CN105071428A - AC and DC stability analysis method considering receiving end excitation system - Google Patents

Abstract

The invention discloses an AC and DC stability analysis method considering a receiving end excitation system. The AC and DC stability analysis method comprises the steps of: determining a control mode and parameters of a DC power transmission system; carrying out expanded load flow calculation on an AC and DC system while considering excitation parameters of a generator and an amplitude limiting link of an excitation link thereof; and analyzing stability of the system according to load variation, receiving end Thevenin equivalent parameter variation and parameters of the DC power transmission system. The AC and DC stability analysis method considers the amplitude limiting link of the excitation system, and illustrates the supporting role of the excitation link of the generator to voltage through the combination of the traditional receiving end Thevenin equivalent parameters; and the supporting capacity of a receiving end system to DC drop-in is embodiment of the interaction of power grid structure, receiving end load and generator excitation.

Description

A kind of alternating current-direct current method for analyzing stability considering receiving end excitation system

Technical field

The present invention relates to electrical engineering field, particularly relate to a kind of alternating current-direct current method for analyzing stability considering receiving end excitation system for power system stability.

Background technology

High voltage direct current transmission is large with its transmission capacity, the advantages such as the electrical network of long distance power transmission and connection different frequency, be rapidly developed in recent years, China has defined alternating current-direct current mixing general layout, meanwhile, the impact of voltage support on the stable operation of high voltage direct current transmission of receiving-end system causes concern.

The patent No. is the Chinese patent of CN201310031426.9: " a kind of analytical method studying alternating-current/interactiveent interactiveent influence mechanism ", give alternating current-direct current interactional analytical method, when large fault occurs AC system by time-domain digital analogue system Main Analysis, cause the problem of direct current transportation commutation failure and receiving end voltage stabilization.The patent No. is the Chinese patent of CN201210454137.5: " computational methods of the power system transient stability under DC transmission system control mode ", analyze the probability that ac and dc systems under different control modes breaks down, calculate the power system transient stability under DC transmission system control mode, this invention achieves the accurate evaluation of DC transmission system control mode to the influence degree of Ac/dc Power Systems transient stability.The patent No. is the Chinese patent of CN201410033099.5: " a kind of honourable fiery bundling direct current sends method for estimating stability outside ", judge the access intensity of each access scheme apoplexy flare up bundling direct current delivery system, judge honourable fiery bundling direct current delivery system and the stability reciprocal effect of networking AC system, mainly rely on the short circuit ratio index of receiving-end system.The stability analysis of alternating current-direct current described in above patent concentrate on AC system intensity and have ignored the excitation situation being at all receiving end generator of its intensity, electric network composition and load number, simple short circuit ratio is difficult to set forth AC system and direct current transportation stability relation.

Summary of the invention

For solving the deficiency that prior art exists, the invention discloses a kind of alternating current-direct current method for analyzing stability considering receiving end excitation system.Relative to the fixing Thevenin's equivalence model of regulating power that can not reflect receiving end, the present invention considers the effect of receiving end excitation system, labor its on the impact of DC transmission system, when pointing out that excitation reaches capacity, it is comparatively large that Receiving End Load fluctuation causes Thevenin's equivalence to change, and affects the fail safe of DC transmission system immediately.

For achieving the above object, concrete scheme of the present invention is as follows:

Consider an alternating current-direct current method for analyzing stability for receiving end excitation system, comprise the following steps:

Step one: determine the control mode of DC transmission system and the parameter of DC transmission system;

Step 2: consider the excitation parameter of generator and the amplitude limit link of its excitation link, expansion Load flow calculation is carried out to ac and dc systems;

Step 3: according to the variation of load, utilizes the stability of the change of receiving end Thevenin's equivalence parameter and the parametric analysis system of DC transmission system.

Further, in described step 2, specifically comprise: the inverter side Equivalent Model setting up DC transmission system, set up the model of excitation system, set up the output power model of synchronous generator, build node power Constraints of Equilibrium equation, build generator power equilibrium equation, each model construction equilibrium equation of system, the basis of extended power flow equations is carried out Load flow calculation and solves unknown state amount, verify the whether out-of-limit process of regulating system excitation simultaneously, if out-of-limit, carry out processing and re-starting Load flow calculation.

The structure of the inverter side Equivalent Model of above-mentioned DC transmission system, the model of excitation system and the output power model of synchronous generator is all the equilibrium equations in order to constructing system, comprises the power balance equation of node, the power balance equation of generator.

