CN115459339A - Improved variational iterative simulation method based on event triggering - Google Patents
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Abstract
The invention discloses an improved variational iterative simulation method based on event triggering, which is characterized in that a mathematical model is established by using a variational iterative method according to the variable relation of distributed photovoltaic in a modern active power distribution network; for a grid-connected inverter module in a two-stage photovoltaic power station, based on a state space correlation principle, performing numerical stability analysis on a system on the basis of establishing a state space expression, and comparing the numerical stability analysis with a traditional simulation algorithm; an improved method for applying the variational iteration method to photovoltaic solving is provided, and errors generated by updating an analytic expression with a fixed step length and numerical stability of the errors are analyzed; the simulation method is based on an event triggering principle, establishes an unequal relation according to the error norm of the state quantity after locking, deduces the triggering condition of the locking, is based on the event triggering principle, takes a variational iteration method as a basic algorithm, provides a basis for designing a high-efficiency simulation method of the distributed photovoltaic power station, achieves the aim of considering both precision and efficiency, and improves the simulation speed of the active power distribution network.
Description
Technical Field
The invention relates to the field of simulation algorithms of distributed power supplies in a power distribution network, in particular to an improved variational iterative simulation method based on event triggering.
Background
A modern power distribution network containing a high-density distributed power supply is a complex nonlinear rigid system, and a solving method of the model, namely a dynamic simulation algorithm, is always the focus of attention in the field of power system simulation. The accuracy and the efficiency of numerical calculation in dynamic simulation have great significance for planning, running, controlling and the like of modern active power distribution networks with high randomness and uncertainty of power generation characteristics. Currently, the solution method of differential equations (ODEs) is a conventional numerical integration algorithm such as a trapezoidal method, and the algorithm is difficult to meet the requirements of simulation for rapidness and stability. Compared with the traditional power distribution network, the active power distribution network has larger difference of dynamic characteristics of components; the time scale difference is obvious, and the rigidity problem exists; the corresponding mathematical model has higher order, higher dimension and stronger nonlinear characteristic. Based on the above, the dynamic simulation of the large-scale power distribution network is faced with more serious challenges, so that on the premise of ensuring the precision and stability, a more efficient and faster simulation algorithm is necessary to be provided.
In recent years, the Variational Iterative Method (VIM) has been distinguished from various approximate analytical methods due to its outstanding advantages, and has been widely applied to solving various nonlinear problems including ages. When the method is applied to the simulation of the distributed power supply of the power distribution network, the efficiency is improved compared with the traditional implicit trapezoidal algorithm, the variable parameter calculation formula of the system is essentially obtained during application, the state quantity expression is updated once in each step length, the calculation resource waste is caused during the steady-state operation, and the optimization space is still provided, so that the improved variational iterative simulation method based on event triggering is provided.
Disclosure of Invention
The invention aims to provide an improved variational iterative simulation method based on event triggering, which is based on a variational iterative approximate analysis method of a differential equation, is applied to an active power distribution network containing high-density distributed photovoltaic, analyzes the numerical stability of the variational iterative approximate analysis method, locks partial state variables in a variational model according to a relevant theory of event triggering, and adopts fixed step length updating or updating when an error vector norm meets a certain condition so as to improve the simulation solving rate of a photovoltaic power station and further improve the simulation operation efficiency of the active power distribution network.
The purpose of the invention can be realized by the following technical scheme:
an improved variation iteration simulation method based on event triggering, comprising the following steps:
step one, according to relevant steps calculated by a variational iterative method, a variational mathematical model is established for the two-stage photovoltaic power station, and then the step two is carried out.
And step two, calculating a state space expression corresponding to the model, carrying out numerical stability analysis on the system according to a state space stability discrimination theory, comparing the maximum simulation step length allowed by the system with a trapezoidal method and an improved Euler method, and then entering step three.
And step three, fixing the step length, updating partial high-order analytic expressions, performing numerical stability analysis and error transmission on the method, expanding the maximum equivalent step length of the variational method, and then entering step four.
