A PARAMETER TUNING APPROACH FOR BYPASS DAMPING FILTER TO SUPPRESS SUBSYNCHRONOUS RESONANCE IN POWER SYSTEMS

Abstract

The present invention discloses a parameter tuning approach for bypass damping filter to suppress subsynchronous resonance in power systems, namely determining the parameters of capacitor, inductor and damping resistor in BDF. Using this approach, the parameters of capacitor and inductor in BDF can be adjusted, so that the frequency where the negative electrical damping of generator reaches minimum can be away from the frequency range of low frequency oscillation mode and typical frequencies of each torsional mode; the parameter of damping resistor in BDF can be further adjusted so that the minimum value of negative electrical damping is in reasonable range. The application of BDF with parameters tuned by the present invention contributes to the suppression of both the torsional interaction effect and the transient torque amplification effect.

Claims

1. A parameter tuning method for a bypass damping filter (BDF) to suppress sub synchronous resonance in power systems, comprising the following steps: (1) calculating typical frequencies of each torsional mode according to turbine-generator shaft parameters, and supposing a low frequency oscillation mode of the shaft is within a frequency range of 0˜2 Hz; (2) choosing the per-unit frequency where negative electrical damping reaches minimum to be f.sub.m*, the f.sub.m* should be away from the frequency range of low frequency oscillation mode and typical frequencies of each torsional mode mentioned in Step (1); (3) according to the chosen f.sub.m* in Step (2), calculating the per-unit capacitance and reactance X.sub.BDF at system rated frequency using the equation below: $X_{\mathrm{BDF}}=\frac{X_C\left(X_L-X_C\right)}{f_e^{*2}.Math.X_L-X_C}-X_C$ $f_e^{*}=1-f_m^{*};$ where X.sub.L is a system per-unit reactance at rated frequency, including generator subtransient reactance, line reactance and equivalent reactance of the receiving power grid; X.sub.C is capacitance of the series capacitor at rated frequency; (4) calculating actual physical parameters of the capacitor and the inductor in BDF according to the above-mentioned X.sub.BDF in Step (3); (5) calculating minimum value of generator negative electrical damping D.sub.e(min).sup.0 without BDF applied; (6) according to the f.sub.m* in Step (2) and the X.sub.BDF in Step (3), calculating the minimum value of generator negative electrical damping D.sub.e(min).sup.BDF with BDF applied; and (7) adjusting the value of damping resistor in BDF to make D.sub.e(min).sup.BDF in reasonable range.

2. The parameter tuning method for BDF to suppress subsynchronous resonance in power systems according to claim 1, characterized in that the per-unit value of f.sub.m* in Step (2) is chosen as the middle frequency between the frequency range from 2 Hz to the lowest typical frequency of the shaft torsional modes.

3. The parameter tuning method for BDF to suppress subsynchronous resonance in power systems according to claim 1, characterized in that in Step (4) the actual physical parameters of the capacitor and the inductor in BDF are calculated using the following equations: $C_{\mathrm{BDF}}=\frac{1}{2.Math.\pi .Math..Math.f_0.Math.Z_B.Math.X_{\mathrm{BDF}}}\times {10}^6.Math..Math.\mathrm{\mu F}$ $L_{\mathrm{BDF}}=\frac{Z_B.Math.X_{\mathrm{BDF}}}{2.Math.\pi .Math..Math.f_0}\times {10}^3.Math..Math.\mathrm{mH}$ where f.sub.0 is the system rated frequency, Z.sub.B is the base value of system impedance, C.sub.BDF and L.sub.BDF are the capacitance and inductance of BDF, respectively.

4. The parameter tuning method for BDF to suppress subsynchronous resonance in power systems according to claim 1, characterized in that in Step (5) the minimum value of generator negative electrical damping D.sub.e(min).sup.0 without BDF applied is calculated using the following equation: $D_{e\left(\min \right)}^0=-{\psi }_0^2.Math.\frac{1-f_m^0}{2.Math.f_m^0}.Math.\frac{1}{R}$ $f_m^0=1-\sqrt{X_C/X_L}$ where ψ.sub.0 is the per-unit air flux linkage of generator and can be chosen as 1.0 for simplification, R is the per-unit resistance of system.

