CN104820751A - Method for analyzing small signal stability of aircraft electric power system based on generalized state space averaging - Google Patents

Abstract

The invention relates to a method for analyzing small signal stability of an aircraft electric power system based on generalized state space averaging, comprising the steps as follows: establishing a power flow equation of the aircraft electric power system according to the structure of the aircraft electric power system, and determining the steady state working point of the aircraft electric power system; establishing an equivalent circuit for modeling the generalized state space averaging of the aircraft electric power system to obtain a nolinear differential equation of the aircraft electric power system; determining the state variable of the nolinear differential equation, and obtaining a generalized state space averaging model described by a fourier coefficient via Fourier decomposition; judging the small signal stability of the aircraft electric power system via calculating according to the model. The method of the invention realizes the analysis of small signal stability of the aircraft electric power system in different states, and realizes the sensitivity analysis of the small signal stability, which provides valuable suggestions for designing and improving the electric power system in large aircraft manufacturing process, and simultaneously provides reliable operation information of the aircraft electric power system for the flight crew.

Description

Based on the aircraft electrical power system small disturbed stability analytical approach of generalized state space average

Technical field

The present invention relates to a kind of aircraft electrical power system small disturbed stability analytical approach, particularly relate to a kind of aircraft electrical power system small disturbed stability analytical approach based on generalized state space average, by taking Fourier coefficient as the state matrix analysis of state variable, aircraft electrical power system small disturbance stability accurately can be realized and judge.

Background technology

For economize energy, the performance reducing costs and improve mobile system, present generation aircraft adopts electric energy to replace hydraulic pressure, the air pressure energy in conventional airplane more and more, and the load by the machinery of engine Direct driver, hydraulic pressure and pneumatic actuation is replaced by and electrically drives load." how electric aircraft (MoreElectric the Aircraft) " concept proposed thus, has become the main trend of airplane industry development.Along with the development of how electric aircraft and increasingly mature, the importance of aircraft electrical power system in aircraft highlights day by day.Aircraft electrical power system comprises consumer three part on aircraft power system, flight sequencing, machine: aircraft power system is equipment combination machine being used for produce electric energy, comprises primary power, accessory power supply, emergency power pack and secondary power supply etc.; Flight sequencing be machine is used for transmit, distributes, conversion and control the combination that the equipment of electric energy and cable undertake by certain way, also claim aircraft electrical network, mainly comprise electric power transmission lead and cable, prevent wire and equipment by the control of the protective device of short circuit or damages of overloading, power distribution equipment, secondary power supply, consumer and conversion equipment and power check instrument etc.; On machine, consumer refers to and relies on electric workable equipment.

Along with coming into operation of the how electric aircraft such as B787, A380, the safe and stable operation problem of aircraft electrical power system have also been obtained increasing attention, and its stability, once wreck, will cause huge economic loss and catastrophic effect.The airplane fault caused due to aircraft electrical power system problem happens occasionally, and as the core of how electric aircraft, the safe and stable operation of aircraft electrical power system is then further important.Due to aircraft electrical power system multi-machine parallel connection, multiple transformer is crosslinked, electrical load character is various, aircraft electrical power system is caused to be a higher-dimension Complex Nonlinear System, its stability not only affects by conventional electric power element dynamic perfromance, and closely related with the dynamic perfromance of power electronic equipment.Simultaneously, because the running environment of aircraft electrical power system varies, aircraft electrical power system operation state is caused to there is very big-difference, therefore be necessary that the mathematical model setting up its dynamic perfromance of reflection also carries out stability analysis based on this, realize aircraft electrical power system determination of stability fast and accurately under normal and fault condition, and determine each component links of aircraft electrical power system electrically and controling parameters to the influence degree of System Small Disturbance, finally the design of electric system in large aircraft manufacturing and improvement are offered suggestions.

Summary of the invention

For the problems referred to above, the object of the present invention is to provide a kind of aircraft electrical power system small disturbed stability analytical approach based on generalized state space average, the small disturbance stability sex determination demand under aircraft electrical power system Different Dynamic characteristic can be realized.

