CN111327054A - Evaluation method for broadband impedance stability margin of power transmission system - Google Patents
Evaluation method for broadband impedance stability margin of power transmission system Download PDFInfo
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Abstract
The invention discloses a broadband impedance stability margin evaluation method of a power transmission system, which comprises the following steps: constructing a power transmission system model which comprises a power transmission line model, a power station side model and a network side model, wherein the power transmission line model is a pi-type circuit model containing a plurality of hyperbolic functions; performing equivalent transformation on the complex hyperbolic function based on the power line model, and performing equivalent transformation on the series impedance and the parallel impedance; converting the source side into a Norton equivalent circuit, constructing an impedance stability criterion analysis circuit model, and obtaining a calculation model of impedance ratio to the source side of the network; and obtaining a polar coordinate track, and obtaining a phase angle margin and an amplitude margin according to a motion rule of the polar coordinate track. The invention has at least the following beneficial effects: on the premise of not violating the application of impedance stability criterion, the relative stability margin of the power transmission system is obtained, and a guidance method is provided for design of a broadband harmonic resonance damping control method and parameter optimization of the broadband harmonic resonance damping control method.
Description
Technical Field
The invention relates to the field of intelligent power distribution, in particular to a method for evaluating broadband impedance stability margin of a power transmission system.
Background
A power transmission line model based on a complex hyperbolic function (namely sinh and cosh terms) is a premise for accurately describing broadband harmonic resonance characteristics. The term "broadband harmonic resonance phenomenon" refers to: the problem of abnormal harmonic current when a renewable energy power station (photovoltaic power station, wind power plant) sends out electric energy through a high-voltage and long-distance power transmission line. Particularly, because a large amount of power electronic interface equipment is arranged in the power station, the output current of the power station contains abundant broadband harmonic waves; even if the current harmonic distortion of the transmission end (power station side) of the transmission line meets the grid-connection requirement, under the influence of the distributed capacitance of the transmission line, the current reaches the receiving end (grid side) of the transmission line through remote propagation, and the condition that the current component of certain order or certain subharmonic is abnormal and prominent occurs.
Theoretically, the scientific evaluation of the cause, the severity and the treatment scheme effectiveness of the broadband harmonic resonance phenomenon can be measured by the impedance stability margin of the power transmission system. However, if the deep level impedance stability margin implied by the broadband harmonic resonance phenomenon is to be evaluated, the sinh and cosh terms in the power line model must be completely reserved. However, these complex hyperbolic functions bring dilemma to the evaluation of the broadband impedance stability margin of the system, which is expressed as: 1) keeping sinh and cosh terms, and then not utilizing an impedance stability criterion to obtain the relative stability margin of the system; 2) the Taylor series approximation linearization of sinh and cosh terms violates the application premise of the impedance stability criterion. How to evaluate the broadband impedance stability margin of the power transmission system containing the complex hyperbolic function is a theoretical problem to be solved in a new normal state of 'power electronics of the power system', and is also an effective way for evaluating the effectiveness of a broadband harmonic resonance damping control method (treatment scheme) and optimizing parameters of the method.
Disclosure of Invention
The present invention is directed to solving at least one of the problems of the prior art. Therefore, the invention provides a method for evaluating the broadband impedance stability margin of a power transmission system, which can obtain the relative stability margin (namely, the phase angle margin and the amplitude margin) of the power transmission system on the premise of not violating the impedance stability criterion.
According to a first aspect of the invention, a method for evaluating a broadband impedance stability margin of a power transmission system comprises the following steps: constructing a power transmission system model, which comprises a power transmission line model, a power station side model and a network side model, wherein the power transmission line model is a pi-shaped circuit model containing a complex hyperbolic function and consists of a series impedance and two same parallel impedances, and the network side model is a Thevenin equivalent circuit and comprises a voltage source and a network side equivalent impedance connected with the voltage source in series; performing equivalent transformation on the plurality of hyperbolic functions based on the power line model, and performing equivalent transformation on the series impedance and the parallel impedance according to the plurality of hyperbolic functions after the equivalent transformation; converting a source side circuit comprising the power station side model and the power line model into a Norton equivalent circuit, wherein the network side model keeps a Thevenin equivalent circuit, and an impedance stability criterion analysis circuit model is constructed to obtain a calculation model of impedance ratio to the source side of the network side; and obtaining a polar coordinate track according to the calculation model of the network side source side impedance ratio, and obtaining a phase angle margin and an amplitude margin according to a motion rule of the polar coordinate track.
The method for evaluating the broadband impedance stability margin of the power transmission system according to the embodiment of the invention has at least the following beneficial effects: through a single pi-shaped circuit model, only the second-order tiny amount of voltage is ignored, and the broadband characteristic of a long-distance power transmission line port can be properly reflected; the calculation is simplified, and the large direction of the broadband impedance stability margin of the power transmission system is not influenced; on the premise of not violating the application of impedance stability criterion, the relative stability margin of the power transmission system is obtained, and a guidance method is provided for design of a broadband harmonic resonance damping control method and parameter optimization of the broadband harmonic resonance damping control method.
According to some embodiments of the invention, the equivalent transformation method of the complex hyperbolic function is:
wherein sinh (γ l) and cosh (γ l) are the complex hyperbolic functions, γ is a propagation constant, l is a transmission line length, ω is a system frequency,
l0inductance of the transmission line per unit length, c0Is the capacitance per unit length of the transmission line. The power transmission line model has broadband behavior description capability; the impedance stability criterion is conveniently applied, and the Nyquist locus of the network side-source side impedance ratio is obtained through MATLAB and other calculation and analysis software, so that the broadband impedance stability margin of the power transmission system is obtained.
According to some embodiments of the invention, the equivalent transformation method of the series impedance and the parallel impedance is:
wherein the content of the first and second substances,
ZLis the series impedance, ZPFor the parallel impedance, s-j ω,
l is the length of the transmission line, omega is the system frequency, r0Is the resistance of the transmission line per unit length, /)0Inductance of the transmission line per unit length, c0Is the capacitance per unit length of the transmission line. The impedance stability criterion is conveniently applied, and the broadband impedance stability margin of the power transmission system is further obtained.
