CN104156542A - Implicit-projection-based method for simulating stability of active power distribution system - Google Patents
Implicit-projection-based method for simulating stability of active power distribution system Download PDFInfo
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Abstract
The invention discloses an implicit-projection-based method for simulating the stability of an active power distribution system. According to an active power distribution system stability simulation model with the rigidity characteristics, based on system simulation parameters and load flow calculation results, the implicit-projection-based method includes the steps that firstly, a plurality of steps of small-step-length integral calculation are carried out through an internal integrator, wherein the step length is h, and any explicit integral algorithm with the accuracy higher than the second order can be adopted; secondly, a step of large-step-length integral calculation is carried out with the step length Mh through an external integrator based on an implicit prediction-correction method according to the calculation result of the internal integrator. By means of the implicit-projection-based method, simulating calculation of system faults can be achieved, the implicit-projection-based method is a second-order accuracy algorithm and has the good numerical stability, a numerical stability domain of the implicit-projection-based method is hardly changed along with changes of the multiple of the step length of the external integrator, the performance of the algorithm is better than that of the explicit projection integral algorithm and that of a traditional implicit trapezoidal method, the implicit-projection-based method is suitable for rapidly achieving the aim of simulating the stability of the active power distribution system with the multi-time scale characteristics, and a foundation is laid for efficiently and reliably developing an active power distribution system simulation program.
Description
Technical field
The present invention relates to a kind of active distribution system Simulation of stability method.Particularly relate to a kind of active distribution system Simulation of stability method based on implicit expression projection being suitable for containing the active distribution system Simulation of stability application of distributed power source and energy storage.
Background technology
The change that the extensive extensively access of distributed power source (DG) and Demand Side Response technology are implemented rear system load characteristic, brings new challenge to the planning of distribution system and operation invariably.The power distribution network containing DG is not " passive ", and the electric energy that access user is used is provided by upper level power transmission network, when power distribution network access DG produces bi-directional current, claims this system for " active distribution system ".Active distribution system is to possess the complicated distribution that various distributed energies (DER, as DG, controllable burden, energy storage etc.) ability is controlled in combination.In the active distribution system in future, the access capacity of DG can surpass the load total amount in (at least in special time period) distribution system easily, now active distribution system as external power source to outside power transmission network transmission of electric energy.Even if DG total volume is no more than load total amount, the extensive access of DG still can cause the dynamic response characteristic of power distribution network to change and then affect the dynamic perfromance of whole electric system, the dynamic perfromance while being particularly subject to large disturbance.In system level, the analysis of relevant issues often cannot directly be tested with research on real system, therefore must adopt effective digital simulation tools as important research means.
Conventional electric power system time-domain-simulation develops respectively electromagnetic transient simulation, electromechanical transient simulation and three kinds of digital dummy method of power systems of long term dynamics emulation for the different time yardstick of system dynamic course, and three has visibly different feature from element mathematical model to emulated computation method.Electromagnetic transient in power system emulation lays particular emphasis on the influence each other fast dynamic changing process of the electric current and voltage that produces of electric field and magnetic field in system; Electromechanical transient simulation mainly study electric system under large disturbance (as fault, cut the situations such as machine, cutting load, reclosing operation) dynamic behaviour and keep the ability of synchronism stability operation, it is transient stability, the time range of paying close attention to is generally several seconds to tens seconds, thereby also referred to as Simulation of stability; Long term dynamics process simulation be after electric system is disturbed compared with the dynamic simulation of growth process, common electric system growth process dynamic stability calculates.
Stability of power system emulation is except paying close attention to the transient stability service ability of conventional electric power system, while also focusing in recent years the active distribution system operation of analyzing containing various distributed power sources and energy storage device, its power frequency quality dynamic response characteristic of (switching manipulation, fault, distributed power source and load fluctuation etc.) under system disturbance, now can be described as active distribution system Simulation of stability.Active distribution system Simulation of stability can be summed up as in essence to the asking for of dynamical system time domain response, and is divided into mathematical modeling and model solution two parts.First according to interelement topological relation, the characteristic equation of active each element of distribution system is formed to system-wide Simulation of stability model, form the differential-Algebraic Equation set of one group of simultaneous, then take steady state condition or trend solution is initial value, solve the numerical solution under disturbance, progressively try to achieve system state amount and algebraic quantity curve over time.
The modeling of active distribution system Simulation of stability is the time scale scope of paying close attention to according to system emulation, is taken out the process of mathematical model by physical prototype.Mathematical model in active distribution system Simulation of stability comprises two parts: the algebraic equation of electrical link between the differential equation of description equipment behavioral characteristics and description equipment.Wherein, electric connecting relation between equipment may change in operational process; as the switching of load, the operations such as start and stop, line disconnection and reclosing of unit, if take into account protective relaying device, also should comprise a large amount of continuous and (or) discrete logic time-varying parameters.
