CN1185496C - Method for pure electrical measuring no-load potential phasor of synchronous electric generator - Google Patents

Abstract

The present invention relates to a pure electrical measurement method for measuring the zero load potential phasor of a synchronous generator, which belongs to the technical fields of electric power systems and the automation thereof. The method relates to the dynamic behavior characteristics of the synchronous generator, and accordingly has high measuring accuracy in a stable state operational process and a transient state (comprises secondary transient state) operational process of the synchronous generator. The method is characterized in that the method comprises the following steps: the values of output phase voltages and output phase currents are collected by an interval of delta T; for data in every new sampling period, the following steps are executed: positive sequence transformation is adopted for obtaining the real parts and the imaginary parts of positive sequence components of the voltages and the currents; the effective values and the output electromagnetism power of the voltages are calculated; a Park equation model is adopted for describing the dynamic process of the synchronous generator, establishing a practical measuring dynamic model, and calculating the zero load potential phasor of the synchronous generator; in the secondary transient state process that a system suffers great disturbance, a load angle is further corrected. Proved by practice, the zero load potential phasor measured by the method has high accuracy in the stable state process and the transient state process.

Description

A kind of pure electric measurement method of synchronous generator no-load emf phasor

Technical field

A kind of pure electric measurement method of synchronous generator no-load emf phasor belongs to the Power System and its Automation technical field.

Background technology

No-load emf E _qAnd phasing degree (being also referred to as rotor electrical angle, merit angle) δ (below be referred to as no-load emf phasor E _q∠ δ) is the important parameter that characterizes the synchronous generator running status and differentiate stability of power system.For many years, numerous research workers have explored measuring of the method that can accurately measure it, particularly merit angle δ always and have paid attention to widely and deep research.In recent years, along with the theoretical research of phasor measurement unit (PMU, Phasor Measurement Unit) and carrying out in a deep going way of application, the measurement of no-load emf phasor is had more importance and urgency.

Existing measuring method is divided into two big classes from principle: class methods realize measuring by non electrical quantity sensor (comprising photoelectricity or magnetoelectricity conversion).The common practice is, mechanical measuring point or measure speed gears are set on armature spindle, photoelectricity or calutron are installed on peritrochanteric, the latter receives the pulse signal that is produced by the former or utilizes electromagnetic induction principle to obtain the amount of certain and rotor-position or velocity correlation, and then realizes the measurement at merit angle by certain conversion.These class methods often need the generator body is carried out in various degree transformation, complex process, and, need signal Processing and Error Compensation Technology by means of more complicated owing to adopt the non electrical quantity sensor, to remove various structural errors, from measurement data, to obtain required characteristic quantity; And, be difficult to be applicable to other generator at the case proposition, cause realizing that cost is bigger.Another kind is pure electric measurement method, and the output voltage, electric current of promptly gathering synchronous generator be or/and other electric parameters, and then by theoretical analysis with calculate and obtain the amplitude of no-load emf or/and the merit angle.The advantage of this method is not contain non-electric sensor, universalization degree height, realize that cost is low.The realization technology that a kind of typical case of these class methods also is simultaneously simplification is based on the analytical Calculation method of motor steady-state operation equation or phasor graph, when it moves at systematic steady state, can calculate the no-load emf phasor more exactly, but in system's transient state process, because the analytic formula that method relied on is untenable, causes the bigger error of calculation.As, according to Simulation results, in the transient state process after generator end generation three phase short circuit fault, its measuring error can reach 50%.

Summary of the invention

The object of the present invention is to provide a kind of pure electric measurement method of synchronous generator no-load emf phasor, this method has been taken into account the dynamic behaviour characteristic of synchronous generator, thereby all has higher measuring accuracy in the stable state of motor and transient state (comprising time transient state) operational process.

The present invention is a kind of pure electric measurement method of synchronous generator no-load emf phasor, comprises the Park equation model of describing the synchronous generator dynamic process, it is characterized in that the method includes the steps of:

At first carry out initialization of variable:

N: AC sampling is counted, the integer greater than 12;

Δ T: in the AC sampling cycle, initial value is the 20/N millisecond, can adopt the sampling of fixed sampling interval technique or changing distance;

The initial zero clearing of each sampling buffer;

With Δ T is the value of gathering output phase voltage and output current phase at interval, converts them to per unit value, when sampling number is less than N, then continues to wait for new sampled point; When sampling number is more than or equal to N, whenever obtain a new sampled point, it and preceding N-1 sampled point form a new sampling period;

To the N point data in each new sampling period, order is carried out following steps;

1) adopt the positive sequence conversion to ask for the positive-sequence component real part and the imaginary part of voltage, electric current; And the sampled data of utilizing the new sampling period is used integral mean method calculating voltage effective value U _iWith output electromagnetic power P _e

2) adopt the Park equation model to describe the dynamic process of synchronous generator, establish on its rotor d-axis (also claiming the d axle) and comprise field copper and damping winding, hand over axle (also claiming the q axle) to comprise two damping winding, the q axle is leading d axle 90 degree on electric phase place; Ignore the influence of stator winding transient state process, rotation speed change to the influence of speed electromotive force and damping winding electric current to no-load emf amplitude E _qWith d axle transient potential increment Delta E ' _dInfluence, set up the practical dynamic model of measuring, this model comprises:

A. Δ E ' _dDynamic process adopt following transport function to describe, wherein input is I _q, output is Δ E ' _d:

${\mathrm{\ΔE}}_d^{\′}=-(X_q-X_q^{\′})(1-\frac{1}{1+{\mathrm{sT}}_{q0}})I_q;$

X _q: the reactance of q axle, adopt per unit value to represent;

X ' _q: q axle subtranient reactance, adopt per unit value to represent;

T _Q0: q axle open circuit time constant, unit are second;

I _q: rotor q shaft current, adopt per unit value to represent;

B.E _q, E ' _qRepresent by following simultaneous equations with the relation of θ:

E _qsinθ＝E′ _qsinθ+(X _d-X′ _d)I _dsinθ，

E _qcosθ＝E′ _qcosθ+(X _d-X′ _d)I _dcosθ，

E′ _qsinθ＝ΔE′ _dcosθ-A+(X′ _d-X _q)sinθ[cosθI _r+sinθI _i]，

E′ _qcosθ＝-ΔE′ _dsinθ+B+(X′ _d-X _q)cosθ[cosθI _r+sinθI _i]，

Parameter A wherein, B is defined as follows:

A＝U _r+RI _r-X _qI _i，

B＝U _i+X _qI _r+RI _i；

R: stator winding resistance, adopt per unit value to represent;

U _r: the real part of terminal voltage positive-sequence component, adopt per unit value to represent;

U _i: the imaginary part of terminal voltage positive-sequence component, adopt per unit value to represent;

I _r: the real part of output current positive-sequence component, adopt per unit value to represent;

I _i: the imaginary part of output current positive-sequence component, adopt per unit value to represent;

E ' _q: q axle transient potential, adopt per unit value to represent;

ω: angular frequency, adopt per unit value to represent;

ω ₀: specified angular frequency, for the 50Hz system, constant is 100 π radian per seconds;

θ: the absolute value of the electric anglec of rotation of no-load emf vector, unit is a radian, that is: $\mathrm{\θ}={\∫}_{t_0}^t{\mathrm{\ω}}_0\mathrm{\ωdt}+{\mathrm{\θ}}_0,$ θ wherein ₀Be corresponding t ₀Initial value constantly;

I _d: rotor d shaft current, adopt per unit value to represent;

X _d: the reactance of d axle, adopt per unit value to represent;

X ' _d: d axle subtranient reactance, adopt per unit value to represent.