For achieving the above object, the technical solution used in the present invention is to provide a kind of aircraft electrical power system small disturbed stability analytical approach based on generalized state space average, described generalized state space average is exactly take Fourier coefficient as a kind of space average of state variable, and the method comprises the following steps:

1) according to aircraft electrical power system structure, set up the alternating current-direct current mixed current equation of power supply in aircraft electrical power system, distribution system, using electricity system, determine the steady operation point of aircraft electrical power system;

$\frac{V_{\mathrm{bus}}{V}_s}{Z}\cos ({\mathrm{\γ}}_Z-\mathrm{\λ})-\frac{V_{\mathrm{bus}}^2}{Z}\cos \left({\mathrm{\γ}}_Z\right)=(P+P_{\mathrm{loss}})/3$

$\frac{V_{\mathrm{bus}}{V}_s}{Z}\sin ({\mathrm{\γ}}_Z-\mathrm{\λ})-\frac{V_{\mathrm{bus}}^2}{Z}\sin \left({\mathrm{\γ}}_Z\right)=Q$

In formula: V _sfor three-phase alternating voltage effective value, V _busfor AC voltage steady-state value, namely vertoro AC input voltage value, λ are phase differential, the Z ∠ γ between above-mentioned two voltages _zfor transmission line of alternation current impedance, comprise the referring reactance of transformer, P, Q be respectively constant power load active power, reactive power, P _lossfor the power attenuation produced due to DC side circuit

2) to step 1) aircraft electrical power system carries out circuit equivalent, and the circuit after equivalence is used for the modeling of generalized state space average, and obtains the nonlinear differential equation of aircraft electrical power system according to this equivalent electrical circuit:

$\stackrel{\·}{x}=\mathrm{\Ψx}+\mathrm{\Γu}$

Wherein, x=[x ₁, x ₂..., x _n] ^tfor system state variables, Ψ is system state variables matrix, is n × n rank matrix, u=[u ₁, u ₂..., u _m] ^tfor system algebraic variable, Γ is system algebraic variable matrix, is n × m rank matrix;

3) according to step 2) nonlinear differential equation of aircraft electrical power system that obtains, determine aircraft electrical power system power-supply system, distribution system, using electricity system nonlinear differential equation state variable, in state variable, aperiodic state variable r is individual, cycle status variable s, and Fourier decomposition is carried out to state variable, according to the Fourier coefficient <x obtained _i> _k(τ), new state variable matrix Q is introduced, Q=[q ₁, q ₂..., q _r+2ks] ^t, each element of Q matrix is as follows:

During 0<i≤r, <x _i> ₀(τ)=q _i

During r<i≤n, <x _i> _k(τ)=q _{2s (k-1)+(2i-r-1)}+ jq _{2s (k-1)+(2i-r)}

4) to step 2) in the nonlinear differential equation of aircraft electrical power system carry out Fourier decomposition, and by step 3) the state variable matrix Q that obtains substitutes into, and finally obtains the aircraft electrical power system generalized state space average equation that Fourier coefficient describes:

$\stackrel{\&CenterDot;}{Q}=\mathrm{AQ}+\mathrm{BY}+U_x=f(Q,Y,U_x)$

In formula: Q represents the system state variables matrix that Fourier coefficient describes, and A represents Fourier coefficient state variable matrix of coefficients, and Y is the output of this link nonlinear differential equation, and its size affects the dynamic perfromance of next link, and B is the matrix of coefficients of Y, U _xfor system cloud gray model controling parameters;

5) according to step 4) the aircraft electrical power system generalized state space average equation that obtains, in step 1) steady operation point place's linearization of aircraft electrical power system of obtaining, obtain the system matrix A of the state equation of linearized system:

6) calculation procedure 5) eigenwert of system matrix that obtains, computing formula is as follows:

det[λI-A]＝0

In formula: A is the system matrix of state equation, I is unit matrix, and λ is eigenwert to be asked.

According to the small disturbed stability of the positive negative judgement aircraft electrical power system of eigenwert real part, the operational parameter control of change system, and according to eigenwert in complex plane with the variation tendency of system cloud gray model controling parameters, if eigenwert is in the left-sided system of the complex plane imaginary axis, be stable, be then unstable in imaginary axis right-sided system, in order to judge that the change of aircraft electrical power system operational parameter control affects small disturbed stability.

The effect that the present invention reaches is this method for analyzing stability, compared to the time-domain-simulation method that can not embody extent of stability, and do not consider the State-space Averaging Principle of aircraft electrical power system dynamic perfromance, realize the small disturbed stability analysis under aircraft electrical power system Different Dynamic, the sensitivity analysis of small disturbance stability can be realized simultaneously, the final design to electric system in large aircraft manufacturing and improvement provide value proposition, can be crew simultaneously and provide reliable aircraft electrical power system operation information

Accompanying drawing explanation

Fig. 1 is aircraft electrical power system sma1l signal stability process flow diagram of the present invention;

Fig. 2 is certain how electric aircraft electrical power system structure diagram;

Fig. 3 is aircraft electrical power system alternating current-direct current Load flow calculation line chart;

Fig. 4 is certain how electric airplane electric system generalized state space average modelled equivalent circuit diagram.