Generally active distribution system mathematical model can be described by the differential-Algebraic Equation set of a high dimensional nonlinear and autonomy continuously, shown in (1).
In formula,
for the differential equation,
for algebraic equation,
for system state variables, represent rotor rotating speed, power electronic devices control system and load dynamic parameter etc.,
for algebraically variable, characterize busbar voltage amplitude and phase angle.Solving generally of mathematical model realizes by specific numerical algorithm and corresponding simulated program.Active distribution system has accessed miscellaneous distributed power source and a large amount of power electronic equipments, comprises electric rotating machine and various static direct current type distributed power source, has obvious Multiple Time Scales feature, on mathematics, can be summed up as stiff problem.Therefore, active distribution system Simulation of stability can be summed up as the initial-value problem that solves a rigidity differential-Algebraic Equation set on mathematics, and its precision and stability to adopted numerical algorithm requires higher.
Active distribution system Simulation of stability algorithm can be divided into alternately solving method and the large class of simultaneous solution method two according to the difference of the differential equation in formula (1) and algebraic equation being resolved to form.Alternately first solving method adopts specific numerical integration algorithm, according to initialization result of calculation, solve the differential equation, obtain the value that this time walks state variable, then be updated in algebraic equation and solved, while obtaining this, walk the value of algebraically variable, finally again the algebraically variable substitution differential equation is carried out walking state variable lower a period of time and solve, realize by that analogy alternately solving of differential-Algebraic Equation set; Simultaneous solution rule is by after differential equation differencing, becomes a complete Algebraic Equation set with algebraic equation simultaneous, simultaneously solving state variable and algebraically variable.
For the differential equation in formula (1), except can obtaining analytic solution under a few cases, most applications can only adopt numerical solution to solve, wherein, method of difference is widely used in active distribution system Simulation of stability, and method of difference can be divided into again single-step process (one step method) and linear multistep method (linear multistep method).According to the difference of solution procedure, single-step process can be divided into explicit integral and implicit expression integration method, explicit integral can directly be calculated next state variable constantly according to current time state variable, and implicit expression integration method needs the equation to containing current time and next moment state variable to solve just can try to achieve next state variable constantly.Common explicit integral comprises Euler method, improved Euler method and Runge-Kutta method, and implicit expression integration method mainly contains backward Euler method and implicit expression trapezoidal method.Active distribution system has obvious rigidity characteristic, for explicit integral, the operand in walking per a period of time is less, but because its numerical stability is poor, therefore solving stiff problem can only take less integration step, and this can seriously limit simulation velocity in stability is calculated; And for implicit expression integration method, although need iterative system of equations in per a period of time in step, it calculates with programing work comparatively complicated to compare progressive failure, but its numerical stability is better, in the solution procedure of stiff problem, when can guarantee numerical stability, by taking larger integration step to promote simulation velocity.
Explicit projection algorithm is the numerical integration derivation algorithm proposing for the initial-value problem of the ordinary differential equation with rigidity characteristic (ODE) shown in formula (2) below, its basic thought is: first carry out the long integral and calculating of small step of some steps, calculate step-length corresponding with the time constant of the fast dynamic process of system; Then, according to the result of calculation of little step-length, adopt formula (3) or the explicit prediction-trimming process based on improved Euler method below to carry out the integral and calculating that a projection walks, projection step-length is corresponding with the time constant of the slow dynamic process of system.Wherein, the long integral and calculating process of small step is called internal integral device, and the explicit fourth-order Runge-Kutta method (explicit four-order Runge-Kutta method) that employing numerical stability is better and precision is higher is to improve stability and the numerical precision of algorithm; Projecting integral's process of large step-length is called outside integrator.Explicit projecting integral algorithm can, when realizing the lifting of traditional explicit integral algorithm numerical stability, further promote simulation calculation speed.However, for the intelligent distribution system with obvious Multiple Time Scales feature, its numerical stability is still limited significantly, and the difficulty that its computing velocity further promotes is very large.
x(t
n+k+1+M)＝(M+1)x(t
n+k+1)-Mx(t
n+k) (3)
Visible, a kind of Simulation of stability method of active distribution system that propose that numerical precision is high, better numerical value stability, counting yield are high, is suitable for having rigidity characteristic is very important.
Summary of the invention
Technical matters to be solved by this invention is, provides that a kind of numerical precision is high, better numerical value stability, counting yield is high and be suitable for having the active distribution system Simulation of stability method based on implicit expression projection of rigidity characteristic.