According to some embodiments of the invention, the computational model of the net side source side impedance ratio, the analysis circuit model in combination with the net side equivalent impedance Z according to the impedance stabilization criteriong＝Rg+jωLgResults, expressed as:
Zgs(jω)/Zss(jω)＝zreal(ω)+jzimag(ω)，
wherein Z isgsIs net side Thevenin equivalent series impedance, ZssIs a source side norton equivalent parallel impedance; zgs(jω)、Zss(j ω) is each Zgs、ZssExpression form of j ω, Zgs＝Zg，ZgIs the net side equivalent impedance, RgIs a pure resistive part, and Lg is a pure inductive part; z is a radical ofreal(ω) is the real part, zimagAnd (ω) is an imaginary part. The complex hyperbolic function is equivalently replaced, and the application of an impedance stability criterion is ensured under the condition that the complex hyperbolic function does not need to be directly calculated, so that the relative stability margin of the system can be obtained.
According to some embodiments of the invention, the computational model of the net-side source-side impedance ratio is:
wherein Z isgsIs net side Thevenin equivalent series impedance, ZssIs a source side norton equivalent parallel impedance; zgs(jω)、Zss(j ω) is each Zgs、ZssJ ω, s ═ j ω, Zgs＝Zg，Zg＝Rg+jωLg，ZgIs the net side equivalent impedance, RgIs a purely resistive part and Lg is a purely inductive part. After the complex hyperbolic function is equivalently replaced, the impedance stability criterion is still applicable, and the correctness of the evaluation method is ensured.
According to some embodiments of the invention, the polar trajectory is obtained by increasing the value of ω from 0rad/s to Max _ order × 100 π rad/s and calculating the real part zreal(ω) and imaginary part zimag(ω), wherein Max _ order is a positive multiple of power frequency; construction of Zgs/ZssWherein the real axis data is zreal(ω) virtual axis data is zimag(ω). And constructing a polar coordinate system to obtain a polar coordinate track, so that the evaluation is facilitated.
According to some embodiments of the invention, Max _ order is a positive integer greater than or equal to 100. The impedance stability evaluation is ensured to be carried out in a wide frequency range, and the reliability of the evaluation method is ensured.
According to some embodiments of the invention, the phase angle margin and the amplitude margin are obtained by: if the polar coordinate track periodically penetrates into and out of the unit circle along with the increase of omega, and the radius of circular motion gradually increases, the phase angle margin is 0 degree, and the amplitude margin is 0 dB; if the polar coordinate track penetrates out of the unit circle along with the increase of omega, then penetrates through the virtual axis, falls on the right half plane and continues to move, the phase angle margin is obtained according to the intersection point of the polar coordinate track on the right half plane and the unit circle, and the amplitude margin is obtained according to the intersection point of the polar coordinate track and the negative real axis of the virtual axis. According to the motion rule of the polar coordinate track, the relative stability margin of the power transmission system can be conveniently evaluated, and a quantitative method is provided for design of a broadband harmonic resonance damping control method and parameter optimization of the broadband harmonic resonance damping control method.
According to some embodiments of the invention, the phase angle margin is calculated by: and obtaining the phase angle margin according to the included angle between the intersection point of the right half plane of the polar coordinate trajectory and the unit circle and the real axis. And calculating to obtain a phase angle margin, so that the relative stability of the power transmission system can be evaluated conveniently.
Drawings
The above and/or additional aspects and advantages of the present invention will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:
FIG. 1 is a schematic illustration of a process flow of an embodiment of the present invention;
FIG. 2 is a model of a power transmission system according to an embodiment of the invention;
FIG. 3a is a plurality of Norton branches of a variation of the plant-side equivalent circuit of an embodiment of the present invention;
FIG. 3b is a variant aggregate Noton branch of a plant side equivalent circuit of an embodiment of the present invention;
FIG. 3c is a modified controlled current source version of the plant side equivalent circuit of an embodiment of the present invention;
FIG. 4a is a model of the power transmission system of FIG. 2 with the inductive-resistive transformer embedded;
fig. 4b is a model of the power transmission system of fig. 2 with the Γ -type transformer embedded therein;
fig. 4c shows a model of the power transmission system of fig. 2 with the Π -type transformer embedded;
FIG. 4d is a model of the power transmission system of FIG. 2 with the T-type transformer embedded;
FIG. 5 is a circuit illustrating an impedance stabilization criterion analysis corresponding to FIG. 2;
FIG. 6 is a table of power line simulation parameters according to an embodiment of the present invention;
FIG. 7a shows Z in an embodiment of the present inventionssThe real part of the zero point is in a relation of changing with the frequency omega and the length l of the transmission line;
FIG. 7b is Z of an embodiment of the present inventionssThe relationship of the imaginary part of the zero point varying with the frequency omega and the length l of the transmission line;
FIG. 8 is a schematic diagram of an impedance stabilization criterion based on a net-side-source-side impedance ratio according to an embodiment of the present invention;
FIG. 9 is Z corresponding to FIG. 2gs/ZssAn exemplary plot of polar trajectories of (a);
FIG. 10 is a diagram of a model of a power transmission system equipped with a broadband harmonic resonance damping specific device in an embodiment of the present invention;
FIG. 11a is Z corresponding to FIG. 10gs/ZssA global map of polar coordinate trajectories of (a);
FIG. 11b is an enlarged view of the polar locus in the unit circle of FIG. 11 a;
fig. 12 is a diagram of a complex power transmission system model according to an embodiment of the invention;
fig. 13a is a table of simulation parameters for the LCL inverter filter system of fig. 12;
FIG. 13b is a table of simulation parameters for the model of the Γ -type transformer of FIG. 12;
FIG. 14a is Z corresponding to FIG. 12gs/ZssA global map of polar coordinate trajectories of (a);
FIG. 14b is an enlarged view of the polar locus in the unit circle of FIG. 11 b;
figure 15 is an enlarged view of the polar locus of the different control coefficients of the damping device of figure 12.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.