3) measure the no-load emf phasor E that dynamic model calculates synchronous generator according to the practicality of synchronous generator _q∠ δ;

4) utilize and practically to measure no-load emf phasor that dynamic model calculates and in the transient state of synchronous generator and steady-state process, have excellent precision, but after system suffers big disturbance, last tens of to hundreds of milliseconds inferior transient state process, the measurement at merit angle has certain error, needs further to revise measured value.

The practicality according to synchronous generator in the described step 3) is measured dynamic model and is calculated the no-load emf phasor, comprises the steps:

A. calculating parameter A, B:

A＝U _r+RI _r-X _qI _i，

B＝U _r+X _qI _r+RI _i；

B. making the d axle transient potential increment of current time temporarily is the value of last sampled point, i.e. Δ E ' _d(t)=Δ E ' _d(t-Δ T), cycle counter Counter=0;

C. cancellation E ' from following simultaneous equations _q:

E′ _qsinθ＝ΔE′ _dcosθ-A+(X′ _d-X _q)sinθ[cosθI _r+sinθI _i]，

E′ _qcosθ＝-ΔE′ _dsinθ+B+(X′ _d-X _q)cosθ[cosθI _r+sinθI _i]，

Obtain equation Acos θ+Bsin θ=Δ E ' _d

If its discriminant $A^{}$ ${}^2+B^2-{\mathrm{\&Delta;E}}_d^{\&prime;2}<0,$ Then make Δ E ' _d=0, Counter is that maximum cycle adds 1, from equation Acos θ+Bsin θ=Δ E ' _dIn solve sin θ and cos θ;

If its discriminant $A^{}$ ${}^2+B^2-{\mathrm{\&Delta;E}}_d^{\&prime;2}\&GreaterEqual;0,$ Then can be from equation Acos θ+Bsin θ=Δ E ' _dIn solve sin θ and cos θ;

After obtaining sin θ and cos θ, calculate E ' according to aforementioned simultaneous equations _qSin θ and E ' _qCos θ;

D. calculate q shaft current I according to the Parker transform _q(t), computing formula is: $I_q\left(t\right)=-\frac{2}{3}[i_a\sin \mathrm{\&theta;}+i_b\sin (\mathrm{\&theta;}-\frac{2}{3}\mathrm{\&pi;})+i_c\sin (\mathrm{\&theta;}+\frac{2}{3}\mathrm{\&pi;})],$ i _a, i _b, i _cBe the synchronous generator output current signal;

E. make Δ E ' temporarily _d(t) ₀=Δ E ' _d(t), according to Δ E ' _dThe dynamic process transport function, utilize numerical method to upgrade

Wherein input is I _q, output is Δ E ' _d:

${\mathrm{\&Delta;E}}_d^{\&prime;}=-(X_q-X_q^{\&prime;})(1-\frac{1}{1+{\mathrm{sT}}_{q0}})I_q;$

If Δ E ' _d(t) with Δ E ' _d(t) ₀Between error exceed maximum cycle less than limits of error η or Counter value, then continue next step f, otherwise, make Counter increase 1, go to step c; Wherein, described limits of error η is 10 ^-4, described maximum cycle is 10;

F. according to Parker transformation calculations d shaft current I _d(t), computing formula is:

$I_d=\frac{2}{3}[i_a\cos \mathrm{\&theta;}+i_b\cos (\mathrm{\&theta;}-\frac{2}{3}\mathrm{\&pi;})+i_c\cos (\mathrm{\&theta;}+\frac{2}{3}\mathrm{\&pi;})],$

i _a, i _b, i _cBe the synchronous generator output current signal, and then calculate E according to following formula _qSin θ and E _qCos θ: E _qSin θ=E ' _qSin θ+(X _d-X ' _d) I _dSin θ, E _qCos θ=E ' _qCos θ+(X _d-X ' _d) I _dCos θ;

G. with E _qSin θ and E _qCos θ sequence multiply by modulates complex carrier signal e ^{-j ω reft}, and ask the mean value of its one-period, and obtain corresponding two vectors, be made as C ₁+ JD ₁, C ₂+ jD ₂Wherein the CALCULATION OF PARAMETERS formula is as follows:

${\mathrm{<figure-callout\; id="1"\; label="C"\; filenames="C0213095500211.png"\; state="\{\{state\}\}">C</figure-callout>}}_1=\frac{2}{T}{\&Integral;}_{t-T}^t\left[E_q\sin \mathrm{\&theta;}\left(\mathrm{\&tau;}\right)\right]\&CenterDot;\sin {\mathrm{\&theta;}}_{\mathrm{ref}}\left(\mathrm{\&tau;}\right)\mathrm{d\&tau;},$

${\mathrm{<figure-callout\; id="1"\; label="D"\; filenames="C0213095500211.png"\; state="\{\{state\}\}">D</figure-callout>}}_1=\frac{2}{T}{\&Integral;}_{t-T}^t\left[E_q\sin \mathrm{\&theta;}\left(\mathrm{\&tau;}\right)\right]\&CenterDot;\cos {\mathrm{\&theta;}}_{\mathrm{ref}}\left(\mathrm{\&tau;}\right)\mathrm{d\&tau;},$

${\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="C0213095500201.png,C0213095500211.png"\; state="\{\{state\}\}">C</figure-callout>}}_2=\frac{2}{T}{\&Integral;}_{t-T}^t\left[E_q\cos \mathrm{\&theta;}\left(\mathrm{\&tau;}\right)\right]\&CenterDot;\sin {\mathrm{\&theta;}}_{\mathrm{ref}}\left(\mathrm{\&tau;}\right)\mathrm{d\&tau;},$

${\mathrm{<figure-callout\; id="2"\; label="D"\; filenames="C0213095500201.png,C0213095500211.png"\; state="\{\{state\}\}">D</figure-callout>}}_2=\frac{2}{T}{\&Integral;}_{t-T}^t\left[E_q\cos \mathrm{\&theta;}\left(\mathrm{\&tau;}\right)\right]\&CenterDot;\cos {\mathrm{\&theta;}}_{\mathrm{ref}}\left(\mathrm{\&tau;}\right)\mathrm{d\&tau;},$

