CN106294993B - A kind of transient energy function analysis method considering inverter current saturation - Google Patents
A kind of transient energy function analysis method considering inverter current saturation Download PDFInfo
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Abstract
The present invention provides a kind of transient energy function analysis method of consideration inverter current saturation, based on inverter virtual synchronous generator control policy grounds, by establishing the virtual synchronous generator amature equation of motion and considering the current saturation factor of inverter, transient energy function is constructed using first integral method, use linear path method approximate for the item that can not accumulate in transient energy function with path-dependent, then critical energy value is obtained using BCU method, and obtains critical clearing time.The present invention considers that the transient energy function analysis method of virtual rotation inertia and inverter current saturation can quantitatively assess the stability of the electric system containing virtual synchronous generator, the transient energy function constructed considers the saturation factor of inverter, closer to reality, it solves the problems, such as that traditional online evaluation conservative causes system unstable, is a kind of important supplement to time-domain simulation method.
Description
Technical field
The present invention designs a kind of power system stability and control technology, especially a kind of to consider the temporary of inverter current saturation
State energy function analysis method.
Background technique
Currently, with distributed generation resource permeability be continuously increased and distributed generation resource is connected with power grid electric power electricity
For sub- device by the way of Digital Circuit Control, transient response speed is fast, and almost without inertia, when DG accounts for certain proportion
When, the small disturbance of power grid can cause safety and stability problem.In this context, domestic and foreign scholars propose virtual synchronous power generation
Machine technology realizes the friendly of distributed generation resource by the operation logic that control inverter simulates synchronous generator and accesses.
Synchronous generator inertia is simulated in gird-connected inverter to the research domestic and foreign scholars focus of virtual synchronous generator
And damping has ignored although some scholars consider the analysis of virtual rotation inertia inverter transient energy function with void
Influence of the current saturation characteristic of the sagging control inverter of quasi- inertia to transient stability, the critical clearing time obtained in this way
It is too conservative, when system online evaluation can because the mute time it is too long so as to cause this unstable significant problem of system,
National economy is directly influenced, therefore, needs to consider that inverter current is saturated factor for instability problem caused by conservative
Influence to transient stability.
Summary of the invention
The purpose of the present invention is to provide a kind of transient energy function analysis methods of consideration inverter current saturation, solve
The critical clearing time that traditional consideration virtual rotation inertia inverter transient energy function analysis method obtains too is protected
It keeps, it can be too long so as to cause this unstable significant problem of system because of the mute time when system online evaluation.
This method the following steps are included:
Step 1, the detail mathematic model of the electric system containing virtual synchronous generator, the model packet are established to inverter
Include the two rank model rotor equations of motion and nonlinear load equation and network equation similar to conventional electric generators；
Step 2, transient energy function is constructed using first integral method, is write equation of rotor motion as first-order system, benefit
Both sides are integrated simultaneously with first integral method, and inverter current saturation factor is taken into account to the energy of construction meter and damping
Amount type liapunov function, in transient energy function and path-dependent can not to accumulate item approximate using linear path method；
Step 3, critical energy value is obtained using BCU method: first calculating failure when path to the fault clearance moment and extremely
Exit point calculates the energy at the moment using the parameter at fault clearance moment, then calculates the minimal gradient point of post-fault system
And unstable uneven point is dominated according to power balance equation acquisition is solved, and by the dotted state gain of parameter critical energy value；
Step 4, when transient state energy be equal to controlling unstable equilibrium point at energy when solve obtain critical clearing time.
The present invention acquires the critical fault mute time and carries out with traditional transition energy that inverter is saturated of ignoring
Comparison is closer in reality.
The present invention is described further with reference to the accompanying drawings of the specification.
Detailed description of the invention
Fig. 1 is to consider virtual rotation inertia inverter transient energy function analysis method flow chart.
Fig. 2 is three virtual synchronous generators, nine node system analogous diagram.
Fig. 3 is that BCU method obtains transition energy and CCT flow chart.
Fig. 4 is system gross energy and kinetic energy and potential energy simulation result diagram.
