CN109149665A - Multi-rate simulating method and system for flexible direct current AC network associative simulation - Google Patents
Multi-rate simulating method and system for flexible direct current AC network associative simulation Download PDFInfo
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J5/00—Circuit arrangements for transfer of electric power between ac networks and dc networks
Abstract
The present invention relates to a kind of multi-rate simulating method and system for flexible direct current AC network associative simulation, establish the electric network model of the large-scale AC-DC hybrid power grid containing VSC based on multi tate；Small step-length VSC model is established according to electric network model；Small step-length VSC model is emulated with AC system emulation interface；Small step-length voltage source converter VSC model is calculated based on discrete Newton method is simplified.This method can use different simulation step lengths to flexible direct current system and AC system, and direct current component step-length is variable, and minimum to can be as small as 0.0001s, AC network uses the typical step-length of electromechanical transient.AC network provides information to VSC in a manner of linear interpolation；VSC injects the mean power that AC network uses multiple time steps.The computational efficiency of the large-scale power grid with different simulation step length models can be improved using multi-rate simulating；Improve alternating iteration convergence problem caused by the high-power injection AC network of VSC with discrete Newton method is simplified.
Description
Technical field
The present invention relates to a kind of Transient-State Analysis of Power System calculation methods, and in particular to one kind is used for flexible direct current alternating current
The multi-rate simulating method and system of net associative simulation.
Background technique
Voltage source converter high voltage direct current (Voltage Source Converter-High Voltage Direct
Current, VSC-HVDC) excellent operation characteristic, necessarily become the important transmission facility of the following ultra-large power grid.Construction
VSC-HVDC machine-electricity transient model with enough accuracy and calculating speed, to support that large scale electric network stability analysis is future
The basis of electric power netting safe running.
VSC machine-electricity transient model is the simplification of electrical-magnetic model, and research at present concentrates on 2 aspects.First is that by large-scale
The custom feature of electromechanical transient simulation software models, as document is based on NETOMAC, document is based on PSASP, document is based on
PSS/E.This model usually ignores a large amount of details, retains converter valve, the dynamic of control system and DC line.Another is to build
Practical VSC-HVDC and DC grid electromechanical model are found, has document to describe and is suitable for any direct current net topology
VSC-HVDC dynamic model；There is document to describe the model of wind power integration DC grid；There is document to give practical based on small
The VSC-HVDC machine-electricity transient model of step-length and quasi-steady state converter valve；Have document list with different the level of detail based on
The VSC-HVDC machine-electricity transient model of fundamental wave average value converter valve model.But above-mentioned document, which does not provide, is suitable for extensive electricity
Network simulation has enough accuracy and reliability VSC-HVDC machine-electricity transient model.By retrieval, related patents Shen is found no
Please.
Summary of the invention
To solve above-mentioned deficiency of the prior art, the object of the present invention is to provide one kind to be used for flexible direct current AC network
The multi-rate simulating method and system of associative simulation, this method is to VSC converter valve and DC grid using different from AC network
Simulation step length guarantee the computational efficiency in computational accuracy and bulk power grid；Improve VSC converter station function with discrete Newton method method is simplified
Rate injects extensive AC network bring convergence problem.
The purpose of the present invention is adopt the following technical solutions realization:
The present invention provides a kind of emulation mode of flexible direct current-AC network, it is improved in that the method packet
It includes:
Establish the electric network model of the large-scale AC-DC hybrid power grid containing VSC based on multi tate；
Small step-length VSC model is established according to electric network model；
Small step-length VSC model is emulated with AC system emulation interface；
Small step-length voltage source converter VSC model is calculated based on discrete Newton method is simplified.
Further, the electric network model for establishing the large-scale AC-DC hybrid power grid containing VSC based on multi tate is as follows
Shown in formula (1)~(6):
0=As(xs,ys,Gs(yf),zs,t) (2)
0=Ls(xs,ys,zs,t) (3)
0=Af(xf,Gf(ys),yf,zf,t) (5)
0=Lf(xf,yf,zf,t) (6)
The electric network model of the large-scale AC-DC hybrid power grid containing VSC based on multi tate includes fast change system and becomes system slowly
System, in which: formula (1)~(3) are followed successively by the differential equation D of slowly varying systems, algebraic equation As and logical equation Ls；X is state
Variable, y are algebraic variable, and z is logical variable；Subscript behalf slowly varying system, f represent fast change system；Gs(yf) it is slowly varying system
Mapping of the algebraic quantity in fast change system；Gf(ys) it is the fast mapping for becoming system algebraic quantity in slowly varying system；xs,ys,zs, t points
Not Wei slowly varying system state variable, algebraic variable, logical variable and time；Formula (4)~(6) are the fast differential side for becoming system
Journey Df, algebraic equation Af and logical equation Lf；xf,yf,zf, t is respectively the fast state variable for becoming system, algebraic variable, logic
Variable and time t represent the time；Fast change system and slowly varying system in formula (1)~(6) only have algebraic quantity coupling, respective system
The convergence of integral is determined by hiding-trapezium integral method and given step-length.
It is further, described that small step-length VSC model is established according to electric network model, comprising:
Determine the voltage interpolation between the n-th step of slowly varying system and n+1 step and the power of receiving；
Speed system alternately solves differential algebraic equations using the hiding-trapezium integral method of fixed step size.