Embodiment

Below in conjunction with drawings and Examples, the aircraft electrical power system small disturbed stability analytical approach based on generalized state space average of the present invention is further illustrated.

Fig. 1 is aircraft electrical power system sma1l signal stability process flow diagram.

Aircraft electrical power system small disturbed stability analytical approach based on generalized state space average of the present invention, described generalized state space average is exactly take Fourier coefficient as a kind of space average of state variable, and the method comprises the following steps:

1) according to aircraft electrical power system structure, set up the alternating current-direct current mixed current equation of power supply in aircraft electrical power system, distribution system, using electricity system, determine the steady operation point of aircraft electrical power system;

$\frac{V_{\mathrm{bus}}{V}_s}{Z}\cos ({\mathrm{\&gamma;}}_Z-\mathrm{\&lambda;})-\frac{V_{\mathrm{bus}}^2}{Z}\cos \left({\mathrm{\&gamma;}}_Z\right)=(P+P_{\mathrm{loss}})/3$

$\frac{V_{\mathrm{bus}}{V}_s}{Z}\sin ({\mathrm{\&gamma;}}_Z-\mathrm{\&lambda;})-\frac{V_{\mathrm{bus}}^2}{Z}\sin \left({\mathrm{\&gamma;}}_Z\right)=Q$

In formula: V _sfor three-phase alternating voltage effective value, V _busfor AC voltage steady-state value, namely vertoro AC input voltage value, λ are phase differential, the Z ∠ γ between above-mentioned two voltages _zfor transmission line of alternation current impedance, comprise the referring reactance of transformer, P, Q be respectively constant power load active power, reactive power, P _lossfor the power attenuation produced due to DC side circuit.

2) to step 1) aircraft electrical power system carries out circuit equivalent, and the circuit after equivalence is used for the modeling of generalized state space average, and obtains the nonlinear differential equation of aircraft electrical power system according to this equivalent electrical circuit:

$\stackrel{\&CenterDot;}{x}=\mathrm{\&Psi;x}+\mathrm{\&Gamma;u}$

Wherein, x=[x ₁, x ₂..., x _n] ^tfor system state variables, Ψ is system state variables matrix, is n × n rank matrix, u=[u ₁, u ₂..., u _m] ^tfor system algebraic variable, Γ is system algebraic variable matrix, is n × m rank matrix.

3) according to step 2) nonlinear differential equation of aircraft electrical power system that obtains, determine aircraft electrical power system power-supply system, distribution system, using electricity system nonlinear differential equation state variable, in state variable, aperiodic state variable r is individual, cycle status variable s, and Fourier decomposition is carried out to state variable, according to the Fourier coefficient <x obtained _i> _k(τ), new state variable matrix Q is introduced, Q=[q ₁, q ₂..., q _r+2ks] ^t, each element of Q matrix is as follows:

During 0<i≤r, <x _i> ₀(τ)=q _i

During r<i≤n, <x _i> _k(τ)=q _{2s (k-1)+(2i-r-1)}+ jq _{2s (k-1)+(2i-r)}.

4) to step 2) in the nonlinear differential equation of aircraft electrical power system carry out Fourier decomposition, and by step 3) the state variable matrix Q that obtains substitutes into, and finally obtains the aircraft electrical power system generalized state space average equation that Fourier coefficient describes:

$\stackrel{\&CenterDot;}{Q}=\mathrm{AQ}+\mathrm{BY}+U_x=f(Q,Y,U_x)$

In formula: Q represents the system state variables matrix that Fourier coefficient describes, and A represents Fourier coefficient state variable matrix of coefficients, and Y is the output of this link nonlinear differential equation, and its size affects the dynamic perfromance of next link, and B is the matrix of coefficients of Y, U _xfor system cloud gray model controling parameters.

5) according to step 4) the aircraft electrical power system generalized state space average equation that obtains, in step 1) steady operation point place's linearization of aircraft electrical power system of obtaining, obtain the system matrix A of the state equation of linearized system:

6) calculation procedure 5) eigenwert of system matrix that obtains, computing formula is as follows:

det[λI-A]＝0

In formula: A is the system matrix of state equation, I is unit matrix, and λ is eigenwert to be asked.

According to the small disturbed stability of the positive negative judgement aircraft electrical power system of eigenwert real part, the operational parameter control of change system, and according to eigenwert in complex plane with the variation tendency of system cloud gray model controling parameters, if eigenwert is in the left-sided system of the complex plane imaginary axis, be stable, be then unstable in imaginary axis right-sided system, in order to judge that the change of aircraft electrical power system operational parameter control affects small disturbed stability.