The technical solution adopted in the present invention is: a kind of active distribution system Simulation of stability method based on implicit expression projection, comprises the steps:
1) according to the dynamic equation of the topological connection relation of system and element, set up active distribution system transient stability realistic model, shape as
In formula,
for the differential equation,
for algebraic equation,
for system state variables,
for system algebraically variable;
2) active distribution system is carried out to trend calculating, obtain system load flow data;
3) reading system parameter and simulation calculation parameter, comprise emulation termination time T, simulation step length h, the outside integrator integration step of the integration step number k of implicit expression projection algorithm internal integral device and implicit expression projection algorithm is with respect to the multiple M of implicit expression projection algorithm internal integral device integration step, k and M are positive integer, emulation fault and operation event information are set, comprise fault generation and checkout time, abort situation and fault type;
4), according to system load flow result of calculation, system-wide dynamic element is carried out to simulation initialisation calculating;
5) simulation time t=0 is set;
6) the integration step number s=1 of current implicit expression projection algorithm internal integral device is set, s is positive integer;
7) simulation time t=t+h is set, h is implicit expression projection algorithm internal integral device integration step, adopts implicit expression projection algorithm internal integral device to calculate a step-length to active distribution system model, obtains the state variable x in this moment of system
n+swith algebraically variable y
n+s, and s=s+1 is set;
8) according to step 3) the emulation fault and the operation event information that arrange judge whether system now breaks down or operate, if the time of origin T of fault and Action Events
event=t, returns to step 6), otherwise carry out next step;
9) judge whether simulation time t reaches emulation termination time T, if t=T, emulation finishes, otherwise carries out next step;
10) whether the integration step number s that judges implicit expression projection algorithm internal integral device is greater than step 3) in the integration step number k+1 of implicit expression projection algorithm internal integral device of user's input, if s≤k+1 returns to step 7), otherwise carry out next step;
11) according to step 3) the emulation fault that arranges and operation event information judge in t～t+Mh time, whether break down or operate, if t<T
event<t+Mh, enters step 13), otherwise carry out next step;
12) the outside integrator integration step of implicit expression projection algorithm H=Mh is set, simulation time t=t+Mh is set, utilize the outside integrator of implicit expression projection algorithm to obtain the state variable x in this moment of system
n+k+1+Hwith algebraically variable y
n+k+1+H, then directly enter step 14);
13) the outside integrator integration step of implicit expression projection algorithm H=T is set
event-t, arranges simulation time t=T
event, utilize the outside integrator of implicit expression projection algorithm to obtain the state variable x of fault or the front system of operation generation
n+k+1+Hwith algebraically variable y
n+k+1+H;
14) judge whether simulation time t reaches emulation termination time T, if t=T, emulation finishes, otherwise returns to step 6), according to step 6) to 14) repeatedly carry out until emulation finishes.
Step 3) described implicit expression projection algorithm internal integral device, be to adopt explicit alternately method for solving to solve active distribution system model, the differential equation in active distribution system model chosen to any explicit numerical integration algorithm with the above precision of second order.
Step 3) the outside integrator of described implicit expression projection algorithm, as follows to describing the concrete solution procedure of differential-algebraic equation of active distribution system in the outside integrator integration step of implicit expression projection algorithm H:
(1) establishing current simulation time is t
n+k+1, wherein, the emulation total step number that n is current time, current time system state variables is x
n+k+1, algebraically variable is y
n+k+1, through step-length H, the system emulation time is t
n+k+1+H, now the state variable of system and algebraically variable are respectively x
n+k+1+Hand y
n+k+1+H, to describing differential-algebraic equation implicit expression differencing of active distribution system model, obtain following formula:
(2) utilize forward direction Euler method to obtain x
n+k+1+Hthe predicted value of initial estimate
be shown below
Substitution equation then
obtain y
n+k+1+Hthe predicted value of initial estimate value
(3) utilize following formula to proofread and correct predicted value, obtain x
n+k+1+Hinitial estimate
Then be updated to algebraic equation
in obtain y
n+k+1+Hinitial estimate
(4) by following formula, obtain x
n+k+1+Hmodified value
Then will
value substitution algebraic equation
in, solve and obtain y
n+k+1+Hmodified value
(5) respectively will
with
substitution following formula judges whether to meet the condition of convergence,
In formula, ξ is the error permissible value being set by the user, if meet the condition of convergence, the outside integrator calculation procedure of implicit expression projection algorithm finishes; Otherwise, respectively will
with
replace
with
return to step (4), repeating step (4) and (5) are until meet the condition of convergence.
A kind of active distribution system Simulation of stability method based on implicit expression projection of the present invention, taken into full account the rigidity characteristic of active distribution system, adopt alternately method for solving alternately to solve describing the differential-Algebraic Equation set of active distribution system realistic model, the differential equation wherein is carried out to difference by implicit expression projection algorithm and solve.Method of the present invention is 2 rank precision algorithms, and algorithm performance is better than traditional implicit expression trapezoidal method.Simultaneously, the method has good numerical stability, its numerical stability territory changes with the change of outside integrator step-length multiple hardly, at more explicit projecting integral algorithm aspect numerical stability and computing velocity, there is obvious advantage, be suitable for having the rapid solving of the active distribution system Simulation of stability problem of obvious Multiple Time Scales feature, for the exploitation of efficient, reliable active distribution system simulated program is had laid a good foundation.