Further, the inverter side Equivalent Model of DC transmission system is:

$\left\{\begin{array}{c}{P}_d={\mathrm{CV}}^2\[cos2\mathrm{\γ}-cos(2\mathrm{\γ}+2\mathrm{\μ})\]\\ Q_d={\mathrm{CV}}^2\[2\mathrm{\μ}+sin2\mathrm{\γ}-sin(2\mathrm{\γ}+2\mathrm{\μ})\]\\ I_d=KV\[\cos \mathrm{\γ}-\cos (\mathrm{\γ}+\mathrm{\μ})\]\\ V_d=P_d/I_d\\ P_{ac}=\[V^2\cos \mathrm{\θ}-EVcos(\mathrm{\δ}+\mathrm{\θ}-\mathrm{\φ})\]/\left|Z\right|\\ Q_{ac}=\[V^2\sin \mathrm{\θ}-EV\sin (\mathrm{\δ}+\mathrm{\θ}-\mathrm{\φ})\]/\left|Z\right|\\ Q_c=V^2{B}_c\end{array}\right.---\left(1\right)$

In formula (1), P _dfor the active power that inverter is carried to AC system; Q _dfor the reactive power that inverter absorbs from AC; I _dfor direct current; V _dfor direct voltage; γ is for closing the angle of rupture; μ is angle of overlap; P _ac, Q _acbe respectively active power, reactive power that bus is carried to receiving end AC system; B _cfor the equivalent admittance of alternating current filter and reactive compensation capacitor; Q _cfor the reactive power that equivalent condenser compensates; V, δ are respectively bus place voltage magnitude and phase angle; E, φ, | Z|, θ are respectively the Thevenin's equivalence electromotive force amplitude of receiving-end system and phase angle, equivalent impedance modulus value, equivalent impedance angle; K is the converter transformers parameter constant relevant with direct current system standard value; C is two constants relevant with direct current with converter transformers parameter.

Wherein, the expression formula of C is such as formula shown in (2):

$C=\frac{3}{4\mathrm{\π}}.\frac{S_T}{P_{dN}}.\frac{1}{U_k\%}.\frac{1}{{\mathrm{\τ}}^2}---\left(2\right)$

In formula (2), S _tfor the capacity of transformer; U _k% is the short-circuit voltage percentage of transformer; τ is the no-load voltage ratio of transformer, P _dNfor nominal DC power.

Further, the change of system frequency do not considered by the model of described excitation system, i.e. the error free adjustment of frequency after frequency modulation frequency modulation, and its model is as follows:

$\left\{\begin{array}{c}{V}_R=K_E{E}_{fd}\\ V_F=K_F{E}_{fd}/T_F\\ E_{fd}=K_A(V_{ref}-V_1)/K_E\\ V_{Rmin}\≤V_R\≤V_{Rmax}\end{array}\right.---\left(3\right)$

In formula (3), wherein V _rmin, V _rmaxrepresent excitation system amplitude limit link bound respectively, V _rfor the exciting voltage of DC exciter; K _efor the self-excitation coefficient of generator; E _fdfor exciting voltage: V _ffor the output of the soft negative feedback links of exciting voltage; K _f, T _fbe respectively gain and the time constant of the soft negative feedback links of exciting voltage; K _athe gain of amplifying element; V _reffor reference voltage; V ₁for the collection value of terminal voltage.

Further, do not consider governing system, the output power model of synchronous generator is as follows:

$\left\{\begin{array}{c}{P}_{gi}=\frac{V_i}{X_{di}}\frac{K_{Ai}}{K_{Ei}}\left(V_{refi}-V_i\right)\sin ({\mathrm{\δ}}_i-{\mathrm{\θ}}_i)+\frac{V_i^2}{2}\sin 2\left({\mathrm{\δ}}_i-{\mathrm{\θ}}_i\right)(\frac{1}{X_{qi}}-\frac{1}{X_{di}})\\ Q_{gi}=\frac{V_i}{X_{di}}\frac{K_{Ai}}{K_{Ei}}\left(V_{refi}-V_i\right)\cos ({\mathrm{\δ}}_i-{\mathrm{\θ}}_i)-\frac{V_i^2}{2}(\frac{1}{X_{di}}+\frac{1}{X_{qi}})+\frac{V_i^2}{2}\cos 2\left({\mathrm{\δ}}_i-{\mathrm{\θ}}_i\right)\left(\frac{1}{X_{qi}}-\frac{1}{X_{di}}\right)\end{array}\right.---\left(4\right)$

In formula (4), P _gi, Q _giexert oneself for synchronous generator i is meritorious, idle; X _di, X _qiand δ _ifor d, q axle synchronous reactance and the merit angle of generator i; K _aifor the multiplication factor of field regulator amplifying element; K _eifor the excitation coefficient of exciter; V _iand θ _ifor Generator end node voltage magnitude and phase angle.Wherein δ _i, θ _idistinguished with δ, the θ of the Equivalent Model in formula 1, avoided the confusion of symbol, V _refifor the reference voltage of i excitation control system.

