CN101866376A - Distinguishing method of PT ferromagnetic resonance - Google Patents

Abstract

The invention provides a distinguishing method of PT ferromagnetic resonance, which comprises the following steps of: 1, converting a distribution network system containing PT into a simple single-phase serial-parallel connection circuit structure; 2, establishing a mathematical model of nonlinear inductances of a capacitor, a resistor and the PT in the equivalent circuit of the step 1; establishing a time-varying vector based state equation of the nonlinear inductances of the capacitor, the resistor and the PT in the equivalent circuit; 4, converting the state equation in the step 3 into a vector relation between the nonlinear inductances of the capacitor, the resistor and the PT and a magnetic flow; 5, solving the relation among the PT, the total voltage at two ends of the capacitor and the magnetic flow according to the time-varying vector based state equation, and converting vector relation into relation between effective values; 6, defining an energy function and calculating stability margin and disturbance quantity of the distribution network system; and 7, distinguishing the PT ferromagnetic resonance. The PT ferromagnetic resonance is distinguished by comparing the stability margin with the disturbance quantity, which has guidance for operators.

Description

The method of discrimination of PT ferroresonance

Technical field

The invention provides a kind of method of discrimination of PT ferroresonance, belong to the power system security analysis field, be applied to the technology of safety analysis of ferroresonance of the PT of distribution network system and electrical transmission network systems especially.

Background technology

The a great problem that ferroresonance is puzzlement Operation of Electric Systems personnel always takes place in PT, brings enormous economic loss also for vast power supply unit and large-scale electricity consumption enterprise.The PT ferroresonance be since electric system in have many electric capacity and inductance element, all can be used as inductance element as transformer, mutual inductor, generator, arc suppression coil, reactor, line wire inductance etc.; The stray capacitance of the ground capacitance of line wire and alternate electric capacity, building-out capacitor, high-tension apparatus etc. all can be used as capacity cell.When system operates or break down, the oscillation circuit that these electric capacity, inductance element form may produce the ferroresonance phenomenon, what the present invention is directed to is the research of ferroresonance problem, and ferroresonance is the resonance problems of refering in particular to nonlinear inductance equipment and capacitance apparatus.Ferroresonance can cause in the system some part or element superpotential and excess current phenomenon to occur.

At present, ferroresonance has been carried out research extensively and profoundly both at home and abroad, some criterions and corresponding analytical approach have been provided, such as Peterson theorem, graphical method, analytical method, Digital Simulation analytic approach, small echo method of identification, nonlinear dynamic analysis method etc., wherein the Peterson theorem ratio range that provided induction reactance under capacitive reactance of circuit zero sequence and the rated line voltage by a large amount of tests is judged the conclusion of ferroresonance type, and its shortcoming is only to have illustrated that the type of ferroresonance does not illustrate the condition of ferroresonance; Graphical method is directly perceived simple to be understood easily, by figure qualitatively the power frequency ferroresonance is analyzed, and has provided the condition that ferroresonance takes place roughly, and its shortcoming is just to analyze qualitatively and does not have a quantitative analysis; Analytical method filters other frequency power frequency is analyzed by the complex mathematical conversion, the critical condition when having drawn a system generation power frequency ferroresonance, and its shortcoming also is just to analyze and the analysis of non-quantitation qualitatively; Digital Simulation analytic approach, small echo method of identification and nonlinear dynamic analysis method are carried out digital simulation by the mode of utilization simulation software and programming, and the industrial frequency resonance type is analyzed, and its shortcoming is not analyze the condition that resonance takes place.

Can up to now, also there be both at home and abroad the analysis that a kind of method be quantitative and the stability of electric system more in all cases?