Specific embodiment
The invention discloses the transient energy function analysis sides of a kind of consideration virtual rotation inertia and inverter current saturation
Method is based on inverter virtual synchronous generator control policy grounds, by establishing the virtual synchronous generator amature equation of motion
And consider the current saturation factor of inverter, transient energy function is constructed using first integral method, in transient energy function
It uses linear path method approximate with the item that can not accumulate of path-dependent, critical energy value is then obtained using BCU method, is finally led to
The crash time for crossing acquisition critical clearing time and time-domain-simulation acquisition is compared.Consideration virtual rotation inertia of the invention
With inverter current saturation transient energy function analysis method can quantitatively to the power train containing virtual synchronous generator
The stability of system is assessed, and the transient energy function constructed considers the saturation factor of inverter, closer to reality, is solved
The problem that traditional online evaluation conservative causes system unstable, is a kind of important supplement to time-domain simulation method.Tool
Body embodiment is following (as shown in Figure 1):
Step 1, the detail mathematic model of the electric system containing virtual synchronous generator, the model packet are established to inverter
Include the two rank model rotor equations of motion and nonlinear load equation and network equation similar to conventional electric generators；
Step 2, transient energy function is constructed using first integral method, is write equation of rotor motion as first-order system, benefit
Both sides are integrated simultaneously with first integral method, and inverter current saturation factor is taken into account to the energy of construction meter and damping
Amount type liapunov function, in transient energy function and path-dependent can not to accumulate item approximate using linear path method；
Step 3, critical energy value is obtained using BCU method: first calculating failure when path to the fault clearance moment and extremely
Exit point calculates the energy at the moment using the parameter at fault clearance moment, then calculates the minimal gradient point of post-fault system
And unstable uneven point is dominated according to power balance equation acquisition is solved, and by the dotted state gain of parameter critical energy value；
Step 4, when transient state energy be equal to controlling unstable equilibrium point at energy when solve obtain critical clearing time.
Specifically
The first step establishes the detail mathematic model containing electric system, including:
1. establishing the equation of rotor motion of virtual synchronous generator.Inverter uses virtual synchronous generator control strategy,
The two rank model rotor equations of motion that foundation is similar to conventional electric generators are as follows；
In formula, E represents node voltage, θi、Respectively i-th generator relative to the center of inertia rotor angle and
Angular frequency, unit are respectively rad, rads-1、MiFor the inertia constant of i-th generator, unit s2·rad-1, PMiIt represents
The mechanical output of i-th virtual synchronous generator, PemiThe electromagnetic power of i-th virtual synchronous generator is represented, inverter is maximum
Electric current is ImaxAndθi=δi-δ0,
In formula, δiFor the rotor velocity of i-th generator, unit rad, ωiFor angular frequency, unit rads-1,
PCOIFor the accelerating power in the center of inertia, m is the quantity of virtual synchronous generator, δ0、ω0The respectively rotor angle speed in the center of inertia
Degree and angular frequency.
2. nonlinear load model
In formula, Pli, QliThe respectively idle and active power of load absorption.
3. network equation
From the active power and reactive power in node i injection network are as follows:
In formula, Pi, QiActive power and reactive power respectively in node i injection network.
Second step obtains transient energy function.
Transient energy function is constructed using first integral method.Equation of rotor motion is write as first-order system, using for the first time
Integration method integrates both sides simultaneously, and inverter current saturation factor is taken into account to energy type Lee of construction meter and damping
Ya Punuofu function such as formula (4)~(7), in transient energy function and path-dependent can not accumulate item using linear path method
Approximation, detailed process is as follows:
VP=VP1+VP2+VP3+VP4+Vdamping (5)
VP4=VP41+VP42+VP43 (6)
Wherein, V is the energy function, VKFor the kinetic energy of virtual synchronous generator, VPFor the total potential energy of system, VP1For
Rotor potential energy caused by whole virtual synchronous generator mechanical power inputs, VP2For potential energy caused by whole active loads, VP3For
Potential energy caused by whole reactive loads, VP4For storage and the potential energy in network, behalf stable equilibrium point, i, j are the index of node
Value, n is node number, DiFor the damping of i-th generator, Bij、BiiTransadmittance and node i respectively between node i, j from
Admittance, Ei、EjIt is node i, the voltage at j respectively,For the angular frequency of i-th generator, θiFor i-th generator relative to
The rotor angle in the center of inertia, wherein a is that constant value is generally 2.
Third step obtains critical energy value.
