CN103972912B - A kind of frequency-domain analysis method containing the response of wind-powered electricity generation power system frequency - Google Patents

Abstract

The present invention relates to a kind of frequency-domain analysis method containing the response of wind-powered electricity generation power system frequency, the method considers generator property, governor characteristic, system network architecture, part throttle characteristics and AGC control characteristic simultaneously, consider the DYNAMIC DISTRIBUTION characteristic of electric power networks medium frequency, solve the lower electric power system of wind power excitation each nodal frequency response explicit expression, frequency-domain result inverse transformation have been fluctuated the power system frequency deviation under encouraging in order to assess wind power to time domain.Simulation result shows that this model can reflect the frequency departure characteristic of the lower each node of wind power excitation quickly and accurately, utilize these scale-model investigation wind power access point, AGC etc. to the affecting laws of system frequency deviation and amplitude-frequency characteristic thereof, the access point of wind energy turbine set is selected, the access capacity planning of wind energy turbine set, in design of filter before wind power access electrical network and system, adjusting etc. of AGC controling parameters has important directive significance, has good promotional value and application prospect.

Description

A kind of frequency-domain analysis method containing the response of wind-powered electricity generation power system frequency

Technical field

The present invention relates to a kind of frequency-domain analysis method of system frequency response, especially relate to a kind of frequency-domain analysis method containing the response of wind-powered electricity generation power system frequency.

Background technology

Along with the fast development of China's Wind Power Generation Industry, the grid-connected problem of large-scale wind power also heals and becomes severe.The wind power connecting system of extensive random fluctuation will cause the unbalanced power in system, and then produce frequency departure.According to GB/T15945-2008 strict regulations, the frequency departure allowed band of large-scale power system is within 4 ‰ of frequency rated value, and the power system frequency deviation allowed band less for capacity suitably can be loosened to 1%.Chinese scholars has done a large amount of work on wind power fluctuation to the impact of system frequency, and its research method roughly can be summarized as two classes:

(1) time-domain simulation method, utilizes simulation software to build the impact of electric power system model emulation wind power fluctuation on power system frequency deviation.Usual simulation software, by solving the differential equation and Load flow calculation carries out simulation calculation, such research method, needs to set up the complete model that electric power system is studied by institute, and along with the expansion of electric power system scale, simulation velocity decline is very fast.

(2) frequency-domain analysis method, the first utilizes SFR model to set up input/output relation between power fluctuation and frequency departure, analyzes the impact of wind power fluctuation on frequency departure.But system is equivalent to unit model by SFR model, have ignored the impact of network configuration, the result obtained is not comprehensive.Its two be by system input swept-frequency signal, record output set up ssystem transfer function, according to wind power fluctuation spectrum density, calculated rate deviation, phase angle information has been lost in calculating due to spectrum density, and make frequency departure result not unique, the result obtained is inaccurate.

Summary of the invention

The present invention mainly solves the technical problem existing for prior art; Provide one and can consider generator property, governor characteristic, system network architecture, part throttle characteristics and AGC control characteristic simultaneously, consider the DYNAMIC DISTRIBUTION characteristic of electric power networks medium frequency, solve the lower electric power system of wind power excitation each nodal frequency response explicit expression, frequency-domain result inverse transformation have been fluctuated the power system frequency deviation under encouraging in order to assess wind power to time domain.Simulation result shows that this model can reflect a kind of frequency-domain analysis method containing the response of wind-powered electricity generation power system frequency of the frequency departure characteristic of the lower each node of wind power excitation quickly and accurately.

Above-mentioned technical problem of the present invention is mainly solved by following technical proposals:

A kind of frequency-domain analysis method containing the response of wind-powered electricity generation power system frequency, it is characterized in that, based on the DYNAMIC DISTRIBUTION characteristic of electric power networks medium frequency, set up and comprise generator and speed regulator, network configuration, load dynamically and the electric power system frequency-domain model of AGC, wherein:

Model one: generator model is based on formula

$G_g\left(s\right)=\frac{\mathrm{\Δ\ω}\left(s\right)}{{\mathrm{\ΔP}}_e\left(s\right)}=\frac{G_r\left(s\right)}{G_r\left(s\right)G_t\left(s\right)-1}$

In formula, G _r(s)=1/ (sT _j+ D) represent the generator equation of motion, T _jfor rotor inertia time constant, D is Generator Damping coefficient, G _ts () is speed regulator transfer function, its expression formula is relevant with the speed regulator type of selection.