Further, node power Constraints of Equilibrium equation:

$\left\{\begin{array}{c}{\mathrm{\ΔP}}_i=P_{gi}-V_i\underset{j=1}{\overset{n}{\Σ}}{V}_j(G_{ij}{\mathrm{cos\θ}}_{ij}+B_{ij}{\mathrm{sin\θ}}_{ij})-P_{Li}+P_{di}=0\\ {\mathrm{\ΔQ}}_i=Q_{gi}-V_i\underset{j=1}{\overset{n}{\Σ}}{V}_j(G_{ij}{\mathrm{sin\θ}}_{ij}-B_{ij}{\mathrm{cos\θ}}_{ij})-Q_{Li}-Q_{di}=0\end{array}\right.---\left(5\right)$

In formula (5), Δ P _i, Δ Q _irepresent meritorious, the reactive power amount of unbalance of node i respectively; If node i connects generator, P _gi, Q _giexpression formula is such as formula shown in (4); If node i does not connect generator, P _gi=0, Q _gi=0, if node i is the receiving end bus nodes of direct current transportation, then P _di, Q _difor the direct current of i node is meritorious, reactive power, the P as shown in (1), (2) _d, Q _d; If node i is for exchanging node, P _di=0, Q _di=0, P _li, Q _lirepresent active power and the reactive power of load bus respectively, G _ij, B _ijrepresent the conductance of node i, j, susceptance respectively, V _i, V _jbe respectively the voltage magnitude of node i, j; θ _ijfor the difference of node i, j voltage phase angle.

Further, generator power equilibrium equation:

Disregard damping coefficient, after frequency modulation frequency modulation, frequency is identical with reference frequency, and prime mover active power balance expression formula of generator corresponding node is:

ΔP _gi＝P _gsi-P _gi＝0(6)

Δ P in formula (6) _gsifor generator amature motion unbalanced power amount; P _gsifor expanding the controlled quentity controlled variable of trend, it is prime mover power output of each generator corresponding node.

Further, extended power flow equations and unknown quantity:

Quantity of state be n node voltage magnitude and except n-1 node voltage phase angle of balance node and m generator's power and angle, therefore the number of unknown quantity is 2n+m-1, legacy network equation number is 2n, generator node is except balance node, the active power balance equation of prime mover is m-1, system power equilibrium equation adds up to 2n+m-1, can a simultaneous solution 2n+m-1 quantity of state.

Further, the out-of-limit process of described excitation:

Constraint AVR (automatic voltage regulator) the output voltage V of synchronous generator rotor electric current _riexpress, if ignore the saturation of excitation system, the output voltage V of AVR when stable state _ribe proportional to the rotor current of generator, therefore, when rotor current reaches maximum, be equivalent to the output voltage V of AVR _rireach maximum V _{ri, max}and remain unchanged, the K namely in formula (4) _ai(V _refi-V _i) use V _{ri, max}substitute.

Further, described alternating current-direct current Load flow calculation step is as follows: given voltage magnitude, angle initial value, and according to the given direct current parameter of the control mode of DC transmission system, as constant-current constant gamma kick mode, given direct current parameter is angle of overlap μ; Utilize node power Constraints of Equilibrium equation and generator power equilibrium equation calculate amount of unbalance and judge whether it meets required precision: if do not meet, to form alternating current-direct current Jacobian matrix, computed correction is until meet; If meet and judge whether the excitation of its receiving end generator reaches the limit values, if reach, then with the output voltage V of AVR _rireach maximum V _{ri, max}re-start Load flow calculation, otherwise calculate end.

In described step 3, load causes the change of system Thevenin's equivalence parameter after increasing, and the generator excitation of receiving-end system is sufficient, in the process that load increases, and V _r≤ V _rmax, when load increases, the generator excitation of receiving end needs constantly to increase, and terminal voltage reduces, the power reduction of direct current conveying; The generator excitation of receiving-end system is limited, in the process of load growth, gets V _r=V _rmax, when the excitation of generator is restricted, the fail safe of system is subject to great threat, and receiving end busbar voltage and power continue to raise.

Beneficial effect of the present invention:

The present invention considers the excitation system of receiving-end system, when ac and dc systems stability analysis, embodies the regulating action of receiving end, improves the method for traditional analysis direct current transportation characteristic.

The present invention considers the amplitude limit link of excitation system, the supporting role of generator excitation link to voltage in conjunction with traditional receiving end Thevenin's equivalence parameter declaration; Receiving-end system to the enabling capabilities that direct current falls into be electric network composition, coefficient embodiment by end load, generator excitation.

Accompanying drawing explanation

Fig. 1 is DC transmission system current conversion station simplified model;

Fig. 2 is IEEEI type field regulator;

Fig. 3 is alternating current-direct current expansion trend flow chart;

Fig. 4 is the simple ac and dc systems considering receiving end excitation;

Fig. 5 is the change curve of direct current transmission power with direct current.