Accompanying drawing explanation
Fig. 1 is the overall flow figure of the inventive method;
Fig. 2 is the numerical stability territory of the inventive method and explicit projection algorithm and traditional explicit 4 rank Runge-Kutta methods;
Fig. 3 is the local enlarged diagram of A in Fig. 2;
Fig. 4 is low-voltage active distribution system example structural drawing;
1: the first accumulator in figure; 2: the first photovoltaic cells; 3: the second photovoltaic cells; 4: the second accumulators; M1: middle pressure bus; S1: switch; L1～L19: low-voltage bus bar; Load1～Load7: load;
Fig. 5 is L17 busbar voltage simulation result and partial enlarged drawing;
Fig. 6 is the second photovoltaic cell active power Output simulation result and partial enlarged drawing;
Fig. 7 is the active distribution system example of IEEE123 node structural drawing;
Fig. 8 is photovoltaic cell active power Output simulation result and the partial enlarged drawing of 56 Nodes;
Fig. 9 is the grid-connected Voltage-output simulation result of the photovoltaic cell of 56 Nodes and partial enlarged drawing;
Figure 10 is the implicit expression trapezoidal method numerical precision comparison (logarithmic coordinate system) that implicit expression projection algorithm and step-length are got 0.5ms;
Figure 11 is the implicit expression trapezoidal method numerical precision comparison (logarithmic coordinate system) that implicit expression projection algorithm and step-length are got 0.02s;
Figure 12 is the implicit expression trapezoidal method numerical precision comparison (logarithmic coordinate system) that implicit expression projection algorithm and step-length are got 0.0025s.
Embodiment
Below in conjunction with embodiment and accompanying drawing, a kind of active distribution system Simulation of stability method based on implicit expression projection of the present invention is described in detail.
A kind of active distribution system Simulation of stability method based on implicit expression projection of the present invention, belongs to explicit, implicit expression parallelopipedal product separating method.Active distribution system has accessed distributed power source of a great variety, dynamic response characteristic differs greatly and a large amount of power electronic equipments, wherein both comprised the alternating current generator of rotation, also contain the static once-through type power supplys such as photovoltaic cell, accumulator, this makes active distribution system have obvious Multiple Time Scales feature, therefore its Digital Simulation problem shows stronger rigidity characteristics, needs to adopt the numerical integration algorithm with good numerical precision and numerical stability to realize its simulation calculation.A kind of active distribution system Simulation of stability method based on implicit expression projection that the present invention proposes, taken into full account the rigidity characteristic of active distribution system, adopt alternately method for solving alternately to solve describing the differential-Algebraic Equation set of active distribution system model, the differential equation wherein is carried out to difference by implicit expression projection algorithm and solve.Method of the present invention is 2 rank precision algorithms, and algorithm performance is better than traditional implicit expression trapezoidal method.Simultaneously, the method has good numerical stability, its numerical stability territory changes with the change of outside integrator step-length multiple hardly, at more explicit projecting integral algorithm aspect numerical stability and computing velocity, there is obvious advantage, be suitable for having the rapid solving of the active distribution system Simulation of stability problem of obvious Multiple Time Scales feature, for the exploitation of efficient, reliable active distribution system simulated program is had laid a good foundation.
The present invention adopts alternately derivation algorithm to realize the calculating to the active distribution system mathematical model based on the description of differential-algebraic equation, to the differential equation wherein, adopt implicit expression projection algorithm to solve, its basic thought is: first carry out the long integral and calculating of some small steps, its simulation step length is corresponding with the fast dynamic process of system; Then, according to the result of the long integral and calculating of small step, utilize implicit expression prediction-bearing calibration to carry out projecting integral's step of the large step-length of a step, step-length is corresponding with the slow dynamic process of system.Wherein, the long integral and calculating process of small step is called internal integral device, can adopt the explicit numerical integration algorithm arbitrarily with the above precision of second order; Large step-length integral and calculating process is called outside integrator.
As shown in Figure 1, a kind of active distribution system Simulation of stability method based on implicit expression projection of the present invention, is characterized in that, comprises the steps:
1) according to the dynamic equation of the topological connection relation of system and element, set up active distribution system transient stability realistic model, shape as
In formula,
for the differential equation,
for algebraic equation,
for system state variables,
for system algebraically variable;
2) active distribution system is carried out to trend calculating, it is to adopt Gaussian processes or Newton-Laphson method to calculate that described trend is calculated.Through trend, calculate system load flow data, comprise node voltage, electric current, load active power and reactive power, the output of power supply active power and reactive power output and Injection Current etc.;
3) reading system parameter and simulation calculation parameter, comprise emulation termination time T, simulation step length h, the outside integrator integration step of the integration step number k of implicit expression projection algorithm internal integral device and implicit expression projection algorithm is with respect to the multiple M of implicit expression projection algorithm internal integral device integration step, k and M are positive integer, emulation fault and operation event information are set, comprise fault generation and checkout time, abort situation and fault type;
Described implicit expression projection algorithm internal integral device, is to adopt explicit alternately method for solving to solve active distribution system model, the differential equation in active distribution system model is chosen to any explicit numerical integration algorithm with the above precision of second order.