T=2 π/ω wherein _Ref

In assumed condition | Δ ω |＜＜ω _RefThink E in [t-T, the t] period down, _qConstant with δ, and make t ₀Constantly, θ _Ref0=0, then following relational expression is set up: E _q=| C ₁+ jD ₁|, δ=arg (C ₁+ jD ₁), E _q=| C ₂+ jD ₂|, δ=arg (C ₂+ jD ₂)-90 °;

Wherein || the mould of expression vector, the angle of arg () expression vector;

ω _Ref: system angle frequency reference value, adopt per unit value to represent, can get and make systematic steady state/specified angular frequency or center of inertia angular frequency;

Δ ω=ω-ω _Ref: angular frequency deviation, adopt per unit value to represent;

θ _Ref: the reference value of the electric anglec of rotation of no-load emf vector, unit is a radian, and ${\mathrm{\&theta;}}_{\mathrm{ref}}={\&Integral;}_{t_0}^t{\mathrm{\&omega;}}_0{\mathrm{\&omega;}}_{\mathrm{ref}}\mathrm{dt}+{\mathrm{\&theta;}}_{\mathrm{ref}0},$ θ wherein _Ref0Be corresponding t ₀Initial value constantly;

δ=θ-θ _Ref: the relative value of the electric anglec of rotation of no-load emf vector, i.e. merit angle, unit is a radian;

Get E _q=(| C ₁+ jD ₁|+| C ₂+ jD ₂|)/2, δ=[arg (C ₁+ jD ₁)+arg (C ₂+ jD ₂)-90 °]/2, thereby the no-load emf phasor E of synchronous generator obtained _q＜δ.

In the pure electric measurement method of synchronous generator no-load emf phasor, the method for revising the measuring power angle value may further comprise the steps:

At first, order is δ (t) according to the merit angle that the practical measurement of synchronous generator dynamic model calculates ₀

Secondly, wave equation according to generator, promptly following transport function equation with numerical calculations angular frequency deviation Δ ω, wherein is input as P _e, be output as Δ ω:

$\mathrm{\&Delta;\&omega;}=-\frac{{\mathrm{sT}}_w}{(2\mathrm{Hs}+D)(1+s{T}_w)}{P}_e,$

T wherein _wBe that a value is 2～10 seconds a time constant;

H: inertia constant, unit is second;

D: ratio of damping, no unit;

Utilize the integral mean method to calculate output electromagnetic power P by the sampled data of nearest one-period _e, computing formula is:

$P_e=\frac{1}{N}\underset{k=0}{\overset{k=N-1}{\mathrm{\&Sigma;}}}[u_a(t-\mathrm{k\&Delta;T})i_a(t-\mathrm{k\&Delta;T})+u_b(t-\mathrm{k\&Delta;T})i_b(t-\mathrm{k\&Delta;T})+u_c(t-\mathrm{k\&Delta;T})i_c(t-\mathrm{k\&Delta;T})],k=\mathrm{0,1},...,N-1;$

Wherein, synchronous generator output phase voltage u _a, u _b, u _c, current i _a, i _b, i _cSignal forms the sampled point sequence, and t is current sampling instant, and k is the numbering of sample sequence, and that k=0 represents is nearest, be t sampled point constantly;

Once more, calculate a coefficient lambda that shows the current running status of system away from inferior transient state degree, the method of calculating λ is: λ → 0 expression system is in time transient state process, inferior transient state process after λ → 1 expression disturbance finishes, (0,1] the reflection running status that λ can be level and smooth between is away from the degree of inferior transient state, and concrete computing formula is as follows:

${\mathrm{\&Delta;U}}_t\left(t\right)=\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}|U_t\left(t\right)-U_t(t-i\&CenterDot;\mathrm{\&Delta;T})|/\left({\mathrm{MU}}_{t,\mathrm{ref}}\right),$

${\mathrm{\&lambda;}}^{\&prime;}\left(t\right)={\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="C0213095500211.png"\; state="\{\{state\}\}">k</figure-callout>}}_1\&CenterDot;e^{-{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="C0213095500201.png,C0213095500211.png"\; state="\{\{state\}\}">k</figure-callout>}}_2\&CenterDot;{\mathrm{\&Delta;U}}_t\left(t\right)},$

λ(t)＝min{1，λ′(t)}，

Integer wherein $M\&ap;2\max (T_{d0}^{\&prime;\&prime;},T_{q0}^{\&prime;\&prime;})/\mathrm{\&Delta;T};$

U _{T, ref}: the reference value of terminal voltage, adopt per unit value to represent;

T " _Q0: q axle open circuit time transient state time constant, unit is second;

T " _D0: d axle open circuit time transient state time constant, unit is second;

Determine coefficient k ₁, k ₂Method be: when the variation value is in the static error scope that allows, promptly | Δ U _t(t) |＜1% o'clock, λ ' was (t) in 0.95～1 scope; When the variation value exceeds the dynamic error scope of permission, promptly | Δ U _t(t) |＞20% o'clock, λ ' was (t) in 0＜λ ' scope (t)≤0.01;

At last, revise the merit angle:

If λ (t)=1 would make merit angle nonce δ ' (t)=δ (t) ₀, otherwise make δ ' (t)=δ ' (t-Δ T)+ω ₀Δ ω Δ T;

And then calculate the merit angle: δ (t)=λ δ (t) according to following formula ₀+ (1-λ) δ ' (t),

Obtain the no-load emf phasor E of synchronous generator time transient state process _q∠ δ.

Coefficient k ₁Preferred value be 1.5, k ₂Preferred value be 40.

Operate in software in the Industrial PC Computer and realized the pure electric measurement method of this synchronous generator no-load emf phasor, in steady-state process, at the parameter of electric machine accurately under the prerequisite, when sampling rate during for 48 in ripple weekly, the steady-state error that algorithm itself causes is no more than 2%; In the inferior transient state process in 300 milliseconds under the generator output rating after the serious disturbance of generation, when sampling rate during for 48 in ripple weekly, the Algorithm Error of measuring power angle is no more than 10%, and in 300 milliseconds of transient state processes in addition after disturbance, the Measurement Algorithm error is no more than 5%.As seen, the pure electric measurement method of this synchronous generator no-load emf phasor all has higher measuring accuracy in the stable state of motor and transient state (comprising time transient state) operational process

Description of drawings

Fig. 1 is for realizing a cover measurement mechanism synoptic diagram of the present invention.

Fig. 2 is the main program block diagram of the embodiment of the invention.

Fig. 3 is for calculating E ' _qSin θ, E ' _qThe subroutine block diagram of cos θ.

Fig. 4 is for upgrading Δ E ' _d(t) subroutine block diagram.

Fig. 5 is for calculating E _qSubroutine block diagram with δ.

The subroutine block diagram of Fig. 6 for merit angle δ is revised.

Embodiment

The pure electric measurement method of the synchronous generator no-load emf phasor that the present invention puts forward can adopt the multiple hardwares scheme to realize, this example is introduced a kind of measuring system that realizes based on Industrial PC Computer more intuitively, comprises relevant hardware configuration and software flow.