Described step 1) the middle aircraft electrical power system alternating current-direct current mixed current equation set up, for exchanging the equation of aerogenerator, transmission line of alternation current, wave filter, vertoro, DC power transmission line, the foundation of inversion link based on 400Hz, the voltage steady-state value of vertoro AC is calculated based on described equation, again according to the ac-dc conversion relation of described vertoro, obtain the steady state voltage value V of vertoro DC side under different capacity P, Q _out.

Described step 2) in set up the equivalent electrical circuit for aircraft electrical power system generalized state spatial modeling and aircraft electrical power system nonlinear differential equation, be based on three phase static abc coordinate system, comprise the alternating current-direct current hybrid equivalent circuit that 400Hz exchanges aerogenerator, transmission line of alternation current, wave filter, vertoro, DC power transmission line link.

Described step 4) in the Generalized State Space Averaging model of aircraft electrical power system that obtains, for comprising the Generalized State Space Averaging model of aircraft electrical power system dynamic perfromance, and the working condition that the dynamic perfromance of aircraft electrical power system is run with aircraft and moment adjustment.

Described step 5) system matrix of state equation of neutral line system is the dynamic perfromance according to aircraft electrical power system, with different rank Fourier coefficient for state variable obtains.

The dynamic perfromance of aircraft electrical power system is started with aircraft, slide, take off, climb, cruise, decline, the operating mode of landing and moment adjustment, comprise that component-level is dynamic, behavioral scaling is dynamic, functional level is dynamic, the dynamic four kinds of levels of structural level, described component-level dynamically refers to the internal dynamics of power electronic devices in aircraft electrical power system, electromagnetic actuator; Described behavioral scaling dynamically refers to that the switch that composition aircraft electrical power system vertoro, chopper, inverter produce in work process is dynamic; Described functional level has dynamically referred to aircraft startup, landing, anti-icing, defrost function, the electric motor starting that aircraft electrical power system carries out, stopping, changing load, switching dynamic behaviour; Described structural level dynamically refers to that the NETWORK STRUCTURE PRESERVING POWER SYSTEM of taking off, climb, cruise, landing produced that aircraft is the different mission phase of reply switches dynamic perfromance.

In described step 6) in, effect characteristics value system cloud gray model controling parameters of variation tendency in complex plane comprises line inductance, electric capacity, active power, reactive power, frequency.

Embodiment

The present embodiment, based on certain how electric aircraft electrical power system, is set up its Generalized State Space Averaging model and carries out small disturbed stability analysis.Fig. 2 is the how electric aircraft electrical power system structure diagram comprising specific link, wherein suppose that GCU governing speed is enough fast, therefore alternator available alternate 400Hz voltage stabilizing AC power replaces, electrical actuation and control system constant power load replaces, all the other building blocks comprise: transmission line of electricity, vertoro, DC filter capacitor.R _eq, L _eq, C _eqbe respectively circuit and transformer equivalent resistance, reactance, electric capacity.

1) according to how electric aircraft electrical power system structure diagram, DC side circuit is converted AC, obtain the aircraft electrical power system alternating current-direct current mixed current shown in Fig. 3 and calculate line chart, computing formula is as follows:

$\frac{V_{\mathrm{bus}}{V}_s}{Z}\cos ({\mathrm{\&gamma;}}_Z-\mathrm{\&lambda;})-\frac{V_{\mathrm{bus}}^2}{Z}\cos \left({\mathrm{\&gamma;}}_Z\right)=(P+P_{\mathrm{loss}})/3$

$\frac{V_{\mathrm{bus}}{V}_s}{Z}\sin ({\mathrm{\&gamma;}}_Z-\mathrm{\&lambda;})-\frac{V_{\mathrm{bus}}^2}{Z}\sin \left({\mathrm{\&gamma;}}_Z\right)=Q$

Wherein, V _sfor three-phase alternating voltage effective value, get 230V;

V _busfor AC voltage steady-state value, i.e. vertoro AC input voltage value, it is amount to be asked;

λ is the phase differential between above-mentioned two voltages, is amount to be asked;

Z ∠ γ _zfor transmission line of alternation current impedance (comprising the referring reactance of transformer), be calculated as follows:

$Z=\sqrt{R_{\mathrm{eq}}^2+{\left({\mathrm{\&omega;L}}_{\mathrm{eq}}\right)}^2}$

${\mathrm{\&gamma;}}_Z={\tan }^{-1}\left(\frac{{\mathrm{\&omega;L}}_{\mathrm{eq}}}{R_{\mathrm{eq}}}\right)$

P, Q are respectively constant power load active power, reactive power, and be the amount changed with load change, its change can affect the change of steady state voltage value.