Summary of the invention

The purpose of this invention is to provide a kind of can overcome above-mentioned defective, accurately and quantitative decision-making system in the method that suffers can enter under the situation of disturbance the ferroresonance state.Its technical scheme is:

A kind of method of discrimination of PT ferroresonance is characterized in that, may further comprise the steps:

(1) the power distribution net system that contains PT is converted into simple single-phase series or equivalent circuit structure in parallel;

(2) mathematical model of the nonlinear inductance of electric capacity, resistance and the PT in establishment step (1) equivalent electrical circuit;

(3) mathematical model in the step (2) is converted into the state equation of each element based on time-varying vector;

(4) state equation of the time-varying vector in the step (3) is converted into electric capacity, resistance and PT nonlinear inductance the time time variant voltage vector with the time funtcional relationship between the change flux vectors;

Vector function relation when (5) obtaining steady-state operation according to the state equation of time-varying vector in the step (4) between PT and electric capacity two ends total voltage and the magnetic flux concerns the funtcional relationship that is converted to vectorial amplitude to vector function then;

(6) the definition energy function is derived the stability margin of system and the computing formula of disturbance quantity according to energy function;

(7) differentiation of PT ferroresonance state.

The method of discrimination of described PT ferroresonance, in step (1), set up the equivalent electrical circuit of system according to structure, actual parameter, the Thevenin's law of the power distribution net system of the whole PT of containing, finally change into simple single-phase series of system or equivalent circuit structure in parallel.

The method of discrimination of described PT ferroresonance, in step (2), the nonlinear inductance characteristic foundation mathematical model separately according to the electric capacity in the equivalent circuit structure, resistance and PT, specifically be,

The mathematical model of capacity cell is:

The mathematical model of resistive element is: U _R=Ri (1.2)

The mathematical model of PT element is:

In the formula: U _LBe the voltage at PT two ends, U _CBe equivalent capacity both end voltage, U _RBe the equivalent resistance both end voltage, i is the main line electric current, and C is an equivalent capacity, and R is an equivalent resistance,

Magnetic flux for the nonlinear inductance of PT.

The method of discrimination of described PT ferroresonance in step (3), is set up the state equation based on time-varying vector of the nonlinear inductance of electric capacity, resistance and PT in the circuit structure according to the mathematical model in the step (2) and Euler's formula, wherein

Be successively

U _L, U _R, U _CThe vector representation form, specifically be,

1. the time-varying vector equation of PT is:

2. the time-varying vector equation of equivalent resistance:

3. the time-varying vector equation of equivalent capacity:

When system is in steady-state operation, promptly

And can get: the state equation of the time-varying vector of capacitance voltage and electric current according to formula (1.4), formula (1.5) and formula (1.6):

The state equation of the time-varying vector of resistive voltage and electric current:

The state equation of the voltage of the nonlinear inductance of PT and the time-varying vector of magnetic flux:

The method of discrimination of described PT ferroresonance is in step (4), according to the exciting characteristic curve of PT

Ask for the exciting characteristic curve model of time-varying vector

$\stackrel{\·}{I}=G\left(\stackrel{\·}{\mathrm{\Φ}}\right)---\left(1.8\right)$

The expression formula of above-mentioned formula (1.8) is updated in the state in the formula (1.7), obtains the voltage of each element of system and the vector relations between the magnetic flux as shown in the formula (1.9)

${\stackrel{\·}{U}}_L=\mathrm{j\ω}\stackrel{\·}{\mathrm{\Φ}},$ ${\stackrel{\·}{U}}_R=G\left(\stackrel{\·}{\mathrm{\Φ}}\right)R,$ ${\stackrel{\·}{U}}_C=\frac{G\left(\stackrel{\·}{\mathrm{\Φ}}\right)}{\mathrm{j\ωC}}---\left(1.9\right)$

The method of discrimination of described PT ferroresonance, in step (5), we are example with the series circuit, just the analysis of ferroresonance is carried out in the series connection closed-loop path that equivalent source, equivalent resistance, equivalent capacity and PT are formed.The nonlinear inductance two ends total voltage of electric capacity and PT and the vector function between magnetic flux relation when obtaining steady-state operation according to the state equation of time-varying vector concerns that the funtcional relationship that is converted between the amplitude is as shown in the formula (1.10) to vector function

$\mathrm{\ΔU}=\mathrm{\ω\Φ}-\frac{G\left(\mathrm{\Φ}\right)}{\mathrm{\ωC}}---\left(1.10\right)$