The outside integrator of described implicit expression projection algorithm, as follows to describing the concrete solution procedure of differential-algebraic equation of active distribution system in the outside integrator integration step of implicit expression projection algorithm H:
(1) establishing current simulation time is t
n+k+1, wherein, the emulation total step number that n is current time, current time system state variables is x
n+k+1, algebraically variable is y
n+k+1, through step-length H, the system emulation time is t
n+k+1+H, now the state variable of system and algebraically variable are respectively x
n+k+1+Hand y
n+k+1+H, to describing differential-algebraic equation implicit expression differencing of active distribution system model, obtain following formula:
(2) utilize forward direction Euler method to obtain x
n+k+1+Hthe predicted value of initial estimate
be shown below
Substitution equation then
obtain y
n+k+1+Hthe predicted value of initial estimate value
(3) utilize following formula to proofread and correct predicted value, obtain x
n+k+1+Hinitial estimate
Then be updated to algebraic equation
in obtain y
n+k+1+Hinitial estimate
(4) by following formula, obtain x
n+k+1+Hmodified value
Then will
value substitution algebraic equation
in, solve and obtain y
n+k+1+Hmodified value
(5) respectively will
with
substitution following formula judges whether to meet the condition of convergence
In formula, ξ is the error permissible value being set by the user, if meet the condition of convergence, the outside integrator calculation procedure of implicit expression projection algorithm finishes; Otherwise, respectively will
with
replace
with
return to step (4), repeating step (4) and (5) are until meet the condition of convergence.
4), according to system load flow result of calculation, system-wide dynamic element is carried out to simulation initialisation calculating;
5) simulation time t=0 is set;
6) the integration step number s=1 of current implicit expression projection algorithm internal integral device is set, s is positive integer;
7) simulation time t=t+h is set, h is implicit expression projection algorithm internal integral device integration step, adopts implicit expression projection algorithm internal integral device to calculate a step-length to active distribution system model, obtains the state variable x in this moment of system
n+swith algebraically variable y
n+s, and s=s+1 is set;
8) according to step 3) the emulation fault and the operation event information that arrange judge whether system now breaks down or operate, if the time of origin T of fault and Action Events
event=t, returns to step 6), otherwise carry out next step;
9) judge whether simulation time t reaches emulation termination time T, if t=T, emulation finishes, otherwise carries out next step;
10) whether the integration step number s that judges implicit expression projection algorithm internal integral device is greater than step 3) in the integration step number k+1 of implicit expression projection algorithm internal integral device of user's input, if s≤k+1 returns to step 7), otherwise carry out next step;
11) according to step 3) the emulation fault that arranges and operation event information judge in t～t+Mh time, whether break down or operate, if t<T
event<t+Mh, enters step 13), otherwise carry out next step;
12) the outside integrator integration step of implicit expression projection algorithm H=Mh is set, simulation time t=t+Mh is set, utilize the outside integrator of implicit expression projection algorithm to obtain the state variable x in this moment of system
n+k+1+Hwith algebraically variable y
n+k+1+H, then directly enter step 14);
13) the outside integrator integration step of implicit expression projection algorithm H=T is set
event-t, arranges simulation time t=T
event, utilize the outside integrator of implicit expression projection algorithm to obtain the state variable x of fault or the front system of operation generation
n+k+1+Hwith algebraically variable y
n+k+1+H;
14) judge whether simulation time t reaches emulation termination time T, if t=T, emulation finishes, otherwise returns to step 6), according to step 6) to 14) repeatedly carry out until emulation finishes.
Provide instantiation below:
For line integral algorithm, it is to linear constant coefficient differential equation
solution and scalar equation
Solution equivalence, wherein, the characteristic root that λ is matrix A, therefore deserving to be called again formula is scalar measured equation.For given numerical integration algorithm, its numerical stability territory refers in s territory, meets numerical stability condition during this Algorithm for Solving scalar measured equation
|σ(hλ)|≤1
The set of h λ.