Thus, the voltage steady-state value of AC can be calculated, then according to the ac-dc conversion relation of vertoro, the steady state voltage value V of DC side under different capacity P, Q can be obtained _out.

2) according to how electric aircraft electrical power system structure diagram, vertoro is carried out circuit equivalent, obtains generalized state space average modelled equivalent circuit diagram, as shown in Figure 4, the nonlinear differential equation that can obtain this equivalent electrical circuit is as follows, and the parameters wherein in formula marks in the drawings:

$I_{\mathrm{dc}}=C_F\frac{{\mathrm{dV}}_{\mathrm{out}}}{\mathrm{dt}}=\frac{P_{\mathrm{CPL}}}{V_{\mathrm{out}}}$

$E_{\mathrm{DC}1}=(r_F+r_{\mathrm{\&mu;}})+L_{\mathrm{eq}}\frac{{\mathrm{dI}}_{\mathrm{dc}}}{\mathrm{dt}}+V_{\mathrm{out}}$

$I_{\mathrm{La}}=C_{\mathrm{eq}}\frac{{\mathrm{dV}}_{\mathrm{Ca}}}{\mathrm{dt}}+I_{\mathrm{ina}}$

$I_{\mathrm{Lb}}=C_{\mathrm{eq}}\frac{{\mathrm{dV}}_{\mathrm{Cb}}}{\mathrm{dt}}+I_{\mathrm{inb}}$

$I_{\mathrm{Lc}}=C_{\mathrm{eq}}\frac{{\mathrm{dV}}_{\mathrm{Cc}}}{\mathrm{dt}}+I_{\mathrm{inc}}$

$V_{\mathrm{sa}}=R_{\mathrm{eq}}{I}_{\mathrm{La}}+L_{\mathrm{eq}}\frac{{\mathrm{dI}}_{\mathrm{La}}}{\mathrm{dt}}+V_{\mathrm{Ca}}$

$V_{\mathrm{sb}}=R_{\mathrm{eq}}{I}_{\mathrm{Lb}}+L_{\mathrm{eq}}\frac{{\mathrm{dI}}_{\mathrm{Lb}}}{\mathrm{dt}}+V_{\mathrm{Cb}}$

$V_{\mathrm{sc}}=R_{\mathrm{eq}}{I}_{\mathrm{Lc}}+L_{\mathrm{eq}}\frac{{\mathrm{dI}}_{\mathrm{Lc}}}{\mathrm{dt}}+V_{\mathrm{Cc}}$

3) according to step 2) in nonlinear differential equation, determine the state variable x=[V of aircraft electrical power system _out, I _dc, I _la, I _lb, I _lc, V _ca, V _cb, V _cc] ^t, wherein aperiodic state variable r=2 is V _out, I _dc, cycle status variable s=6 is I _la, I _lb, I _lc, V _ca, V _cb, V _cc, carry out Fourier decomposition to state variable, get k=1, and ignore DC ripple, then in the new state variable matrix Q introduced, element is as follows:

<V _out> ₀＝q ₁

<I _dc> ₀＝q ₂

<I _La> ₁＝q ₃+jq ₄

<I _Lb> ₁＝q ₅+jq ₆

<I _Lc> ₁＝q ₇+jq ₈

<V _Ca> ₁＝q ₉+jq ₁₀

<V _Cb> ₁＝q ₁₁+jq ₁₂

<V _Cc> ₁＝q ₁₃+jq ₁₄

4) to step 2) the aircraft electrical power system nonlinear differential equation that obtains carries out Fourier decomposition, and substitute into step 3) the new state variable matrix Q that obtains, finally obtain the aircraft electrical power system generalized state space average equation that Fourier coefficient describes:

${\stackrel{\&CenterDot;}{q}}_1=-\frac{P_{\mathrm{CPL}}}{C_F{q}_1}+\frac{1}{C_F}{q}_2$

