Journal of Energy and Power Engineering 6 (2012) 833-839
Mitigating Subsynchronous Resonance Torques Using Dynamic Braking Resistor
Sherif Helmy1, Amged S. El-Wakeel1, Mohammed Abdel Rahman2 and Mohammed A.L. Badr2
1. Department of Electric Power and Energy, Military Technical College, Cairo 11311, Egypt
2. Department of Electric Power and Machines, Ain-Shams University, Cairo 11517, Egypt
Received: April 28, 2011 / Accepted: August 31, 2011 / Published: May 31, 2012.
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.
Key words: Dynamic braking resistor, First Benchmark Model, fuzzy logic control, subsynchronous resonance.
1. Introduction
Since the two shaft failures at Mohave station in 1970 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 (subsynchronous resonance) 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 (VA reactive) compensators as well as many other countermeasures [2]. Moreover, dynamic braking resistor is used as a powerful countermeasure for SSR [3, 4]. 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 Corresponding author: Sherif Helmy, Ph.D. candidate, lecturer, research fields: real time simulation, power system control,HVDC.E-mail:*********************.dynamic braking resistor is the FLC (fuzzy logic controller) [5]. The proposed 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. [5] 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 behavior 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 FBM (IEEE First Benchmark Model) [6]. The results show that the proposed controller is adequate for damping SSR.
2. Dynamic Braking Resistor
Dynamic braking resistor has previously been
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Mitigating Subsynchronous Resonance Torques Using Dynamic Braking Resistor 834
considered for augmenting system stability as well as for improving the transient response of power systems following major system disturbances [7]. The resistor bank is connected to the machine terminals. Fig. 1 shows a schematic of dynamically controlled 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 turbo-generator. After the torsional oscillations decay to a small level, the resistor bank is again disabled from service. BPA (Bonneville Power Administration) has implemented dynamic braking resistor for enhancing transient stability [7]. The resistor is 1,400 MW, 240 kV. It consists of 45,000 ft of 1/2 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 [8].
3. Case Study
The system under study is the IEEE FBM (IEEE First Benchmark Model) which is shown in Fig. 2.reactive materials studies
Fig. 1 Dynamically controlled three-phase resistor bank.
Fig. 2  IEEE First Benchmark Model with dynamic braking resistor.
The synchronous machine model is developed with three-phase ac armature windings on the stator, one field winding on the rotor, and three damper windings on the rotor [9].
The parameters of the equivalent circuit of synchronous generator are calculated using Canay’s conversion [10]. The parameters of the synchronous generator are stated in Ref. [6]. These parameters are in the form of IEEE and IEC standards [11, 12]. Hence, Canay’s conversion [10] is used to transform these parameters into equivalent circuit parameters.
The voltage equation is given in Refs. [13, 14]:
d a d d
q a q q
0a00
f f f f
g g g g
D D D D
Q Q Q Q
V R000000iψ
V0R00000iψ
V00R0000iψ
d
V000R000iψ
=  -  -
d t
V0000R00iψ
V00000R0iψ
V000000R iψ
⎡⎤⎡⎤⎡⎤⎡⎤
⎢⎥⎢⎥⎢⎥⎢⎥
⎢⎥⎢⎥⎢⎥⎢⎥
⎢⎥⎢⎥⎢⎥⎢⎥
⎢⎥⎢⎥⎢⎥⎢⎥
⎢⎥⎢⎥⎢⎥⎢⎥
⎢⎥⎢⎥⎢⎥⎢⎥
⎢⎥⎢⎥⎢⎥⎢⎥
⎢⎥⎢⎥⎢⎥⎢⎥
⎢⎥⎢⎥⎢⎥⎢⎥
⎣⎦⎣⎦⎣⎦⎣⎦
d
q
U
U
+0
⎡⎤
⎢⎥
⎢⎥
⎢⎥
⎢⎥
⎢⎥
⎢⎥
⎢⎥
⎢⎥
⎢⎥
⎣⎦
(1)
where:
V d, V q and V0: d-axis, q-axis, 0-axis voltages;
V f, V g, V D and V Q: field and damper bars voltages respectively;
R a: armature resistance;
R f, R g, R D and R Q: field and damper bars resistances respectively;
I d, I q and I0: d-axis, q-axis, 0-axis currents;
I f, I g, I D and I Q:field and damper bars currents respectively;
Ψd, Ψq and Ψ0: d-axis, q-axis, 0-axis flux linkages respectively;
Ψf, Ψg, ΨD and ΨQ: field and damper bars flux linkages respectively;
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:
[][][][][][][]
2
d d
T=Jθ + Dθ + Kθ
dt dt
(2) where:
[θ]: vector of angular positions;
[J]: diagonal matrix of moments of inertia;
[D]: tridiagonal matrix of damping coefficients;
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Mitigating Subsynchronous Resonance Torques Using Dynamic Braking Resistor 835
[K]: tridiagonal matrix of stiffness coefficients; [T]: vector of turbine and electromagnetic torques.
4. Simulation Algorithm
The algorithm for the simulation is outlined as follows [9]:
(1)The parameters of the synchronous machine are computed from the IEEE standard parameters usi
ng Canay’s conversion [10]. 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 Eq. (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 dq0 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 dq0 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 tur
bine stages by solving Eq. (2);
(9)The computed generator speed is used as an input to the FLC;
(10) The output of the FLC is obtained according to the generator speed;
(11) Steps from (3) to (10) are repeated till t = t max.
5. Proposed Fuzzy Logic Controller
5.1 FLC Linguistic V ariables 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. The universe of discourse is normalized to be in the range of -1 to 1. Fig. 4 shows the membership functions of the CE (change of error). 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 (P b. The membership functions of P b are similar to those of E and CE. The universe of discourse is in the range of 0 to 3.
5.2 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:
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 four linguistic variables for E and four linguistic variables for CE the resulting rule table would have 16 rules. Table 1 shows rule table of the proposed fuzzy logic control.
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 [7].
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Mitigating Subsynchronous Resonance Torques Using Dynamic Braking Resistor
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Fig. 3  Membership function for the error (E).
Fig. 4  Membership function for the CE (change of error).
Fig. 5  Membership function for the braking power (P b ).
Table 1  Rule table of proposed FLC.
PM PB PB PB PM PS PB PB PM PS ZE PB PM PS ZE
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.
6. Simulation Results
The torsional interaction case is the IEEE FBM [6] with 3-phase short circuit located at point B at time 0 and the fault is cleared at time 0.075 sec. The results of simulation are presented with and without controller. Fig. 6 shows the generator terminal voltage with and without control. The solid line represents the generator terminal voltage with control, while the dashed line represents the voltage 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). For all next curves, the dashed line is the case where no controller exists, while the solid line represents the controller case.
Figs. 8-13 show the speed deviations for different masses. Figs. 14-18 show the torsional torques for different shaft sections.
The results show good damping behavior for proposed controller. Both electrical and mechanical transients are mitigated down to acceptable range.
Fig. 6  Generator terminal voltage deviation.
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Mitigating Subsynchronous Resonance Torques Using Dynamic Braking Resistor
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Fig. 7 Generator terminal current.
Fig. 8 High pressure turbine speed deviation.
Fig. 9
Intermediate pressure turbine speed deviation. Fig. 10 Low pressure turbine stage A speed deviation.
Fig. 11 Low pressure turbine stage B speed deviation.
Fig. 12 Generator speed deviation.
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