In the description of the present invention, the meaning of a plurality of means is one or more, the meaning of a plurality of means is two or more, and larger, smaller, larger, etc. are understood as excluding the number, and larger, smaller, inner, etc. are understood as including the number. If the first and second are described for the purpose of distinguishing technical features, they are not to be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated or implicitly indicating the precedence of the technical features indicated.
Referring to fig. 1, a method of an embodiment of the invention includes: constructing a power transmission system model, which comprises a power transmission line model, a power station side model and a network side model, wherein the power transmission line model is a pi-shaped circuit model containing a complex hyperbolic function and consists of a series impedance and two same parallel impedances, and the network side model is a Thevenin equivalent circuit and comprises a voltage source and a network side equivalent impedance of the series voltage source; performing equivalent transformation on the plurality of hyperbolic functions based on the power transmission line model, and performing equivalent transformation on the series impedance and the parallel impedance according to the plurality of hyperbolic functions after the equivalent transformation; converting a source side circuit comprising a power station side model and a power line model into a Noton equivalent circuit, maintaining a Thevenin equivalent circuit on a network side, constructing an impedance stability criterion analysis circuit model, and obtaining a calculation model of impedance ratio to the source side of the network side; and obtaining a polar coordinate track according to a calculation model of the impedance ratio at the side of the network source, and obtaining a phase angle margin and an amplitude margin according to a motion rule of the polar coordinate track. In the embodiment of the invention, by constructing a power transmission system model, the relative stability margin of the system can be acquired by using the equivalent transformation form of the complex hyperbolic function instead of directly reserving the complex hyperbolic function; and the relative stability of the system can be evaluated only by the impedance ratio at the source side of the network side, and the method is simple to implement.
The method and its principles in the embodiments of the present invention will be described in detail below.
In the embodiment of the invention, a power transmission system model needs to be constructed firstly, and the power transmission system model is a power transmission system model containing a complex hyperbolic function with reference to fig. 2. Wherein the transmission line is a pi-type circuit model containing complex hyperbolic function and composed of series impedance ZLAnd a parallel impedance ZPComposition is carried out; the transmitting end is communicated with a renewable energy power station (namely a power station side model); the receiving end is in communication with the power grid (i.e., the grid-side model). Ideal current source I for power stationrefRepresents; thevenin equivalent circuit for net side model (comprising impedance Z)gSeries voltage source Ug) And (4) showing.
In fig. 2, the transmission line is represented by a pi-type circuit, rather than a series of pi-type circuit models as in conventional power system analysis to represent a long-distance transmission line; this is because: the power transmission line model containing the complex hyperbolic function is obtained by solving a differential equation set of voltage and current of a uniform power transmission line port, and only second-order tiny quantity of the voltage is ignored, so that the broadband characteristic of the long-distance power transmission line port can be properly reflected. In contrast, in conventional power system analysis, since the impedance characteristics of the transmission line at power frequency (i.e., 50Hz) are only discussed, the series impedance Z is set in the conventional pi-type circuit model of the transmission lineLAnd a parallel resistoranti-ZPThe sinh and cosh terms in the expression are only approximated by respective taylor series first order terms, which has the following disadvantages: 1) the impedance characteristics of the transmission line near the power frequency can be reproduced only; 2) when modeling a long-distance power transmission line, a plurality of pi-shaped circuits are required to be connected in series for representation.
It should be noted that in fig. 2, the renewable energy power station (power station side) is simplified to an ideal current source IrefThe reason is as follows:
(1) the broadband harmonic resonance phenomenon is caused by the distribution parameters of the power transmission line, but not the equivalent impedance of a renewable energy power station; the high-order, complex and accurate model of the renewable energy power station does not cause qualitative change to the system broadband impedance stability margin information hidden behind the broadband harmonic resonance phenomenon;
(2) the power station contains a large number of power electronic devices, the control modes of the devices of various manufacturers are different, and the power station is blackened; if a high-order, complex and accurate power station model is forcibly established, the problem only falls into the problem of dimension disaster analysis of the system, the main contradiction cannot be effectively solved, and the method is inverted at the end.
(3) This simplification does not change the large direction of the wide-band impedance stability margin of the power transmission system.
Fig. 3a to 3c are various variants of the station side (renewable energy station) equivalent circuit, including but not limited to: multiple Norton branches, a converged Norton branch, a controlled current source type. In FIG. 3a, Gs,1For the 1 st power generation unit Nutton equivalent current source coefficient, Zs,1Is the Noton equivalent parallel impedance of the 1 st power generation unit Iref,1The 1 st power generation unit reference current and the subscript n is the nth power generation unit. In FIG. 3b, GsFor aggregating Noton equivalent current source coefficient of power generation unit, ZsFor polymerization of the Noton equivalent parallel impedance of the power generating unit, IrefIs a reference current of the polymerization generating unit; the polymerization power generation unit refers to: the power generation effect of a plurality of (cluster) power generation units is represented by one power generation unit. Fig. 3c differs from fig. 3b in that: in fig. 3c, the plant-side equivalent circuit is represented as a controlled current source parallel impedance ZsIn the form of (since the power generating unit generally adopts a current control mode))。
The multiple variants of the equivalent circuit at the power station side do not change the large direction of the broadband impedance stability margin of the power transmission system containing the complex hyperbolic function; thus, referring to FIG. 2, the side-of-station model is simplified to an ideal current source Iref。
It should be noted that the power transmission system model in fig. 2 omits the transformer models of the transmitting end and the receiving end of the power transmission line. FIG. 4 shows a power transmission system model with complex hyperbolic functions after embedding a transformer model; wherein, fig. 4a shows a resistance-inductance transformer model embedded; FIG. 4b shows a transformer model with embedded gamma shapes; fig. 4c shows a pi-type transformer model embedded; fig. 4d shows an embedded T-type transformer model.