$\begin{array}{c}{\stackrel{\&CenterDot;}{q}}_2=-\frac{1}{L_F}{q}_1-\frac{(r_{\mathrm{\&mu;}}+r_F)}{L_F}{q}_2-\frac{2\sqrt{3}}{{\mathrm{\&pi;L}}_F}\sin {\mathrm{\&lambda;q}}_9-\frac{2\sqrt{3}}{{\mathrm{\&pi;L}}_F}\cos {\mathrm{\&lambda;q}}_{10}\\ -\frac{2\sqrt{3}}{{\mathrm{\&pi;L}}_F}\sin (\frac{2\mathrm{\&pi;}}{3}+\mathrm{\&lambda;})q_{11}-\frac{2\sqrt{3}}{{\mathrm{\&pi;L}}_F}\cos (\frac{2\mathrm{\&pi;}}{3}+\mathrm{\&lambda;})q_{12}\\ -\frac{2\sqrt{3}}{{\mathrm{\&pi;L}}_F}\sin (\frac{4\mathrm{\&pi;}}{3}+\mathrm{\&lambda;})q_{13}-\frac{2\sqrt{3}}{{\mathrm{\&pi;L}}_F}\cos (\frac{4\mathrm{\&pi;}}{3}+\mathrm{\&lambda;})q_{14}\end{array}$

${\stackrel{\&CenterDot;}{q}}_3=-\frac{R_{\mathrm{eq}}}{L_{\mathrm{eq}}}{q}_3+{\mathrm{\&omega;q}}_4-\frac{1}{L_{\mathrm{eq}}}{q}_9$

${\stackrel{\&CenterDot;}{q}}_4={-\mathrm{\&omega;q}}_3-\frac{R_{\mathrm{eq}}}{L_{\mathrm{eq}}}{q}_4-\frac{1}{L_{\mathrm{eq}}}{q}_{10}-\frac{V_m}{{2L}_{\mathrm{eq}}}$

${\stackrel{\&CenterDot;}{q}}_5=-\frac{R_{\mathrm{eq}}}{L_{\mathrm{eq}}}{q}_5+{\mathrm{\&omega;q}}_6-\frac{1}{L_{\mathrm{eq}}}{q}_{11}-\frac{\sqrt{3}}{{4L}_{\mathrm{eq}}}$

${\stackrel{\&CenterDot;}{q}}_6={-\mathrm{\&omega;q}}_5-\frac{R_{\mathrm{eq}}}{L_{\mathrm{eq}}}{q}_6-\frac{1}{L_{\mathrm{eq}}}{q}_{12}-\frac{V_m}{{4L}_{\mathrm{eq}}}$

${\stackrel{\&CenterDot;}{q}}_7=-\frac{R_{\mathrm{eq}}}{L_{\mathrm{eq}}}{q}_7+{\mathrm{\&omega;q}}_8-\frac{1}{L_{\mathrm{eq}}}{q}_{13}-\frac{\sqrt{3}}{{4L}_{\mathrm{eq}}}$

${\stackrel{\&CenterDot;}{q}}_8={-\mathrm{\&omega;q}}_7-\frac{R_{\mathrm{eq}}}{L_{\mathrm{eq}}}{q}_8-\frac{1}{L_{\mathrm{eq}}}{q}_{14}-\frac{V_m}{{4L}_{\mathrm{eq}}}$

${\stackrel{\&CenterDot;}{q}}_9=\frac{\sqrt{3}}{{\mathrm{\&pi;C}}_{\mathrm{eq}}}\sin {\mathrm{\&lambda;q}}_2+\frac{1}{C_{\mathrm{eq}}}{q}_3+{\mathrm{\&omega;q}}_{10}$

${\stackrel{\&CenterDot;}{q}}_{10}=\frac{\sqrt{3}}{{\mathrm{\&pi;C}}_{\mathrm{eq}}}\cos {\mathrm{\&lambda;q}}_2+\frac{1}{C_{\mathrm{eq}}}{q}_4-{\mathrm{\&omega;q}}_9$

${\stackrel{\&CenterDot;}{q}}_{11}=\frac{\sqrt{3}}{{\mathrm{\&pi;C}}_{\mathrm{eq}}}\sin (\frac{2\mathrm{\&pi;}}{3}+\mathrm{\&lambda;})q_2+\frac{1}{C_{\mathrm{eq}}}{q}_5+{\mathrm{\&omega;q}}_{12}$

${\stackrel{\&CenterDot;}{q}}_{12}=\frac{\sqrt{3}}{{\mathrm{\&pi;C}}_{\mathrm{eq}}}\cos (\frac{2\mathrm{\&pi;}}{3}+\mathrm{\&lambda;})q_2+\frac{1}{C_{\mathrm{eq}}}{q}_6-{\mathrm{\&omega;q}}_{11}$

${\stackrel{\&CenterDot;}{q}}_{13}=\frac{\sqrt{3}}{{\mathrm{\&pi;C}}_{\mathrm{eq}}}\sin (\frac{4\mathrm{\&pi;}}{3}+\mathrm{\&lambda;})q_2+\frac{1}{C_{\mathrm{eq}}}{q}_7+{\mathrm{\&omega;q}}_{14}$