Model two: network structure model DC power flow is based on formula

$\left[\begin{array}{c}\mathrm{\Δ}{P}_e\\ \mathrm{\Δ}{P}_L\end{array}\right]=\left[\begin{array}{cc}{B}_{\mathrm{ee}}& B_{\mathrm{eL}}\\ B_{\mathrm{Le}}& B_{\mathrm{LL}}\end{array}\right]\left[\begin{array}{c}\mathrm{\Δ\δ}\\ \mathrm{\Δ\θ}\end{array}\right]$

In formula, Δ P _efor the input power of synchronous generator node, Δ P _lfor load bus injecting power, wind power fluctuation can be regarded as on this category node injects negative load, and Δ δ is the merit angle of generator node, and Δ θ is the phase angle of load bus, B _ee, B _eL, B _le, B _lLfor power system network matrix in block form.

Model three: load fluctuation model is based on formula

ΔP _L1(s)＝K _LP _l0Δω _L(s)

In formula, P _l0for rated load, represent the active power of load under rated frequency, K _lrepresent the frequency regulation characteristics of load.Δ ω _lthe frequency domain form of the frequency fluctuation of (s) load bus.

Model four: AGC model $G_{\mathrm{AGC}}\left(s\right)=\frac{1}{1+s{T}_{\mathrm{agc}}}(K_P+\frac{K_I}{s})$

In formula, T _agcfor AGC time constant, K _pand K _ifor the adjustment factor of AGC.

Step 1, according to set up electric power system frequency-domain model, solves the transfer function H (ω) of each nodal frequency response of the lower electric power system of wind power excitation, wherein makes s=j ω, just can be converted into H (ω) by H (s);

Wherein the frequency response transfer function of generator node is based on formula

$H_e\left(s\right)=\frac{\mathrm{\Δ}{\mathrm{\ω}}_e\left(s\right)}{{\mathrm{\ΔP}}_{\mathrm{wind}}\left(s\right)}=\frac{{\mathrm{\ω}}_0}{s}G\·B_{\mathrm{eL}}\·K\·P_{\mathrm{location}}$

The transfer function of load bus response wind power fluctuation is based on formula

$H_L\left(s\right)=\frac{\mathrm{\Δ}{\mathrm{\ω}}_L\left(s\right)}{\mathrm{\Δ}{P}_{\mathrm{wind}}\left(s\right)}=[{\left(\frac{{\mathrm{\ω}}_0}{s}\right)}^{2}K\·B_{\mathrm{eL}}G\·B_{\mathrm{eL}}K-K]\·P_{\mathrm{location}}$

Wherein $K={(-P_{L0}{K}_L-\frac{{\mathrm{\ω}}_0}{s}{B}_{\mathrm{LL}})}^{-1}$

$G={({\mathrm{sT}}_J-G_t\left(s\right)+\frac{{\mathrm{\ω}}_0}{s}{B}_{\mathrm{ee}}+{\left(\frac{{\mathrm{\ω}}_0}{s}\right)}^2{B}_{\mathrm{eL}}\·K\·B_{\mathrm{Le}})}^{-1}$

P _locationrepresent the vector of wind power access point position, define system has n node, its interior joint 1,2,3 ..., m is generator node m altogether, node m+1, m+2 ..., n is load bus n-m altogether, then P _locationfor n-m dimensional vector, have the node that wind power accesses, corresponding vector element gets 1, otherwise is taken as 0.

Step 2, by known wind power time series Δ P _windt () carries out the spectral characteristic Δ P that Fourier transform obtains wind power fluctuation _wind(ω);

Step 3, according to Δ Ω (ω)=H (ω) Δ P _wind(ω) frequency departure frequency-domain result Δ Ω (ω) of electric power system response wind power fluctuation is calculated;

Step 4, carries out Fourier inversion to frequency departure frequency-domain result Δ Ω (ω), calculates power system frequency deviation signal delta ω (t) in the time domain, and then assessment to be fluctuated the power system frequency deviation caused by wind power.

Therefore, tool of the present invention has the following advantages: the DYNAMIC DISTRIBUTION characteristic considering each nodal frequency in electric power system, utilizes the power system frequency deviation under the method assessment wind-powered electricity generation excitation of time-frequency conversion.And utilize carry the affecting laws to system frequency deviation and amplitude-frequency characteristic thereof such as the methods analyst of model wind power access point, AGC, the access point of wind energy turbine set is selected, in the access capacity Intention of Plan of wind energy turbine set and system, the contention of AGC controling parameters has important directive significance, has good promotional value and application prospect.

Accompanying drawing explanation

Accompanying drawing 1 is generator feedback circuit diagram of the present invention.