In conjunction with Fig. 3, obtaining critical energy value using BCU method, steps are as follows
Step 3-1 writes out its pinch system such as formula (8) for formula (1) electric power system model
Then path when failure is usedSeek exit point θEP, it is that there are pinch systems is steady for projection path
It is fixed more borderline, path when its failure available by formula (1).Detect exit point θEPIt is to reach first by projection path
A potential energy of local maximum value.Power deviation amount equation after failure is namely brought by the θ value that formula (1) obtains:
When meeting condition fi* θ=0 d, namelyAfter obtain θEP.In order to correctly obtain exit point, detect
Precision chooses 10-5。
Step 3-2 integrates formula (8) resulting pinch system, using exit point θ EP as initial point along integral
Curve looks for first minimum value shown in formula (10):
First obtained minimum value is known as minimal gradient point θMGP。
Step 3-3, with minimal gradient point θEPFor initial value, (m-1) a failure is iteratively solved with Newton-Raphson method
Power deviation amount equation afterwards:
Obtain the controlling unstable equilibrium point CUEP of pinch system.The state parameter of CUEP is substituted into formula (7) transient state energy
Function calculates critical energy value Vcr。
4th step obtains critical clearing time and assesses transient stability.
The resulting transient state energy value of formula (7) is enabled to be equal to critical energy value V obtained in third stepcr, to acquire critical
Fault clearing time simultaneously carries out stability assessment.
Consideration virtual rotation inertia inverter transient energy function analysis method proposed by the present invention is analyzed by emulating
Validity.Generator based on traditional 3 machine of IEEE, 9 node system changes virtual synchronous generator into and contains current limit
On device, is analyzed respectively in different route setting three phase short circuit faults, obtain different critical clearing times and system
Energy includes the kinetic energy of system and potential energy is shown in attached drawing 4, and the CCT result obtained with time-domain-simulation compares.Analogue system figure
See attached drawing 2, the parameter of virtual synchronous generator is as shown in table 1, and obtained critical clearing time is as shown in table 2.
The different virtual synchronous generator parameters of table 1
| Parameter | Size |
| Filter capacitor | 35uF |
| Dead resistance | 0.5′Ω |
| Load | 50′Ω |
| DC voltage | 650V |
| Network voltage | 380V |
| Line impedance | 0.01+j0.377′Ω |
| PR proportionality constant kp | 150 |
| PR integration time constant ki | 4 |
| Mains frequency f0 | 50Hz |
| Reactive-power control coefficient kq | 1×10-4 |
| Voltage regulation coefficient kv | 3.5×10-2 |
| Rated capacity S1 | 247.5MVA |
| Rated capacity S2 | 192.0MVA |
| Rated capacity S3 | 128.0MVA |
Table 2 considers that inverter current is saturated different route three phase short circuit faults and obtains CCT
| Malfunctioning node | Faulty line | CCT transient energy function | CCT time-domain-simulation |
| 4 | 4-5 | 0.160 | 0.162 |
| 4 | 4-6 | 0.155 | 0.160 |
| 5 | 5-7 | 0.165 | 0.168 |
| 6 | 6-9 | 0.174 | 0.179 |
| 7 | 7-8 | 0.175 | 0.18 |
| 8 | 8-9 | 0.130 | 0.135 |
Table 3 does not consider that inverter current is saturated different route three phase short circuit faults and obtains CCT
| Malfunctioning node | Faulty line | CCT transient energy function | CCT time-domain-simulation |
| 4 | 4-5 | 0.164 | 0.168 |
| 4 | 4-6 | 0.159 | 0.164 |
| 5 | 5-7 | 0.169 | 0.173 |
| 6 | 6-9 | 0.178 | 0.182 |
| 7 | 7-8 | 0.180 | 0.184 |
| 8 | 8-9 | 0.136 | 0.140 |
According to table 2 and the comparison of table 3 it is found that traditional transient energy function analysis for not considering inverter current saturation factor
The critical clearing time that method obtains is longer than the time for considering inverter current saturation factor, if fault clearing time is long
It will cause the unstable of system, and the critical clearing time (CCT) and time-domain-simulation that are obtained using transient energy function method are obtained
The error very little arrived, also the verifying present invention considers the transient energy function analysis side of virtual rotation inertia and inverter current saturation
The validity of method.Therefore, for the method for the present invention closer to reality, solving traditional online evaluation conservative causes system unstable
The problem of, it is a kind of important supplement to time-domain simulation method.