${\stackrel{\&CenterDot;}{q}}_{14}=\frac{\sqrt{3}}{{\mathrm{\&pi;C}}_{\mathrm{eq}}}\cos (\frac{4\mathrm{\&pi;}}{3}+\mathrm{\&lambda;})q_2+\frac{1}{C_{\mathrm{eq}}}{q}_8-{\mathrm{\&omega;q}}_{13}$

5) for step 4) Generalized State Space Averaging model that obtains, steady operation point place under a certain certain power P, Q that step 1 obtains carries out linearization, obtains the system matrix A of the state equation of the linearized system described for Fourier coefficient.

In formula, P _cPLfor the active power of constant power load.

6) eigenwert of formula det [λ I-A]=0 compute matrix A is utilized, according to the small disturbed stability of the positive negative judgement aircraft electrical power system of eigenwert real part, and by P in difference transformation matrix _cPL, L _f, C _f, r _f, R _eq, L _eq, C _eqetc. parameter, obtain eigenwert follows above-mentioned different parameters variation tendency at complex plane, and then determine that each Parameters variation of aircraft electrical power system is on the impact of small disturbed stability.

Thus, present invention achieves the aircraft electrical power system small disturbed stability analysis based on generalized state space average, can meet Different Dynamic condition get off the plane electric system small disturbed stability analyze demand.

Finally should be noted that: in conjunction with above-described embodiment, technical scheme of the present invention be only described but not be limited.Those of ordinary skill in the field are to be understood that: those skilled in the art can modify to embodiments of the present invention or equivalent replacement, but these amendments or change are all being applied within the claims awaited the reply.

Claims (7)

1., based on an aircraft electrical power system small disturbed stability analytical approach for generalized state space average, described generalized state space average is exactly take Fourier coefficient as a kind of space average of state variable, and the method comprises the following steps:

1) according to aircraft electrical power system structure, set up the alternating current-direct current mixed current equation of power supply in aircraft electrical power system, distribution system, using electricity system, determine the steady operation point of aircraft electrical power system;

$\frac{V_{\mathrm{bus}}{V}_s}{Z}\cos ({\mathrm{\&gamma;}}_Z-\mathrm{\&lambda;})-\frac{V_{\mathrm{bus}}^2}{Z}\cos \left({\mathrm{\&gamma;}}_Z\right)=(P+P_{\mathrm{loss}})/3$

$\frac{V_{\mathrm{bus}}{V}_s}{Z}\sin ({\mathrm{\&gamma;}}_Z-\mathrm{\&lambda;})-\frac{V_{\mathrm{bus}}^2}{Z}\sin \left({\mathrm{\&gamma;}}_Z\right)=Q$

In formula: V _sfor three-phase alternating voltage effective value, V _busfor AC voltage steady-state value, namely vertoro AC input voltage value, λ are phase differential, the Z ∠ γ between above-mentioned two voltages _zfor transmission line of alternation current impedance, comprise the referring reactance of transformer, P, Q be respectively constant power load active power, reactive power, P _lossfor the power attenuation produced due to DC side circuit

2) to step 1) aircraft electrical power system carries out circuit equivalent, and the circuit after equivalence is used for the modeling of generalized state space average, and obtains the nonlinear differential equation of aircraft electrical power system according to this equivalent electrical circuit:

$\stackrel{\&CenterDot;}{x}=\mathrm{\&Psi;x}+\mathrm{\&Gamma;u}$

Wherein, x=[x ₁, x ₂..., x _n] ^tfor system state variables, Ψ is system state variables matrix, is n × n rank matrix, u=[u ₁, u ₂..., u _m] ^tfor system algebraic variable, Γ is system algebraic variable matrix, is n × m rank matrix;

3) according to step 2) nonlinear differential equation of aircraft electrical power system that obtains, determine aircraft electrical power system power-supply system, distribution system, using electricity system nonlinear differential equation state variable, in state variable, aperiodic state variable r is individual, cycle status variable s, and Fourier decomposition is carried out to state variable, according to the Fourier coefficient <x obtained _i> _k(τ), new state variable matrix Q is introduced, Q=[q ₁, q ₂..., q _r+2ks] ^t, each element of Q matrix is as follows:

During 0<i≤r, <x _i> ₀(τ)=q _i

During r<i≤n, <x _i> _k(τ)=q _{2s (k-1)+(2i-r-1)}+ jq _{2s (k-1)+(2i-r)}

4) to step 2) in the nonlinear differential equation of aircraft electrical power system carry out Fourier decomposition, and by step 3) the state variable matrix Q that obtains substitutes into, and finally obtains the aircraft electrical power system generalized state space average equation that Fourier coefficient describes:

$\stackrel{\&CenterDot;}{Q}=\mathrm{AQ}+\mathrm{BY}+U_x=f(Q,Y,U_x)$

In formula: Q represents the system state variables matrix that Fourier coefficient describes, and A represents Fourier coefficient state variable matrix of coefficients, and Y is the output of this link nonlinear differential equation, and its size affects the dynamic perfromance of next link, and B is the matrix of coefficients of Y, U _xfor system cloud gray model controling parameters;

5) according to step 4) the aircraft electrical power system generalized state space average equation that obtains, in step 1) steady operation point place's linearization of aircraft electrical power system of obtaining, obtain the system matrix A of the state equation of linearized system:

6) calculation procedure 5) eigenwert of system matrix that obtains, computing formula is as follows:

det[λI-A]＝0

In formula: A is the system matrix of state equation, I is unit matrix, and λ is eigenwert to be asked;

According to the small disturbed stability of the positive negative judgement aircraft electrical power system of eigenwert real part, the operational parameter control of change system, and according to eigenwert in complex plane with the variation tendency of system cloud gray model controling parameters, if eigenwert is in the left-sided system of the complex plane imaginary axis, be stable, be then unstable in imaginary axis right-sided system, in order to judge that the change of aircraft electrical power system operational parameter control affects small disturbed stability.

2. the aircraft electrical power system small disturbed stability analytical approach based on generalized state space average according to claim 1, it is characterized in that: described step 1) the middle aircraft electrical power system alternating current-direct current mixed current equation set up, for exchanging aerogenerator based on 400Hz, transmission line of alternation current, wave filter, vertoro, DC power transmission line, the equation that inversion link is set up, the voltage steady-state value of vertoro AC is calculated based on described equation, again according to the ac-dc conversion relation of described vertoro, obtain vertoro DC side at different capacity P, steady state voltage value V under Q _out.

3. the aircraft electrical power system small disturbed stability analytical approach based on generalized state space average according to claim 1, it is characterized in that: described step 2) in set up the equivalent electrical circuit for aircraft electrical power system generalized state spatial modeling and aircraft electrical power system nonlinear differential equation, be based on three phase static abc coordinate system, comprise the alternating current-direct current hybrid equivalent circuit that 400Hz exchanges aerogenerator, transmission line of alternation current, wave filter, vertoro, DC power transmission line link.

4. the aircraft electrical power system small disturbed stability analytical approach based on generalized state space average according to claim 1, it is characterized in that: described step 4) in the Generalized State Space Averaging model of aircraft electrical power system that obtains, for comprising the Generalized State Space Averaging model of aircraft electrical power system dynamic perfromance, and the working condition that the dynamic perfromance of aircraft electrical power system is run with aircraft and moment adjustment.

5. the aircraft electrical power system small disturbed stability analytical approach based on generalized state space average according to claim 1, it is characterized in that: described step 5) system matrix of the state equation of neutral line system, the dynamic perfromance according to aircraft electrical power system, with different rank Fourier coefficient for state variable obtains.

6. the aircraft electrical power system small disturbed stability analytical approach based on generalized state space average according to claim 4, it is characterized in that: the dynamic perfromance of aircraft electrical power system is started with aircraft, slide, take off, climb, cruise, decline, the operating mode of landing and moment adjustment, comprise that component-level is dynamic, behavioral scaling is dynamic, functional level is dynamic, the dynamic four kinds of levels of structural level, described component-level dynamically refers to the internal dynamics of power electronic devices in aircraft electrical power system, electromagnetic actuator; Described behavioral scaling dynamically refers to that the switch that composition aircraft electrical power system vertoro, chopper, inverter produce in work process is dynamic; Described functional level has dynamically referred to aircraft startup, landing, anti-icing, defrost function, the electric motor starting that aircraft electrical power system carries out, stopping, changing load, switching dynamic behaviour; Described structural level dynamically refers to that the NETWORK STRUCTURE PRESERVING POWER SYSTEM of taking off, climb, cruise, landing produced that aircraft is the different mission phase of reply switches dynamic perfromance.

7. the aircraft electrical power system small disturbed stability analytical approach based on generalized state space average according to claim 1, it is characterized in that: in described step 6) in, effect characteristics value system cloud gray model controling parameters of variation tendency in complex plane comprises line inductance, electric capacity, active power, reactive power, frequency.