The above, but not limited to, four transformer models do not change the large direction of the wide-frequency impedance stability margin of the power transmission system containing the complex hyperbolic function. The reason is as follows: when current is transmitted on the power transmission line, the broadband harmonic resonance characteristic of the current is dominated by power transmission line distribution parameters, and the equivalent impedance of the transformer hardly works; more colloquially, transformers cannot cause substantial current distortion. Therefore, in order to concentrate on obtaining the wide-frequency impedance stability margin of the power transmission system containing the complex hyperbolic function, the transformer model is not considered.
In FIG. 2, the series impedance Z of a power line model containing a complex hyperbolic functionLAnd a parallel impedance ZPThe expressions are respectively formula (1) and formula (2).
ZL＝Zcsinh(γl) (1)
Zp＝[Zcsinh(γl)]/[cosh(γl)-1](2)
In the above formula 2, ZcIs the wave impedance, gamma is the propagation constant, l is the transmission line length; zcAnd γ are respectively expressed by formula (3) and formula (4).
In the above formula 2, r0、l0、c0Respectively the resistance, inductance and capacitance of the unit length transmission line; ω is the system frequency. ZcBoth γ are complex variable functions, and in consideration of the relation of s ═ j ω (s is both a differential operator and a complex variable), expressions (3) and (4) can be expressed as expressions (5) and (6), respectively, in the s domain.
Zc＝a+b/s (5)
γ＝c+ds (6)
In the above-mentioned formula 2, the compound,
in the transmission line model, series impedance ZLParallel impedance ZPBoth contain sinh (gamma l) and cosh (gamma l) terms, and the impedance stability criterion can be applied only after the sinh (gamma l) terms and the cosh (gamma l) terms are equivalently transformed; on the contrary, directly approximating sinh (γ l) and cosh (γ l) by taylor series would violate the application premise of the impedance stabilization criterion.
Therefore, in order to apply the criterion of impedance stabilization, in the embodiment of the present invention, the equivalent transformation is required to be performed on sinh (γ l) and cosh (γ l) terms, and the steps are as follows:
first, according to equation (6), sinh (γ l) and cosh (γ l) terms can be respectively converted into the forms of sinh [ (c + ds) l ] and cosh [ (c + ds) l ];
next, using the relationships:
and
to transform sinh [ (c + ds) l equivalently]And cosh [ (c + ds) l](ii) a After transformation, the expressions are respectively:
then, in the expression
In, s is replaced by j ω; after replacement, the expressions are respectively:
finally, in the expression
In, using euler's formula: e.g. of the typejxCosx + j sinx, eliminating ejxAnd (4) obtaining the calculation results of the formula (7) and the formula (8).
The specific process is as follows:
the formula (7) and the formula (8) are equivalent transformation formulas of complex hyperbolic function sinh (gamma l) and cosh (gamma l) terms respectively; the advantage of the equivalent transformation is represented by:
1) compared with Taylor series approximation sinh and cosh terms, the equivalent transformation enables the power line model to have broadband behavior description capacity;
2) the numerator and the denominator of the transmission function of the power transmission line model can be arranged into a form of s polynomial;
3) the Nyquist (namely polar coordinate system) locus of the network side-source side impedance ratio can be obtained conveniently through MATLAB and other calculation analysis software, and further the broadband impedance stability margin of the power transmission system can be obtained.
Carrying the formula (5) and the formula (7) into the formula (1), carrying the formula (5), the formula (7) and the formula (8) into the formula (2), and finishing to obtain the formula (9) and the formula (10) respectively.
The formula (9) and the formula (10) are power transmission line models after complex hyperbolic function equivalent transformation; wherein k is1、k2、k3Is an s polynomial coefficient, and the specific expression is as follows:
and then, evaluating the broadband impedance stability margin of the power transmission system by applying an impedance stability criterion.
In the embodiment of the present invention, first, an impedance stabilization criterion analysis circuit is constructed. Referring to fig. 5, the dotted line is used as a boundary, the left side is networked into a norton equivalent circuit, and the right side is kept with a thevenin equivalent circuit, so that the broadband impedance stability criterion analysis circuit applied to the power transmission system is obtained.
In FIG. 5, the net-side equivalent impedance ZgsAnd network side voltage source UgsRespectively satisfy: zgs＝Zg、Ugs＝Ug；GssIs the source side norton equivalent current source coefficient; zssIs the source side norton equivalent parallel impedance. GssAnd ZssAre respectively formula (12) and formula (13).
Gss＝ZP/(ZL+ZP) (12)
Zss＝ZP(ZL+ZP)/(ZL+2ZP) (13)
Bringing formula (9) and formula (10) into formula (12) to obtain:
bringing formula (9) and formula (10) into formula (13) to obtain:
equations (14) and (15) are G obtained by equivalently transforming complex hyperbolic functions (sinh and cosh terms), respectivelyssAnd Zss。
It should be understood that: g in formulae (12) to (15)ssAnd ZssThe expressions are all obtained under 3 simplified conditions; these simplifying conditions are: 1) many variations of the station-side (renewable energy plant) equivalent circuit (represented typically in the form of the circuit listed in fig. 3) are not considered; 2) the transformer model of the transmission end and the receiving end of the transmission line is omitted; 3) no specific means for broadband harmonic resonance damping is provided. If the 3 simplifying conditions are abandoned, the impedance stability criterion analysis circuit applied to the power transmission system can still be arranged into the form shown in fig. 5, only GssAnd ZssThere are differences in the specific expressions of (a).
According to FIG. 5, readily available IgAn expression; and will IgArranged as a net side-source side impedance ratio (i.e., Z)gs/Zss) In the standard form of (a), i.e., formula (16).