Accompanying drawing 2-1 is the wind power fluctuation of the embodiment of the present invention.

Accompanying drawing 2-2 is the wind power random fluctuation spectral characteristic of the embodiment of the present invention.

Accompanying drawing 3 is AGC model framework charts of the embodiment of the present invention.

Accompanying drawing 4 is IEEE tri-machine nine node system structure charts of the embodiment of the present invention.

Accompanying drawing 5-1 is the generator nodal frequency deviation transfer function amplitude-frequency characteristic of the embodiment of the present invention.

Accompanying drawing 5-2 is the sub-load nodal frequency deviation transfer function amplitude-frequency characteristic of the embodiment of the present invention.

Node 2 frequency response transfer function amplitude-frequency characteristic when accompanying drawing 6-1 is the different node access of the embodiment of the present invention.

Node 7 frequency response transfer function amplitude-frequency characteristic when accompanying drawing 6-2 is the different node access of the embodiment of the present invention.

Accompanying drawing 7 is that the AGC of the embodiment of the present invention is on the impact of transfer function amplitude-frequency characteristic.

The accompanying drawing 8a frequency fluctuation that to be the frequency of the embodiment of the present invention be under the wind power fluctuation excitation of 0.01rad/s.

The accompanying drawing 8b frequency fluctuation that to be the frequency of the embodiment of the present invention be under the wind power fluctuation excitation of 0.52rad/s.

The accompanying drawing 8c frequency fluctuation that to be the frequency of the embodiment of the present invention be under the wind power fluctuation excitation of 15.6rad/s.

The accompanying drawing 8d frequency fluctuation that to be the frequency of the embodiment of the present invention be under the wind power fluctuation excitation of 23.5rad/s.

The accompanying drawing 8e frequency fluctuation that to be the frequency of the embodiment of the present invention be under the wind power fluctuation excitation of 100rad/s.

Accompanying drawing 9 is frequency dynamic curves of the node 7 sudden increase in load node 2 of the embodiment of the present invention.

Accompanying drawing 10 is time-domain calculation relative errors of the embodiment of the present invention.

Accompanying drawing 11 is different nodal frequency deviations utilizing time-frequency conversion to calculate of the embodiment of the present invention.

Accompanying drawing 12 is time-frequency conversion result and the time-domain calculation Comparative result figure of the embodiment of the present invention.

Accompanying drawing 13 is relative errors of the time-frequency conversion result of calculation of the embodiment of the present invention.

Embodiment

Below by embodiment, and by reference to the accompanying drawings, technical scheme of the present invention is described in further detail.

Embodiment:

Below in conjunction with drawings and Examples, technical scheme of the present invention is further illustrated.

One. containing the Modeling In Frequency Domain of wind-powered electricity generation electric power system.

1.1 containing each element Modeling In Frequency Domain of wind-powered electricity generation electric power system.

1.1.1 synchronous generator and governor model

After ignoring excitation link, normal power supplies generally comprises two parts: prime mover and governor model thereof, synchro generator model, and its simplified model as shown in Figure 1 ^[1].

Synchro generator model can describe with equation of rotor motion, shown in (1):

$\left\{\begin{array}{c}\frac{\mathrm{d\Δ\δ}}{\mathrm{dt}}=\mathrm{\Δ\ω}\·{\mathrm{\ω}}_0\\ T_J\frac{\mathrm{d\Δ\ω}}{\mathrm{dt}}={\mathrm{\ΔP}}_m-\mathrm{\Δ}{P}_e-D\·\mathrm{\Δ\ω}\end{array}\right.---\left(1\right)$

In formula, ω ₀=2 π f ₀for fundamental frequency angular speed, T _j=diag{T _1J, T _2J..., T _mJbe the rotor moment of inertia of n synchronous generator, D=diag{D ₁, D ₂... D _mrepresent n synchronous generator rotor damping coefficient.

Formula (1) is carried out Laplace transform, and under its complex frequency domain, expression formula is such as formula shown in (2):

$\left\{\begin{array}{c}\mathrm{s\Δ\δ}\left(s\right)-\mathrm{\Δ\δ}\left(0_{-}\right)={\mathrm{\ω}}_0\·\mathrm{\Δ\ω}\left(s\right)\\ \mathrm{\Δ\ω}\left(s\right)={(T_{J}s+D)}^{-1}[\mathrm{\Δ}{P}_m\left(s\right)-\mathrm{\Δ}{P}_e\left(s\right)+T_J\mathrm{\Δ\ω}\left(0_{-}\right)\end{array}\right.---\left(2\right)$

In formula: Δ ω (0 _-) be t=0 _-the value of moment Δ ω, Δ δ (0 _-) be t=0 _-the value of moment δ.Generally, initial value Δ ω (0 is got _-)=0, Δ δ (0 _-)=0 item can obtain the transfer function G of separate unit synchronous generator rotor dynamic process _r(s).