Embodiment:

Below in conjunction with accompanying drawing, the present invention is described in detail:

Consider an alternating current-direct current method for analyzing stability for receiving end excitation system, comprise the following steps:

(1) control mode of direct current transportation and the relevant parameter of control is determined;

(2) consider the excitation parameter of generator and the amplitude limit link of its excitation link, expansion Load flow calculation is carried out to ac and dc systems;

(3) according to the variation of load, analyze the change of its receiving end Thevenin's equivalence parameter and the parameter of DC transmission system, analyze its stability.

In described step (1), the control mode of the change of current has four kinds: Given current controller mode, constant dc power control mode, determine gamma kick mode, determine voltage control mode.For convenience of the stability of research receiving-end system, the control mode of DC transmission system has following four kinds: rectifier is determined current inverter and determined voltage; Rectifier is determined current inversion and to be stood firm extinguish angle; Rectifier is determined power inverting and to be stood firm voltage; Rectifier is determined power inverting and to be stood firm extinguish angle.

In described step (2), consider that the alternating current-direct current expansion power flow algorithm of generator excitation restriction is as follows:

1) the inverter side Equivalent Model of DC transmission system is as shown in Figure 1, and receiving-end system is equivalent by Dai Weinan parameter, and the excitation of receiving-end system acts in model subsequently and can embody, and its mathematical expression is as follows:

$\left\{\begin{array}{c}{P}_d={\mathrm{CV}}^2\[cos2\mathrm{\γ}-cos(2\mathrm{\γ}+2\mathrm{\μ})\]\\ Q_d={\mathrm{CV}}^2\[2\mathrm{\μ}+sin2\mathrm{\γ}-sin(2\mathrm{\γ}+2\mathrm{\μ})\]\\ I_d=KV\[\cos \mathrm{\γ}-\cos (\mathrm{\γ}+\mathrm{\μ})\]\\ V_d=P_d/I_d\\ P_{ac}=\[V^2\cos \mathrm{\θ}-EVcos(\mathrm{\δ}+\mathrm{\θ}-\mathrm{\φ})\]/\left|Z\right|\\ Q_{ac}=\[V^2\sin \mathrm{\θ}-EV\sin (\mathrm{\δ}+\mathrm{\θ}-\mathrm{\φ})\]/\left|Z\right|\\ Q_c=V^2{B}_c\end{array}\right.---\left(1\right)$

In formula (1), P _dfor the active power that inverter is carried to AC system; Q _dfor the reactive power that inverter absorbs from AC; I _dfor direct current; V _dfor direct voltage; γ is for closing the angle of rupture; μ is angle of overlap; P _ac, Q _acbe respectively active power, reactive power that bus is carried to receiving end AC system; B _cfor the equivalent admittance of alternating current filter and reactive compensation capacitor; Q _cfor the reactive power that equivalent condenser compensates; V, δ are respectively bus place voltage magnitude and phase angle; E, φ, | Z|, θ are respectively the Thevenin's equivalence electromotive force amplitude of receiving-end system and phase angle, equivalent impedance modulus value, equivalent impedance angle; K is the converter transformers parameter constant relevant with direct current system standard value; C is two constants relevant with direct current with converter transformers parameter, and wherein the expression formula of C is such as formula shown in (2).

$C=\frac{3}{4\mathrm{\π}}.\frac{S_T}{P_{dN}}.\frac{1}{U_k\%}.\frac{1}{{\mathrm{\τ}}^2}---\left(2\right)$

In formula (2), S _tfor the capacity of transformer; U _k% is the short-circuit voltage percentage of transformer; τ is the no-load voltage ratio of transformer.

2) model of excitation system

This patent does not consider the effect of governing system, does not limit the meritorious situation of exerting oneself of each generator, does not namely consider the change of system frequency, i.e. the error free adjustment of frequency after frequency modulation frequency modulation.IEEE-I excitation model in accompanying drawing 2, its model is as follows:

$\left\{\begin{array}{c}{V}_R=K_E{E}_{fd}\\ V_F=K_F{E}_{fd}/T_F\\ E_{fd}=K_A(V_{ref}-V_1)/K_E\\ V_{Rmin}\≤V_R\≤V_{Rmax}\end{array}\right.---\left(3\right)$

In formula (3), wherein V _rmin, V _rmaxrepresent excitation system amplitude limit link bound respectively.