The hardware configuration of measuring system comprises Industrial PC Computer as shown in Figure 1, ABC threephase potential transformer (PT) summation current transformer (CT), and from the A/D capture card on the Industrial PC Computer of being installed in of the secondary side of little PT and little CT output image data.

Synchronous generator outlet bus place, PT and CT be measuring machine end ABC three-phase voltage and electric current respectively, obtains ± the interior ac voltage signal of 120V scope, delivers to little PT and little CT, is converted to ± the interior voltage signal of 5V scope by it; The A/D capture card carries out low-pass filtering, AC sampling and digital-to-analog conversion with little PT and little CT secondary side voltage signal, and the digital signal that obtains is transferred to Industrial PC Computer CPU by pci bus, handle by corresponding software programs, finish the measurement of no-load emf phasor, and then output to user's monitoring interface.

Measuring method proposed by the invention mainly is embodied on the software that operates in the Industrial PC Computer, the master routine of software as shown in Figure 2,

Measuring method may further comprise the steps:

1. initialization

A. the parameter of pointing out the user must want from the computer interface input comprises the synchronous generator parameter: stator winding resistance R, q axle reactance X _q, d axle reactance X _d, q axle subtranient reactance X ' _q, d axle subtranient reactance X ' _d, q axle open circuit time constant T _Q0, q axle open circuit time transient state time constant T " _Q0, d axle open circuit time transient state time constant T " _D0, inertia constant H, ratio of damping D, the specified angular frequency of system ₀, the system reference angular frequency _Ref(default value is ω ₀); If input is famous value, then the user also must provide voltage base value U _BaseWith power base value S _Base, the famous value that Automatic Program will be correlated with changes into per unit value, and conversion formula is: per unit value=famous value/base value.The selection of base value is according to voltage base value U _BaseBe the specified phase voltage of generator, power base value S _BaseBe the generator rated capacity, electric current base value I _Base=P _Base/ (3U _Base), the impedance base value $Z_{\mathrm{base}}={3U}_{\mathrm{base}}^2/S_{\mathrm{base}},$ The base value of angular frequency is ω ₀The R=0.0181 Ω of system in this example, $U_{\mathrm{base}}=13.8/\sqrt{3}\mathrm{kV},$ S _Base=30/0.95MVA, the then base value of impedance $Z_{\mathrm{base}}=U_{\mathrm{base}}^2/S_{\mathrm{base}}=6.0306\mathrm{\&Omega;},$ The per unit value of R is 0.0181/6.0306=0.003.

B. the sampling number N that points out the user to set every power frequency period (50Hz system), this routine N=48 represents every power frequency period (20 milliseconds) sampling 48 points, thus sampling interval Δ T=20/48 millisecond.

C. point out the relevant configured parameter of user's input measurement device, comprising: (this example is the PT no-load voltage ratio $(13.8/\sqrt{3})\mathrm{kV}/120V)$ , CT no-load voltage ratio (this example is 600A/120V), little PT no-load voltage ratio (this example is 120V/5V), little CT no-load voltage ratio (this example is 120V/5V), filtering scale-up factor (this example is 0.95) and A/D conversion coefficient (this example is 5V/3FFFh) etc.

D. parameter initialization in the algorithm: d axle transient potential increment initial value Δ E ' _d(0)=0, calculates rotor q shaft current initial value I _q(0); Each sampling buffer zero clearing:

u _a(t-kΔT)＝0，u _b(t-kΔT)＝0，u _c(t-kΔT)＝0，

i _a(t-kΔT)＝0，i _b(t-kΔT)＝0，i _c(t-kΔT)＝0，k＝0，...，N-1，

They are used for circulating and deposit the synchronous generator output phase voltage u that collects _a, u _b, u _c, current i _a, i _b, i _cSignal forms the sampled point sequence, and wherein t is current sampling instant, and k is the numbering of sample sequence, and that k=0 represents is nearest, be t sampled point constantly.

2. under the driving of AC sampling data, carry out following link successively:

A. obtain new sampling number certificate from A/D sampling card, at first they are marked change, that is: consider the factors such as no-load voltage ratio, filtering scale-up factor and A/D conversion coefficient of PT/CT and little PT/CT, the digital quantity that obtains is converted to the actual physics value of synchronous generator outlet bus place correspondence, again according to formula: per unit value=famous value/base value obtains corresponding per unit value.

After obtaining the per unit value of voltage, electric current, with one of the value of voltage/current sample sequence pusher successively, nearest sampled point leaves on the data point of k=0 correspondence.

B. when sampling number is less than N, then continue to wait for new sampled point, otherwise, whenever obtaining a new sampled point, it and preceding N-1 sampled point form a new sampling period; To the N point data in each new sampling period, order is carried out following steps and is measured calculating.

1) calculates following parameter.

A. utilize the positive sequence conversion to ask for the real part and the imaginary part of the positive-sequence component of voltage, electric current, be respectively U _r, U _iAnd I _r, I _i, computing formula is:

$U_r=2/3u_a-1/3u_b-1/{3u}_c,U_i=1/\sqrt{3}(u_b-u_c),$

$I_r=2/3i_a-1/3i_b-1/{3i}_c,I_i=1/\sqrt{3}(i_b-i_c).$

B. utilize integral mean method calculating voltage effective value U by the sampled data of nearest one-period _iWith output electromagnetic power P _e, computing formula is:

$U_t=\sqrt{\frac{1}{3N}\underset{k=0}{\overset{k=N-1}{\mathrm{\&Sigma;}}}[u_a^2(t-\mathrm{k\&Delta;T})+u_b^2(k-\mathrm{k\&Delta;T})+u_c^2(t-\mathrm{k\&Delta;T})]},k=\mathrm{0,1},...,N-1;$

$P_e=\frac{1}{N}\underset{k=0}{\overset{k=N-1}{\mathrm{\&Sigma;}}}[u_a(t-\mathrm{k\&Delta;T})i_a(t-\mathrm{k\&Delta;T})+u_b(t-\mathrm{k\&Delta;T})i_b(t-\mathrm{k\&Delta;T})+u_c(t-\mathrm{k\&Delta;T})i_c(t-\mathrm{k\&Delta;T})],k=\mathrm{0,1},...,N-1;$

2) establish on the rotor d axle of synchronous generator and comprise field copper and damping winding, the q axle comprises two damping winding, ignores the influence of stator winding transient state process, rotation speed change to the influence of speed electromotive force and damping winding electric current to no-load emf amplitude E _qWith d axle transient potential increment Delta E ' _dInfluence, set up the practical dynamic model of measuring:

A. Δ E ' _dDynamic process adopt following transport function to describe, wherein input is I _q, output is Δ E ' _d:

${\mathrm{\&Delta;E}}_d^{\&prime;}=-(X_q-X_q^{\&prime;})(1-\frac{1}{1+{\mathrm{sT}}_{q0}})I_q;$

B.E _q, E ' _qRepresent by following simultaneous equations with the relation of θ:

E _qsinθ＝E′ _qsinθ+(X _d-X′ _d)I _dsinθ，

E _qcosθ＝E′ _qcosθ+(X _d-X′ _d)I _dcosθ，

E′ _qsinθ＝ΔE′ _dcosθ-A+(X′ _d-X _q)sinθ[cosθI _r+sinθI _i]，

E′ _qcosθ＝-ΔE′ _dsinθ+B+(X′ _d-X _q)cosθ[cosθI _r+sinθI _i]，

Parameter A wherein, B is defined as follows:

A＝U _r+RI _r-X _qI _i，

B＝U _i+X _qI _r+RI _i；

E ' _q: q axle transient potential, adopt per unit value to represent;

ω: angular frequency, adopt per unit value to represent;

θ: the absolute value of the electric anglec of rotation of no-load emf vector, unit is a radian, that is: $\mathrm{\&theta;}={\&Integral;}_{t_0}^t{\mathrm{\&omega;}}_0\mathrm{\&omega;dt}+{\mathrm{\&theta;}}_0,$ θ wherein ₀Be corresponding t ₀Initial value constantly;

3) measure the no-load emf phasor E that dynamic model calculates synchronous generator according to the practicality of synchronous generator _q∠ δ:

3.1) calculating parameter A, B

A＝U _r+RI _r-X _qI _i，

B＝U _i+X _qI _r+RI _i；

3.2) to make the d axle transient potential increment of current time temporarily be the value of last sampled point, i.e. Δ E ' _d(t)=Δ E ' _d(t-Δ T), counter Counter=0; Maximum cycle is 10 in this example.

3.3) cancellation E ' from following simultaneous equations _q:

E′ _qsinθ＝ΔE′ _dcosθ-A+(X′ _d-X _q)sinθ[cosθI _r+sinθI _i]，

E′ _qcosθ＝-ΔE′ _dsinθ+B+(X′ _d-X _q)cosθ[cosθI _r+sinθI _i]，

Obtain equation Acos θ+Bsin θ=Δ E ' _d, therefrom solve sin θ and cos θ.

As shown in Figure 3,

If $A^2+B^2-{\mathrm{\&Delta;E}}_d^{\&prime;2}<0,$ Then make Δ E ' _d=0,

Counter=11;

If $A^2+B^2-{\mathrm{\&Delta;E}}_d^{\&prime;2}\&GreaterEqual;0,$ Then

Calculate sin θ and cos θ according to x:

sinθ＝2x/(1+x ²)，cosθ＝(1-x ²)/(1+x ²)。

Note, when x=∞, sin θ=0, cos θ=-1.

And then according to above-mentioned simultaneous equations formula calculating E ' _qSin θ, E ' _qCos θ.

3.4) according to Parker transformation calculations q shaft current I _q(t), computing formula is:

$I_q\left(t\right)=-\frac{2}{3}[i_a\sin \mathrm{\&theta;}+i_b\sin (\mathrm{\&theta;}-\frac{2}{3}\mathrm{\&pi;})+i_c\sin (\mathrm{\&theta;}+\frac{2}{3}\mathrm{\&pi;})].$

3.5) make Δ E ' temporarily _d(t) ₀=Δ E ' _d(t), according to Δ E ' _dThe dynamic process transport function, utilize numerical method to upgrade Δ E ' _d(t), as shown in Figure 4, wherein input is I _q, output is Δ E ' _d:

${\mathrm{\&Delta;E}}_d^{\&prime;}=-(X_q-X_q^{\&prime;})(1-\frac{1}{1+{\mathrm{sT}}_{q0}})I_q;$

Promptly calculate according to following formula successively, obtain new Δ E ' _d(t), z wherein, pz is a temporary variable.

z(t-ΔT)＝ΔE′ _d(t-ΔT)/(X _q-X′ _q)+I _q(t-ΔT)，

pz(t-ΔT)＝1/T _q0[z(t-ΔT)-I _q(t-ΔT)]，

z(t)＝ΔE′ _d(t)/(X _q-X′ _q)+I _q(t)，

pz(t)＝1/T _q0[z(t)-I _q(t)]，

z(t)＝z(t-ΔT)+[pz(t-ΔT)+pz(t)]/2·ΔT，

ΔE _d(t)＝-(X _q-X′ _q)[I _q(t)-z(t)]；

If | Δ E ' _d(t)-Δ E ' _d(t) _o| (η is the limits of error to＜η, and this example gets 10 ^-4) or Counter＞10 item continue next step 3.6), otherwise, make Counter=Counter+1, go to 3.3);

3.6) according to Parker transformation calculations d shaft current I _d(t), computing formula is:

$I_q\left(t\right)=\frac{2}{3}[i_a\cos \mathrm{\&theta;}+i_b\cos (\mathrm{\&theta;}-\frac{2}{3}\mathrm{\&pi;})+i_c\cos (\mathrm{\&theta;}+\frac{2}{3}\mathrm{\&pi;})];$

And then according to following formula calculating E _qSin θ and E _qCos θ:

E _qsinθ＝E′ _qsinθ+(X _d-X′ _d)I _dsinθ，

E _qcosθ＝E′ _qcosθ+(X _d-X′ _d)I _dcosθ。

3.7) calculating E _qAnd δ, its subroutine block diagram as shown in Figure 5:

A. with E _qSin θ and E _qCos θ sequence multiply by modulates complex carrier signal e ^{-j ω reft}, and ask the mean value of its one-period, and obtain corresponding two vectors, be made as C ₁+ jD ₁, C ₂+ jD ₂, wherein the CALCULATION OF PARAMETERS formula is as follows:

${\mathrm{<figure-callout\; id="1"\; label="C"\; filenames="C0213095500211.png"\; state="\{\{state\}\}">C</figure-callout>}}_1=\frac{2}{T}{\&Integral;}_{t-T}^t\left[E_q\sin \mathrm{\&theta;}\left(\mathrm{\&tau;}\right)\right]\&CenterDot;\sin {\mathrm{\&theta;}}_{\mathrm{ref}}\left(\mathrm{\&tau;}\right)\mathrm{d\&tau;},$

${\mathrm{<figure-callout\; id="1"\; label="D"\; filenames="C0213095500211.png"\; state="\{\{state\}\}">D</figure-callout>}}_1=\frac{2}{T}{\&Integral;}_{t-T}^t\left[E_q\sin \mathrm{\&theta;}\left(\mathrm{\&tau;}\right)\right]\&CenterDot;\cos {\mathrm{\&theta;}}_{\mathrm{ref}}\left(\mathrm{\&tau;}\right)\mathrm{d\&tau;},$

${\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="C0213095500201.png,C0213095500211.png"\; state="\{\{state\}\}">C</figure-callout>}}_2=\frac{2}{T}{\&Integral;}_{t-T}^t\left[E_q\cos \mathrm{\&theta;}\left(\mathrm{\&tau;}\right)\right]\&CenterDot;\sin {\mathrm{\&theta;}}_{\mathrm{ref}}\left(\mathrm{\&tau;}\right)\mathrm{d\&tau;},$

