the case of fuzzy logic control. REFERENCES Fig. 18. LPTA-LPTB shaft torque deviation) Fig. 19. LPTB-Gen shaft torque deviation Fig. 2. Gen-Exc Shaft torque deviation The results show good damping behavior for proposed controller. Both electrical and mechanical transients are mitigated down to acceptable range. [1] IEEE Subsynchronous Resonance Working Group of the System Dynamic Performance Subcommittee, "Terms, Definitions And Symbols For Subsynchronous Oscillations," IEEE Transactions on Power Apparatus and Systems, vol. PAS-14, No. 6, pp. 1326-1333, June 1985. [2] E. T. Ooi and M. M. Sartawi, "Concepts on field excitation control of subsynchronous resonance in synchronous machines," IEEE Transaction on Power Apparatus and Systems, vol. PAS-97, No. 5, pp. 1637-1645, Sept. / Oct. 1978. [3] IEEE Subsynchronous Resonance Working Group of the System Dynamic Performance Subcommittee, "Countermeasures to subsynchronous resonance problem," IEEE Transactions on Power Apparatus and Systems, vol. PAS-99, No. 5, pp. 181-1818, Sept/Oct 198. [4] L. Wang and Y.-Y. Hsu, "Damping of subsynchronous resonance using excitation controllers ans static Var compensators: A comparative study," IEEE Transaction on Energy conversion, vol. 3, No.1, pp. 6-13, 1988. [5] M. K. Donnelly, et al., "Control of a dynamic brake to reduce turbine-generator shaft transient torques," IEEE Transactions on Power Systems, vol. 8, No. 1, pp. 67-73, February 1993. [6] O. Wasynczuk, "Damping shaft torsional oscillations using a dynamically controlled resistor bank," IEEE Transactions on Power Apparatus and Systems, vol. PAS-1, No. 7, pp. 334-3349, July 1981. [7] A. H. M. A. Rahim, "A minimum-time based fuzzy logic dynamic braking resistor control for sub-synchronous resonance," Electrical Power and Energy Systems, vol. 26, pp. 191 198, 24. [8] IEEE Subsynchronous Resonance Working Group of the System Dynamic Performance Subcommittee, "First Benchmark Model for computer simulation of Subsynchronous resonance," IEEE Transactions on Power Apparatus and Systems, vol. PAS-96, No. 5, pp. 1566-1572, September/October 1977. [9] M. L. Shelton, W. A. Mittelstadt, P. F. Winkelman, and W. J. Bellerby, "Bonneville Power Administration 14-MW Braking Resistor," IEEE Transaction on Power Apparatus and Systems, vol. PAS-94, No. 2, pp. 62-611, 1975. [1] CIGRE. (May 1988) State of the art in non classical means to improve power system stability. Electra. 88-113. [11] S. Helmy, Amged S. El-Wakeel, M. Abdel Rahman, and M. A. L. Badr, "Real-Time Modeling of Synchronous Generators based on PC," in 13 th International Middle East Power System Conference MEPCON '9, Assuit, Egypt, 29, pp. 337, 343. [12] I. M. Canay, "Determination of model parameters of synchronous machines," IEE Proceeding, vol. 13, Pt. B, No. 2, pp. 86-94, March 1983. [13] IEEE, "Test procedures fo synchronous machines," in standard 115, ed, 1965. [14] IEC, "Recommecdations for rotating electric machinery," in Publ. 34-4A, ed, 1972. [15] P. Kundur, Power system stability and control. New York: McGraw-Hill Inc., 1994. [16] Y.-n. Yu, Electric Power System Dynamics: Academic Press, 1983 421