G _r(s)＝Δω(s)/[ΔP _m(s)-ΔP _e(s)](3)＝1/(sT _J+D)

The complex frequency domain model of prime mover and governor model thereof can be represented by formula (4):

ΔP _m(s)＝G _t(s)Δω(s)(4)

Wherein: G _ts transfer function that () is prime mover and speed regulator, G _ts embodying of () is relevant with the selection of prime mover and governor model.Choosing prime mover governor model is herein:

$G_t\left(s\right)=-\frac{1+F_{\mathrm{\μ}}{T}_{R}s}{R(1+T_{R}s)}---\left(5\right)$

According to Fig. 1, convolution (3) and (4) can obtain the transfer function G of generator model _g(s):

$G_g\left(s\right)=\frac{\mathrm{\Δ\ω}\left(s\right)}{\mathrm{\Δ}{P}_e\left(s\right)}=\frac{G_r\left(s\right)}{G_r\left(s\right)G_t\left(s\right)-1}---\left(6\right)$

1.1.2 power network model.

In the process of system frequency fluctuation, the frequency at diverse location place is different, namely has the distribution character of space-time, therefore the impact of network on frequency be can not ignore.Owing to only considering the impact of wind power fluctuation on nodal frequency, therefore need to consider the relation between the phase angle of node and input active power, this pass can be described with DC power flow ^[12]:

P＝Bθ(7)

In formula: P is the vector power of each node, matrix B is the susceptance matrix of network.For ease of calculating, above formula is write as following matrix in block form form ^[9]:

$\left[\begin{array}{c}\mathrm{\Δ}{P}_e\\ \mathrm{\Δ}{P}_L\end{array}\right]=\left[\begin{array}{cc}{B}_{\mathrm{ee}}& B_{\mathrm{eL}}\\ B_{\mathrm{Le}}& B_{\mathrm{LL}}\end{array}\right]\left[\begin{array}{c}\mathrm{\Δ\δ}\\ \mathrm{\Δ\θ}\end{array}\right]---\left(8\right)$

In formula, Δ P _efor the input power of synchronous generator node, Δ P _lfor load bus injecting power, wind power fluctuation can be regarded as on this category node injects negative load, and Δ δ is the merit angle of generator node, and Δ θ is the phase angle of load bus.

1.1.3 load frequency-domain model.

Ignore the impact of voltage on load active power, then adopt power index model to describe load model and can be reduced to shown in formula (9):

P _L＝P _L0(1+K _LΔω _L)(9)

In formula: P _l0for rated load, represent the active power of load under rated frequency, K _lrepresent the frequency regulation characteristics of load.Laplace transform is done to formula (9), only considers load fluctuation part, the complex frequency domain model of load shown in formula (10) can be obtained.

ΔP _L1(s)＝K _LP _l0Δω _L(s)(10)

1.1.4 wind power frequency-domain model.

Because the controlling unit of actual wind energy turbine set is complicated, and the factor affecting output of wind electric field is a lot, and the Mathematical Modeling setting up wind energy turbine set is very complicated.System response under main research wind power fluctuation herein, therefore its wind power exported of wind energy turbine set describes, and can be expressed as:

P _wind(t)＝P _wind0(t)+ΔP _wind(t)(11)

In formula, P _wind0t () is wind power mean value, Δ P _windt () is wind power random fluctuation.Main consideration wind power random fluctuation Δ P herein _wind(t) on the impact of nodal frequency, then:

ΔP _L2(s)＝-ΔP _wind(s)(12)

Δ P _winds Laplace transform result that () is wind power random fluctuation.

Figure 2 shows that the wind power curve of actual measurement in certain wind energy turbine set 10min.Figure 3 shows that and will survey wind power curve in Fig. 2 and carry out the result of Fourier transform, reflection be the spectral characteristic of wind power random fluctuation part.As shown in Figure 3, wind power random fluctuation mainly concentrates on low frequency region, and along with the increase of frequency, the wind power content of this frequency range reduces gradually.

1.1.5AGC model.

The main purpose of AGC comprises adjustment generator output to be made it and load balancing, maintains near rated value with keeping system frequency.When disturbance appears in system, ACE (district control deviation) value according to system regulates the active power of AGC unit, and ACE controls within the scope of regulation the most at last.For isolated system, can think that the generally general form of ACE is such as formula shown in (13).