${\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="C0213095500201.png,C0213095500211.png"\; state="\{\{state\}\}">C</figure-callout>}}_2=\frac{2}{T}{\&Integral;}_{t-T}^t\left[E_q\cos \mathrm{\&theta;}\left(\mathrm{\&tau;}\right)\right]\&CenterDot;\cos {\mathrm{\&theta;}}_{\mathrm{ref}}\left(\mathrm{\&tau;}\right)\mathrm{d\&tau;},$

T=2 π/ω wherein _Ref

B. in multi-machine power system, because the relative value at merit angle is just meaningful, at its definition δ=θ-θ _RefIn, θ _RefTo choose mainly be to decide on convenient, it can be taken as certain with reference to the rotor electrical angle of unit or the equivalent phasing degree of system inertia center (COI), or even the integration of stable state (specified) angular frequency.Because $\mathrm{\&theta;}={\&Integral;}_{t_0}^t{\mathrm{\&omega;}}_0\mathrm{\&omega;dt}+{\mathrm{\&theta;}}_0,$ ${\mathrm{\&theta;}}_{\mathrm{ref}}={\&Integral;}_{t_0}^t{\mathrm{\&omega;}}_0{\mathrm{\&omega;}}_{\mathrm{ref}}\mathrm{dt}+{\mathrm{\&theta;}}_{\mathrm{ref}0},$ Thereby $\mathrm{\&delta;}={\&Integral;}_{t_0}^t{\mathrm{\&omega;}}_0\mathrm{\&Delta;\&omega;}\mathrm{dt}+{\mathrm{\&theta;}}_0-{\mathrm{\&theta;}}_{\mathrm{ref}0}.$ Make t ₀Constantly, θ _Ref0=0, then $\mathrm{\&delta;}={\&Integral;}_{t_0}^t{\mathrm{\&omega;}}_0\mathrm{\&Delta;\&omega;}\mathrm{dt}+{\mathrm{\&theta;}}_0.$ In assumed condition | Δ ω |＜＜ω _RefThink E in [t-T, the t] period down, _qConstant with δ, thus there is following relational expression:

C ₁＝E _qcosδ，D ₁＝E _qsinδ；C ₂＝-E _qsinδ，D ₂＝E _qcosδ；

By C ₁(C ₂) be real part, D ₁(D ₂) for imaginary part constitutes vector, then have:

E _q＝|C ₁+jD ₁|，δ＝arg(C ₁+jD ₁)，

E _q＝|C ₂+jD ₂|，δ＝arg(C ₂+jD ₂)-90°；

Wherein || the mould of expression vector, the angle of arg () expression vector; Get:

E _q＝(|C ₁+jD ₁|+|C ₂+jD ₂|)/2，δ＝[arg(C ₁+jD ₁)+arg(C ₂+jD ₂)-90°]/2；

Thereby obtain the no-load emf phasor E of synchronous generator _q∠ δ.

4) the no-load emf phasor E that obtains according to above-mentioned steps _q∠ δ has excellent precision in the transient state of synchronous generator and steady-state process; But after system suffers big disturbance, last tens ofly to hundreds of milliseconds inferior transient state processes, the measurement at merit angle has certain error, needs further correction measured value, the subroutine block diagram that merit angle δ is revised as shown in Figure 6:

A. making the merit angle that calculates according to the practical measurement of synchronous generator dynamic model is δ (t) ₀

B. wave equation according to generator, promptly following transport function equation with numerical calculations angular frequency deviation Δ ω, wherein is input as P _e, be output as Δ ω:

$\mathrm{\&Delta;\&omega;}=-\frac{{\mathrm{sT}}_w}{(2\mathrm{Hs}+D)(1+s{T}_w)}{P}_e,$

T wherein _wBe that a value is 2～10 seconds a time constant;

C. calculate one and show that the current running status of system is made as λ away from the coefficient of inferior transient state degree.The method of calculating λ is: λ → 0 expression system is in time transient state process, inferior transient state process after λ → 1 expression disturbance finishes substantially, [0,1] λ can smoothly hang down the reflection running status away from inferior transient state degree between, can adopt parameters such as voltage, inferior transient state time constant in the λ computing method.The λ computing method that this example adopts are as follows:

${\mathrm{\&Delta;U}}_t\left(t\right)=\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}|U_t\left(t\right)-U_t(t-i\&CenterDot;\mathrm{\&Delta;T})|/\left({\mathrm{MU}}_{t,\mathrm{ref}}\right),$

${\mathrm{\&lambda;}}^{\&prime;}\left(t\right)={\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="C0213095500211.png"\; state="\{\{state\}\}">k</figure-callout>}}_1\&CenterDot;e^{-{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="C0213095500201.png,C0213095500211.png"\; state="\{\{state\}\}">k</figure-callout>}}_2\&CenterDot;{\mathrm{\&Delta;U}}_t\left(t\right)},{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="C0213095500211.png"\; state="\{\{state\}\}">k</figure-callout>}}_1=1.5,{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="C0213095500201.png,C0213095500211.png"\; state="\{\{state\}\}">k</figure-callout>}}_2=40,$

λ(t)＝min{1，λ′(t)}：

Integer wherein $M\&ap;2\max (T_{d0}^{\&prime;\&prime;},T_{q0}^{\&prime;\&prime;})/\mathrm{\&Delta;T};$

D. revise the merit angle:

If λ (t)=1 would make merit angle nonce δ ' (t)=δ (t) ₀, otherwise make δ ' (t)=δ ' (t-Δ T)+ω ₀Δ ω Δ T;

And then according to following formula correction merit angle:

δ(t)＝λδ(t) ₀+(1-λ)δ′(t)，

Obtain the no-load emf phasor E of synchronous generator time transient state process _q∠ δ.

Above-mentioned measuring method all can obtain very high precision at inferior transient state, transient state and the steady-state process of synchronous generator, and can be on the monitor of Industrial PC Computer dynamic refresh measurement result E _q∠ δ.