Using the premise of impedance-stability criterion, otherwise known as Zgs/ZssThe relative stability of the Nyquist (polar coordinates) trajectory evaluation system is premised on: in the s right half plane, GssNo pole and ZssThere is no zero point. In other words, each term in the parentheses on the right side of the equal sign of equation (16) cannot inject any s-right half-plane poles into the system. In a popular way, if the interface power supply and the power grid are required to be stably interconnected, the premise is that the interface power supply and the power grid are stable when the interface power supply and the power grid independently operate; this is not difficult to understand. Finally, I must also be defaultedref(generating side reference Current) and Ug(grid voltage) is stable.
Referring to fig. 6, power line simulation parameters are shown. These parameters come from LGJ-185 type transmission lines; the novel wind power station is also a line model commonly selected by a 35kV bus system of a typical wind power station. Next, verification is required: by equivalent transformation Z of formula (7) and formula (8)LAnd ZPAfter the sinh (gamma l) and cosh (gamma l) terms are in the middle, whether the impedance stability criterion is applied or not is judgedCan still be satisfied. When the forms of the formulae (14) and (15) are observed, it is found that: gssThe method is only a complex variable related to omega, so that no pole or zero exists; zssIt contains 1 pole fixed at the origin and 1 zero.
Z is shown in FIGS. 7a to 7bssZero-point variation with frequency ω and transmission line length l, where FIGS. 7a and 7b correspond to Z, respectivelyssReal and imaginary coordinate information of the zero point. The data in the figure is that the power transmission line parameter and the power grid impedance simulation parameter in the figure 6 are set as ZgObtained under the condition of 0.002+ j ω 0.0012 Ω.
As can be seen from fig. 7a to 7 b: only when resonance occurs, ZssThe real part of the zero point will move slightly at the position of the negative real axis-66.4 of the s-plane. Thus, GssAnd ZssInjecting an s-right half-plane pole and an s-right half-plane zero into the system respectively; the following can be concluded: using formulae (9) and (10), i.e. ZLAnd ZPAfter the sinh (gamma l) and cosh (gamma l) terms in the expression are equivalently replaced by the formula (7) and the formula (8), the impedance stability criterion is still applicable; further, Z can be utilizedgs/ZssThe nyquist (polar) trajectory of (a) evaluates the relative stability of the system.
As explained below, Z can be utilizedgs/ZssThe nyquist (polar) locus of (a) evaluates the principle of the relative stability of the system. If, in the s right half plane, GssNo pole and ZssIf no zero point exists, all items in brackets on the right side of the equal sign of the formula (16) are absolutely stable; in fig. 5, if the series connection between the source side circuit and the network side circuit is stable, the rest is enclosed on the right side by the equation (16):
and (6) determining. In fact, it is possible to use,
it can be understood that: the transfer function of the antecedent channel is 1, and the negative feedback channel is Zgs/ZssSee fig. 8; from the perspective of Nyquist stability criterion, closed-loop subsystem
Stability of by subsystem open loop transfer function Zgs/ZssThe Nyquist curve of is in [ Z ]gs/Zss]The plane (hereinafter referred to as "complex plane") is judged as a surrounding characteristic of the point (-1+ j 0).
The impedance stabilization criterion application rule is as follows:
in the right half-plane, due to ZssThere is no zero point (this has been concluded from fig. 7), which is equivalent to: open loop transfer function Zgs/ZssNo pole exists; at this time, the stability of the power transmission system is represented by Zgs/ZssNyquist (polar coordinate) trajectory determination of; the determination method comprises the following steps:
(1) if Z isgs/ZssThe Nyquist (polar coordinate) locus of (A) encompasses the (-1+ j0) point in the complex plane, the system is unstable; at the moment, the impedance stability margin of the power transmission system, including the phase angle margin and the amplitude margin, is negative;
(2) if Z isgs/ZssThe Nyquist (polar coordinate) curve of (1 + j0) point in the complex plane is not enclosed, then the system is stable; at the moment, the impedance stability margin of the power transmission system, including the phase angle margin and the amplitude margin, is positive.
In fact, in a power transmission system, each power generation unit in the station side (renewable energy station) should be operated stably, and the grid side (power grid) should also be operated stably; based on the above general knowledge, the source-side circuit and the grid-side circuit should be absolutely stable in series, and only the relative stability of the interconnected system needs to be analyzed. Then, the above "rule of applying the impedance stabilization criterion" only needs to apply item (2). Thus, make Zgs/ZssAnd obtaining the intersection points of the track, the unit circle and the negative real axis, and further respectively calculating the phase angle margin and the amplitude margin of the power transmission system, namely the stability margin of the evaluation system.
Considering the net-side equivalent impedance Zg＝Rg+jωLg(ii) a Wherein R isgIs a purely resistive part, LgIs a pure sensory part; in the s domain, Zg＝Rg+sLg(ii) a And Z isgs＝Zg(ii) a Binding formula (15) to give Zgs/ZssThe transfer function of (c):
replacing the complex variable s in formula (17) with s ═ j ω, resulting in:
in fact, at a specific ω, Zgs(jω)/Zss(j ω) is a specific complex number, i.e.
Zgs(jω)/Zss(jω)＝zreal(ω)+jzimag(ω) (19)
In the formula (19), zreal(omega) is Zgs(jω)/ZssReal part of (j ω), zimag(omega) is Zgs(jω)/ZssThe imaginary part of (j ω). Then, Zgs(jω)/ZssThe mode and phase angle of (j ω) are shown in formula (20) and formula (21), respectively.
The operator atan2 is an arctangent function that takes into account the quadrant; in other words, atan2 may represent the phase angle at any point in the four quadrants in polar coordinates, with the radian range (- π, + π).
Using equation (19), Z is calculated when ω increases from 0rad/s to Max _ order × 100 π rad/sgs(jω)/Zss(j ω), where Max _ order refers to a positive multiple of power frequency (50 Hz); subsequently, using the calculated zreal(ω) and zimag(omega) data making Zgs/ZssA polar coordinate graph of (a); wherein the real axis data is zreal(ω) virtual axis data is zimag(ω)。
The impedance stability evaluation of the power electronic power system needs to be discussed in a wide frequency range, so that the Max _ order value is suggested as follows: max _ order ≧ 100, i.e., the range of frequencies from the power frequency up to frequencies greater than or equal to the 100 th harmonic is considered.