And step four, based on an event trigger correlation theory, taking the norm of the error vector as a trigger discrimination condition to obtain an error threshold, improving the original variation iteration method, and further improving the operation efficiency of the simulation system.
Further, in the first step, in modeling of the two-stage photovoltaic power station, a mathematical model of the two-stage photovoltaic including the photovoltaic array, the boost chopper circuit and the grid-connected inverter is established according to related steps calculated by a variational iteration method, and the specific operation includes the following steps:
s11, introducing a variational iteration method to solve a general form of a differential equation in the two-stage photovoltaic power station, wherein the form is as follows:
ly (t) + Ny (t) = f (t) formula (1)
Wherein y (t) is a function to be solved, and L and N are respectively a linear operator and a nonlinear operator. According to the VIM principle, the corresponding correction functional of this equation is:
wherein n is the number of iterations, λ (τ) is the Lagrangian, which is a pending function,
denotes y n The constraint variation of (τ) is subjected to a variation operation, resulting in 0.
S12: mathematical modeling is respectively carried out on a photovoltaic array, a boost chopper and a grid-connected inverter in a two-stage photovoltaic power station, and an algebraic-differential equation (D-Es) model corresponding to each part is as follows:
a photovoltaic array:
wherein u is PV 、i PV Respectively photovoltaic voltage, current i Two oost, L Chopping the input current for boosting, C PV Is a photovoltaic equivalent capacitance;
a boost chopper:
wherein u is Two oost To output a voltage, i Two oost For output current, D is chopping duty cycle, L Two oost 、C Two oost Respectively an inductance, a capacitance u in the chopper M For photovoltaic maximum power point corresponding to voltage, k p1 、k i1 Is the controller parameter of the two oost circuit.
Grid-connected inverter (single-ring PQ control, when park conversion is performed, the d axis is taken to be consistent with one phase):
u Boost i Boost ＝u id i d +u iq i q formula (14)
Wherein u is mdq 、u idq 、u sdq 、i dq Dq components, k, of the modulated wave voltage, inverter output voltage, grid-connected point voltage, current, respectively 0 Is the modulation ratio. k is a radical of p2 、k i2 Is the controller parameter of the inverter circuit. When SPWM is adoptedIn the modulation mode, k 0 Get the
If u is Two oost Is 800V, U A C 380V, then m =2.227.
S13: all differential equations in the expressions (3) to (13) are solved by using a variation iteration method, the variation iteration format is calculated by taking the expression (8) as an example, and the correction functional is as follows according to the expression (2):
in consideration of the alternative solution of algebraic-differential equation, u is used for calculating differential equation sd 、u id 、L f All are known quantities, so the quantities are combined into a parameter one, and the variational operation is carried out on the formula (15):
according to the variational principle, as the iteration proceeds, the left side of equation (16) gradually approaches 0, then for the right side, there is a constraint:
and lambda = -1, an iterative format of id can be obtained by substituting formula (15), an initial function is substituted, and an approximate analytical solution can be obtained by iteration. The same can be said of the variant iteration formats corresponding to the equations (4) - (11).
Further, in the second step, based on a state space theory, a state space expression corresponding to the grid-connected inverter is calculated, and the numerical stability of the state space expression is analyzed, and the specific steps include:
s21, listing a mathematical model corresponding to the grid-connected inverter after the variational iteration is applied, wherein the inverter adopts PQ single-ring control, and the variational iteration method adopts a second-order expression, and the model is as follows:
wherein, the subscript contains 0 to indicate that the variable is the updated initial value.
S22: the simulation calculation is carried out on a single simulation step length by adopting alternative solution, because u in the control system md1 、u md2 The integral equation has no coupling of state quantity, and can be discretized directly by adopting an Euler method, and the other variables adopt a variational format, i is taken d 、i q 、u md1 、u mq1 As state variables, the state space expression of the system can be obtained after arrangement:
where Δ t is the simulation step size, and C is a constant matrix related to the parameters of the inverter input, output, etc. And m is the ratio of the output voltage of the inverter to the modulation voltage. According to the state space theory, when the state matrix spectrum radius is smaller than 1, the system can be stable, so that whether the system can be stable can be calculated under the condition that each parameter in the matrix is known. Thus, the state iteration matrix can be used for the determination of the maximum simulation step size when the remaining pending parameters are known.