The method of discrimination of described PT ferroresonance, in step (6), obtain according to formula (1.10) | Δ U| is about the curve of Ф.If it is E (t)=U that system suffers the voltage before the disturbance ₁, the voltage after the disturbance raises and is E (t)=U ₂, with U ₂Electric pressure is an example, and there are three equilibrium points in system, and wherein A ' is that normal operating point, B ' are that transient stability point, C ' are stable state resonance equilibrium point.According to Fig. 3, the definition energy function

The stability margin S of computing system _DmaxThe time, make S _Dmax=S, a are A ' horizontal ordinate, and b is the horizontal ordinate of B '; During the disturbance quantity of computing system, make S _a=S, a are the horizontal ordinate of A, and b is the horizontal ordinate of A ', and stability margin that can computing system also can calculate the disturbance quantity of system.

The method of discrimination of described PT ferroresonance is in step (7), according to the disturbance quantity S of system _aWith stability margin S _DmaxThe comparison of size judges that can PT enter the ferroresonance state, and its criterion is as follows:

Work as S _a＞S _DmaxThe time, system can enter resonant condition in fault-time when suitable, reaches the ferroresonance equilibrium point, the general rising of electric current this moment is tens times or tens times of primary current, cause apparatus overheat even burn, general two to three times of raising to primary voltage of voltage simultaneously, the insulation that jeopardizes equipment;

Work as S _a＜S _DmaxThe time, system can not enter the ferroresonance state, finally arrives stable equilibrium point A ', only is the influence of the perturbation process of transient state to system, and is less to the influence of system comparatively speaking, relatively safety;

Work as S _a=S _DmaxThe time, system is the critical conditions that ferroresonance takes place.

The present invention compared with prior art, its advantage is: determine that by quantitative mode can system be subjected to entering the ferroresonance state under certain disturbed condition.Time-varying vector mathematical model from system, obtain the electric capacity in the system and the relation of PT two ends total voltage and magnetic flux, define the energy function of voltage then to magnetic flux, obtain the stability margin of system and the size of disturbance quantity by quantitative mode, by relatively the two size so that judge whether system has possessed the condition that enters resonant condition, for the removing method of avoiding of follow-up more deep analysis ferroresonance has proposed crucial theoretical foundation, judged result is accurate, has good practical value.

Description of drawings

Fig. 1 is a principle of work block diagram of the present invention;

Fig. 2 is the circuit diagram of equivalent series circuit of the present invention;

Fig. 3 is the nonlinear inductance of PT and the graph of a relation between electric capacity two ends total voltage and the magnetic flux.

Embodiment

Be example with certain power distribution network below, elaborate specific embodiments of the present invention:

As shown in Figure 1: the PT resonance method of discrimination that the present invention embodied can be realized according to following steps successively: set up system equivalent circuit structure, set up each element of system mathematical model, set up system the state equation based on time-varying vector, the time-varying vector state equation is carried out the stability margin of the conversion of electric current and magnetic flux, the relation of asking for electric capacity and PT two ends total voltage and magnetic flux, computing system and the differentiation that disturbance quantity, the system of making enter ferroresonance.Specifically:

Step 1: set up the equivalent series circuit structure of system, its equivalent series circuit such as Fig. 2, each component parameters sees the following form

Wherein C is the equivalent capacity of circuit, and R is the equivalent resistance of circuit, U ₁The voltage of voltage source before the disturbance, U ₂Be supply voltage after the disturbance, U _BBe voltage reference value, I _BBe current reference value, ω _BReference value for angular frequency.R is the perunit value of R, and c is the perunit value of C, u ₁Be U ₁Perunit value, u ₂Be U ₂Perunit value.