Claims (5)
1. a kind of transient energy function analysis method for considering inverter current saturation, comprising the following steps:
Step 1, the detail mathematic model of the electric system containing virtual synchronous generator is established to inverter, which includes class
It is similar to the two rank model rotor equations of motion and nonlinear load equation and network equation of conventional electric generators；
Step 2, transient energy function is constructed using first integral method, is write equation of rotor motion as first-order system, utilizes head
Secondary integration method integrates both sides simultaneously, and inverter current saturation factor is taken into account to the energy type of construction meter and damping
Liapunov function, in transient energy function and path-dependent can not to accumulate item approximate using linear path method；
Step 3, obtain critical energy value using BCU method: path is exported to the fault clearance moment and extremely when calculating failure first
Point calculates the energy at the moment using the parameter at fault clearance moment, then calculates the minimal gradient point and root of post-fault system
Unstable uneven point is dominated according to power balance equation acquisition is solved, and by the dotted state gain of parameter critical energy value；
Step 4, when transient state energy be equal to controlling unstable equilibrium point at energy when solve obtain critical clearing time.
2. the method according to claim 1, wherein the mathematical model in step 1 is
In formula, E represents node voltage, Ei、EjIt is node i, the voltage at j, θ respectivelyi、Respectively i-th generator relative to
The rotor angle and angular frequency in the center of inertia, MiFor the inertia constant of i-th generator, PMiRepresent i-th virtual synchronous power generation
The mechanical output of machine, PemiRepresent the electromagnetic power of i-th virtual synchronous generator, IijThe line current between node i and node j,
Inverter maximum current is Imax；
In formula, δiFor the rotor velocity of i-th generator, ωiFor angular frequency, PCOIFor the accelerating power in the center of inertia, m is void
The quantity of quasi- synchronous generator, δ0、ω0The respectively rotor velocity and angular frequency in the center of inertia.
3. according to the method described in claim 2, it is characterized in that, inverter current saturation factor is taken into account in step 2
Construction meter and the energy type liapunov function of damping are as follows:
VP=VP1+VP2+VP3+VP4+Vdamping (3)
Wherein, V is the energy function, VKFor the kinetic energy of virtual synchronous generator, VPFor the total potential energy of system, VP1For whole
Rotor potential energy caused by virtual synchronous generator mechanical power input, VP2For potential energy caused by whole active loads, VP3For whole
Potential energy caused by reactive load, VP4To store and the potential energy in network, behalf stable equilibrium point, the index value of i, j for node, n
For node number, DiFor the damping of i-th generator, Bij、BiiThe self-admittance of transadmittance and node i respectively between node i, j,
Ei、EjIt is node i, the voltage at j respectively,For the angular frequency of i-th generator, θiIt is i-th generator relative to inertia
The rotor angle at center, wherein a is that constant value is generally 2.
4. according to the method described in claim 3, it is characterized in that, the detailed process of the step 3 are as follows:
Step 3.1, its pinch system such as following formula is obtained to formula (1)
Path when step 3.2, with failureSeek exit point θEP, θEPIt is that there are pinch systems is steady for projection path
It is fixed more borderline, specially
θ is obtained by the detail mathematic model of electric systemEPPath when failure, power is inclined after bringing failure by the θ value that formula (1) obtains
Residual quantity equation detects exit point θEPIt is that first potential energy of local maximum value is reached by projection path；Wherein departure equation is
When meeting condition fi* θ is obtained behind θ=0 dEP；
Step 3.3, with exit point θEPFor initial point, formula (6) resulting pinch system is integrated, is gone along the curve of integral
First minimum value shown in seeking (7)
First obtained minimum value is minimal gradient point θMGP；
Step 3.4, with minimal gradient point θMGPFor initial value, function after (m-1) a failure is iteratively solved with Newton-Raphson method
Rate departure equation
Obtain the controlling unstable equilibrium point CUEP of pinch system；
Step 3.4, state parameter θ, ω of CUEP are substituted into formula (2) and obtains critical energy value Vcr。
5. according to the method described in claim 4, it is characterized in that, in step 4, if the critical energy value V that step 3.4 obtainscr
Equal to the resulting transient state energy value of formula (2), obtain corresponding θ, ω, found in time-domain-simulation θ, ω obtained it is corresponding when
Between value be critical clearing time.
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