CN106611069A - Variable-step-size element companion model with constant impedance - Google Patents
Variable-step-size element companion model with constant impedance Download PDFInfo
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Abstract
The invention provides a variable-step-size element companion model with constant impedance. An element model in an electromagnetic transient simulated program can be presented in a Norton equivalence or Thevenin equivalent way; and voltage and current in the Norton equivalence or the Thevenin equivalent can be subjected to linear interpolation so as to obtain the element companion model with constant impedance or admittance. Therefore, changes of a system admittance matrix at an accurate event capturing moment and a numerical value oscillation suppression moment can be avoided, so that computing efficiency is greatly improved; and meanwhile, the newly obtained element model has the same structural way as the original element model, so that the realization of the element model can be performed easily without adjusting the existing structure of the program.
Description
Technical field
The present invention relates to a kind of element associated model in step-size change with constant impedance, can be used in simulation calculation
Event handling and numerical value concussion suppress, and belong to the necks such as electromagnetic transient in power system emulation and computer-aided circuit analysis technology
Domain.
Background technology
In electromagnetic transients program, in order to emulate the non-linear elements such as power electronic equipment, generally can be opened using ideal
Close or the simulation of piece-wise linearization nonlinear resistance；Electromagnetic transients program needs effectively to be located in these power electronic equipment units of reason
Event caused by the state change institute of part.Traditional electromagnetic transients program is emulated using fixed step size, and power electronic devices
Action moment may but fall between emulation step, and many situations of accurate simulation of the action moment for power electronic devices
Under be but necessary.Can easily in the action moment insertion simulated point of power electronic devices, in order to obtain using variable step
Preferable numerical stability, electromagnetic transients program would generally use the numerical method (conventional trapezoidal method) of implicit expression, change imitative
True step-length can cause the admittance of the associated model of element to change, and this is accomplished by the admittance battle array for re-forming system equation, and
LU decomposition is re-started, the efficiency of emulation is reduced.In order to solve this problem, the electromagnetic transients program of current main flow
All it is that simulated point is inserted between step-length by the method for interpolation：Electromagnetic transients program is still emulated using fixed step-length,
But when finding that certain device there occurs event between step-length, the shape of event generation time system is obtained by linear interpolation
State.
Electromagnetic transients program would generally adopt trapezoidal method, and although trapezoidal method is that A is stable, but is not but that L is stable；
When having quick transient process in system, if simulation step length is too big relative to transient process, non-state variable can be produced
The raw phenomenon shaken around Exact Solutions back and forth.Solving electromagnetic transients program numerical value concussion problem at present mainly has two methods：
Document " Neville Watson and Jos Arrillaga, " Power System Electromagnetic Transients Simulation "
The NOS of Published by Institute of Engineering and Technology, London, United Kingdom, 2003. "
Method (Numerical Oscillation Suppression) and document " Marti, Jose R.；Lin,Jiming,"Suppression
of numerical oscillations in the EMTP,"in Power Systems,IEEE Transactions on,vol.4,no.2,
CDA methods (Critical Damping Adjustment) in pp.739-747, May 1989. ".The principle of NOS is simply straight
See, since variable is to be shaken around accurate value back and forth, then the centre position that adjacent two calculate point is inevitable very close to standard
Really it is worth, therefore NOS suppresses using the interpolation of half step-length numerical value to shake.Due to for accurate simulation event generation time,
Each element has been carried out interpolation function, therefore suppresses numerical value concussion by half step-length interpolation, is easier to realize, electro-magnetic transient
Simulated program PSCAD/EMTDC is exactly this mode for using.CDA suppresses numerical value using the backward-Euler method of half step-length
Concussion, as backward-Euler method is the stable methods of L, it can effectively suppress the numerical value caused due to fast transient process to shake
Swing, and using the promise obtained by trapezoidal method of the equivalent admittance of the promise obtained by the backward-Euler method of half step-length with synchronizing length
Equivalent admittance of pausing is the same, can so avoid modification and decompose again admittance matrix, and some electro-magnetic transient softwares are (such as：
EMTP-RV) it is exactly this kind of method that uses.