This example be take implicit expression projection algorithm internal integral device, and to get explicit 4 rank Runge-Kutta methods (hereinafter to be referred as RK4 algorithm) be example, according to numerical stability condition, obtain respectively implicit expression projection algorithm under different parameters, traditional RK4 algorithm and the numerical stability territory of explicit projection algorithm in h λ plane, as shown in accompanying drawing 2, Fig. 3, wherein explicit projection algorithm internal integral device adopts RK4 algorithm, and outside integrator adopts the explicit prediction-bearing calibration based on improved Euler method.As seen from the figure, along with the increase of the multiple M of outside integrator step-length, the numerical stability territory of explicit projection algorithm significantly reduces, and is split into gradually several less regions by a large region.And the numerical stability territory of implicit expression projection algorithm and the numerical stability territory of traditional RK4 algorithm are basically identical, and the change with M changes hardly, at M, get under 10000 egregious cases, the numerical stability territory of implicit expression projection algorithm still overlaps with the numerical stability territory of traditional RK4 algorithm substantially.The numerical stability of the implicit expression projecting integral algorithm that therefore, the present invention proposes is better than explicit projecting integral algorithm.
Digital Simulation and electrical network calculation procedure (DIgSILENT PowerFactory) are a commercial power system simulation softwares of German DIgSLENTGmbH company exploitation.This example has been realized a kind of active distribution system Simulation of stability method based on implicit expression projection that the present invention proposes in C++ programmed environment, and by the simulation result of implicit expression projecting integral method and business software DIgSILENT PowerFactory and calculated performance being compared to verify correctness and the validity of the method, the hardware platform of carrying out emulation testing is Intel (R) Core (TM) i5-3470CPU@3.20GHz, the PC of 4GB RAM; Software environment is 32-bit Windows 7 operating systems.This example is tested method of the present invention by choosing different algorithm parameters, and algorithm parameter can meet any value under the condition of numerical precision according to actual conditions when specific implementation, and enforcement of the present invention does not limit this.
First, this example adopts a low-voltage active distribution system example containing distributed power source to carry out testing authentication to method of the present invention, as shown in Figure 4.Low-voltage active distribution system example electric pressure is 400V, main feeder is connected to middle pressure bus M1 place by 0.4/10kV transformer, the DYn11 bind mode that transformer adopting is conventional, and low-pressure side is provided with reactive compensation capacitor, main feeder nodal pitch is 50m, adopts three-phase symmetrical circuit and load.In addition, in example, accessed polytype distributed power source, having comprised: possess photovoltaic generating system and energy-storage system of accumulator that maximal power tracing is controlled, each distributed power source control mode, access capacity and active power output are as shown in table 1.
Table 1 distributed power source control mode, access capacity and output power
Adopt a kind of active distribution system Simulation of stability method based on implicit expression projection of the present invention to carry out Simulation of stability calculating to test example, it is 9s that simulation time is set, and simulation step length is 0.5ms.2.0s constantly low-voltage active distribution system switch S1 disconnects, and system switches to islet operation pattern by the pattern of being incorporated into the power networks; 4.7s constantly S1 switch is closed, and system switches to by islet operation pattern the pattern of being incorporated into the power networks.
By a kind of active distribution system Simulation of stability method based on implicit expression projection of the present invention, wherein algorithm parameter is got k=3, M=4, compare with the fixed step size simulation result of DIgSILENT PowerFactory and traditional implicit expression trapezoidal method, wherein, implicit expression projection algorithm internal integral step-length is got 0.5ms, outside integration step H=Mh=0.002s, the simulation step length of DIgSILENT is identical with implicit expression projection algorithm internal integral step-length, and the simulation step length of traditional implicit expression trapezoidal method is identical with outside integration step.The simulation result of L17 busbar voltage and No. 2 accumulator active power outputs and partial enlarged drawing are as shown in accompanying drawing 5 and accompanying drawing 6.Can find out, simulation result and the DIgSILENT of implicit expression projection algorithm are basically identical.In addition, by more known with traditional implicit expression trapezoidal method, be subject to the impact of the long integral and calculating of internal integral device small step, traditional implicit expression trapezoidal method that the numerical precision of the inventive method is better than step-length while getting outside integration step.
For verifying that implicit expression of the present invention projecting integral algorithm is for the adaptability with the extensive active distribution system of rigidity characteristic, this example be take IEEE123 node power distribution network standard example (as shown in Figure 7) as basis, from aspects such as numerical precision and calculated performances, this algorithm is carried out to integration test.IEEE123 node example has been described a baroque radial distribution networks network, has 123 nodes, and electric pressure is 4.16kV, and the load of various ways has been considered in its inside, and is connected with external network at node 150 places.It is 30kWp that this example Nodes in dotted line frame in accompanying drawing 7 accesses 50 capacity altogether, and active power is output as the photovoltaic generating system of 20.4kW.
Adopt a kind of active distribution system Simulation of stability method based on implicit expression projection of the present invention to carry out Simulation of stability calculating to IEEE123 node example, it is 9s that simulation time is set, simulation step length is 0.5ms, and the initial intensity of illumination of example environment of living in is set to 1000W/m
2, 1.5s, 3.5s and 6s constantly intensity of illumination become respectively 1025W/m
2, 1010W/m
2and 1000W/m
2.