ACE＝-B(f-f _ref)＝-BΔf(13)

Wherein, Δ f is frequency departure; B is the frequency bias coefficient of electrical network or control area.

AGC has various control model, and often kind of corresponding different control characteristic of control model, thus its control performance, control block diagram are also different, if AGC transfer function is GAGC (s), then control characteristic is such as formula shown in (14).

ΔP _C(s)＝G _AGC(s)ACE(s)(14)

In formula: Δ P _cs () is unit generation variable quantity.

Figure (4) is typical AGC control block diagram, and consider that it simplifies statement, ignore the time-lag action of AGC, then its transfer function can be write as formula (15) form.

$G_{\mathrm{AGC}}\left(s\right)=\frac{1}{1+s{T}_{\mathrm{agc}}}(K_P+\frac{K_I}{s})---\left(15\right)$

Two. the frequency-domain model containing wind-powered electricity generation electric power system solves.

2.1 do not solve containing the system frequency-domain model of AGC.

Similar generator node, according to the definition of load bus frequency, can obtain its frequency domain and be described as:

ω ₀·Δω _L(s)＝sΔθ(s)(16)

According to network model formula (8), simultaneous (1) and (16) can obtain

${\mathrm{\ΔP}}_e=B_{\mathrm{ee}}\mathrm{\Δ\δ}+B_{\mathrm{eL}}\mathrm{\Δ\θ}=\frac{{\mathrm{\ω}}_0}{s}(B_{\mathrm{ee}}\mathrm{\Δ}{\mathrm{\ω}}_e+B_{\mathrm{eL}}{\mathrm{\Δ\ω}}_L)---\left(17\right)$

${\mathrm{\ΔP}}_L=B_{\mathrm{Le}}\mathrm{\Δ\δ}+B_{\mathrm{LL}}\mathrm{\Δ\θ}=\frac{{\mathrm{\ω}}_0}{s}(B_{\mathrm{Le}}\mathrm{\Δ}{\mathrm{\ω}}_e+B_{\mathrm{LL}}{\mathrm{\Δ\ω}}_L)---\left(18\right)$

Wind power regards so have the load that load bus access is negative as

ΔP _L(s)＝-(ΔP _L1+ΔP _L2)＝-(P _l0K _LΔω _L(s)-ΔP _wind(s))(19)

Simultaneous formula (18) and (19) can obtain

$\mathrm{\Δ}{\mathrm{\ω}}_L={({-P}_{L0}{K}_L-\frac{{\mathrm{\ω}}_0}{s}{B}_{\mathrm{LL}})}^{-1}\·(\frac{{\mathrm{\ω}}_0}{s}{B}_{\mathrm{Le}}\mathrm{\Δ}{\mathrm{\ω}}_e+\mathrm{\Δ}{P}_{\mathrm{wind}})---\left(20\right)$

Can obtain according to formula (2) and (17)

$(\mathrm{sM}-G_t\left(s\right)+\frac{{\mathrm{\ω}}_0}{s}{B}_{\mathrm{ee}}){\mathrm{\Δ\ω}}_e=-\frac{{\mathrm{\ω}}_0}{s}{B}_{\mathrm{eL}}{\mathrm{\Δ\ω}}_L---\left(21\right)$

Simultaneous formula (20) and formula (21) can in the hope of the frequency response expression formulas of node, and formula (22) is the response of generator nodal frequency, and formula (17) is load bus frequency response:

$\mathrm{\Δ}{\mathrm{\ω}}_e\left(s\right)=\frac{{\mathrm{\ω}}_0}{s}G\·B_{\mathrm{eL}}\·K\·\mathrm{\Δ}{P}_{\mathrm{wind}}\left(s\right)---\left(22\right)$

$\mathrm{\Δ}{\mathrm{\ω}}_L\left(s\right)=[{\left(\frac{{\mathrm{\ω}}_0}{s}\right)}^{2}K\·B_{\mathrm{eL}}G\·B_{\mathrm{eL}}K-K]{\mathrm{\ΔP}}_{\mathrm{wind}}\left(s\right)---\left(23\right)$

Wherein,

$K={({-P}_{L0}{K}_L-\frac{{\mathrm{\ω}}_0}{s}{B}_{\mathrm{LL}})}^{-1}---\left(18\right)$

$G={(s{T}_J-G_t\left(s\right)+\frac{{\mathrm{\ω}}_0}{s}{B}_{\mathrm{ee}}+{\left(\frac{{\mathrm{\ω}}_0}{s}\right)}^2{B}_{\mathrm{eL}}\·K\·B_{\mathrm{Le}})}^{-1}---\left(19\right)$

In order to characterize the impact of wind power access point on system, definition P _locationfor the vector of wind power access point position, if such as system has n node, its interior joint 1,2,3 ..., m is generator node m altogether, node m+1, m+2 ..., n is load bus n-m altogether, then P _locationfor n-m dimensional vector, have the node that wind power accesses, corresponding vector element gets 1, otherwise is taken as 0.