The present invention can be expressed as the form of promise equivalence or Thevenin's equivalence for component models in electromagnetic transients program,
Voltage and current in or Thevenin's equivalence equivalent to promise carries out linear interpolation, so as to obtain with constant impedance or admittance
Element associated model, it is to avoid change of the admittance matrix of system when accurate event moment is caught and suppress numerical value to shake, greatly
Improve greatly computational efficiency；Simultaneously because the component models for newly obtaining have same version with original component models, its
It is implemented without being adjusted program existing structure, it is easy to accomplish.
The content of the invention
The present invention proposes element associated model during a kind of variable step with constant impedance or admittance, it is to avoid system admittance matrix
Re-form and decompose, substantially increase computational efficiency.The method clear physics conception, implementation are simple, for electromagnetism
Transient emulation and computer-aided circuit analysis software development have certain meaning.Technical scheme is as follows：
The equivalence of equivalent and Thevenin's equivalence due to promise, for the ease of narration, it is assumed that element associated model is using promise
Equivalence, when element is described using Thevenin's equivalence, is as a result similar.In electromagnetic transients program or area of computer aided
In Circuit analyzer, the associated model of element may finally be expressed as the promise as shown in Fig. 1 and (1) formula equivalent form.
I (t+ Δ t)=gu (t+ Δ t)+is(t) (1)
Wherein g is element promise Equivalent admittance, isT the promise equal currents of () for element, it is according to the currently known state of system
Calculate.When (1) formula is used to calculate the state of t+ Δ t systems from t, during for t to t+ Δ t
Any moment t ' ∈ between quarter (t, t+ Δ t], it is assumed that
T '=t+k Δ t, k ∈ (0,1] (2)
It is assumed that electric current is linear change in t to t+ Δ ts, then have：
Can further obtain：
Similarly, for voltage can be obtained：
(4) and (5) formula is substituted into into (1), can be obtained：
I (t ')=gu (t ')+kiS(t)+(1-k)[i(t)-gu(t)] (6)
The promise equal currents of wherein new associated model are given by (7) formula
i′s(t)=kiS(t)+(1-k)[i(t)-gu(t)] (7)
Consider：
ihist(t- Δ t)=i (t)-gu (t) (8)
(6) formula can also be expressed as：
I (t ')=gu (t ')+kihist(t)+(1-k)ihist(t-Δt) (9)
By assuming voltage and current in t to linear change between t+ Δ ts, equivalent by existing promise (can appoint
The promise equivalence what numerical method is obtained), (6) or (9) formula gives etching system shape when a system mode by t calculates t '
One new promise of state is equivalent, and (6) or (9) formula gives a kind of mode of new variable step emulation in other words.Due to its form
It is just the same with classical electromagnetic transients program, therefore its realization can indiscriminately imitate the flow process of existing program, Er Qieyou completely
In the equivalent admittance of new promise with original just the same, it is to avoid the modification of admittance matrix and decompose again.
When the original associated model in formula (1) is obtained using trapezoidal method, and the coefficient k in (2) formula is when taking 1/2, passes through
(6) the new associated model or obtained by (9) formula is complete with the associated model obtained using the retrogressing Euler's method of half step-length
Consistent, therefore there is as retreating Euler's method suppression numerical value by the new associated model obtained by (6) or (9) formula
The effect of concussion.
Description of the drawings
Fig. 1 promises equivalent circuit structure chart.
Fig. 2 inductance elements.