5. The parameter tuning method for BDF to suppress subsynchronous resonance in power systems according to claim 1, characterized in that in Step (6) the minimum value of generator negative electrical damping D.sub.e(min).sup.BDF with BDF applied is calculated using the following equation: $D_{e\left(\min \right)}^{\mathrm{BDF}}=-{\psi }_0^2.Math.\frac{1-f_m^{*}}{2.Math.f_m^{*}}.Math.\frac{1}{R^{*}}$ $R^{*}=R+\frac{R_{\mathrm{BDF}}.Math.X_C^2}{f_e^{*2}.Math.R_{\mathrm{BDF}}^2+{\left[k_f^{*}.Math.f_e^{*}.Math.X_{\mathrm{BDF}}-X_C\right]}^2}$ $k_f^{*}=\frac{f_e^{*}}{\left(1-f_e^{*2}\right)}$ where ψ.sub.0 is the per-unit air flux linkage of generator and can be chosen as 1.0 for simplification, R is the per-unit resistance of system and R.sub.BDF is the resistance of the damping resistor in BDF.

6. The parameter tuning method for BDF to suppress subsynchronous resonance in power systems according to claim 1, characterized in that in Step (7) the reasonable range of D.sub.e(min).sup.BDF is chosen as
D.sub.e(min).sup.0<D.sub.e(min).sup.BDF<D.sub.e(min).sup.0/2 where D.sub.e(min).sup.0 is minimum value of generator negative electrical damping without BDF applied.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0021] FIG. 1 is a structural diagram of bypass damping filter.

[0022] FIG. 2 is a diagram of subsynchronous resonance benchmark model with BDF applied. In the diagram, X.sub.d′ is the subtransient reactance of generator, X.sub.T is the leakage reactance of transformer, X.sub.Line is the inductive reactance of transmission line, R is the resistance of transmission line, X.sub.C is the capacitive reactance of series capacitor, X.sub.S is the equivalent reactance of receiving power grid.

[0023] FIG. 3 is a comparison diagram of electrical damping with and without BDF applied under 40% compensation.

[0024] FIG. 4(a) is a diagram of fault response of shaft LPB-GEN segment under 40% compensation without BDF applied.

[0025] FIG. 4(b) is a diagram of fault response of shaft LPB-GEN segment under 40% compensation with BDF applied.

PREFERRED EMBODIMENTS OF THE INVENTION

[0026] The present invention will be described in detail with reference to the accompanying drawings and specific embodiments thereof, in order to more specifically describe the present invention.

[0027] FIG. 2 is a diagram of subsynchronous resonance benchmark model with BDF applied. The rated frequency of the model is 60 Hz, other electrical parameters are labeled with base impedance value 325.55Ω. The series compensation level is set as 40% (0.20 p.u.). The detailed structure of BDF is shown in FIG. 1.

[0028] In this preferred embodiment, the turbine generator shaft has five torsional modes with typical frequency 15.71 Hz, 20.21 Hz, 25.55 Hz, 32.28 Hz and 47.46 Hz. Considering the low frequency oscillation mode is with frequency 0˜2 Hz, choose the frequency where negative electrical damping reaches minimum as the middle frequency of the frequency range 2˜15.71 Hz, namely f.sub.m*=0.1417 p.u. (8.5 Hz). Noticed that the method of choosing the frequency where negative electrical damping reaches minimum includes but not limited to the method used in the preferred embodiment.

[0029] According to the choosing method of BDF capacitor and inductor proposed in the present invention, the per-unit capacitance and reactance X.sub.BDF at system rated frequency is calculated as below:

[00005]$X_{\mathrm{BDF}}=\frac{X_C\left(X_L-X_C\right)}{f_e^{*2}.Math.X_L-X_C}-X_C$

Where f.sub.e*=1−f.sub.m*=0.8583 p.u.; X.sub.L is the system per-unit reactance at rated frequency (including generator subtransient reactance, line reactance and equivalent reactance of the receiving power grid), X.sub.L=0.869 p.u.; X.sub.C is capacitance of the series capacitor at rated frequency, X.sub.C=0.20 p.u.; The calculation results is listed in Table 1.

TABLE-US-00001 TABLE 1 X.sub.BDF/p.u. 0.1039 Inductor/mH 89.754 Capacitor/uF 78.394

[0030] According to the choosing method of BDF resistor proposed in the present invention, the minimum value of generator negative electrical damping D.sub.e(min).sup.DBF with BDF applied should satisfy the following relationship.