Furthermore, the analytic expression is updated in the third step through a fixed step length, so that a certain simulation speed is increased, and the method is characterized in that:
and acquiring a state space expression corresponding to the fixed step length update. By the method, the equivalent step length can be enlarged to n delta t. For the improved form of numerical stability, the spectral radius of the state matrix one' can be used to perform the numerical stability determination.
Further, the fourth step is based on the event triggering correlation theory, and i is locked when the system state quantity meets a certain condition dq So as to omit the calculation of the secondary expression in the simulation calculation time step, and the specific operation steps comprise:
s41: the state space expression corresponding to equation (19) is simplified as follows:
y(k+1)＝Ay(k)+C 1 formula (21)
And assume its steady state value of y ∞ Deviation e between the state quantity and the steady state value 0 The state matrix after locking is one 1 Then the new state space expression is:
y ∞ +e(k+1)＝A 1 [y ∞ +e(k)]+C 2 formula (22)
Remember one 1 = one + Δ one, which can be modified by substituting equation (26), i.e.:
the left side and the right side simultaneously eliminate the steady-state component, and the iterative expression of the obtained error is as follows:
e(k+1)＝A 1 e(k)+ΔAy ∞ +C 2 -C 1 ＝A 1 e(k)+C 3 and (3) formula (24).
And S42, converting the error iteration format of the formula (24) into a continuous form for solving, wherein according to the conversion relation between the discrete form and the continuous form:
taking norm to obtain inequality constraint:
solving the differential inequality can obtain the condition of event triggering, namely the constraint condition of the error norm is as follows:
the invention has the beneficial effects that:
1. according to the simulation method, the method is compared with the traditional numerical integration algorithm through the numerical stability verification, the error calculation and the event triggering method, and the variational iteration method in the mathematical field is combined with the distributed photovoltaic in the active power distribution network, so that the simulation algorithm combining the variational method and the traditional numerical integration method is established, the approximate analytic characteristic of the variational method is utilized, and the simulation calculation efficiency is improved;
2. the simulation method of the invention uses the state space theory to carry out numerical stability analysis on the mathematical model established by the variational method, thereby obtaining the maximum simulation step length allowed by the simulation method as the basis of simulation design;
3. the simulation method provided by the invention is improved by aiming at the problem that the expression is updated once per step length in the existing variation simulation method, an improved form based on event triggering is provided, and the simulation efficiency of the system is further improved.
4. The algorithm iteration format in the simulation method is simple to construct and has higher universality;
5. the simulation method has the advantages of high precision close to that of the traditional simulation algorithm, larger allowable step length, higher simulation speed and certain application prospect in the modern active power distribution network accessed by the high-density distributed power supply.
Drawings
The invention will be further described with reference to the accompanying drawings.
FIG. 1 is a flow chart of a simulation method of the present invention;
FIG. 2 is a grid-connected inverter simulation system employed in the simulation method of the present invention;
FIG. 3 is a graph of active power comparison of variational modeling in different step lengths according to the simulation method of the present invention;
FIG. 4 is a simulation result diagram of active power comparison of three algorithms in the simulation method under a near-limit step length;
FIG. 5 is a graph comparing the active power output by the inverter under different triggering modes in the simulation method of the present invention;
FIG. 6 is a graph comparing the voltages output by the inverter under different triggering modes in the simulation method of the present invention;
FIG. 7 is a block diagram of an improved IEEE-33 node active power distribution network test system employed in the simulation method of the present invention;
FIG. 8 is a comparison graph of active power waveforms of different simulation methods of the test system node 8 in the simulation method of the present invention;
FIG. 9 is a comparison graph of reactive power waveforms of different simulation methods of the test system node 8 in the simulation method of the present invention;
fig. 10 is a comparison graph of voltage waveforms of different simulation methods of the test system node 8 in the simulation method of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In the description of the present specification, reference is made to the term an improved variational iterative simulation method based on event triggering, as shown in fig. 1, the simulation method includes the following steps:
step one, establishing a mathematical model of a variational form for the two-stage photovoltaic power station according to related steps calculated by a variational iterative method, and then entering step two.