Further, the voltage interpolation expression between n-th step of slowly varying system and n+1 step is as follows:
The power such as following formula that slowly varying system receives:
Wherein: setting the fast system step-length that becomes as h, slowly varying system step-length is H=mh, and m is integer；It is fast to become each time step outlet of system
Busbar voltage is obtained by the corresponding busbar voltage interpolation of slowly varying system, VfIt (nm+i) is the fast voltage interpolation for becoming the i-th step of system；Vs
It (n) is the voltage interpolation of the n-th step of slowly varying system；VsIt (n+1) is the voltage interpolation of the (n+1)th step of slowly varying system；GfIt is fast to become system generation
Mapping of the quantity in slowly varying system；The expression step-length of n slowly varying system；Slowly varying system from the power that fast change system receives be fast
M walks the average value of power, S before change systems(n+1) power received for the (n+1)th step of slowly varying system；Is(n+1) become system to be slow
The electric current that (n+1)th step of uniting receives；The conjugation for the power that the (n+1)th step of slowly varying system receives；For slowly varying system
The conjugation of the voltage interpolation of (n+1)th step；
It is as follows using hiding-trapezium integral method and differential algebraic equations the alternating solution of fixed step size to speed system:
Wherein: according to implicit trapezoidal rule, formula (1), (4) difference turn to algebraic expression (10), (11), x respectivelys(n+1)、xs
(n) be respectively slowly varying system the (n+1)th step and the n-th step state variable；ys(n+1)、ysIt (n) is respectively the (n+1)th step of slowly varying system
With the algebraic variable of the n-th step；zs(n+1)、zsIt (n) is the logical variable of slowly varying system the (n+1)th step and the n-th step； xf(k+1)、xf
It (k) is respectively the fast state variable for becoming+1 step of system kth and kth step；yf(k+1)、yfIt (k) is respectively fast change+1 step of system kth
With the algebraic variable of kth step；zf(k+1)、zf(k) logical variable walked for+1 step of slowly varying system kth and kth；Df(xf(k+
1))、Df(xfIt (k)) is respectively the fast differential equation for becoming the state variable that+1 step of system kth and kth walk； Ds(xs(n+1))、Ds
(xs(n)) be respectively the (n+1)th step of slowly varying system and the n-th step state variable the differential equation.
It is further, described that small step-length VSC model is emulated with AC system emulation interface, comprising:
1) the n-th step of slowly varying system solves the logical equation Ls unrelated with quantity of state in slowly varying system it is known that solve a step,
And update the differential equation D of slowly varying systemsWith algebraic equation As；
2) assume that whole network voltage remains unchanged in slow system, by element complexity successively or in iterative solution slowly varying system
Equation relevant with component models and by differential equation D in logical equation Ls relevant to quantity of state, algebraic equation AssDifference
Break up obtained formula, calculates each element injection AC network electric current；
3) small step-length VSC model is carried out from the n-th m+1 to (n by the voltage interpolation between the n-th step of slowly varying system and n+1 step
+ 1) the port voltage difference of m step, successively carries out the interpolation of of ac；
4) small step-length emulation is carried out, formula, the fast algebraic equation for becoming system of the Df differencing of the formula differential equation are iteratively solved
Af and logical equation Lf m times, obtain to walk from the n-th m+1 to (n+1) m and walk inverter inside state and output active reactive；
5) inverter injects power network current in the small step-length VSC model of power calculation received by slowly varying system；
6) network equation in Solving Algebraic Equation As updates whole network voltage；
7) whether inspection state amount and algebraic quantity restrain, if having restrained, enable n=n+1, calculate into next step, otherwise return
To step 2) iteration.
Further, described constringent based on the small step-length voltage source converter VSC model of discrete Newton method progress is simplified
It calculates, comprising:
A, when the number of iterations k is 0, small step-length VSC model is solved；
B, judge whether electric current residual error is less than setting value, if satisfied, then exporting current flow and voltage；Otherwise, it is walked
Rapid C；
C, the number of iterations k=k+1 is enabled, and judges whether updated the number of iterations k is less than k1, if being less than, returns to step
Rapid A；Otherwise, step D is carried out；
D, it solves with discrete Newton method formula is simplified, judges whether electric current residual error meets the requirements；If so, the current electricity of output
Stream and voltage；Otherwise, another the number of iterations k=k+1；
E, judge whether updated the number of iterations k is less than k2, if so, return step D；Otherwise the minimum electricity of output residual error
Stream and corresponding voltage；K1, k2 are the number of iterations upper limit of setting.
Further, in the step A, the D dimension Nonlinear System of Equations and Iteration of small step-length VSC model are public as follows
Formula:
F (x)=0 (12)
x(k+1)=x(k)-J(x(k),h(k))-1F(x(k)) (15)
Wherein: its mathematics, which is in the nature that D dimension is non-linear, to be determined to the network equation formed in the algebraic equation As of slowly varying system
Equation group, such as formula (12), Iteration is formula (13)~(15)；N indicates step-length；X is Injection Current column vector, and dimension D is
Bus number；F(x(k)) be kth time iteration demand solution Nonlinear System of Equations, element f1(x(k))、f2(x(k))、…fn(x(k))；H is independent variable deviation；J is quasi- Jacobian matrix；e1It is the 1st D Wiki our unit vector, j=1,2 ..., n；h(k)
For the independent variable deviation of kth time iteration；The independent variable deviation for being j for kth time iteration step length；x(k)For the note of kth time iteration
Enter the independent variable of electric current column vector.