Claims (4)

1. the pure electric measurement method of a synchronous generator no-load emf phasor comprises the Park equation model of describing the synchronous generator dynamic process, it is characterized in that the method includes the steps of:

At first carry out initialization of variable:

N: AC sampling is counted, the integer greater than 12;

Δ T: in the AC sampling cycle, initial value is the 20/N millisecond, can adopt the sampling of fixed sampling interval technique or changing distance;

The initial zero clearing of each sampling buffer;

With Δ T is the value of gathering output phase voltage and output current phase at interval, converts them to per unit value, when sampling number is less than N, then continues to wait for new sampled point; When sampling number is more than or equal to N, whenever obtain a new sampled point, it and preceding N-1 sampled point form a new sampling period;

To the N point data in each new sampling period, order is carried out following steps;

1) adopt the positive sequence conversion to ask for the positive-sequence component real part and the imaginary part of voltage, electric current; And the sampled data of utilizing the new sampling period is used integral mean method calculating voltage effective value U _tWith output electromagnetic power P _e

2) adopt the Park equation model to describe the dynamic process of synchronous generator, establish on its rotor d axle and comprise field copper and damping winding, the q axle comprises two damping winding, and the q axle is leading d axle 90 degree on electric phase place; Ignore the influence of stator winding transient state process, rotation speed change to the influence of speed electromotive force and damping winding electric current to no-load emf amplitude E _qWith d axle transient potential increment Delta E ' _dInfluence, set up the practical dynamic model of measuring, this model comprises:

A. Δ E ' _dDynamic process adopt following transport function to describe, wherein input is I _q, output is Δ E ' _d:

$\mathrm{\&Delta;}{E}_d^{\&prime;}=-(X_q-X_q^{\&prime;})(1-\frac{1}{1+s{T}_{q0}})I_q;$

X _q: the reactance of q axle, adopt per unit value to represent;

X ' _q: q axle subtranient reactance, adopt per unit value to represent;

T _Q0: q axle open circuit time constant, unit are second;

I _q: rotor q shaft current, adopt per unit value to represent;

B.E _q, E ' _qRepresent by following simultaneous equations with the relation of θ:

E _q?sinθ＝E′ _qsinθ+(X _d-X′ _d)I _d?sinθ，

E _q?cosθ＝E′ _qcosθ+(X _d-X′ _d)I _d?cosθ，

E′ _qsinθ＝ΔE′ _dcosθ-A+(X′ _d-X _q)sinθ[cosθI _r+sinθI _i]，

E′ _qcosθ＝ΔE′ _dsinθ+B+(X′ _d-X _q)cosθ[cosθI _r+sinθI _i]，

Parameter A wherein, B is defined as follows:

A＝U _r+RI _r-X _qI _i，

B＝U _i+X _qI _r+RI _i；

R: stator winding resistance, adopt per unit value to represent;

U _r: the real part of terminal voltage positive-sequence component, adopt per unit value to represent;

U _t: the imaginary part of terminal voltage positive-sequence component, adopt per unit value to represent;

I _r: the real part of output current positive-sequence component, adopt per unit value to represent;

I _i: the imaginary part of output current positive-sequence component, adopt per unit value to represent;

E ' _q: q axle transient potential, adopt per unit value to represent;

ω: angular frequency, adopt per unit value to represent;

ω ₀: specified angular frequency, for the 50Hz system, constant is 100 π radian per seconds;

θ: the absolute value of the electric anglec of rotation of no-load emf vector, unit is a radian, that is: $\mathrm{\&theta;}={\&Integral;}_{t_0}^t{\mathrm{\&omega;}}_0\mathrm{\&omega;}+\mathrm{dt}+{\mathrm{\&theta;}}_0,$ θ wherein ₀Be corresponding t ₀Initial value constantly;

I _d: rotor d shaft current, adopt per unit value to represent;

X _d: the reactance of d axle, adopt per unit value to represent;

X ' _d: d axle subtranient reactance, adopt per unit value to represent;

3) measure the no-load emf phasor E that dynamic model calculates synchronous generator according to the practicality of synchronous generator _q∠ δ;

4) utilize and practically to measure no-load emf phasor that dynamic model calculates and in the transient state of synchronous generator and steady-state process, have excellent precision, but after system suffers big disturbance, last tens of to hundreds of milliseconds inferior transient state process, the measurement at merit angle has certain error, needs further to revise measured value.

2. the pure electric measurement method of synchronous generator no-load emf phasor according to claim 1 is characterized in that dynamic model calculating no-load emf phasor is measured in the practicality according to synchronous generator in the described step 3), comprises the steps:

A. calculating parameter A, B:

A＝U _r+RI _r-X _qI _i，

B＝U _i+X _qI _r+RI _i；

B. making the d axle transient potential increment of current time temporarily is the value of last sampled point, i.e. Δ E ' _d(t)=Δ E ' _d(t-Δ T), cycle counter Counter=0;

C. cancellation E ' q from following simultaneous equations:

E′ _q?sinθ＝ΔE′ _d?cosθ-A+(X′ _d-X _q)sinθ[cosθI _r+sinθI _i]，

E′ _q?cosθ＝-ΔE′ _d?sinθ+B+(X′ _d-X _q)cosθ[cosθI _r+sinθI _i]，

Obtain equation Acos θ+Bsin θ=Δ E ' _d

If its discriminant $A^2+B^2-\mathrm{\&Delta;}{E}_d^{\&prime;2}<0,$ Then make Δ E ' _d=0, Counter is that maximum cycle adds 1, from equation Acos θ+Bsin θ=Δ E ' _dIn solve sin θ and cos θ;

If its discriminant $A^2+B^2-\mathrm{\&Delta;}{E}_d^{\&prime;2}\&GreaterEqual;0,$ Then can be from equation Acos θ+Bsin θ=Δ E ' _dIn solve sin θ and cos θ; After obtaining sin θ and cos θ, calculate E ' according to aforementioned simultaneous equations _qSin θ and E ' _qCos θ;

D. calculate q shaft current I according to the Parker transform _q(t), computing formula is: $I_q\left(t\right)=-\frac{2}{3}[i_a\sin \mathrm{\&theta;}+i_b\sin (\mathrm{\&theta;}-\frac{2}{3}\mathrm{\&pi;})+i_c\sin (\mathrm{\&theta;}+\frac{2}{3}\mathrm{\&pi;})],$ i _a, i _b, i _cBe the synchronous generator output current signal;

E. make Δ E ' temporarily _d(t) ₀=Δ E ' _d(t), according to Δ E ' _dThe dynamic process transport function, utilize numerical method to upgrade Δ E ' _d(t), wherein input is I _q, output is Δ E ' _d:

$\mathrm{\&Delta;}{E}_d^{\&prime;}=-(X_q-X_q^{\&prime;})(1-\frac{1}{1+s{T}_{q0}})I_q;$

If Δ E ' _d(t) with Δ E ' _d(t) ₀Between error exceed maximum cycle less than limits of error η or Counter value, then continue next step f, otherwise, make Counter increase 1, go to step c; Wherein, described limits of error η is 10 ^-4, described maximum cycle is 10;

F. according to Parker transformation calculations d shaft current I _d(t), computing formula is: $I_d=\frac{2}{3}[i_a\cos \mathrm{\&theta;}+i_b\cos (\mathrm{\&theta;}+\frac{2}{3}\mathrm{\&pi;})+i_c\cos (\mathrm{\&theta;}+\frac{2}{3}\mathrm{\&pi;})],$ i _a, i _b, i _cBe the synchronous generator output current signal, and then calculate E according to following formula _qSin θ and E _qCos θ: E _qSin θ=E ' _qSin θ+(X _d-X ' _d) I _dSin θ, E _qCos θ=E ' _qCos θ+(X _d-X ' _d) I _dCos θ;