In modeling of a two-stage photovoltaic power station, a mathematical model of the two-stage photovoltaic power station comprising a photovoltaic array, a boost chopper circuit and a grid-connected inverter is established according to relevant steps calculated by a variational iteration method, and the method specifically comprises the following steps:
s11, introducing a variational iteration method to solve a general form of a differential equation in the two-stage photovoltaic power station, wherein the form is as follows:
ly (t) + Ny (t) = f (t) formula (1)
Wherein y (t) is a function to be solved, L and N are respectively a linear operator and a nonlinear operator, and according to the VIM principle, the corresponding correction functional of the equation is as follows:
wherein n is the number of iterations, λ (τ) is the Lagrangian, which is a pending function,
denotes y n The constraint variation of (τ) is subjected to a variation operation, resulting in 0.
S12: mathematical modeling is respectively carried out on a photovoltaic array, a boost chopper and a grid-connected inverter in a two-stage photovoltaic power station, and an algebraic-differential equation (D-Es) model corresponding to each part is as follows:
photovoltaic array:
wherein u is PV 、i PV Respectively photovoltaic voltage, current i Two oost, L Chopping the input current for boosting, C PV Is a photovoltaic equivalent capacitance.
A boost chopper:
wherein u is Two oost To output a voltage, i Two oost For output current, D is chopping duty cycle, L Two oost 、C Two oost Respectively an inductance, a capacitance u in the chopper M For photovoltaic maximum power point corresponding to voltage, k p1 、k i1 Is the controller parameter of the two oost circuit.
Grid-connected inverter (single-loop PQ control, when carrying out park transformation, taking d axis to be consistent with one phase):
u Boost i Boost ＝u id i d +u iq i q formula (14)
Wherein u is mdq 、u idq 、u sdq 、i dq Respectively are the dq components of the modulated wave voltage, the inverter output voltage, the grid-connected point voltage and the current,k 0 is the modulation ratio. k is a radical of p2 、k i2 Is the controller parameter of the inverter circuit. When the SPWM modulation mode is adopted, k 0 Get
If u is Two oost Is 800V, U A C 380V, then m =2.227.
S13: all the differential equations in the formulas (3) to (13) are solved by using a variational iteration method, and the variational iteration format is calculated by taking the formula (8) as an example. According to equation (2), the correction functional is:
considering u in the alternative solution of algebraic-differential equation sd 、u id 、L f All are known quantities, so the parameters are combined into a parameter one, and the variational operation is carried out on the formula (15):
according to the variation principle, as the iteration proceeds, the left side of equation (16) gradually approaches 0, and then for the right side, there is a constraint condition:
further, λ = -1 is easily known, an iterative format of id can be obtained by substituting formula (15), and an approximate analytical solution can be obtained by substituting an initial function and iteration. The same can be said of the variant iteration formats corresponding to the equations (4) - (11). For other distributed power generation equipment in the active power distribution network, such as water turbines, fans and the like, corresponding variational iteration formats and expressions of each order can be obtained by adopting the same method.
And step two, calculating a state space expression corresponding to the model, carrying out numerical stability analysis on the system according to a state space stability discrimination theory, comparing the maximum simulation step length allowed by the system with a trapezoidal method and an improved Euler method, and then entering step three.
Based on a state space theory, calculating a state space expression corresponding to the grid-connected inverter, and analyzing the numerical stability of the state space expression, wherein the specific operations comprise the following steps:
s21, listing a mathematical model corresponding to the grid-connected inverter after the variational iteration is applied, wherein the inverter adopts PQ single-ring control, the variational iteration method adopts a second-order expression, and the model is as follows:
wherein, the subscript contains 0 to indicate that the variable is the updated initial value.