In general, Zgs/ZssThe following 2 laws exist in the motion mode of the polar coordinate track:
1) with increasing ω, Zgs/ZssPeriodically pass in and out of the unit circle, and the radius of circular motion gradually increases.
The 1 st motion mode corresponds to the circuit structure shown in fig. 2, namely a power transmission system model ① does not consider multiple variants of a power station side equivalent circuit, a power transmission terminal and receiving terminal transformer model ② is omitted, ③ is not provided with a specific device for damping broadband harmonic resonance, and the condition can directly adopt an equation (18) to make the situation that when omega is increased from 0rad/s to 100 × 100 pi rad/s, Z is increased from 100 rad/sgs(jω)/Zss(j ω) in FIG. 9. As can be seen from the parameters in equation 18, the polar trajectory is actually related only to the following variables: zgIs the grid impedance; l is the length of the transmission line; omega is the system frequency; r is0Is the resistance of the transmission line per unit length, /)0Inductance of the transmission line per unit length, c0Is the capacitance of the transmission line per unit length; for a particular transmission line, the polar locus is associated only with ZgL and ω. FIG. 9 is a power line parameter set to Z for the grid impedance simulation using the power line parameter of FIG. 6g0.002+ j ω 0.0012 Ω, and a transmission line length l of 50 km.
2) With increasing ω, Zgs/ZssAfter the polar coordinate track passes through the unit circle, the polar coordinate track passes through the virtual axis again and falls on the right half plane to continue moving.
The 2 nd motion mode can correspond to the circuit structure shown in the figure 10, namely a power transmission system model ① does not consider multiple variants of a power station side equivalent circuit, a power transmission line transmitting end and receiving end transformer model ② is omitted, ③ is provided with a broadband harmonic resonance damping specific device, the condition can not adopt the formula (18) directly, but can imitate the acquisition formula(12) The ideas of equations (15) and (17) to (18) are to find Z corresponding to fig. 10g(jω)/Zss(j ω), the detailed calculation process is no longer a list of equations, described only by text:
first, with the dotted line in fig. 10 as a boundary, the left side is networked into a norton equivalent circuit (obtained by norton's equivalent theorem), and the right side branch holds a thevenin equivalent circuit to find the corresponding source side norton equivalent current source coefficient GssSource side norton equivalent parallel impedance ZssAn expression;
next, replacing G by following the equivalent transformation process of formula (12) and formula (13)ssAnd ZssComplex hyperbolic functions (sinh and cosh terms);
then, the actual net-side equivalent impedance Z is combinedg＝Rg+sLgCalculating Zgs(s)/Zss(s) expression (Z)gs＝Zg)；
Again, replacing Z with the s ═ j ω relationshipgs(s)/Zss(s) and calculating Z when ω increases from 0rad/s to Max _ order × 100 π rad/sgs(jω)/ZssReal part z of (j ω)real(ω) and imaginary part zimag(ω)；
Finally, the calculated z is utilizedreal(ω) and zimag(omega) data making Zgs/ZssA polar coordinate trajectory of; wherein the real axis data is zreal(ω) virtual axis data is zimag(ω)。
In fig. 10, the broadband harmonic resonance damping specific device is equivalent to 2 impedances, respectively impedance Z connected in parallel to the receiving end of the transmission linepdAnd a virtual impedance Z connected in series to the receiving terminalad；ZpdAnd ZadAre respectively:
Zpd＝jω×17×10-3+1/(jω×600×10-6) (22)
Zad＝KAZparallel/Zpd(23)
in the formula: zparallel＝[ZP(ZL+ZP)/(ZL+2ZP)]||ZpdThe symbol | | represents the impedance in parallel; zparallelIs represented by ZpdAs a starting point, the equivalent input impedance of the network on the left side thereof; kAIs the control coefficient of the damping device.
According to the circuit configuration shown in FIG. 10, Z is made when ω is incremented from 0rad/s to 100 × 100 π rad/sgs(jω)/Zss(j ω) in the polar locus, see FIGS. 11 a-11 b. Fig. 11a to 11b are diagrams of a power transmission line parameter and a grid impedance simulation parameter set to Z in fig. 6g0.002+ j omega 0.0012 omega, the length of the transmission line is set to be l 50 kilometers, and the control coefficient K of the damping deviceAObtained under 4 conditions.
The 2 nd law of motion may also correspond to the circuit structure shown in fig. 12, i.e. the power transmission system model ① considers a variant of the equivalent circuit on the side of the power station, specifically, the polymeric norton branch circuit shown in fig. 3b, ② considers the transformer model of the transmitting end and the receiving end of the power transmission line, ③ is equipped with a specific device for broadband harmonic resonance damping, in this case, the formula (18) may not be directly adopted, but the Z corresponding to fig. 12 may be found in the same way (i.e. the transformation method from the formula (12) to the formula (15) and from the formula (17) to the formula (18))gs(jω)/Zss(j ω), the detailed calculation process and the text description are not repeated. In fig. 12, the plant-side equivalent circuit is a convergent norton branch; gsAnd ZsRespectively are a polymerization Noton equivalent current source coefficient and an equivalent impedance; zDKAnd ZDMAll the parameters are T-shaped model parameters of the transformer at the side of the power station; zMKAnd ZMMAre all the parameters of the T-shaped model of the network side transformer.
If the power station side distributed generation unit is an LCL type inversion filtering system, and the control mode adopts: proportional quasi-resonant outer ring + filter capacitor current proportional feedback, and corresponding GsAnd ZsThe expressions are respectively formula (24) and formula (25).
