IEEE Power Engineering Society 2001 Winter Meeting Columbus, OH. Panel Session. Data for Modeling System Transients

Transcription

1 IEEE Power Engineering Society 2001 Winter Meeting Columbus, OH Panel Session Data for Modeling System Transients Parameters for Modeling Transmission Lines and Transformers in Transient Studies Bruce Mork Michigan Technological University January 29, 2001

2 Simulation of Transient Behaviors EMTP-like programs are used. Simulation results are as good as the model that is implemented. We must consider Frequency range of the behavior being simulated Available models for each component in the simulation package being used. You must correctly choose and implement each model, within the capabilities of available models. Not all component models are mature, so some intelligence must be used. Models representing components are at various stages of maturity.

3 A Question of Time How much time is spent on each of the following activities? Constructing the overall system model. Obtaining parameters for components. Benchmarking the component models. Benchmarking the overall system model. Running the simulations and getting results.

4 Transmission Line Models The model chosen depends on line length and the highest frequency to be simulated. For short or medium lines, a simple lumped coupled-b or several cascaded in series may be sufficient. Distributed parameter lines are typically used except for some of the shortest line sections. Various distributed line models exist, each using different representations of characteristic impedance and frequency dependence.

5 Basic Features of Distributed Parameter Line Models Based on text book traveling wave equations [2,3]: v = i = Z i Y v x x v and i are the vectors of node voltage and line currents at distance x from receiving end of line.

6 Model Derivation Details given in references [2,4,5,6,7] Basic approach: Derive model in frequency domain. Use Modal Transformations to decouple phases. Use convolution/deconvolution methods to convert frequency domain solution to time-domain equivalent that can be implemented via numerical integration methods. Problematic realizations Problems: Derived model is only valid for the frequency at which the Modal Transformation was done. Frequency fitting techniques can be used to improve results [7]. Newer models are based in the phase domain and avoid the Modal Transformation [8].

7 Transmission Line Data - A Dilemma Existing transmission line data may exist only in a format useful for load flow, short circuit, and stability studies. Short-circuit data: positive and zero sequence per-phase series impedances.. For double- circuit lines, you will also have the mutual impedance -- the zero-sequence coupling between circuits. Total positive sequence line-charging MVA may be known. For load flow and stability studies, you will have short-circuit data as above, plus positive and negative sequence capacitive coupling.

8 A Data Base of Physical Design Parameters Must be Developed (x, y) coordinates of conductors and shield wires. Bundle spacings,, orientations. Phase (A,B,C) and circuit (1,2,3) designation of each conductor Phase rotation or swapping at each transposition Physical dimensions of each conductor (both inner and outer radii for bus bar and stranded conductor). Earth resistivity of the ground return path. Other information such as segmented grounds, transpositions.

9 Transmission Lines - Two Examples 345-kV Single-Circuit 345-kV Double-Circuit

10 345-kV Single-Circuit Physical Input Parameters Acknowledgement: Sung Don Cho for putting together these examples Typical set of input, representative of most so-called LINE CONSTANTS programs or supporting routines.

11 Comments on Parameters Conductor Numbers 1,2,3 ==> phase A,B,C Conductors Numbered 0 ==> shield wire Inner Radius: Radius of steel stranded core or radius of inner tube diameter of bus bar. DC Resistance: usually choose to be at 50 C or higher, not at 25 C Horizontal (x-axis) value: relative horizontal position of each conductor. Absolute value is not important. Typical height at tower and height at midspan are used to determine average height above terrain assuming a catenary sag. Bundled conductors are usually handled as a group: number in bundle, separation, orientation of bundle.

12 Choice of Model to Implement Accuracy of model for given range of frequencies is key concern. Several standard choices, available in the original EMTP program are discussed here. Other models may be available in various simulation packages. Lumped parameter coupled PI. Bergeron (distributed parameter, constant Z C. ), also referred to as Constant Parameter which is built on the paper by Snelson [4] and developed by Meyer and Dommel [5]. J-Marti Model (distributed parameter, constant Z C. ) With physical parameters entered, various models for a given line section can be implemented and benchmarked until satisfied.

13 Steady-State Benchmarking Single Phase Model Utility SC Data Length (miles) R0 (ohms) X0 (ohms) R1 (ohms) X1 (ohms) Charging MVar ATP % difference 0.0% 5.2% -2.5% -2.0% -1.4% 4.3% A utility s existing transmission line data base contains some information that should be used to verify that you ve developed a model which is basically correct.

14 Steady-State Benchmarking Double-Circuit Line Utility S.C. Data Length (miles) R0 (ohms) X0 (ohms) R1 (ohms) X1 (ohms) Charging MVar R00 (ohms) X00 (ohms) ATP % difference 0.0% 4.4% -2.0% -2.3% 0.0% 1.9% 3.8% -3.1% Zero-Sequence coupling between phases is also a consideration in this case [2].

15 Frequency Scan Benchmarking A pair of frequency scans can be performed on the developed line model, determining input impedance with the receiving end open- circuited. First perform frequency scan on the model you ve developed, stepping the source through the desired frequency range in discrete steps. Next, perform a series of open-circuit simulations on the ideal coupled PI model (redevelop coupled- PI model for each frequency). This result is assumed to be the true frequency response. Overplot the two frequency scan results.