Then the transfer function of system frequency response wind power fluctuation is:

$H_e\left(s\right)=\frac{{\mathrm{\Δ\ω}}_e\left(s\right)}{{\mathrm{\ΔP}}_{\mathrm{wind}}\left(s\right)}=\frac{{\mathrm{\ω}}_0}{s}G\·B_{\mathrm{eL}}\·K\·P_{\mathrm{location}}$

$H_L\left(s\right)=\frac{{\mathrm{\Δ\ω}}_L\left(s\right)}{{\mathrm{\ΔP}}_{\mathrm{wind}}\left(s\right)}=[{\left(\frac{{\mathrm{\ω}}_0}{s}\right)}^{2}K\·B_{\mathrm{eL}}G\·B_{\mathrm{eL}}K-K]\·P_{\mathrm{location}}$

The 2.2 system frequency-domain models containing AGC solve.

When considering AGC effect, only G need be modified to:

$G={(s{T}_J-G_t\left(s\right)+\frac{{\mathrm{\ω}}_0}{s}{B}_{\mathrm{ee}}+{\left(\frac{{\mathrm{\ω}}_0}{s}\right)}^2{B}_{\mathrm{eL}}\·K\·B_{\mathrm{Le}}+G_{\mathrm{AGC}}\left(s\right))}^{-1}---\left(20\right)$

Three. sample calculation analysis.

This patent has carried out simulation calculation and analysis for IEEE tri-machine nine node system.

3.1 frequency-domain analysis.

1.1 Analysis of Magnitude-Frequency Characteristic.

When only having a node access wind power in system, the unit impulse response according to formula (22) and (23) can obtain system transter H (s)=Δ ω (s)/Δ P _winds (), it is input as wind power fluctuation, exports the frequency departure into each node.The inherent characteristic that transfer function H (s) is system, for giving, the transfer function H (s) of fixed system same nodal frequency response is certain.Due to the distribution character of frequency dynamic, between the transfer function of different nodal frequency response, there is certain otherness.Analytical system, in the characteristic of different nodal frequency response pass function H (s), is convenient to the frequency response of each node of system studied under multi-form wind power fluctuation excitation.As shown in figure (5), when access point is No. 7 nodes, the amplitude-frequency characteristic of the frequency response transfer function of generator node and load bus.

As seen from the figure, the amplitude-frequency characteristic of each nodal frequency response pass function has three extreme points, and Frequency point corresponding to the extreme point of different node is identical, and namely system frequency is certain, but extreme value exists certain otherness.When wind power vibration frequency is lower than in the low-frequency range of 1rad/s, the frequency departure of each node of system is identical, and namely under low-frequency fluctuation, the frequency dynamic of each node is consistent.In 1rad/s ~ 100rad/s frequency range, there is otherness in the frequency departure of each node, and frequency distribution characteristic is obvious, and occurs peak value, and the wind power fluctuation of this frequency band on frequency fluctuation impact obviously.High frequency wind power fluctuation higher than 100rad/s causes system frequency to produce deviation hardly, and the fluctuation of high frequency wind power is negligible on the impact of frequency departure.

Figure (6) gives and sets forth wind power when node 4,5 and No. 7 node accesses, the amplitude-frequency characteristic of the frequency departure transfer function of node 2 and node 7.As seen from the figure, natural frequency not with access point change and change, and from access point more close to, the impact that wind power produces nodal frequency deviation is larger.

This example low frequency region stationary value is 0.016, the maximum of low frequency range is 0.053, and when node 7 has disturbance, it is 0.069 that the maximum of the frequency transfer function amplitude-frequency characteristic of node 2 appears at intermediate frequency zone, be about 1.3 times of low frequency maximum, be about 4.31 times of low frequency stationary value.When wind power frequency is consistent with system frequency, system responses wind power fluctuates and has obvious amplification to frequency departure, when the wind power fluctuation of this frequency reaches certain value, easily make system frequency deviation out-of-limit, system stable operation is produced serious influence.In order to reduce the impact of wind power fluctuation on frequency departure, can carry out filtering process to the wind power before access electrical network makes it more level and smooth, according to Bode diagram, after the wind power fluctuation of filtering 0.1rad/s ~ 1rad/s and 10rad/s ~ 30rad/s frequency band, the impact of wind power fluctuation on frequency departure can be effectively reduced, be conducive to system safety stable operation.