Specific embodiment
The present invention is further remarked additionally below by embodiment：
For example, discretization is carried out using trapezoidal method to inductance as shown in Figure 2, the parameter of the associated model of element can be obtained
For：
is(t)=gu (t)+i (t) (11)
(6) formula of use or (9) formula can obtain new associated model parameter and be：
Admittance g is not changed in, and is still calculated by (10) formula；And promise equal currents then can be calculated by (12) formula.
i′s(t)=i (t)+(2k-1) gu (t) (12)
When k takes 1/2, it is known that new associated model just with the direct discretization inductance of backward-Euler method using half step-length obtained by companion
It is on all four with model.
Claims (1)
1. the variable step element associated model generation method of a kind of constant impedance, it is characterised in that：
1) in electromagnetic transient simulation and computer-aided circuit analysis class method, all elements may finally be expressed as that promise is equivalent or the form of Thevenin's equivalence, and formula (1) gives the associated model represented with promise form：
I (t+ Δ t)=gu (t+ Δ t)+is(t) (1)
Wherein g is element promise Equivalent admittance, isThe promise equal currents of (t) for element, it be according to the currently known state computation of system out.Based on the Nuo Dun or Thevenin's equivalence of element, new associated model is built by linear interpolation is carried out to voltage and current.
2) for t between t+ Δ ts any moment t ' ∈ (t, t+ Δ t], it is assumed that
T '=t+k Δ t, k ∈ (0,1] (2)
And assume that voltage and current is linear transformation in t in t+ Δ ts, by linear interpolation formula, the relation that can be obtained between t ' moment and t+ Δ t voltages and electric current is as follows：
3) (3) and (4) formula is substituted into into (1), the new associated model that can obtain element is as follows：
I (t ')=gu (t ')+kiS(t)+(1-k)[i(t)-gu(t)] (5)
The promise equal currents of wherein new associated model are given by (6) formula
i′S(t)=kiS(t)+(1-k)[i(t)-gu(t)] (6)
4) if it is considered that a upper time step historical current, between voltage, electric current have following relation：
ihist(t- Δ t)=i (t)-gu (t) (7)
Another form that new associated model can also be obtained is as follows：
I (t ')=gu (t ')+kihist(t)+(1-k)ihist(t-Δt) (8) 。
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Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101625389A (en) * | 2009-08-06 | 2010-01-13 | 中国电力科学研究院 | Method for analyzing stability of power system by considering change characteristic of load |
| CN102799765A (en) * | 2012-06-19 | 2012-11-28 | 中国电力科学研究院 | Method for timely computing unfixed-point interpolation of switch within step size |
| CN103678900A (en) * | 2013-12-06 | 2014-03-26 | 云南电力试验研究院（集团）有限公司电力研究院 | Network decoupling calculation method used for regional power distribution network real-time simulation |
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Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101625389A (en) * | 2009-08-06 | 2010-01-13 | 中国电力科学研究院 | Method for analyzing stability of power system by considering change characteristic of load |
| CN102799765A (en) * | 2012-06-19 | 2012-11-28 | 中国电力科学研究院 | Method for timely computing unfixed-point interpolation of switch within step size |
| CN103678900A (en) * | 2013-12-06 | 2014-03-26 | 云南电力试验研究院（集团）有限公司电力研究院 | Network decoupling calculation method used for regional power distribution network real-time simulation |
Non-Patent Citations (2)
| Title |
|---|
| 朱翊: "电力变压器电磁暂态仿真模型与算法研究", 《中国优秀硕士学位论文全文数据库工程科技Ⅱ辑》 * |
| 李亚楼 等: "直流电网模型和仿真的发展与挑战", 《电力系统自动化》 * |
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Effective date of registration: 20171206 Address after: Room 3, unit 401, family courtyard, family hospital of Peony District, 1010 people road, Heze City, Shandong Province Applicant after: Fan Shengtao Applicant after: Integrated Electronic Co., Ltd. Address before: Room 3, unit 401, family courtyard, family hospital of Peony District, 1010 people road, Heze City, Shandong Province Applicant before: Fan Shengtao |
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