3) do not consider governing system, the output power model of synchronous generator is as follows:

$\left\{\begin{array}{c}{P}_{gi}=\frac{V_i}{X_{di}}\frac{K_{Ai}}{K_{Ei}}\left(V_{refi}-V_i\right)\sin ({\mathrm{\δ}}_i-{\mathrm{\θ}}_i)+\frac{V_i^2}{2}\sin 2\left({\mathrm{\δ}}_i-{\mathrm{\θ}}_i\right)(\frac{1}{X_{qi}}-\frac{1}{X_{di}})\\ Q_{gi}=\frac{V_i}{X_{di}}\frac{K_{Ai}}{K_{Ei}}\left(V_{refi}-V_i\right)\cos ({\mathrm{\δ}}_i-{\mathrm{\θ}}_i)-\frac{V_i^2}{2}(\frac{1}{X_{di}}+\frac{1}{X_{qi}})+\frac{V_i^2}{2}\cos 2\left({\mathrm{\δ}}_i-{\mathrm{\θ}}_i\right)\left(\frac{1}{X_{qi}}-\frac{1}{X_{di}}\right)\end{array}\right.---\left(4\right)$

In formula (4), P _gi, Q _giexert oneself for synchronous generator i is meritorious, idle; X _di, X _qiand δ _ifor d, q axle synchronous reactance and the merit angle of generator i; K _aifor the multiplication factor of field regulator amplifying element; K _eifor the excitation coefficient of exciter; V _iand θ _ifor Generator end node voltage magnitude and phase angle.Wherein δ _i, θ _idistinguished with δ, the θ of the Equivalent Model in formula 1, avoided the confusion of symbol.

4) node power Constraints of Equilibrium:

$\left\{\begin{array}{c}{P}_{gi}-V_i\underset{j=1}{\overset{n}{\Σ}}{V}_j(G_{ij}{\mathrm{cos\θ}}_{ij}+B_{ij}{\mathrm{sin\θ}}_{ij})-P_{Li}+P_{di}=0\\ Q_{gi}-V_i\underset{j=1}{\overset{n}{\Σ}}{V}_j(G_{ij}{\mathrm{sin\θ}}_{ij}-B_{ij}{\mathrm{cos\θ}}_{ij})-Q_{Li}-Q_{di}=0\end{array}\right.---\left(5\right)$

In formula (5), if node i connects generator, P _gi, Q _giexpression formula is such as formula shown in (4); If node i does not connect generator, P _gi=0, Q _gi=0.If node i is the receiving end bus nodes of direct current transportation, then P _di, Q _dias shown in (1), (2); If node i is for exchanging node, P _di=0, Q _di=0.P _li, Q _lirepresent active power and the reactive power of load bus respectively.G _ij, B _ijrepresent the conductance of node i, j, susceptance respectively.

5) generator power equilibrium equation

Disregard damping coefficient, after frequency modulation frequency modulation, frequency is identical with reference frequency, and prime mover active power balance expression formula of generator corresponding node is:

P _gsi-P _gi＝0(6)

P in formula (6) _gsifor expanding the controlled quentity controlled variable of trend, it is prime mover power output of each generator corresponding node.

6) extended power flow equations and unknown quantity

Quantity of state be n node voltage magnitude and except n-1 node voltage phase angle of balance node and m generator's power and angle, therefore the number of unknown quantity is 2n+m-1.Legacy network equation number is 2n, and generator node is except balance node, and the active power balance equation of prime mover is m-1, and system power equilibrium equation adds up to 2n+m-1, can a simultaneous solution 2n+m-1 quantity of state.

7) the out-of-limit process of excitation

The constraint AVR of synchronous generator rotor electric current exports V _riexpress, if ignore the saturation of excitation system, the output voltage V of AVR when stable state _ribe proportional to the rotor current of generator.Therefore, when rotor current reaches maximum, be equivalent to the output voltage V of AVR _rireach maximum V _{ri, max}and remain unchanged, the K namely in formula (4) _ai(V _refi-V _i) use V _{ri, max}substitute.

8) the expansion trend of alternating current-direct current

As shown in Figure 3, alternating current-direct current Load flow calculation step is as follows: given voltage magnitude, angle initial value and direct current parameter; Calculate amount of unbalance and judge whether it meets required precision: if do not meet, forming alternating current-direct current Jacobian matrix, computed correction is until meet; If meet and judge whether the excitation of its receiving end generator reaches the limit values, if reach, then with V _{ri, max}re-start Load flow calculation, otherwise calculate end.

In described step (3), load causes the change of system Thevenin's equivalence parameter after increasing, the real-time tracing of Thevenin's equivalence parameter is very ripe, does not repeat them here.Analyze its stability, the voltage magnitude not only comprising receiving end voltage bus also comprises maximum power curve.