In the above formula 2, KPWMIs the inverter gain; kcIs a filter capacitor current proportional feedback coefficient; hd＝KPWMKcCf/L1；G1(s)＝1/(sL1+R1)；G2(s)＝1/(sL2+R2)；Gc(s)＝1/sCf。L1、R1Respectively an inverter side filter inductor and an equivalent resistor thereof; l is2、R2Respectively a network side filter inductor and an equivalent resistor thereof; kDTIs the turns ratio of the transformer 1; gPRBeing a proportional quasi-resonant controller, a transfer function of
In the formula, KpIs a proportional gain; kiIs the resonant gain; omegacIs the cut-off frequency; omeganIs the fundamental frequency.
LCL inversion filter system simulation parameters are shown in FIG. 13a, transformer simulation data are shown in FIG. 13b, according to the circuit structure shown in FIG. 12, Z is made when omega is increased from 0rad/s to 100 × 100 π rad/sgs(jω)/Zss(j ω) in fig. 14a and 14 b. It should be understood that since the range of the abscissa and ordinate of fig. 14a is too large, the unit circle (with the origin as the center and radius of 1) is too small to be identified in the drawing. FIGS. 14a and 14b show the transmission line parameters of FIG. 6 with the net-side impedance simulation parameter set to Zg0.0066+ j omega 0.004 omega, the length of the transmission line is set to be l 50 kilometers, and the control coefficient K of the damping deviceAThe power station side inverter filter system adopts the proportion quasi-resonant outer ring + filter capacitor current proportion feedback scheme and the simulation parameters in fig. 13a, and adopts the transformer simulation parameters in fig. 13b, and the conditions are obtained under the conditions.
In an embodiment of the present invention, the evaluation of the wide-band impedance stability margin of the system is as follows, in terms of Zgs/ZssThe motion law of the polar coordinate trajectory is divided into the following 2 types.
In the first case of the process, the first,Zgs/Zssthe polar coordinate trajectory of (a) satisfies the first motion law, namely: with increasing ω, Zgs(jω)/ZssThe polar locus of (j ω) periodically passes in and out of the unit circle with a radius of circular motion that gradually increases. Referring to fig. 9, a first exemplary case of the embodiment of the present invention is shown, which satisfies a first motion rule. Zgs(jω)/Zss(j ω) starting from the origin of coordinates with a polar (nyquist) trajectory; as omega increases, the Nyquist locus circularly moves anticlockwise and is tangent to the origin; the radius of the new arc is increased every time the circular motion is performed. As can be surmised from FIG. 9, as ω continues to increase, it will cause the intersection of the trajectory with the right half-unit circle to move closer to the negative real axis; when omega increases and approaches + ∞, the newly added intersection point of the track and the right semi-unit circle approaches (-1+ j 0); due to the open loop system Zgs/ZssThe polar coordinate curve and the unit circle have infinite gain boundary frequencies, and the phase margin is measured at the highest gain boundary frequency, namely the point (-1+ j 0); obviously, the phase margin of the system is 0 °. Open-loop system Z as ω increases and approaches + ∞gs/ZssThe newly added intersection point of the polar coordinate trajectory and the right half unit circle is infinitely close to the point (-1+ j0), so the gain margin is measured at the point (-1+ j 0); obviously, the gain margin of the system is 0 dB. Therefore, the evaluation conclusion of the wide-frequency impedance stability margin of the power transmission system using fig. 9 as a typical case is as follows: the phase angle margin is 0 degrees, the amplitude margin is 0dB, and the relative stability of the system is seriously insufficient.
Second case, Zgs/ZssSatisfies the motion law two, i.e. as omega increases, Zgs(jω)/ZssAnd (j omega) enabling the polar coordinate track to pass through the unit circle, then pass through the virtual axis, fall on the right half plane and continue to move. Referring to fig. 11a and 11b, and fig. 14a and 14b, which are exemplary embodiments of the present invention, a second exemplary case is shown, which satisfies the second motion rule, Zgs(jω)/Zss(j ω) the polar (nyquist) locus begins within the unit circle; as ω increases, the trajectory will pass out of the unit circle, then through the imaginary axis, and continue to move falling in the right half plane.
In FIG. 11aAnd 11b in, Zgs(jω)/ZssThe intersection 1 of the polar coordinate trajectory of (j ω) and the cell circle is located at (-0.0426+ j 0.9966). Calculating formula by phase angle margin:
will zimag(jω1) 0.9966 and zreal(jω1) The phase angle margin is 87.5 degrees after the-0.0426 insertion. Since the intersection of the trajectory and the negative real axis is only the origin, the amplitude margin is + ∞ dB. Therefore, the evaluation conclusion of the wide-band impedance stability margin of the power transmission system corresponding to fig. 11a and 11b is as follows: the phase angle margin is 87.5 degrees, the amplitude margin is + ∞ dB, namely, the system has sufficient phase angle and amplitude margin, and the relative stability of the system is sufficient.
In FIGS. 14a and 14b, Zgs(jω)/ZssThe intersection 1 of the polar coordinate trajectory of (j ω) and the cell circle is located at (-0.908+ j 0.413). Calculating formula by phase angle margin:
will zimag(jω1) 0.413 and zreal(jω1) -0.908; the phase angle margin is obtained as follows: 24.5 degrees. Since the intersection of the trajectory and the negative real axis is only the origin, the amplitude margin is + ∞ dB. Therefore, the evaluation conclusion of the wide-band impedance stability margin of the power transmission system corresponding to fig. 14a and 14b is as follows: the phase angle margin is 24.5 degrees and the amplitude margin is + ∞ dB.
