CN106611069B - Variable-step-size element adjoint model generation method for constant impedance - Google Patents
Variable-step-size element adjoint model generation method for constant impedance Download PDFInfo
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Abstract
The invention provides a variable-step-size element adjoint model of constant impedance, which can be used for carrying out linear interpolation on voltage and current in a Norton equivalent value or a Thevenin equivalent value aiming at an element model in an electromagnetic transient simulation program, so that the element adjoint model with the constant impedance or admittance is obtained, the change of an admittance matrix of a system in capturing an accurate event moment and inhibiting numerical value oscillation can be avoided, and the calculation efficiency is greatly improved; meanwhile, because the newly obtained element model has the same structural form as the original element model, the realization of the element model does not need to adjust the existing structure of the program, and the element model is easy to realize.
Description
Technical Field
The invention relates to a method for generating an element adjoint model with constant impedance when the step length is changed, which can be used for event processing and numerical value oscillation suppression in simulation calculation and belongs to the fields of electromagnetic transient simulation of a power system, computer-aided circuit analysis technology and the like.
Background
In an electromagnetic transient simulation program, in order to simulate a nonlinear element such as a power electronic device, an ideal switch or a piecewise linear nonlinear resistance simulation can be generally used; electromagnetic transient simulation programs need to efficiently handle events caused by changes in the state of these power electronics components. The traditional electromagnetic transient simulation program adopts fixed-step simulation, but the action time of the power electronic device can fall between simulation steps, and the accurate simulation of the action time of the power electronic device is necessary in many cases. The electromagnetic transient simulation program usually uses an implicit numerical method (usually a trapezoidal method) to obtain better numerical stability, and changing the simulation step length causes the admittance of the accompanying model of the element to change, which requires to reform the admittance array of the system equation and perform LU decomposition again to reduce the simulation efficiency. In order to solve the problem, the currently mainstream electromagnetic transient simulation program inserts simulation points between step lengths by an interpolation method: the electromagnetic transient simulation program still uses fixed step size simulation, but when finding that an event occurs between step sizes of a certain device, the state of the system at the event occurrence time is obtained through linear interpolation.
The electromagnetic transient simulation program usually adopts a trapezoidal method, and the trapezoidal method is A stable but not L stable; when there is a fast transient in the system, the non-state variables can oscillate around the exact solution if the simulation step size is too large relative to the transient. At present, two methods are mainly used for solving the problem of numerical value oscillation of an electromagnetic transient simulation program: the NOS method (numerical OscillationsSuppression) of the document "Neville Watson and JosArrillaga," Power System Electromagnetics transduction Simulination "public knowledge institute of engineering and technology, London, UnitedKingdom, 2003" and the document "Marti, Joser; CDA method (Critical DamppingAdjustment) in Lin, Jiming, "suppression of numerically located EMTP," InPower systems, IEEETransactionson, vol.4, No.2, pp.739-747, May1989. The principle of NOS is simple and intuitive, since variables oscillate around the exact value, the intermediate position of two adjacent computation points must be very close to the exact value, and therefore NOS uses half step interpolation to suppress numerical oscillations. Because each element already realizes the interpolation function in order to accurately simulate the occurrence time of an event, the numerical oscillation is restrained by half-step interpolation, and the realization is easier, and the electromagnetic transient simulation program PSCAD/EMTDC is the mode used. The CDA uses a half-step back-off Euler method to restrain numerical value oscillation, because the back-off Euler method is an L stable method, it can effectively restrain numerical value oscillation caused by fast transient process, and the Norton equivalent admittance obtained by using the half-step back-off Euler method is the same as that obtained by using the whole-step ladder method, thus avoiding modifying and re-decomposing admittance matrix, and some electromagnetic transient software (such as EMTP-RV) is the method.
According to the method, for the element model in the electromagnetic transient simulation program, which can be expressed in a form of a Norton equivalent or a Thevenin equivalent, linear interpolation is carried out on the voltage and the current in the Norton equivalent or the Thevenin equivalent, so that an element accompanying model with constant impedance or admittance is obtained, the change of an admittance matrix of a system in capturing an accurate event moment and inhibiting numerical value oscillation is avoided, and the calculation efficiency is greatly improved; meanwhile, because the newly obtained element model has the same structural form as the original element model, the realization of the element model does not need to adjust the existing structure of the program, and the element model is easy to realize.