D.sub.e(min).sup.0<D.sub.e(min).sup.BDF<D.sub.e(min).sup.0/2

where D.sub.e(min).sup.0 is the minimum value of generator negative electrical damping without BDF applied. Suppose the per-unit air flux linkage of generator is 1.17 p.u., then D.sub.e(min).sup.0 cam be calculated as below.

[00006]$f_m^0=1-\sqrt{X_C/X_L}=0.5203$$D_{e\left(\min \right)}^0=-{\psi }_0^2.Math.\frac{1-f_m^0}{2.Math.f_m^0}.Math.\frac{1}{R}=-{1.17}^2.Math.\frac{1-0.5203}{2\times 0.5203}.Math.\frac{1}{0.0181}=-34.86$

[0031] As a result, the minimum value of generator negative electrical damping D.sub.e(min).sup.BDF with BDF applied should be −34.86<D.sub.e(min).sup.BDF<−17.43. In this preferred embodiment, the damping resistor R.sub.BDF is chosen as 15Ω (0.0461 p.u.), then D.sub.e(min).sup.BDF is calculated as below.

[00007]$f_e^{*}=1-f_m^{*}=1-0.1417=0.8583$$k_f^{*}=f_e^{*}/\left(1-f_e^{*2}\right)=0.8583/\left(1-{0.8583}^2\right)=3.2595$$R^{*}=R+\frac{R_{\mathrm{BDF}}.Math.X_C^2}{f_e^{*2}.Math.R_{\mathrm{BDF}}^2+{\left[k_f^{*}.Math.f_e^{*}.Math.X_{\mathrm{BDF}}-X_C\right]}^2}=0.2376$$D_{e\left(\min \right)}^{\mathrm{BDF}}=-{\psi }_0^2.Math.\frac{1-f_m^{*}}{2.Math.f_m^{*}}.Math.\frac{1}{R^{*}}=-17.45$

[0032] The above-mentioned relationship −34.86<D.sub.e(min).sup.BDF<−17.43 is satisfied.

[0033] For the above-mentioned condition of 40% compensation level, respectively, to further demonstrate the effectiveness of the present invention, the electrical damping of the generator with and without BDF is tested, shown in FIG. 3. Note that the subfigure in FIG. 3 is the amplification diagram of the electrical damping with BDF between 5 Hz and 12 Hz. The comparison result shows that, without BDF applied the negative electrical damping appears within the frequency range of 25˜35 Hz, which contributes to the excitation of 25.55 Hz and 32.28 Hz torsional modes. After BDF applied, the negative electrical damping is shifted to about 8.5 Hz, which is away from any of the torsional modes and the low frequency oscillation mode; the shift of the negative electrical damping is helpful for the suppression of torsional interaction. Also note that the minimum value of negative electrical damping is about half of that without BDF.

[0034] Time domain simulation of the system is applied, in order to better illustrate the BDF parameter tuning method of the invention on the shaft torsional interaction and transient torque amplification of the inhibition. FIG. 2 bus B at the application of three-phase short-circuit fault, fault clearance time 0.1 s. FIG. 4(a) shows the torque response of the BDF without the BDF, and FIG. 4(b) shows the torque response of the BDF. FIG. 4 (a) shows the torque response of the BDF.

[0035] FIG. 4(a) shows that, without BDF applied, the torsional interaction effect of shaft LPB-GEN segment is significantly stimulated. The torque diverges rapidly, which is adverse to the stable operation of shaft. FIG. 4(b) shows that, with BDF applied using the preferred embodiment, the torque of shaft LPB-GEN segment converges rapidly, which means that the torsional interaction is suppressed. Besides, the comparison of FIG. 4(a) and FIG. 4(b) shows that the transient torque decreases significantly with BDF applied; this means that the application of BDF using the preferred embodiment can not only help suppressing torsional interaction, but also contribute to the reduction of transient torque.

[0036] The foregoing description of the embodiments is intended to facilitate the understanding and application of the invention by one of ordinary skill in the art. It will be apparent to those skilled in the art that various modifications may be made to the above-described embodiments and that the generic principles set forth herein are applied to other embodiments without the need for creative work. Accordingly, the present invention is not limited to the above-described embodiments, and modifications and modifications of the present invention are intended to be within the scope of the present invention, as disclosed by those skilled in the art in view of the present invention.