This example is got implicit expression projection algorithm parameter and is respectively k=3, M=4, and internal integral step-length is 0.5ms, outside integration step H=Mh=0.002s.By implicit expression projection algorithm and step-length is got the DIgSILENT of internal integral step-length and the fixed step size simulation result of traditional implicit expression trapezoidal method that step-length is got outside integration step compares, the simulation result of the output of the photovoltaic active power of 56 Nodes and grid-connected busbar voltage and partial enlarged drawing are as illustrated in Figure 8 and 9 reference.From simulation result, can find out, the simulation result of implicit expression projection algorithm is still basically identical with DIgSILENT.Meanwhile, by more known with traditional implicit expression trapezoidal method, the numerical precision of implicit expression projection algorithm of the present invention is better than traditional implicit expression trapezoidal method that step-length is got outside integration step.
For the numerical precision of comparison implicit expression projection algorithm from traditional implicit expression trapezoidal method under different step-lengths, it is k=6 that this example arranges projection algorithm parameter, M=40, and internal integral step-length is got 0.5ms, outside integration step H=Mh=0.02s.If the simulation step length of traditional implicit expression trapezoidal method is h
tR, step-length is got respectively h
tR=0.5ms, h
tR=0.02s and h
tR=0.0025s, the explicit fourth-order Runge-Kutta method that the step-length of take is 0.1ms is benchmark, in logarithmic coordinate system, compare respectively the absolute error of the relative RK4 algorithm simulating of the simulation result result of implicit expression projection algorithm and implicit expression trapezoidal method under different step-lengths, if accompanying drawing 10 is to as shown in accompanying drawing 12.As can be seen from the figure, work as h
tRwhen identical with implicit expression projection algorithm internal integral step-length, the absolute error of trapezoidal method simulation result is less than implicit expression projection algorithm, and numerical precision is higher; Work as h
tRwhen identical with outside integration step, the numerical precision of projection algorithm is higher than trapezoidal method; Work as h
tRwhile getting 0.0025s, the absolute error of projection algorithm is a little less than trapezoidal method.
By accompanying drawing 2, Fig. 3, can be found out, a kind of active distribution system Simulation of stability method based on implicit expression projection of the present invention, the more explicit projecting integral of its numerical stability algorithm has larger advantage, therefore can further realize by getting larger M value the lifting of simulation calculation speed.This example is usingd the active distribution system of IEEE123 node as test example, the explicit fourth-order Runge-Kutta method that the step-length of take is got 0.5ms is benchmark, choose different simulation step length and algorithm parameter, compare respectively the counting yield of implicit expression projection algorithm, explicit projection algorithm, DIgSILENT and the emulation of traditional implicit expression trapezoidal method fixed step size, comparative result is as shown in table 2.
The comparison of table 2 algorithm performance
As can be seen from Table 2, along with reducing or the increase of M value of k value, the calculating used time of implicit expression projection algorithm reduces gradually.When projection algorithm parameter is identical, because the more explicit projection algorithm of computation process of the outside integrator of implicit expression projection algorithm is slightly complicated, can expend more computational resource, so the counting yield of implicit expression projection algorithm is a little less than explicit projection algorithm.But, work as k=3, during M=8 explicit projection algorithm numerical value do not restrain, and even implicit expression projection algorithm M gets and still can keep numerical stability at 60 o'clock, now, speed-up ratio can reach more than 7 times much smaller than traditional RK4 algorithm and DIgSILENT the emulation used time of implicit expression projection algorithm.In addition, by algorithm parameter, be k=6, the implicit expression projection algorithm of M=40 respectively with h
tRimplicit expression trapezoidal method while equaling internal integral step-length, outside integration step and 0.0025s compares.Can find out, work as h
tRwhile getting implicit expression projection algorithm internal integral step-length, the counting yield of implicit expression projection algorithm is far above trapezoidal method; Work as h
tRwhile getting outside integration step, the counting yield of implicit expression projection algorithm is a little less than trapezoidal method; Work as h
tRwhile getting 0.0025s, the counting yield of projection algorithm is higher than trapezoidal method.By finding out accompanying drawing 10 to the analysis of accompanying drawing 12 and table 2, for the traditional implicit expression trapezoidal method under different simulation step length, implicit expression projection algorithm all has certain advantage compared with implicit expression trapezoidal method aspect numerical precision or counting yield, and when implicit expression trapezoidal method is got certain intermediate step, the numerical precision of implicit expression projection algorithm and counting yield are better than trapezoidal method simultaneously.Therefore a kind of more traditional implicit expression trapezoidal method of active distribution system Simulation of stability method based on implicit expression projection that, the present invention proposes has better algorithm performance.
In sum, a kind of active distribution system Simulation of stability method based on implicit expression projection of the present invention, there is good numerical precision and numerical stability, can realize the significantly lifting of counting yield, be particularly useful for having the extensive active distribution system Simulation of stability calculating of rigidity characteristic, for the exploitation of efficient, reliable active distribution system simulated program is had laid a good foundation.