As shown in Figure 4, a kind of alternating current-direct current stability analysis of single system, it specifically comprises the steps:

1) parameter and the control mode of DC transmission system is determined

If under rated condition, system parameters is as follows: direct voltage V under rated condition _dn=1, direct current I under rated condition _dn=1, rated condition ShiShimonoseki angle of rupture γ _n=18 °, the meritorious P that exerts oneself of synchronous generator under rated condition _gn=1, cos φ=0.9, Z=1/3, θ=90 °, U _k%=18%, τ=1.Under rated condition, through type (1) obtains μ, Q _dnthe reactive power that under rated condition, inverter absorbs from AC, Q _cnthe reactive power of equivalent capacitor compensation under rated condition, Q _dn=Q _cn, draw building-out capacitor B _c; Through type (1) obtains K, gets θ=90 °, and through type (1) obtains E, δ; Calculate active power, reactive power P that bus is carried to receiving end AC system _ac, Q _ac, generator end electric current I under rated condition _gfor I ∠ 0 °, the meritorious P that exerts oneself of generator end under rated condition _g=EIcos φ, formula calculates I thus _g; Get excitation parameter K _a=50, K _e=1, X _d=0.2495, X _q=0.237, obtain reference voltage V by formula (5) and machine end power balance equation _refand initial load active power and reactive power P _ln, Q _ln.

2) consider the excitation parameter of generator and the amplitude limit link of its excitation link, expansion Load flow calculation is carried out to ac and dc systems.

Set up two kinds of situations: a class is that the generator excitation of receiving-end system is sufficient, in the process that load increases, V _r≤ V _rmax; One class is that the generator excitation of receiving-end system is limited, in the process of load growth, gets V _r=V _rmax.

3) according to the variation of load, analyze the change of its receiving end Thevenin's equivalence parameter and the parameter of DC transmission system, analyze its stability.

Along with P _l, Q _lby constant power factor increase, direct current system operates in constant current I _d=1, permanent extinguish angle γ=18 °, carry out Load flow calculation, P _l=9, step-length is 0.2, carries out the exciting voltage V that 5 Load flow calculation draw the exciter of generator _rand direct current relevant parameter is as table 1.As can be seen from Load flow calculation, when load increases, the generator excitation of receiving end needs constantly to increase, and terminal voltage reduces, the power reduction of direct current conveying.

The abundant lower exciting voltage of table 1 excitation and DC parameter are with the change of load

When the excitation of generator arrives V _rmax=3.6, simulate its impact on direct current transportation, as shown in table 2.When the excitation of generator is restricted, the fail safe of system is subject to great threat, and receiving end busbar voltage continues to raise.

Table 2 excitation is by the change with load of in limited time exciting voltage and DC parameter

At generator excitation by limited time, along with the variation direct current transportation receiving end busbar voltage of load is unstable.In fact namely excitation situation have impact on the Thevenin's equivalence parameter of receiving-end system, and then affects the running status of direct current transportation, and in traditional analysis, just changes the parameters such as E, Z according to Fig. 1 and observes its impact on direct current transportation.Excitation is key one ring affecting Thevenin's equivalence, observes the contrast of Dai Weinan parameter in above-mentioned two situations, as table 3.

Thevenin's equivalence parameter under table 3 two kinds of situations

Calculate by above-mentioned Part Methods, keep initial load, get K _a=50, K _e=1, X _d=0.25, X _q=0.2, change direct current I _dvalue, make maximum power curve as accompanying drawing 5.

Curve 1 represents the maximum power curve during effect not considering excitation system; Curve 2 represents maximum power curve when excitation abundance; Curve 3 represents that excitation limit value is V _rmaxmaximum power curve when=1.2.Can find out by contrasting 1,2, the effect of excitation still limits the maximum of DC transmission system can transmission power; Contrast 2,3 can be found out, the limited direct current transmission power that causes of excitation reduces.

By reference to the accompanying drawings the specific embodiment of the present invention is described although above-mentioned; but not limiting the scope of the invention; one of ordinary skill in the art should be understood that; on the basis of technical scheme of the present invention, those skilled in the art do not need to pay various amendment or distortion that creative work can make still within protection scope of the present invention.

Claims (10)

1. consider an alternating current-direct current method for analyzing stability for receiving end excitation system, it is characterized in that, comprise the following steps:

Step one: determine the control mode of DC transmission system and the parameter of DC transmission system;

Step 2: consider the excitation parameter of generator and the amplitude limit link of its excitation link, expansion Load flow calculation is carried out to ac and dc systems;

Step 3: according to the variation of load, utilizes the stability of the change of receiving end Thevenin's equivalence parameter and the parametric analysis system of DC transmission system.

2. a kind of alternating current-direct current method for analyzing stability considering receiving end excitation system as claimed in claim 1, it is characterized in that, in described step 2, specifically comprise: the inverter side Equivalent Model setting up DC transmission system, set up the model of excitation system, set up the output power model of synchronous generator, build node power Constraints of Equilibrium equation, build generator power equilibrium equation, each model construction equilibrium equation of system, the basis of extended power flow equations is carried out Load flow calculation and solves unknown state amount, verify the whether out-of-limit process of regulating system excitation simultaneously, if out-of-limit, carry out processing and re-starting Load flow calculation.