The curve of the excitation property under the PT perunit value is:

Step 2 is set up mathematical model, wherein in the series circuit configuration

The mathematical model of electric capacity:

The mathematical model of resistive element: U _R=Ri (2.2)

The mathematical model of PT element:

Step 3 is set up the state equation based on time-varying vector of system according to the time-varying vector relation of the mathematical model in the step 2, Euler's formula and each element;

${\stackrel{\·}{U}}_L=j\stackrel{\·}{\mathrm{\Φ}},$ ${\stackrel{\·}{U}}_R=0.0026\stackrel{\·}{I},$ $\stackrel{\·}{I}=\mathrm{jC}{\stackrel{\·}{U}}_C---\left(2.4\right)$

Step 4 is according to the exciting characteristic curve of non-linear equipment

Ask for the exciting characteristic curve model of time-varying vector

$\stackrel{\·}{I}=G\left(\stackrel{\·}{\mathrm{\Φ}}\right)=2.8478\stackrel{\·}{\mathrm{\Φ}}-3.2216{\stackrel{\·}{\mathrm{\Φ}}}^3+1.8190{\stackrel{\·}{\mathrm{\Φ}}}^5-0.0868{\stackrel{\·}{\mathrm{\Φ}}}^7---\left(2.5\right)$

The expression formula of above-mentioned formula (2.5) is updated in the vector model in the formula (2.4), obtains the relation between each voltage vector and the flux vectors;

${\stackrel{\·}{U}}_L=\mathrm{j\ω}\stackrel{\·}{\mathrm{\Φ}},$ ${\stackrel{\·}{U}}_R=G\left(\stackrel{\·}{\mathrm{\Φ}}\right)R,$ ${\stackrel{\·}{U}}_C=\frac{G\left(\stackrel{\·}{\mathrm{\Φ}}\right)}{\mathrm{j\ωC}}---\left(2.6\right)$

Relation when step 5 is obtained steady-state operation according to the mathematical model of time-varying vector between the nonlinear inductance of PT and electric capacity two ends total voltage effective value and the magnetic flux effective value;

$\mathrm{\ΔU}=\mathrm{\ω\Φ}-\frac{G\left(\mathrm{\Φ}\right)}{\mathrm{\ωC}}---\left(2.7\right)$

Step 6 definition energy function, and the stability margin of computing system and disturbance quantity

Get by formula (2.5), formula (2.6) and formula (2.7):

Make | Δ U|, u ₁And u ₂About

Curve such as figure two, wherein because R is very little comparatively speaking, then the voltage got of resistance can be ignored, and calculates the stability margin S of system _Dmax=0.0212, disturbance quantity S _a=0.008;

The differentiation of step 7 PT ferroresonance

Result of calculation by step 6 is learnt S _Dmax＞S _a, then in this case, system can not enter resonant condition, the transient state resonant process only occurs, and is less relatively to the harm of system.

Claims (8)

1. the method for discrimination of a PT ferroresonance is characterized in that, may further comprise the steps:

(1) distribution network system that contains PT is converted into simple serial or parallel connection circuit structure;

(2) mathematical model of the nonlinear inductance of electric capacity, resistance and the PT in establishment step (1) equivalent electrical circuit;

(3) set up the state equation based on time-varying vector of the nonlinear inductance of electric capacity, resistance and PT in the equivalent electrical circuit;

(4) state equation in the step (3) is converted into the nonlinear inductance voltage of electric capacity, resistance and PT and the relation between the magnetic flux;

Relation when (5) obtaining steady-state operation according to the state equation of time-varying vector between PT and electric capacity two ends total voltage and the magnetic flux is converted to relation between the effective value to vector relations;

(6) define energy function, and calculate the stability margin and the disturbance quantity of system;

(7) differentiation of PT ferroresonance state.

2. as the method for discrimination of claims 1 described PT ferroresonance, it is characterized in that: in the step (1), set up the equivalent electrical circuit of system according to structure, actual parameter, the Thevenin's law of the power distribution net system of the whole PT of containing, finally change into the circuit structure of the single-phase simple serial or parallel connection of system.

3. as the method for discrimination of claims 1 described PT ferroresonance, it is characterized in that: in the step (2), the nonlinear inductance characteristic foundation mathematical model separately according to the electric capacity in the circuit structure, resistance and PT, specifically be,

The mathematical model of capacity cell is:

The mathematical model of resistive element is: U _R=Ri (1.2)

The mathematical model of PT element is:

In the formula: U _LBe the voltage at PT two ends, U _CBe electric capacity both end voltage, U _RBe the resistance both end voltage, i is the main line electric current, and C is an equivalent capacity, and R is an equivalent resistance, Magnetic flux for the nonlinear inductance of PT.