Claims (3)
1. the active distribution system Simulation of stability method based on implicit expression projection, is characterized in that, comprises the steps:
1) according to the dynamic equation of the topological connection relation of system and element, set up active distribution system transient stability realistic model, shape as
In formula,
for the differential equation,
for algebraic equation,
for system state variables,
for system algebraically variable;
2) active distribution system is carried out to trend calculating, obtain system load flow data;
3) reading system parameter and simulation calculation parameter, comprise emulation termination time T, simulation step length h, the outside integrator integration step of the integration step number k of implicit expression projection algorithm internal integral device and implicit expression projection algorithm is with respect to the multiple M of implicit expression projection algorithm internal integral device integration step, k and M are positive integer, emulation fault and operation event information are set, comprise fault generation and checkout time, abort situation and fault type;
4), according to system load flow result of calculation, system-wide dynamic element is carried out to simulation initialisation calculating;
5) simulation time t=0 is set;
6) the integration step number s=1 of current implicit expression projection algorithm internal integral device is set, s is positive integer;
7) simulation time t=t+h is set, h is implicit expression projection algorithm internal integral device integration step, adopts implicit expression projection algorithm internal integral device to calculate a step-length to active distribution system model, obtains the state variable x in this moment of system
n+swith algebraically variable y
n+s, and s=s+1 is set;
8) according to step 3) the emulation fault and the operation event information that arrange judge whether system now breaks down or operate, if the time of origin T of fault and Action Events
event=t, returns to step 6), otherwise carry out next step;
9) judge whether simulation time t reaches emulation termination time T, if t=T, emulation finishes, otherwise carries out next step;
10) whether the integration step number s that judges implicit expression projection algorithm internal integral device is greater than step 3) in the integration step number k+1 of implicit expression projection algorithm internal integral device of user's input, if s≤k+1 returns to step 7), otherwise carry out next step;
11) according to step 3) the emulation fault that arranges and operation event information judge in t～t+Mh time, whether break down or operate, if t<T
event<t+Mh, enters step 13), otherwise carry out next step;
12) the outside integrator integration step of implicit expression projection algorithm H=Mh is set, simulation time t=t+Mh is set, utilize the outside integrator of implicit expression projection algorithm to obtain the state variable x in this moment of system
n+k+1+Hwith algebraically variable y
n+k+1+H, then directly enter step 14);
13) the outside integrator integration step of implicit expression projection algorithm H=T is set
event-t, arranges simulation time t=T
event, utilize the outside integrator of implicit expression projection algorithm to obtain the state variable x of fault or the front system of operation generation
n+k+1+Hwith algebraically variable y
n+k+1+H;
14) judge whether simulation time t reaches emulation termination time T, if t=T, emulation finishes, otherwise returns to step 6), according to step 6) to 14) repeatedly carry out until emulation finishes.
2. a kind of active distribution system Simulation of stability method based on implicit expression projection according to claim 1, it is characterized in that, step 3) described implicit expression projection algorithm internal integral device, be to adopt explicit alternately method for solving to solve active distribution system model, the differential equation in active distribution system model chosen to any explicit numerical integration algorithm with the above precision of second order.
3. a kind of active distribution system Simulation of stability method based on implicit expression projection according to claim 1, it is characterized in that, step 3) the outside integrator of described implicit expression projection algorithm, as follows to describing the concrete solution procedure of differential-algebraic equation of active distribution system in the outside integrator integration step of implicit expression projection algorithm H:
(1) establishing current simulation time is t
n+k+1, wherein, the emulation total step number that n is current time, current time system state variables is x
n+k+1, algebraically variable is y
n+k+1, through step-length H, the system emulation time is t
n+k+1+H, now the state variable of system and algebraically variable are respectively x
n+k+1+Hand y
n+k+1+H, to describing differential-algebraic equation implicit expression differencing of active distribution system model, obtain following formula:
(2) utilize forward direction Euler method to obtain x
n+k+1+Hthe predicted value of initial estimate
be shown below
Substitution equation then
obtain y
n+k+1+Hthe predicted value of initial estimate value
(3) utilize following formula to proofread and correct predicted value, obtain x
n+k+1+Hinitial estimate
Then be updated to algebraic equation
in obtain y
n+k+1+Hinitial estimate
(4) by following formula, obtain x
n+k+1+Hmodified value
Then will
value substitution algebraic equation
in, solve and obtain y
n+k+1+Hmodified value
(5) respectively will
with
substitution following formula judges whether to meet the condition of convergence,
In formula, ξ is the error permissible value being set by the user, if meet the condition of convergence, the outside integrator calculation procedure of implicit expression projection algorithm finishes; Otherwise, respectively will
with
replace
with
return to step (4), repeating step (4) and (5) are until meet the condition of convergence.
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