3. a kind of alternating current-direct current method for analyzing stability considering receiving end excitation system as claimed in claim 2, it is characterized in that, the inverter side Equivalent Model of DC transmission system is:

$\left\{\begin{array}{c}{P}_d={\mathrm{CV}}^2\[cos2\mathrm{\γ}-cos(2\mathrm{\γ}+2\mathrm{\μ})\]\\ Q_d={\mathrm{CV}}^2\[2\mathrm{\μ}+sin2\mathrm{\γ}-sin(2\mathrm{\γ}+2\mathrm{\μ})\]\\ I_d=KV\[\cos \mathrm{\γ}-\cos (\mathrm{\γ}+\mathrm{\μ})\]\\ V_d=P_d/I_d\\ P_{ac}=\[V^2\cos \mathrm{\θ}-EVcos(\mathrm{\δ}+\mathrm{\θ}-\mathrm{\φ})\]/\left|Z\right|\\ Q_{ac}=\[V^2\sin \mathrm{\θ}-EV\sin (\mathrm{\δ}+\mathrm{\θ}-\mathrm{\φ})\]/\left|Z\right|\\ Q_c=V^2{B}_c\end{array}\right.---\left(1\right)$

In formula (1), P _dfor the active power that inverter is carried to AC system; Q _dfor the reactive power that inverter absorbs from AC; I _dfor direct current; V _dfor direct voltage; γ is for closing the angle of rupture; μ is angle of overlap; P _ac, Q _acbe respectively active power, reactive power that bus is carried to receiving end AC system; B _cfor the equivalent admittance of alternating current filter and reactive compensation capacitor; Q _cfor the reactive power that equivalent condenser compensates; V, δ are respectively bus place voltage magnitude and phase angle; E, φ, | Z|, θ are respectively the Thevenin's equivalence electromotive force amplitude of receiving-end system and phase angle, equivalent impedance modulus value, equivalent impedance angle; K is the converter transformers parameter constant relevant with direct current system standard value; C is two constants relevant with direct current with converter transformers parameter.

4. a kind of alternating current-direct current method for analyzing stability considering receiving end excitation system as claimed in claim 2, it is characterized in that, the change of system frequency do not considered by the model of described excitation system, i.e. the error free adjustment of frequency after frequency modulation frequency modulation, and its model is as follows:

$\left\{\begin{array}{c}{V}_R=K_E{E}_{fd}\\ V_F=K_F{E}_{fd}/T_F\\ E_{fd}=K_A(V_{ref}-V_1)/K_E\\ V_{Rmin}\≤V_R\≤V_{Rmax}\end{array}\right.---\left(3\right)$

In formula (3), wherein V _rmin, V _rmaxrepresent excitation system amplitude limit link bound respectively, V _rfor the exciting voltage of DC exciter; K _efor the self-excitation coefficient of generator; E _fdfor exciting voltage: V _ffor the output of the soft negative feedback links of exciting voltage; K _f, T _fbe respectively gain and the time constant of the soft negative feedback links of exciting voltage; K _athe gain of amplifying element; V _reffor reference voltage; V ₁for the collection value of terminal voltage.

5. a kind of alternating current-direct current method for analyzing stability considering receiving end excitation system as claimed in claim 2, it is characterized in that, do not consider governing system, the output power model of synchronous generator is as follows:

$\left\{\begin{array}{c}{P}_{gi}=\frac{V_i}{X_{di}}\frac{K_{Ai}}{K_{Ei}}\left(V_{refi}-V_i\right)\sin ({\mathrm{\δ}}_i-{\mathrm{\θ}}_i)+\frac{V_i^2}{2}\sin 2\left({\mathrm{\δ}}_i-{\mathrm{\θ}}_i\right)(\frac{1}{X_{qi}}-\frac{1}{X_{di}})\\ Q_{gi}=\frac{V_i}{X_{di}}\frac{K_{Ai}}{K_{Ei}}\left(V_{refi}-V_i\right)\cos ({\mathrm{\δ}}_i-{\mathrm{\θ}}_i)-\frac{V_i^2}{2}(\frac{1}{X_{di}}+\frac{1}{X_{qi}})+\frac{V_i^2}{2}\cos 2\left({\mathrm{\δ}}_i-{\mathrm{\θ}}_i\right)\left(\frac{1}{X_{qi}}-\frac{1}{X_{di}}\right)\end{array}\right.---\left(4\right)$

In formula (4), P _gi, Q _giexert oneself for synchronous generator i is meritorious, idle; X _di, X _qiand δ _ifor d, q axle synchronous reactance and the merit angle of generator i; K _aifor the multiplication factor of field regulator amplifying element; K _eifor the excitation coefficient of exciter; V _iand θ _ifor Generator end node voltage magnitude and phase angle, V _refifor the reference voltage of i excitation control system.