Further, to before needing the large-scale power grid emulation of multiple differential algebra alternating iteration, arranged as follows:
1) residual error of Injection Current is represented with D dimension Nonlinear System of Equations, i.e. certain currents combination injects power grid, solves each mother
Line voltage, then update the difference that after currents combination and primary current combines；If residual error is 0, small step-length VSC model is able to maintain power
For given value；Since the electric current of non-control power component injection bus is constant always, D ties up Nonlinear System of Equations such as:
In formula, x is Injection Current column vector, and dimension n is bus number；Xvsc retains VSC by x and exports bus corresponding element
Element, other elements are all set 0 and are obtained；Y is node admittance battle array；Diag () indicates column vector turning to diagonal matrix；Svsc is column
Vector, only in the outlet VSC, bus corresponding position has non-zero element, is worth the apparent energy to obtain；
Simple Iteration is carried out to formula (16), as follows:
2) difference for intending the currents combination that Jacobian matrix element is 2 injection power grids, is the electricity of kth time and the 0th iteration
Flow the difference of combination, expression formula are as follows:
Large-scale power grid emulation to multiple differential algebra alternating iteration is needed, formula (14) generate quasi- Jacobian, formula (15)
In the calculation amount inverted to quasi- Jacobian is excessive need to take approximation, it is as follows:
The diagonal element of right side matrix is as follows:
After above-mentioned restriction and assuming, it is simplified the formula of discrete Newton method, it is as follows；
The variation of bus Injection Current will not cause other bus current residual errors to change, i.e. matrix non-diagonal on the right side of formula (14)
Line element is 0, becomes diagonal matrix；The electric current residual error of bus is determined that the variation of currents combination is in bus by bus Injection Current
Caused residual error variation is identical as the residual error that the variation of bus Injection Current generates only is retained；
Wherein: formula (19) is to emulate to the large-scale power grid for needing multiple differential algebra alternating iteration, is generated to formula (14) quasi-
The approximation that Jacobian is taken；For the Injection Current column vector of kth time iteration and the 0th iteration；Point
Not Wei+1 iteration of kth and kth time iteration voltage source converter VSC mold exit bus corresponding element and other members retained by x
Element is set 0 and is obtained.
The present invention also provides a kind of analogue systems of flexible direct current-AC network, the improvement is that: including:
First building module, for establishing the electric network model of the large-scale AC-DC hybrid power grid containing VSC based on multi tate；
Second building module, for establishing small step-length VSC model according to electric network model；
Emulation module, for being emulated to small step-length VSC model with AC system emulation interface；
Computing module, for calculating small step-length voltage source converter VSC model based on simplified discrete Newton method.
Further: the second building module further comprises:
Determining module, for determining the voltage interpolation between the n-th step of slowly varying system and n+1 step and the power of receiving；
Module is solved, for alternately being asked differential algebraic equations using the hiding-trapezium integral method of fixed step size speed system
Solution；
The emulation module, is also used to:
1) the n-th step of slowly varying system solves the logical equation Ls unrelated with quantity of state in slowly varying system it is known that solve a step,
And update the differential equation D of slowly varying systemsWith algebraic equation As；
2) assume that whole network voltage remains unchanged in slow system, by element complexity successively or in iterative solution slowly varying system
Equation relevant with component models and by differential equation D in logical equation Ls relevant to quantity of state, algebraic equation AssDifference
Break up obtained formula, calculates each element injection AC network electric current；
3) small step-length VSC model is carried out from the n-th m+1 to (n by the voltage interpolation between the n-th step of slowly varying system and n+1 step
+ 1) the port voltage difference of m step, successively carries out the interpolation of of ac；
4) small step-length emulation is carried out, formula, the fast algebraic equation for becoming system of the Df differencing of the formula differential equation are iteratively solved
Af and logical equation Lf m times, obtain to walk from the n-th m+1 to (n+1) m and walk inverter inside state and output active reactive；
5) inverter injects power network current in the small step-length VSC model of power calculation received by slowly varying system；
6) network equation in Solving Algebraic Equation As updates whole network voltage；
7) whether inspection state amount and algebraic quantity restrain, if having restrained, enable n=n+1, calculate into next step, otherwise return
To step 2) iteration.
Compared with the immediate prior art, technical solution provided by the invention is had the beneficial effect that
Provided by the present invention for the alternating current-direct current power grid transient emulation method containing flexible HVDC transmission system.This method can be right
Flexible direct current system and AC system use different simulation step lengths, and direct current component step-length is variable, minimum to can be as small as 0.0001s, hand over
Flow network uses the typical step-length of electromechanical transient.AC network provides information to VSC in a manner of linear interpolation；VSC injection exchange
Power grid uses the mean power of multiple time steps.The large size electricity with different simulation step length models can be improved using multi-rate simulating
The computational efficiency of net；It is asked with alternating iteration convergence caused by the discrete Newton method improvement high-power injection AC network of VSC is simplified
Topic.
Detailed description of the invention
Fig. 1 is that simplified discrete Newton method provided by the invention solves flow chart；
Fig. 2 is the one sided network wiring diagram of specific embodiment provided by the invention；
Fig. 3 is the three-phase fault sending end state diagram of specific embodiment provided by the invention；Wherein: (a) active/MW；(b) nothing
Function/MVR；(c) DC voltage/p.u.；(d) change of current power transformation voltage on line side/p.u.；P.u. per unit value is indicated；
Fig. 4 is the three-phase fault receiving end state diagram of specific embodiment provided by the invention；Wherein: (a) active/MW；(b) nothing
Function/MVR；(c) DC voltage/p.u.；(d) change of current power transformation voltage on line side/p.u.；P.u. per unit value is indicated；
Fig. 5 is the process provided by the present invention for the multi-rate simulating method of flexible direct current AC network associative simulation
Figure.
Specific embodiment
Specific embodiments of the present invention will be described in further detail with reference to the accompanying drawing.
The following description and drawings fully show specific embodiments of the present invention, to enable those skilled in the art to
Practice them.Other embodiments may include structure, logic, it is electrical, process and other change.Implement
Example only represents possible variation.Unless explicitly requested, otherwise individual component and function are sequences that is optional, and operating
It can change.The part of some embodiments and feature can be included in or replace part and the feature of other embodiments.
The range of embodiment of the present invention includes obtained by the entire scope of claims and all of claims
Equivalent.Herein, these embodiments of the invention individually or can be indicated generally with term " invention ", this
Just for the sake of convenient, and if in fact disclosing the invention more than one, it is not meant to automatically limit the model of the application
It encloses for any single invention or inventive concept.