16 Frequency Scan Verification Single-Circuit Line, 1 Hz - 5 khz

17 Miscellaneous Comments on Line Models Frequency dependency of resistance typically assumes a solid conductor (or hollow conductor) and applies skin effect corrections. Skin effect assumes that highest current density is at surface. However, for stranded conductors having 3 or more layers of aluminum, this is not true. Other more advanced line models are being developed, but are not generally available in all transients packages. Taku Noda - phase-domain frequency dependent [8]. Other models and frequency fitting techniques by Gustavsen and others.

18 Miscellaneous Comments on Line Models Choose integration timestep to be smaller than the smallest propagation time for all modes. Segmented ground? Transpositions? Full vs.. approximate. Choosing real vs.. complex transformation matrix affects numerical stability. Usually choose real for transient studies.

19 Key References Key References [1] Modeling and Analysis of Power System Transients Using Digital Programs, IEEE Special Publication TP-133-0, IEEE Catalog No. 99TP133-0, [2] H.W. Dommel, EMTP Theory Book, Microtran Power System Analysis Corporation, Vancouver, BC, May [3] A. Greenwood, Electrical Transients in Power Systems, 2 nd Edition, John Wiley & Sons, Inc., [4] J.K. Snelson, Propagation of Travelling Waves on Transmission Lines Frequency Dependent Parameters, IEEE Trans. PAS, Vol. 91, pp , [5] W.S. Meyer and H.W. Dommel, Numerical Modeling of Frequency- Dependent Transmission Line Parameters in an Electromagnetic Transients Program, IEEE Trans. PAS, Vol. PAS-93, pp , [6] A. Semlyen and A. Dabuleanu, Fast and Accurate Switching Transient Calculations on Transmission Lines with Ground Return Using Recursive Convolutions, IEEE Trans. PAS, Vol. PAS-94, pp , [7] J.R. Marti, Accurate Modeling of Frequency-Dependent Transmission Lines in Electromagnetic Transient Simulations, Power Industry Computer Applications, pp , [8] T. Noda, N. Nagaoka, A. Ametani, Phase Domain Modeling of Frequency- Dependent Transmission Lines by Means of an ARMA Model, IEEE Trans. Power Delivery, Vol. 11, No. 1, January [9] G.R. Slemon, Equivalent Circuits for Transformers and Machines Including Non-Linear Effects, Proc. IEE, Vol. 100, part IV, pp , [10] V. Brandwajn, H.W. Dommel, I.I. Dommel, Matrix Representation of Three- Phase N-Winding Transformers for Steady-State and Transient Studies, IEEE Trans. PAS, Vol. PAS-101, No. 6, pp , June 1982.

20 Example of BCTran BCTran Modeling Acknowledgement: Sung Don Cho for putting together this example Grd.Y/ Grd.Y/ Delta Open-Circuit Exciting Current Test Short-Circuit Impedance Test P-S: 6.85% P-T: S-T: No Load Loss Loss P-S: kW P-T: S-T: Verify steady-state exciting currents and no-load loss. Verify the Binary Short Circuit currents and losses.

21 Short-Circuit Representation v v M v 1 2 = R 11 0 L 0 0 R L 0 22 M M O M 0 0 L N NN N R i1 i2 M i + L L L L N L L L L N M M O M L L L L d dt i1 i 2 M i N 1 N 2 NN N For N-Winding Transformer Represents short-circuit effects as equivalent winding resistance and leakage reactance.

22 Inclusion of Core Saturation & Loss Standard factory test reports typically report on the total open-circuit losses at 100% and at 110% rated voltage. Standard factory test reports typically report the average of the RMS exciting currents of the three phases. This data is only useful if you have a bank of three single phase transformers. Otherwise, the core configuration should be taken into account. An approximate core representation can be attached (usually to the low-voltage terminals of the BCTRAN model).

23 Core Configurations

24 Development of an Approximate Equivalent Core Basic calculations are given in [2]. 161MVA MVA1 φ = = 53.7MVA 3 161MVA Ib = = 3,889A kV 0.34%@100% V I = 3889A 0.34% 0.73%@110% V I E E = 3889A 0.73% = 13.2A = 28.4A V = I 2 E PE 3V 2 = = 12.82A = pu V = = A = pu

25 Using SATURATION Routine Input RMS V-I saturation curve, including (0,0) point at origin. Run EMTP supporting routine SATURATION to get corresponding peak (current, flux-linked) C SATURATION C $ERASE C C 3.296e-3 1. C 7.240e C E E E E

26 Incorporating with BCTRAN The output of SATURATION can then be pasted into a nonlinear inductance element. Suggest either type-98 or type-93 inductance. The hysteretic type-96 has problems reproducing loop area (losses) over the full range of excitation. This is bad, especially for CT core models. Core representation can be connected either in Wye or Delta. Problems with convergence of nonlinear inductance operation points can be a problem when connected in Delta. Include core loss resistance in parallel with core inductance. Losses are quite dependent on voltage.

27 CLOSING COMMENTS Have an intuitive feel for what you re doing. Always at least verify the model s steady- state performance. Confirm that model should be valid within the range of frequencies you will be simulating. Sometimes this requires that you first run the simulation. In cases involving nonlinearities, it is impossible to predict all frequencies present. Run simulation, find out what the natural response frequencies are. Adjust model if need be.

28 COMMENTS? QUESTIONS?