3.1.2AGC impact

In three machine nine node systems, add AGC model carry out simulation in the frequency-domain analysis, contrast with without during AGC effect, as shown in figure (9).AGC effect does not change the natural frequency of system, and has obvious reduction effect to extreme value, and the amplitude of the low-frequency range of amplitude-frequency characteristic is obviously reduced, and lower than 0.01rad/s frequency band, amplitude is almost reduced to zero.Visible AGC access has larger impact to system response, can pass through its frequency modulation frequency modulation effect, effectively suppresses the frequency departure that low-frequency fluctuation causes.

3.2 time-domain-simulation checkings.

In order to verify the correctness of above frequency-domain analysis, and considering the deficiency of some simulation softwares on frequency conversion calculates, in MATLAB, building the Model in Time Domain corresponding with frequency domain, carrying out simulating, verifying by solving the differential equation.First built Model in Time Domain is verified, increase the load of 50MW at node 7, observe the frequency response of any one node, contrast with PSASP simulation result, as shown in figure (9).Figure (10) gives the relative error of calculating, wherein maximum relative error is 0.26%, the mean absolute percentage error (MAPE) calculated by formula (21) is 0.038%, demonstrates the correctness of Model in Time Domain thus.

$\mathrm{MAPE}=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}\left|\frac{F_m\left(i\right)-F_p\left(i\right)}{F_p\left(i\right)}\right|---\left(21\right)$

Wherein N is total amount of data, F _mi () is i-th measured value, F _pi () is corresponding i-th true value.

For checking frequency domain amplitude-frequency characteristic, the wind power fluctuation that form is y=sin (ω t) is accessed at node 7, getting ω is different values, obtains the frequency fluctuation result of different node respectively, and Fig. 8 lists the frequency fluctuation result of different frequency wind power excitation lower node 1,2,3.When wind power vibration frequency is lower, the frequency change of each node of system is consistent; When wind power vibration frequency is higher, the frequency fluctuation of each node of system presents significant otherness, and when driving frequency is consistent with system frequency, shows as resonance oscillations; And under high frequency pumping, frequency departure is almost nil.Steady frequency deviate under the excitation of different frequency wind power and the amplitude one_to_one corresponding under amplitude-frequency characteristic respective frequencies, and then demonstrate the correctness of frequency-domain analysis.

3.3 actual wind power fluctuation excitation results.

According to the definition of transfer function, can obtain, under wind power excitation, system frequency deviation is:

ΔF(s)＝H(s)×ΔP _wind(s)

For different access points and observation station, H (s) value is different.Make s=j ω, the frequency domain form Δ F (j ω) of frequency departure can be obtained, carried out frequency fluctuation Δ F (t) that namely Fourier inversion obtains forms of time and space.Still for IEEE tri-machine nine node system, simulation calculation obtains system frequency fluctuation as shown in figure (11).Figure (12) says that frequency-domain calculations result and time domain Output rusults contrast, calculate relative error as shown in figure (13), wherein maximum relative error is 0.0485%, mean absolute percentage error (MAPE) is 0.0247%, and frequency-domain analysis result and result in time domain are almost consistent.

The present invention considers the DYNAMIC DISTRIBUTION characteristic of each nodal frequency in electric power system, sets up the electric power system model comprising electric power networks, utilizes the power system frequency deviation under the method assessment wind-powered electricity generation excitation of time-frequency conversion.Relative to conventional method, the analytical method that the present invention carries can significantly promote computational analysis speed.This is because power system frequency response function amplitude H (s) only needs once to be stored afterwards by calculated off-line, need the difference according to wind power fluctuation afterwards, use fast Fourier transform (FFT) and inverse fast Fourier transform (IFFT) to calculate the frequency departure of electric power system.Traditional analytical method then needs the frequency departure being analyzed electric power system by numerical solution subordination principle.Obviously the time needed for fast Fourier transform of solving is much smaller than the time solved needed for subordination principle.