The VSC-HVDC machine-electricity transient model that the present invention establishes is based on multi-rate simulating method, to VSC converter valve and direct current
Power grid guarantees the computational efficiency in computational accuracy and bulk power grid using the simulation step length different from AC network；It is discrete with simplification
Newton method method improves VSC converter station power and injects extensive AC network bring convergence problem.This method has been used for country
The daily simulation analysis work of power grid.The flow chart of method of the invention is as shown in Figure 5, comprising:
1. the alterating and direct current network simulation frame containing flexible direct current system based on multi tate method
Multi tate method is a kind of method for solving ordinary differential system, is proposed by Gear, and is containing power electronics, high voltage direct current
There is extensive application in the emulation fields such as transmission of electricity.This method is suitable for the system with broad time response, its main feature is that different changes
Amount takes different simulation step lengths, to meet computational efficiency and guarantee precision, passes through the methods of interpolation coupling between slow-fast variables
It closes.
Large-scale AC-DC hybrid power grid containing VSC has the apparent two kinds of response speeds of difference, is applicable in multi tate method, but
The weak coupling of its complicated power grid characteristic and inverter and AC network, forms special restriction to algorithm.The electric network model is such as
Formula (1)~(6).
0=As(xs,ys,Gs(yf),zs,t) (2)
0=Ls(xs,ys,zs,t) (3)
0=Af(xf,Gf(ys),yf,zf,t) (5)
0=Lf(xf,yf,zf,t) (6)
Formula (1)~(3) are followed successively by the differential equation D of slowly varying systems, algebraic equation As and logical equation Ls；X is state change
Amount, y is algebraic variable, and z is logical variable；Subscript behalf slowly varying system, f represent fast change system；Gs(yf) it is slowly varying system generation
Mapping of the quantity in fast change system；Gf(ys) it is the fast mapping for becoming system algebraic quantity in slowly varying system；xs,ys,zs, t difference
For the state variable of slowly varying system, algebraic variable, logical variable and time；Formula (4)~(6) are the fast differential equation for becoming system
Df, algebraic equation Af and logical equation Lf；xf,yf,zf, t is respectively the fast state variable for becoming system, algebraic variable, logic change
Amount and time .t represent the time.
The differential equation describes the dynamic changing process of quantity of state, is typically found in inside element and (power grid is considered as AC network
Network and the element 2 being connected to thereon are most of)；Algebraic equation characterizes the positive connection for being unrelated with the time or ignoring time effects, main
Refer to the topological constraints of AC network, the algebra in generally linear nodal voltage equation and certain component models closes
System；Logical equation refers to the condition of satisfaction there is a phenomenon where jumping, such as failure occurs, out-of-limit judgement, protection act.It is fast to become system
Refer to VSC and DC grid (other equipment containing power electronic element can be analogized by context of methods, not propose individually), power grid is surplus
Remaining part point is slowly varying system.Although the problem of variation speed is not present in algebra, logical variable, in simulations following state
The every time step of variable updates, and corresponding with state variable need to divide.Speed system is mutually coupled in the outlet VSC bus by algebraic quantity.
2. small step-length VSC model and AC system emulation interface and calculation process:
If becoming system step-length fastly as h, slowly varying system step-length is H=mh, and m is integer.The fast each time step of system that becomes exports bus
Voltage corresponds to busbar voltage interpolation by slowly varying system and obtains, and formula (7) describes the voltage between the n-th step of slowly varying system and n+1 step
Interpolation.For convenience, the vectorial of voltage is saved, hereafter apparent energy, electric current etc. also save.Other slowly varying systems are transmitted to
The fast of ac for becoming system uses linear interpolation, similar with formula (7).
Wherein: VfIt (nm+i) is the fast voltage interpolation for becoming the i-th step of system；VsIt (n) is the voltage interpolation of the n-th step of slowly varying system；
VsIt (n+1) is the voltage interpolation of the (n+1)th step of slowly varying system；GfThe fast mapping for becoming system algebraic quantity in slowly varying system；N becomes slowly
The expression step-length of system；
M walks the average value of power before slowly varying system is fast change system from the power that fast change system receives.Formula (8) is slow becomes
The power that the (n+1)th step of system receives, corresponding electric current such as formula (9).Wherein, apparent energy S=P+jQ, " * " indicate conjugation.Cause
Voltage and current remains unchanged in one step-length, and formula (8), (9) mean in a slow variable step, and slowly varying system receives and fast change
The energy of system output is equal.
Wherein: Ss(n+1) power received for the (n+1)th step of slowly varying system；Is(n+1) receive for the (n+1)th step of slowly varying system
Electric current；The conjugation for the power that the (n+1)th step of slowly varying system receives；It is inserted for the voltage of the (n+1)th step of slowly varying system
The conjugation of value；
Since logical variable exists, differential in electric network model, there are discontinuous points for Algebraic Equation set, and being largely can not be pre-
The discontinuous point known.Power grid scale is bigger, and discontinuous point is more.This makes the various continuitys based on equation, and needs to consider as a whole
Formula (1)~(6) solution, such as Variable Step Algorithm[17], differential algebraic equations simultaneous solution method[18], need to often identify interruption, weight
New starting, processing is complicated, and efficiency is lower[17].Therefore the hiding-trapezium integral method of fixed step size and micro- is mainly used to speed system
Algebraic equation is divided alternately to solve[18].According to implicit trapezoidal rule, formula (1), (4) difference turn to algebraic expression (10), (11).