Embodiments of the present invention may also be used for control parameter optimization for various damping schemes. Taking the power transmission system corresponding to fig. 14a and 14b (see fig. 12) as an example, if the phase angle margin of the system is further improved, the control coefficient K of the damping device may be increasedAThis is achieved. Referring to FIG. 15, in an embodiment of the present invention, K is givenAUnder three conditions of 4, 6 or 8, Zgs(jω)/Zss(j ω) polar coordinate trace. When K isA4, 6 or 8, the intersection of the trajectory with the unit circleRespectively point 1, point 2, point 3. The coordinates of point 1 are the same as those of FIG. 14b, and are (-0.908+ j0.413), and the coordinates of point 2 and point 3 are: (-0.8063+ j0.5906), (-0.6672+ j 0.7412). Using a phase angle margin calculation formula:
to obtain KAWhen 6, the phase angle margin of the system is 36.2 degrees; kAThe phase angle margin of the system is 48 deg. when it is 8 deg.. Therefore, the evaluation method for the broadband impedance stability margin of the power transmission system provided by the embodiment of the invention not only can conveniently evaluate the relative stability margin of the power transmission system, but also provides a quantitative method for designing a broadband harmonic resonance damping control method and optimizing parameters of the broadband harmonic resonance damping control method.
The embodiments of the present invention have been described in detail with reference to the accompanying drawings, but the present invention is not limited to the above embodiments, and various changes can be made within the knowledge of those skilled in the art without departing from the gist of the present invention.
Claims (9)
1. A method for evaluating a broadband impedance stability margin of a power transmission system is characterized by comprising the following steps:
constructing a power transmission system model, which comprises a power transmission line model, a power station side model and a network side model, wherein the power transmission line model is a pi-shaped circuit model containing a complex hyperbolic function and consists of a series impedance and two same parallel impedances, and the network side model is a Thevenin equivalent circuit and comprises a voltage source and a network side equivalent impedance connected with the voltage source in series;
performing equivalent transformation on the plurality of hyperbolic functions based on the power line model, and performing equivalent transformation on the series impedance and the parallel impedance according to the plurality of hyperbolic functions after the equivalent transformation;
converting a source side circuit comprising the power station side model and the power line model into a Norton equivalent circuit, wherein the network side model keeps a Thevenin equivalent circuit, and an impedance stability criterion analysis circuit model is constructed to obtain a calculation model of impedance ratio to the source side of the network side;
and obtaining a polar coordinate track according to the calculation model of the network side source side impedance ratio, and obtaining a phase angle margin and an amplitude margin according to a motion rule of the polar coordinate track.
2. The evaluation method for broadband impedance stability margin of a power transmission system according to claim 1, wherein the equivalent transformation method of the complex hyperbolic function is as follows:
wherein sinh (γ l) and cosh (γ l) are the complex hyperbolic functions, γ is a propagation constant, l is a transmission line length, ω is a system frequency,
l0inductance of the transmission line per unit length, c0Is the capacitance per unit length of the transmission line.
3. The evaluation method for the broadband impedance stability margin of the power transmission system according to claim 2, wherein the equivalent transformation method for the series impedance and the parallel impedance is as follows:
wherein the content of the first and second substances,
ZLis the series impedance, ZPFor the parallel impedance, s-j ω,
l is the length of the transmission line, omega is the system frequency, r0Is the resistance of the transmission line per unit length, /)0Inductance of the transmission line per unit length, c0Is the capacitance per unit length of the transmission line.
4. The evaluation method for broadband impedance stability margin of a power transmission system according to claim 3, wherein the calculation model of the grid-side source-side impedance ratio is analyzed by combining a circuit model with the grid-side equivalent impedance Z according to the impedance stability criteriong＝Rg+jωLgResults, expressed as:
Zgs(jω)/Zss(jω)＝zreal(ω)+jzimag(ω)，
wherein Z isgsIs net side Thevenin equivalent series impedance, ZssIs a source side norton equivalent parallel impedance; zgs(jω)、Zss(j ω) is each Zgs、ZssExpression form of j ω, Zgs＝Zg，ZgIs the net side equivalent impedance, RgIs a pure resistive part, and Lg is a pure inductive part; z is a radical ofreal(ω) is the real part, zimagAnd (ω) is an imaginary part.
5. The evaluation method for broadband impedance stability margin of a power transmission system according to claim 4, wherein the calculation model of the grid-side source-side impedance ratio is:
wherein Z isgsIs net side Thevenin equivalent series impedance, ZssIs a source side norton equivalent parallel impedance; zgs(jω)、Zss(j ω) is each Zgs、ZssJ ω, s ═ j ω, Zgs＝Zg，Zg＝Rg+jωLg，ZgIs the net side equivalent impedance, RgIs a purely resistive part and Lg is a purely inductive part.
6. The evaluation method for the broadband impedance stability margin of the power transmission system according to claim 4, wherein the polar coordinate trajectory is obtained by:
the value of omega is increased from 0rad/s to Max _ order × 100 pi rad/s, and the real part z is calculatedreal(ω) and imaginary part zimag(ω), wherein Max _ order is a positive multiple of power frequency;
construction of Zgs/ZssWherein the real axis data is zreal(ω) virtual axis data is zimag(ω)。
7. The evaluation method for the broadband impedance stability margin of the power transmission system according to claim 6, wherein Max _ order is a positive integer greater than or equal to 100.
8. The method for evaluating the broadband impedance stability margin of the power transmission system according to claim 1, wherein the phase angle margin and the amplitude margin are obtained by:
if the polar coordinate track periodically penetrates into and out of the unit circle along with the increase of omega, and the radius of circular motion gradually increases, the phase angle margin is 0 degree, and the amplitude margin is 0 dB;
if the polar coordinate track penetrates out of the unit circle along with the increase of omega, then penetrates through the virtual axis, falls on the right half plane and continues to move, the phase angle margin is obtained according to the intersection point of the polar coordinate track on the right half plane and the unit circle, and the amplitude margin is obtained according to the intersection point of the polar coordinate track and the negative real axis of the virtual axis.
9. The method for evaluating the wide-frequency impedance stability margin of the power transmission system according to claim 8, wherein the phase angle margin is calculated by:
and obtaining the phase angle margin according to the included angle between the intersection point of the right half plane of the polar coordinate trajectory and the unit circle and the real axis.
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