6. a kind of alternating current-direct current method for analyzing stability considering receiving end excitation system as claimed in claim 2, is characterized in that, node power Constraints of Equilibrium equation:

$\left\{\begin{array}{c}{\mathrm{\ΔP}}_i=P_{gi}-V_i\underset{j=1}{\overset{n}{\Σ}}{V}_j(G_{ij}{\mathrm{cos\θ}}_{ij}+B_{ij}{\mathrm{sin\θ}}_{ij})-P_{Li}+P_{di}=0\\ {\mathrm{\ΔQ}}_i=Q_{gi}-V_i\underset{j=1}{\overset{n}{\Σ}}{V}_j(G_{ij}{\mathrm{sin\θ}}_{ij}-B_{ij}{\mathrm{cos\θ}}_{ij})-Q_{Li}-Q_{di}=0\end{array}\right.---\left(5\right)$

In formula (5), Δ P _i, Δ Q _irepresent meritorious, the reactive power amount of unbalance of node i respectively; If node i connects generator, P _gi, Q _giexpression formula is such as formula shown in (4); If node i does not connect generator, P _gi=0, Q _gi=0, if node i is the receiving end bus nodes of direct current transportation, then P _di, Q _difor the direct current of i node is meritorious, reactive power, the P as shown in (1), (2) _d, Q _d; If node i is for exchanging node, P _di=0, Q _di=0, P _li, Q _lirepresent active power and the reactive power of load bus respectively, G _ij, B _ijrepresent the conductance of node i, j, susceptance respectively, V _i, V _jbe respectively the voltage magnitude of node i, j; θ _ijfor the difference of node i, j voltage phase angle.

7. a kind of alternating current-direct current method for analyzing stability considering receiving end excitation system as claimed in claim 2, is characterized in that, generator power equilibrium equation:

Disregard damping coefficient, after frequency modulation frequency modulation, frequency is identical with reference frequency, and prime mover active power balance expression formula of generator corresponding node is:

ΔP _gi＝P _gsi-P _gi＝0(6)

Δ P in formula (6) _gsifor generator amature motion unbalanced power amount; P _gsifor expanding the controlled quentity controlled variable of trend, it is prime mover power output of each generator corresponding node.

8. a kind of alternating current-direct current method for analyzing stability considering receiving end excitation system as claimed in claim 5, is characterized in that, extended power flow equations and unknown quantity:

Quantity of state be n node voltage magnitude and except n-1 node voltage phase angle of balance node and m generator's power and angle, therefore the number of unknown quantity is 2n+m-1, legacy network equation number is 2n, generator node is except balance node, the active power balance equation of prime mover is m-1, system power equilibrium equation adds up to 2n+m-1, can a simultaneous solution 2n+m-1 quantity of state;

The out-of-limit process of described excitation:

The constraint AVR and automatic voltage regulator output voltage V of synchronous generator rotor electric current _riexpress, if ignore the saturation of excitation system, the output voltage V of AVR when stable state _ribe proportional to the rotor current of generator, therefore, when rotor current reaches maximum, be equivalent to the output voltage V of AVR _rireach maximum V _{ri, max}and remain unchanged, the K namely in formula (4) _ai(V _refi-V _i) use V _{ri, max}substitute.

9. a kind of alternating current-direct current method for analyzing stability considering receiving end excitation system as claimed in claim 2, it is characterized in that, described alternating current-direct current Load flow calculation step is as follows: according to the given direct current parameter of the control mode of DC transmission system, node power Constraints of Equilibrium equation and generator power equilibrium equation is utilized to calculate amount of unbalance and judge whether it meets required precision: if do not meet, form alternating current-direct current Jacobian matrix, computed correction is until meet; If meet and judge whether the excitation of its receiving end generator reaches the limit values, if reach, then with the output voltage V of AVR _rireach maximum V _{ri, max}re-start Load flow calculation, otherwise calculate end.

10. a kind of alternating current-direct current method for analyzing stability considering receiving end excitation system as claimed in claim 1, is characterized in that, in described step 3, load causes the change of system Thevenin's equivalence parameter after increasing, the generator excitation of receiving-end system is sufficient, in the process that load increases, and V _r≤ V _rmax, when load increases, the generator excitation of receiving end needs constantly to increase, and terminal voltage reduces, the power reduction of direct current conveying; The generator excitation of receiving-end system is limited, in the process of load growth, gets V _r=V _rmax, when the excitation of generator is restricted, the fail safe of system is subject to great threat, and receiving end busbar voltage and power continue to raise.