Wherein: xs(n+1)、xs(n) be respectively slowly varying system the (n+1)th step and the n-th step state variable；ys(n+1)、ys(n)
The respectively algebraic variable of slowly varying system the (n+1)th step and the n-th step；zs(n+1)、zsIt (n) is the (n+1)th step of slowly varying system and the n-th step
Logical variable；xf(k+1)、xfIt (k) is respectively the fast state variable for becoming+1 step of system kth and kth step； yf(k+1)、yf(k)
Respectively become the algebraic variable of+1 step of system kth and kth step fastly；zf(k+1)、zf(k) it is walked for+1 step of slowly varying system kth and kth
Logical variable；Df(xf(k+1))、Df(xfIt (k)) is respectively the fast differential for becoming the state variable that+1 step of system kth and kth walk
Equation；Ds(xs(n+1))、Ds(xs(n)) be respectively the (n+1)th step of slowly varying system and the n-th step state variable the differential equation.
Since each element is almost independently connected to AC network, using alternately solving method, not only differential, algebraic equation be on the whole
It solves respectively, the differential equation group of each element can also be handled individually.It has no progeny between appearance, corresponding modification differential or algebraic equation
It successively solves again, processing is simple, high-efficient.Speed system in formula (1)~(6) only has algebraic quantity coupling, respective system integral
Convergence guaranteed by hiding-trapezium integral method and given step-length, the influence to solution procedure similar to common components with exchange
The coupling of power grid.To sum up, by slow the n-th step of system it is known that the grid simulation process of multi tate method is as follows for solving a step.
1) logical equation unrelated with quantity of state in formula (3) is solved；
2) newer (1), (2)；
3) assume that whole network voltage remains unchanged in slow system；
4) by element complexity equation relevant to quantity of state sequentially or in iterative solution formula (3), in formula (2) with element
The relevant equation of model and the formula (10) obtained by formula (1) differencing calculate each element injection AC network electric current；
5) port voltage walked by formula (7) interpolation VSC from the n-th m+1 to (n+1) m, other of acs that need to be used and formula
(7) similar interpolation；
6) small step-length emulation is carried out, iterative solution formula (11), (5), (6) m time obtain to walk from the n-th m+1 to (n+1) m and change
Flow device internal state and output active reactive；
7) inverter is calculated by formula (8), (9) inject power network current；
8) network equation in formula (2) is solved, whole network voltage is updated；
9) whether inspection state amount and algebraic quantity restrain, if having restrained, enable n=n+1, calculate into next step, otherwise return
To step 4) iteration.
The process takes into account the complex characteristics and different emulation rates of large-scale power grid, there is stronger practicability.But in large disturbances
In the process, converter power changes greatly, often convergence difficulties.
3. based on the VSC Model Calculating Method for simplifying discrete Newton method
After step (8) updates whole network voltage in large disturbances, the injection calculated by the newest end VSC busbar voltage and electric current is electric
Often deviation is larger for the power that the power and formula (8) of net provide, and leads to convergence difficulties.Substantially, the phenomenon is by differential and algebra
Equation alternating iteration causes, and belongs to handover error.Intuitive ameliorative way is simultaneous difference equations and algebraic equation, uses newton
Method solves.But as above described in section, simultaneous solution method needs frequently modification Nonlinear System of Equations in Bulk power system simulation, and again
Factorization, calculation amount are excessive.And the equation group scale after simultaneous sharply expands, and Newton method cannot guarantee that extensive non-
The convergence of system of linear equations.Therefore practical large-scale electromechanical transient simulation program is all based on differential algebraic equations alternating iteration and asks
Solution.
Based on alternative iteration method, if the power that can guarantee VSC injection power grid is current iteration calculated value, be conducive to power grid
State is quickly adjusted to adapt to inverter output, improves convergence.Therefore formula (2) network equation is changed in VSC bus power
Balance, other bus current balances, i.e. VSC is control power module, and network equation group is from linearly becoming non-linear.In fact, passing
System electric network element also has control power module, but because the reasons such as power is smaller, variation is slow are without specially treated, this section is mentioned
The convergence of these elements equally can be improved in the solution of confession.It should be understood that when outlet busbar voltage is very low, control
The electric current that power module is injected to power grid is excessive, may cause not convergence, should use control current system instead.
Solution Nonlinear System of Equations often uses 3 kinds of methods: Simple iterative method, Newton method, all kinds of quasi-Newton methods.Simple iterative method is received
It holds back relatively slow；Newton method needs every iteration step to update Jacobian matrix, computationally intensive；Quasi-Newton method is replaced with various approximate matrixs
Jacobian is compromised in calculation amount and convergence efficiency.Discrete Newton method belongs to one kind of quasi-Newton method, ties up to D non-thread
Property equation group (12), Iteration be formula (13)~(15).
F (x)=0 (12)
x(k+1)=x(k)-J(x(k),h(k))-1F(x(k)) (15)
Wherein: n indicates step-length；X is the independent variable of Injection Current column vector, D dimension；F(x(k)) it is kth time iteration demand solution
Nonlinear System of Equations, element f1(x(k))、f2(x(k))、…fn(x(k))；H is independent variable deviation；J is quasi- Jacobean matrix
Battle array；e1It is the 1st D Wiki our unit vector, j=1,2 ..., n；h(k)For the independent variable deviation of kth time iteration；For kth
Secondary iteration step length is the independent variable deviation of j；x(k)For the independent variable of the Injection Current column vector of kth time iteration；
The e of formula (14)jIt is j-th of D Wiki our unit vector.The Iteration core be replaced with difference coefficient it is refined in Newton method
Than matrix element, quasi- Jacobian matrix is constituted, is calculated with simplifying.Nonlinear network equation is solved using discrete Newton method, first
Arranged as follows.
1) residual error of Injection Current is represented with formula (12), i.e. certain currents combination injects power grid, each busbar voltage is solved, then
It is updated after currents combination with formula (9) and the difference that combines of primary current.If residual error is that be able to maintain power be given value to 0, VSC.Due to
The electric current of non-control power component injection bus is constant always, formula (12) writeable accepted way of doing sth (16).