The simulation results show correctness of institute's extracting method, and show:

(1) model set up considers generator and governor characteristic, system network architecture to the impact of each nodal frequency response of system, and energy analysis frequency DYNAMIC DISTRIBUTION characteristic, clearly can be analyzed the impact of wind power on frequency departure of different frequency by system point amplitude-frequency characteristic, provide foundation to the filtering before wind power access electrical network;

(2) there is frequency division characteristic in the lower system frequency response of wind power excitation: consistent at the frequency departure of each node of low-frequency range system; The each nodal frequency deviation of Mid Frequency has otherness, and frequency distribution characteristic is obvious, and occurs maximum in this frequency range; High band fluctuation causes the frequency departure of system hardly.When wind power vibration frequency is close to system frequency, the resonance oscillations of system can be evoked, the enlarge-effect of system frequency of occurrences deviation, easily make system frequency out-of-limit, serious threat system stable operation;

(3) for specific system, its natural frequency is relevant with system parameters, amplitude under this frequency is not only by the impact of system parameters, also closely related with factors such as the position of wind power access point and the positions of frequency observation point, for avoiding the resonance oscillations phenomenon of wind power wave excitation system to occur, need the interaction mechanism furtheing investigate wind power fluctuation and system response;

(4) AGC effectively can suppress the system frequency deviation size that wind power fluctuation low-frequency range causes, and is conducive to system frequency and stablizes.

Specific embodiment described herein is only to the explanation for example of the present invention's spirit.Those skilled in the art can make various amendment or supplement or adopt similar mode to substitute to described specific embodiment, but can't depart from spirit of the present invention or surmount the scope that appended claims defines.

Claims (1)

1. the frequency-domain analysis method containing the response of wind-powered electricity generation power system frequency, it is characterized in that, based on the DYNAMIC DISTRIBUTION characteristic of electric power networks medium frequency, set up and comprise generator and speed regulator, network configuration, load dynamically and the electric power system frequency-domain model of AGC, wherein:

Model one: generator model is based on formula

In formula, G _gs transfer function that () is generator model, Δ P _es electromagnetic power that () exports for generator, G _r(s)=1/ (sT _j+ D) represent the generator equation of motion, T _jfor rotor inertia time constant, D is Generator Damping coefficient, G _ts () is speed regulator transfer function, its expression formula is relevant with the speed regulator type of selection;

Model two: network structure model DC power flow is based on formula

In formula, Δ P _efor the input power column vector of synchronous generator node, Δ P _lfor load bus injecting power column vector, wind power fluctuation is regarded as this category node is injected negative load, and Δ δ is the merit angle column vector of generator node, and Δ θ is the phase angle column vector of load bus, B _ee, B _eL, B _le, B _lLfor power system network matrix in block form;

Model three: load fluctuation model is based on formula

ΔP _L1(s)＝K _LP _L0Δω _L(s)

In formula, Δ P _l1s active power column vector that () is load, P _l0for rated load, represent the active power column vector of load under rated frequency, K _lrepresent the frequency regulation characteristics diagonal matrix of load, Δ ω _ls frequency departure column vector that () is load bus;

Model four: AGC model

In formula, G _agcs transfer function that () is AGC, T _agcfor AGC time constant, K _pand K _ifor the adjustment factor of AGC;

Specifically comprise the following steps:

Step 1, according to set up electric power system frequency-domain model, solves the transfer function H (ω) of each nodal frequency response of the lower electric power system of wind power excitation, wherein makes s=j ω, be just converted into H (ω) by H (s);

Wherein the frequency response transfer function of generator node is based on formula

The transfer function of load bus response wind power fluctuation is based on formula

Wherein

H _es frequency response transfer function that () is generator node, Δ ω _es frequency departure column vector that () is generator node, Δ P _winds wind power undulate quantity that () is access point, ω ₀for fundamental frequency angular speed, H _ls () is the transfer function of load bus response wind power fluctuation, Δ ω _ls frequency departure column vector that () is load bus, P _locationrepresent the vector of wind power access point position, define system has n node, its interior joint 1,2,3 ..., m is generator node m altogether, node m+1, m+2 ..., n is load bus n-m altogether, then P _locationfor n-m dimensional vector, have the node that wind power accesses, corresponding vector element gets 1, otherwise is taken as 0;

Step 2, by known wind power time series Δ P _windt () carries out the spectral characteristic Δ P that Fourier transform obtains wind power fluctuation _wind(ω);

Step 3, according to Δ Ω (ω)=H (ω) Δ P _wind(ω) frequency departure frequency-domain result Δ Ω (ω) of electric power system response wind power fluctuation is calculated;

Step 4, carries out Fourier inversion to frequency departure frequency-domain result Δ Ω (ω), calculates power system frequency deviation signal delta ω (t) in the time domain, and then assessment to be fluctuated the power system frequency deviation caused by wind power.