4. as the method for discrimination of claims 1 described PT ferroresonance, it is characterized in that: in the step (3), set up the state equation based on time-varying vector of the nonlinear inductance of electric capacity, resistance and PT in the circuit structure according to the mathematical model in the step (2) and Euler's formula, wherein Be successively

U _L, U _R, U _CThe vector representation form, specifically be,

1. the time-varying vector equation of PT is:

2. the time-varying vector equation of equivalent resistance:

3. the time-varying vector equation of equivalent capacity:

When system is in steady-state operation, promptly

And can get the state equation of the time-varying vector of capacitance voltage and electric current according to formula (1.4), formula (1.5) and (1.6):

The state equation of the time-varying vector of resistive voltage and electric current:

The state equation of the voltage of the nonlinear inductance of PT and the time-varying vector of electric current:

5. as the method for discrimination of claims 1 described PT ferroresonance, it is characterized in that: in the step (4), according to the exciting characteristic curve of PT

Ask for the exciting characteristic curve model of time-varying vector

$\stackrel{.}{I}=G\left(\stackrel{.}{\mathrm{\Φ}}\right)---\left(1.8\right)$

The expression formula of above-mentioned formula (1.8) is updated in the state in the formula (1.7), obtains the relation between each voltage and the magnetic flux;

${\stackrel{.}{U}}_L=\mathrm{j\ω}\stackrel{.}{\mathrm{\Φ}},$ ${\stackrel{.}{U}}_R=G\left(\stackrel{.}{\mathrm{\Φ}}\right)R,$ ${\stackrel{.}{U}}_C=\frac{G\left(\stackrel{.}{\mathrm{\Φ}}\right)}{\mathrm{j\ωC}}---\left(1.9\right).$

6. as the method for discrimination of claims 1 described PT ferroresonance, it is characterized in that: in the step (5), we are example with the series circuit, equivalent source, equivalent resistance, equivalent capacity and PT are followed in series to form a closed-loop path, it is carried out the analysis of ferroresonance, the nonlinear inductance two ends total voltage of electric capacity and PT and the relation between the magnetic flux when obtaining steady-state operation according to the state equation of time-varying vector are converted to relation following (1.10) formula between the amplitude to vector relations

$\mathrm{\ΔU}=\mathrm{\ω\Φ}-\frac{G\left(\mathrm{\Φ}\right)}{\mathrm{\ωC}}---\left(1.10\right)$

7. as the method for discrimination of claims 1 described PT ferroresonance, it is characterized in that: in the step (6), obtain according to (1.10) formula | Δ U| is about the curve of Φ, according to the definition of the voltage before and after disturbance energy function

Utilize the stability margin of energy function define system and the notion of disturbance quantity then, and calculate the stability margin S of system _DmaxWith disturbance quantity S _a, when the stability margin of computing system, make S _Dmax=S; When the disturbance quantity of computing system, make S _a=S.

8. as the method for discrimination of claims 1 described PT ferroresonance, it is characterized in that: in the step (7),, judge that can PT enter the ferroresonance state, can obtain to draw a conclusion according to the comparison of the disturbance quantity and the stability margin size of system:

Work as S _a＞S _DmaxThe time, system can enter resonant condition in fault-time when suitable, reaches the ferroresonance equilibrium point, the general rising of electric current this moment is tens times or tens times of primary current, cause apparatus overheat even burn, general two to three times of raising to primary voltage of voltage simultaneously, the insulation that jeopardizes equipment;

Work as S _a＜S _DmaxThe time, system can not enter the ferroresonance state, finally arrives stable equilibrium point A ', only is the influence of the perturbation process of transient state to system, and is less to the influence of system comparatively speaking, relatively safety;

Work as S _a=S _DmaxThe time, system is the critical conditions that ferroresonance takes place.

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