In formula (16), x is Injection Current column vector, and dimension n is bus number；xvscVoltage source converter VSC is retained by x
Mold exit bus corresponding element and other elements are set 0 and are obtained；Y is node admittance battle array；Diag () is indicated column vector
For diagonal matrix；svscFor column vector, only in the outlet VSC, bus corresponding position has non-zero element, is worth and is obtained according to formula (8)
Apparent energy；For the conjugation of column vector, y-1For the inverse matrix of node admittance battle array；
Formula (16) slight variation, as simple Iteration, such as formula (17).
2) difference for intending the currents combination that Jacobian matrix element is 2 injection power grids in formula (13), such as kth time and the 0th time
The difference of the currents combination of iteration, expression formula are formula (18):
Large-scale power grid emulation to multiple differential algebra alternating iteration is needed, formula (14) generate quasi- Jacobian, formula (15)
In the calculation amount inverted to quasi- Jacobian it is still excessive, therefore take such as lower aprons.
1) the electric current residual error of certain bus is mainly determined by the bus Injection Current, therefore the variation of currents combination is in certain bus
Caused residual error variation is identical as the residual error that bus Injection Current variation generates only is retained, i.e., pair of matrix on the right side of formula (14)
Angle element can are as follows:
2) variation of certain bus Injection Current will not cause other bus current residual errors to change, i.e., matrix is non-on the right side of formula (14)
Diagonal entry is 0, becomes diagonal matrix, inverts and greatly simplifies.
After above-mentioned restriction and assuming, Iteration becomes formula (16), (20), (21), referred to as simplifies discrete Newton method.
Wherein:For the Injection Current column vector of kth time iteration and the 0th iteration；
Simplify the main calculation amount of discrete Newton method and concentrate on asking the solution Linear Network equation in electric current residual error, i.e., in formula (16)
Y-1x.The factor table after admittance battle array triangle decomposition is temporarily generally stored in steady emulation, solution network equation only needs former generation back substitution, counts
Calculation amount is little.Simplifying the hypothesis that discrete Newton method uses prevents its result from being trusted completely, practical middle using including simply repeatedly
In generation, repeatedly solves inside, takes the strategy of optimal solution.VSC Injection Current method such as Fig. 1 is sought with discrete Newton method is simplified.Wherein k1,
K2 is the number of iterations upper limit of setting.It is not restrained still when the complete k2 of iteration is walked, exports the smallest currents combination of residual error in k2 iteration
And corresponding busbar voltage, it is transferred to the alternating iteration of differential algebraic equations next time.Therefore step 7 changes in upper section emulation mode
Are as follows: inverter, which is calculated, by formula (8) injects grid power；Step 8 is changed to inject power network current by Fig. 1 workflow management VSC and update
Whole network voltage.
Embodiment one
The pseudo- bipolar MMC DC transmission system example in 2 ends is built with the mentioned method of the present invention, with electro-magnetic transient mould in PSCAD
Type comparison.One side structure of example such as Fig. 2.It is as follows as the mark parameter of base value using power system capacity to exchange each element in side: change of current power transformation
Hinder Rt=0, reactance Lt=0.075, generator reactance 0.082, commutating resistance resistance Rc=0, reactance Lc=0.083.AC line
5.683 Europe of road resistance, inductance 0.376 is prosperous, 132 microfarad of capacitor.Converter valve level number 31,600 microfarad of submodule capacitor.D axis is adopted
With master & slave control, q axis is to determine Reactive Power Control.Three-phase ground, ground connection electricity occur for 1.8s receiving end transformer power grid side bus
0.01 Europe is hindered, 0.1s is continued.
Fig. 3,4 respectively indicate sending end and receiving end inverter is active and reactive, change of DC voltage and change of current power transformation voltage on line side
Change.
Fig. 3, PSASP1 refers to all element 0.0001s step-lengths in 4, i.e. whole simulation results of small step-lengths；PSASP2 is
Converter station, DC network 0.0001s step-length, rest part 0.01s step-length, the i.e. simulation result of multi tate；PSCAD is
Electrical-magnetic model simulation result.Compare known to three kinds of the model calculations:
1) in most cases, multi-rate simulating and small step-length simulation result are almost overlapped, and illustrate the calculation of multi-rate simulating
Method is highly effective.The main distinction occurs to jump moment: the ac bus brownout of converter station at failure in failure, by control function
The duration that rate model switchs to control current model is different, and power waveform is caused to be had any different.Since the process is very of short duration, and
Inverter output power does not enter AC network substantially at failure during failure continues, and influences on stability analysis very small.
2) machine-electricity transient model and PSCAD simulation result integrally approach, and are able to satisfy engineering calculation requirement.
Emulation difference is electromechanical transient to keep calculating speed, carries out the cost that model simplification is necessarily paid.Divide from stablizing
From the point of view of analysis, these losss of significance are acceptable.On the other hand, above-mentioned simulation comparison is not consider protective device
The lower progress of effect.The protection operation of actual electric network band, will not allow so big perturbation process.This model is configured with commonly
Protective device, and the phantom error of protective device is very small, thus in Bulk power system simulation VSC and DC grid model it is whole
Body phantom error is simultaneously little.
3) example PSASP1 used time 10.847 seconds, the PSASP2 used time 0.413 second, PSCAD was more than 20 minutes.Illustrate herein
Method has higher efficiency to the processing of VSC and DC grid itself.
Example is planned to the State Grid Corporation of China of different scales, in processor frequencies 2.5GHz, memory 4GB, 64 bit manipulations
In the PC machine of system, 400 fault scannings of a length of 20s, averagely used time are as shown in table 1 when with emulation.Two are removed in each data
There are also a small amount of power frequency static characteristic loads etc. to control power module outside back-to-back VSC model.These control power modules simplify discrete ox
The method of pausing realization, referred to as algorithm 1；Unused is algorithm 2.From calculating in terms of effect, calculating effect can be effectively improved by simplifying discrete Newton method
Rate.