Disclosure of Invention
The invention provides an element adjoint model generation method with constant impedance or admittance at variable step length, which avoids the reformation and decomposition of a system admittance matrix and greatly improves the calculation efficiency. The method has clear physical concept and simple implementation mode, and has certain significance for electromagnetic transient simulation and computer-aided circuit analysis software development. The technical scheme of the invention is as follows:
because of the equivalence of norton and thevenin equivalents, for ease of description, assuming that the component accompanying models all use norton equivalents, the results are similar when the components are described using thevenin equivalents. In an electromagnetic transient simulation program or a computer-aided circuit analysis program, the adjoint model of an element can be finally expressed in a norton equivalent form as shown in fig. 1 and (1).
i(t+Δt)＝gu(t+Δt)+is(t) (1)
Where g is the element norton's equivalent admittance, is(t) is the norton equivalent current of the element, which is calculated from the current known state of the system. When equation (1) is used to calculate the state of the system at time t + Δ t from time t, for any time t' ∈ (t, t + Δ t) between time t and time t + Δ t]Suppose that
t′＝t+kΔt,k∈(0,1] (2)
Assuming that the current varies linearly from time t to time t + Δ t, then:
further, the method can be obtained as follows:
similarly, for the voltages available:
substituting equations (4) and (5) into equation (1) yields:
i(t′)＝gu(t′)+kiS(t)+(1-k)[i(t)-gu(t)] (6)
wherein the Norton equivalent current of the new adjoint model is given by equation (7)
i′s(t)＝kiS(t)+(1-k)[i(t)-gu(t)] (7)
Consider that:
ihist(t-Δt)＝i(t)-gu(t) (8)
(6) formula (la) can also be expressed as:
i(t′)＝gu(t′)+kihist(t)+(1-k)ihist(t-Δt) (9)
by assuming that the voltage and current vary linearly from time t to time t + Δ t, a new norton equivalent (which may be any numerical method) is calculated from the system state at time t by using the existing norton equivalent (equation 6) or (9), or a new way of varying the step size simulation is provided by using equation (6) or (9). Because the form of the method is completely the same as that of a classical electromagnetic transient simulation program, the realization of the method can completely take the same actions as the existing program, and because the new Norton equivalent admittance is completely the same as the original admittance, the modification and the re-resolution of the admittance matrix are avoided.
When the original adjoint model in expression (1) is obtained by using the trapezoidal method and the coefficient k in expression (2) is 1/2, the new adjoint model obtained by expression (6) or (9) is completely consistent with the adjoint model obtained by the back euler method using a half step, and therefore the new adjoint model obtained by expression (6) or (9) has the effect of suppressing numerical oscillation like the back euler method.
Drawings
Figure 1 shows a structure of the norton equivalent circuit.
Fig. 2 an inductive component.
DETAILED DESCRIPTION OF EMBODIMENT (S) OF INVENTION
The invention is further illustrated by the following examples:
for example, when the inductance shown in fig. 2 is discretized by the trapezoidal method, parameters of the accompanying model of the element can be obtained as follows:
is(t)＝gu(t)+i(t) (11)
the new adjoint model parameters can be obtained by using the formula (6) or the formula (9):
the admittance g is not changed and is still calculated by the formula (10); the norton equivalent current can be calculated by equation (12).
i′s(t)＝i(t)+(2k-1)gu(t) (12)
When k is 1/2, the new adjoint model is exactly consistent with the adjoint model obtained by directly discretizing the inductance by using a half-step backward eulerian method.
Claims (1)
1. A method for generating a constant-impedance variable-step-size element adjoint model is characterized in that:
1) all elements in the electromagnetic transient simulation and computer-aided circuit analysis class program can be finally expressed in the form of norton equivalence or thevenin equivalence, and the accompanying model expressed in norton form is given by equation (1):
i(t+Δt)＝gu(t+Δt)+is(t) (1)
wherein g is the element norton, etcValue admittance, is(t) the norton equivalent current of the element, which is calculated from the current known state of the system, and a new adjoint model is constructed by linear interpolation of the voltage and current based on the norton or thevenin equivalent of the element;
2) for any time t' ∈ (t, t + Δ t ] from time t to time t + Δ t, assume that
t′＝t+kΔt,k∈(0,1] (2)
And assuming that the voltage and the current are linearly transformed from the time t to the time t + delta t, the relationship between the voltage and the current at the time t' and the time t + delta t can be obtained through a linear interpolation formula as follows:
3) substituting equations (3) and (4) into equation (1) yields a new adjoint model of the element as follows:
i(t′)＝gu(t′)+kiS(t)+(1-k)[i(t)-gu(t)] (5)
wherein the Norton equivalent current of the new adjoint model is given by equation (6)
i′S(t)＝kiS(t)+(1-k)[i(t)-gu(t)] (6)
4) If the historical current, voltage and current of the last time step are considered to have the following relationship:
ihist(t-Δt)＝i(t)-gu(t) (7)
another form of obtaining a new adjoint model is as follows:
i(t′)＝gu(t′)+kihist(t)+(1-k)ihist(t-Δt) (8)。
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| 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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| 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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| 电力变压器电磁暂态仿真模型与算法研究;朱翊;《中国优秀硕士学位论文全文数据库工程科技Ⅱ辑》;20120715(第7期);正文第10-12页 * |
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