G. with E _qSin θ and E _qCos θ sequence multiply by modulates complex carrier signal e ^{-j ω reft}, and ask the mean value of its one-period, and obtain corresponding two vectors, be made as C ₁+ jD ₁, C ₂+ jD ₂Wherein the CALCULATION OF PARAMETERS formula is as follows:

$C_1=\frac{2}{T}{\&Integral;}_{t-T}^t\left[E_q\sin \mathrm{\&theta;}\left(\mathrm{\&tau;}\right)\right]\&CenterDot;\sin {\mathrm{\&theta;}}_{\mathrm{ref}}\left(\mathrm{\&tau;}\right)\mathrm{d\&tau;},$

$C_1=\frac{2}{T}{\&Integral;}_{t-T}^t\left[E_q\sin \mathrm{\&theta;}\left(\mathrm{\&tau;}\right)\right]\&CenterDot;\sin {\mathrm{\&theta;}}_{\mathrm{ref}}\left(\mathrm{\&tau;}\right)\mathrm{d\&tau;},$

$C_2=\frac{2}{T}{\&Integral;}_{t-T}^t\left[E_q\cos \mathrm{\&theta;}\left(\mathrm{\&tau;}\right)\right]\&CenterDot;\sin {\mathrm{\&theta;}}_{\mathrm{ref}}\left(\mathrm{\&tau;}\right)\mathrm{d\&tau;},$

$D_2=\frac{2}{T}{\&Integral;}_{t-T}^t\left[E_q\cos \mathrm{\&theta;}\left(\mathrm{\&tau;}\right)\right]\&CenterDot;\cos {\mathrm{\&theta;}}_{\mathrm{ref}}\left(\mathrm{\&tau;}\right)\mathrm{d\&tau;},$

T=2 π/ω wherein _Ref

In assumed condition | Δ ω |＜＜ω _RefThink E in [t-T, the t] period down, _qConstant with δ, and make t ₀Constantly, θ _Ref0=0, then following relational expression is set up:

E _q＝|C ₁+jD ₁|，δ＝arg(C ₁+jD ₁)，E _q＝|C ₂+jD ₂|，δ＝arg(C ₂+jD ₂)-90°；

Wherein || the mould of expression vector, the angle of arg () expression vector;

ω _Ref: system angle frequency reference value, adopt per unit value to represent, can get and make systematic steady state/specified angular frequency or center of inertia angular frequency;

Δ ω=ω-ω _Ref: angular frequency deviation, adopt per unit value to represent;

θ _Ref: the reference value of the electric anglec of rotation of no-load emf vector, unit is a radian, and ${\mathrm{\&theta;}}_{\mathrm{ref}}={\&Integral;}_{t_0}^t{\mathrm{\&omega;}}_0{\mathrm{\&omega;}}_{\mathrm{ref}}\mathrm{dt}+{\mathrm{\&theta;}}_{\mathrm{ref}0},$ θ wherein _Ref0Be corresponding t ₀Initial value constantly;

δ=θ-θ _Ref: the relative value of the electric anglec of rotation of no-load emf vector, i.e. merit angle, unit is a radian;

Get E _q=(| C ₁+ jD ₁|+| C ₂+ jD ₂|)/2, δ=[arg (C ₁+ jD ₁)+arg (C ₂+ jD ₂)-90 °]/2, thereby the no-load emf phasor E of synchronous generator obtained _q∠ δ.

3. the pure electric measurement method of synchronous generator no-load emf phasor according to claim 1 is characterized in that may further comprise the steps the method for the described correction measuring power angle value in the step 4):

At first, order is δ (t) according to the merit angle that the practical measurement of synchronous generator dynamic model calculates ₀

Secondly, wave equation according to generator, promptly following transport function equation with numerical calculations angular frequency deviation Δ ω, wherein is input as P _e, be output as Δ ω:

$\mathrm{\&Delta;\&omega;}=-\frac{s{T}_w}{(2\mathrm{Hs}+D)(1+s{T}_w)}{P}_e,$

T wherein _wBe that a value is 2～10 seconds a time constant;

H: inertia constant, unit is second;

D: ratio of damping, no unit;

Utilize the integral mean method to calculate output electromagnetic power P by the sampled data of nearest one-period _e, computing formula is:

$P_e=\frac{1}{N}\underset{k=0}{\overset{k=N-1}{\mathrm{\&Sigma;}}}[u_a(t-\mathrm{k\&Delta;T})i_a(t-\mathrm{k\&Delta;T})+u_b(t-\mathrm{k\&Delta;T})i_b(t-\mathrm{k\&Delta;T})+u_c(t-\mathrm{k\&Delta;T})i_c(t-\mathrm{k\&Delta;T})],k=\mathrm{0,1}...,N-1;$

Wherein, synchronous generator output phase voltage u _a, u _b, u _c, current i _a, i _b, i _cSignal forms the sampled point sequence, and t is current sampling instant, and k is the numbering of sample sequence, and that k=0 represents is nearest, be t sampled point constantly;

Once more, calculate a coefficient lambda that shows the current running status of system away from inferior transient state degree, the method of calculating λ is: λ → 0 expression system is in time transient state process, inferior transient state process after λ → 1 expression disturbance finishes, (0,1] the reflection running status that λ can be level and smooth between is away from the degree of inferior transient state, and concrete computing formula is as follows:

$\mathrm{\&Delta;}{U}_t\left(t\right)=\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}|U_t\left(t\right)-U_t(t-i\&CenterDot;\mathrm{\&Delta;T})|/\left(M{U}_{t,\mathrm{ref}}\right),$

${\mathrm{\&lambda;}}^{\&prime;}\left(t\right)=k_1\&CenterDot;e^{-k_2\&CenterDot;\mathrm{\&Delta;}{U}_t\left(t\right)},$

λ(t)＝min{1，λ′(t)}，

Wherein integer M ≈ 2max (T " _D0, T " _Q0)/Δ T;

U _{T, ref}: the reference value of terminal voltage, adopt per unit value to represent;

T " _Q0: q axle open circuit time transient state time constant, unit is second;

T " _D0: d axle open circuit time transient state time constant, unit is second;

Determine coefficient k ₁, k ₂Method be: when the variation value is in the static error scope that allows, promptly | Δ U _t(t) |＜1% o'clock, λ ' was (t) in 0.95～1 scope; When the variation value exceeds the dynamic error scope of permission, promptly | Δ U _t(t) |＞20% o'clock, λ ' was (t) in 0＜λ ' scope (t)≤0.01;

At last, revise the merit angle:

If λ (t)=1 would make merit angle nonce δ ' (t)=δ (t) ₀, otherwise make δ ' (t)=δ ' (t-Δ t)+ω ₀Δ ω Δ T; And then calculate the merit angle according to following formula:

δ(t)＝λδ(t) ₀+(1-λ)δ′(t)，

Obtain the no-load emf phasor E of synchronous generator time transient state process _q∠ δ.

4. the pure electric measurement method of synchronous generator no-load emf phasor according to claim 3 is characterized in that coefficient k ₁Be 1.5, k ₂Be 40.

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