Table 1 simplifies discrete Newton method and calculates effect
The above embodiments are merely illustrative of the technical scheme of the present invention and are not intended to be limiting thereof, although referring to above-described embodiment pair
The present invention is described in detail, and those of ordinary skill in the art still can be to a specific embodiment of the invention
It is modified or replaced equivalently, these are without departing from any modification of spirit and scope of the invention or equivalent replacement, in Shen
Within claims of the invention that please be pending.
Claims (10)
1. a kind of multi-rate simulating method for flexible direct current AC network associative simulation, which is characterized in that the method packet
It includes:
Establish the electric network model of the large-scale AC-DC hybrid power grid containing VSC based on multi tate；
Small step-length VSC model is established according to electric network model；
Small step-length VSC model is emulated with AC system emulation interface；
Small step-length voltage source converter VSC model is calculated based on discrete Newton method is simplified.
2. multi-rate simulating method as described in claim 1, which is characterized in that it is described foundation based on multi tate containing VSC's
Shown in the electric network model of large-scale AC-DC hybrid power grid such as following formula (1)~(6):
0=As(xs,ys,Gs(yf),zs,t) (2)
0=Ls(xs,ys,zs,t) (3)
0=Af(xf,Gf(ys),yf,zf,t) (5)
0=Lf(xf,yf,zf,t) (6)
The electric network model of the large-scale AC-DC hybrid power grid containing VSC based on multi tate includes becoming system and slowly varying system fastly,
In: formula (1)~(3) are followed successively by the differential equation D of slowly varying systems, algebraic equation As and logical equation Ls；X is state variable, y
For algebraic variable, z is logical variable；Subscript behalf slowly varying system, f represent fast change system；Gs(yf) it is slowly varying system algebraic quantity
Mapping in fast change system；Gf(ys) it is the fast mapping for becoming system algebraic quantity in slowly varying system；xs,ys,zs, t is respectively slow
The state variable of change system, algebraic variable, logical variable and time；Formula (4)~(6) are the fast differential equation Df for becoming system, generation
Number equation Af and logical equation Lf；xf,yf,zf, t is respectively the fast state variable for becoming system, algebraic variable, logical variable and when
Between t represent the time；Fast change system and slowly varying system in formula (1)~(6) only have algebraic quantity coupling, the convergence of respective system integral
Property is determined by hiding-trapezium integral method and given step-length.
3. multi-rate simulating method as described in claim 1, which is characterized in that described to establish small step-length according to electric network model
VSC model, comprising:
Determine the voltage interpolation between the n-th step of slowly varying system and n+1 step and the power of receiving；
Speed system alternately solves differential algebraic equations using the hiding-trapezium integral method of fixed step size.
4. multi-rate simulating method as claimed in claim 3, which is characterized in that between n-th step of slowly varying system and n+1 step
Voltage interpolation expression it is as follows:
The power such as following formula that slowly varying system receives:
Wherein: setting the fast system step-length that becomes as h, slowly varying system step-length is H=mh, and m is integer；The fast each time step of system that becomes exports bus
Voltage is obtained by the corresponding busbar voltage interpolation of slowly varying system, VfIt (nm+i) is the fast voltage interpolation for becoming the i-th step of system；Vs(n) it is
The voltage interpolation of the n-th step of slowly varying system；VsIt (n+1) is the voltage interpolation of the (n+1)th step of slowly varying system；GfThe fast system algebraic quantity that becomes exists
Mapping in slowly varying system；The expression step-length of n slowly varying system；Slowly varying system from the power that fast change system receives be fast change system it
The average value of preceding m step power, Ss(n+1) power received for the (n+1)th step of slowly varying system；IsIt (n+1) is the (n+1)th step of slowly varying system
The electric current of receiving；The conjugation for the power that the (n+1)th step of slowly varying system receives；For the (n+1)th step of slowly varying system
The conjugation of voltage interpolation；
It is as follows using hiding-trapezium integral method and differential algebraic equations the alternating solution of fixed step size to speed system:
Wherein: according to implicit trapezoidal rule, formula (1), (4) difference turn to algebraic expression (10), (11), x respectivelys(n+1)、xs(n) divide
Not Wei slowly varying system the (n+1)th step and the n-th step state variable；ys(n+1)、ysIt (n) is respectively the (n+1)th step of slowly varying system and the n-th step
Algebraic variable；zs(n+1)、zsIt (n) is the logical variable of slowly varying system the (n+1)th step and the n-th step；xf(k+1)、xf(k) it is respectively
The fast state variable for becoming+1 step of system kth and kth step；yf(k+1)、yfIt (k) is respectively the fast generation for becoming+1 step of system kth and kth step
Number variable；zf(k+1)、zf(k) logical variable walked for+1 step of slowly varying system kth and kth；Df(xf(k+1))、Df(xf(k)) divide
The differential equation of the state variable of+1 step of system kth and kth step Wei not become fastly；Ds(xs(n+1))、Ds(xsIt (n)) is respectively slow become
The differential equation of the state variable of the (n+1)th step of system and the n-th step.
5. multi-rate simulating method as described in claim 1, which is characterized in that it is described to small step-length VSC model with exchange system
System emulation interface is emulated, comprising:
1) the n-th step of slowly varying system is it is known that one step of solution, solves logical equation Ls unrelated with quantity of state in slowly varying system, and more
The differential equation D of new slowly varying systemsWith algebraic equation As；
2) assume that whole network voltage remains unchanged in slow system, by element complexity successively or iteratively solve in slowly varying system with shape
Equation relevant to component models and by differential equation D in the relevant logical equation Ls of state amount, algebraic equation AssDifferencing obtains
The formula arrived calculates each element injection AC network electric current；
3) small step-length VSC model is carried out from the n-th m+1 to (n+1) m by the voltage interpolation between the n-th step of slowly varying system and n+1 step
The port voltage difference of step successively carries out the interpolation of of ac；
4) carry out small step-length emulation, iteratively solve the formula of formula differential equation Df differencing, the fast algebraic equation Af for becoming system and
Logical equation Lfm times is obtained and is walked from the n-th m+1 to (n+1) m step inverter inside state and output active reactive；
5) inverter injects power network current in the small step-length VSC model of power calculation received by slowly varying system；
6) network equation in Solving Algebraic Equation As updates whole network voltage；
7) whether inspection state amount and algebraic quantity restrain, if having restrained, enable n=n+1, calculate into next step, otherwise return to step
Rapid 2) iteration.
6. multi-rate simulating method as described in claim 1, which is characterized in that described small based on discrete Newton method progress is simplified
The constringent calculating of step size voltage source inverter VSC model, comprising:
A, when the number of iterations k is 0, small step-length VSC model is solved；
B, judge whether electric current residual error is less than setting value, if satisfied, then exporting current flow and voltage；Otherwise, step C is carried out；
C, the number of iterations k=k+1 is enabled, and judges whether updated the number of iterations k is less than k1, if being less than, return step A；
Otherwise, step D is carried out；
D, it solves with discrete Newton method formula is simplified, judges whether electric current residual error meets the requirements；If so, output current flow and
Voltage；Otherwise, another the number of iterations k=k+1；
E, judge whether updated the number of iterations k is less than k2, if so, return step D；Otherwise output residual error minimum current and
Corresponding voltage；K1, k2 are the number of iterations upper limit of setting.
7. multi-rate simulating method as claimed in claim 6, which is characterized in that in the step A, the D of small step-length VSC model
Tie up Nonlinear System of Equations and the following formula of Iteration:
F (x)=0 (12)
x(k+1)=x(k)-J(x(k),h(k))-1F(x(k)) (15)
Wherein: its mathematics, which is in the nature D dimension nonlinear equation, to be determined to the network equation formed in the algebraic equation As of slowly varying system
Group, such as formula (12), Iteration is formula (13)~(15)；N indicates step-length；X is Injection Current column vector, and dimension D is bus
Number；F(x(k)) be kth time iteration demand solution Nonlinear System of Equations, element f1(x(k))、f2(x(k))、…fn(x(k))；h
For independent variable deviation；J is quasi- Jacobian matrix；e1It is the 1st D Wiki our unit vector, j=1,2 ..., n；h(k)For kth time
The independent variable deviation of iteration；The independent variable deviation for being j for kth time iteration step length；x(k)For the Injection Current column of kth time iteration
The independent variable of vector.
8. multi-rate simulating method as claimed in claim 7, which is characterized in that the multiple differential algebra alternating iteration of needs
Large-scale power grid emulation before, arranged as follows:
1) residual error of Injection Current is represented with D dimension Nonlinear System of Equations, i.e. certain currents combination injects power grid, solves each bus electricity
Pressure, then update the difference that after currents combination and primary current combines；If residual error is 0, it is given that small step-length VSC model, which is able to maintain power,
Value；Since the electric current of non-control power component injection bus is constant always, D ties up Nonlinear System of Equations such as:
In formula, x is Injection Current column vector, and dimension n is bus number；Xvsc retains VSC by x and exports bus corresponding element,
Its element is all set 0 and is obtained；Y is node admittance battle array；Diag () indicates column vector turning to diagonal matrix；Svsc is column vector,
Only in the outlet VSC, bus corresponding position has non-zero element, is worth the apparent energy to obtain；
Simple Iteration is carried out to formula (16), as follows:
2) difference for intending the currents combination that Jacobian matrix element is 2 injection power grids, is the set of currents of kth time and the 0th iteration
The difference closed, expression formula are as follows:
Large-scale power grid emulation to multiple differential algebra alternating iteration is needed, formula (14), which generates, intends Jacobian, right in formula (15)
The calculation amount that quasi- Jacobian is inverted is excessive need to take approximation, as follows:
The diagonal element of right side matrix is as follows:
After above-mentioned restriction and assuming, it is simplified the formula of discrete Newton method, it is as follows；
The variation of bus Injection Current will not cause other bus current residual errors to change, i.e. matrix non-diagonal line element on the right side of formula (14)
Element is 0, becomes diagonal matrix；The electric current residual error of bus is determined that the variation of currents combination causes in bus by bus Injection Current
Residual error variation with only retain a bus Injection Current variation generation residual error it is identical；
Wherein: formula (19) is to emulate to the large-scale power grid for needing multiple differential algebra alternating iteration, formula (14) are generated intend it is refined can
The approximation taken than battle array；For the Injection Current column vector of kth time iteration and the 0th iteration；Respectively
+ 1 iteration of kth and kth time iteration retain voltage source converter VSC mold exit bus corresponding element by x and other elements are equal
0 is set to obtain.
9. a kind of multi-rate simulating system for flexible direct current AC network associative simulation, it is characterised in that: include:
First building module, for establishing the electric network model of the large-scale AC-DC hybrid power grid containing VSC based on multi tate；
Second building module, for establishing small step-length VSC model according to electric network model；
Emulation module, for being emulated to small step-length VSC model with AC system emulation interface；
Computing module, for calculating small step-length voltage source converter VSC model based on simplified discrete Newton method.
10. multi-rate simulating system as claimed in claim 9, it is characterised in that: the second building module further comprises:
Determining module, for determining the voltage interpolation between the n-th step of slowly varying system and n+1 step and the power of receiving；
Module is solved, for alternately solving using the hiding-trapezium integral method of fixed step size to differential algebraic equations to speed system.
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