S22: the simulation calculation is carried out on a single simulation step length by adopting alternative solution, because u in the control system md1 、u md2 The integral equation has no coupling of state quantity, and can be discretized directly by adopting an Euler method, and the other variables adopt a variational format, i is taken d 、i q 、u md1 、u mq1 As state variables, the state space expression of the system can be obtained after the arrangement:
where Δ t is the simulation step size, and C is a constant matrix related to parameters such as inverter input and output. And m is the ratio of the output voltage of the inverter to the modulation voltage. According to the state space theory, when the spectrum radius of the state matrix is less than 1, the system can be stable, so that whether the system can be stable can be calculated under the condition that each parameter in the matrix is known. Thus, the state iteration matrix can be used for the determination of the maximum simulation step size when the remaining pending parameters are known.
And step three, fixing the step length, updating partial high-order analytic expressions, performing numerical stability analysis and error transmission on the method, expanding the maximum equivalent step length of the variational method, and then entering step four.
The analytic formula is updated through fixed step length, certain simulation speed is improved, and the analytic formula is as follows:
and acquiring a state space expression corresponding to fixed step length updating, expanding the equivalent step length to n delta t by the method, and judging the numerical stability of the improved form by using the spectrum radius of the state matrix I'.
And step four, based on an event trigger correlation theory, taking the norm of the error vector as a trigger discrimination condition to obtain an error threshold, improving the original variation iteration method, and further improving the operation efficiency of the simulation system.
Based on the event trigger correlation theory, locking i when the system state quantity meets a certain condition dq The value of (3) is obtained, so that the calculation of a quadratic expression in the simulation calculation time step is omitted, the increase of errors can be restrained, and the simulation efficiency is improved.
S41: the state space expression corresponding to equation (19) is simplified as follows:
y(k+1)＝Ay(k)+C 1 formula (21)
And assume its steady state value of y ∞ Deviation e between the state quantity and the steady state value 0 The state matrix after locking is one 1 Then the new state space expression is:
y ∞ +e(k+1)＝A 1 [y ∞ +e(k)]+C 2 formula (22)
Remember one 1 = one + Δ one, which can be modified by substituting equation (26), i.e.:
the left side and the right side simultaneously eliminate the steady-state component, and the iterative expression of the obtained error is as follows:
e(k+1)＝A 1 e(k)+ΔAy ∞ +C 2 -C 1 ＝A 1 e(k)+C 3 formula (24)
And S42, converting the error iteration format of the formula (24) into a continuous form for solving, wherein according to the conversion relation between the discrete form and the continuous form:
taking the norm of the vector, obtaining the inequality constraint:
solving the differential inequality can obtain the condition of event triggering, namely the constraint condition of the error norm is as follows:
the simulation method is applied to the reality, and the simulation system is shown as fig. 2, wherein: the circuit on the left direct current side of the converter is connected with 800V direct current input, and the right side of the converter is connected with the filter inductor and is connected with the grid through a line. The effective value of the grid line voltage is 380V, and the frequency is 50Hz. Filter inductor L f Is 4mH, line resistance R line 0.1 omega, inductance L line Is 1mH. The simulation time of the system is 5s, the converter adopts PQ control, and the power reference value P ref Is 20kw, where Q is changed to 15kw at 2-3s ref Is 20 kv-r. Controller parameter setting k p ＝1.5，k i =30. According to the improved variational iterative simulation method based on event triggering, the distributed photovoltaic grid-connected inverter is designed, a simulation model is built based on an M-TL-I-II platform, the stability of each algorithm and the event triggering effect are simulated, and the feasibility of the method is verified.
According to the active comparison diagram modeled by the variational method under different step lengths, 1ms, 1.7ms, 1.73ms and 1.74ms are respectively adopted as simulation step lengths for comparison, the inverter output active power is shown in figure 3, when the simulation step length is less than 1.73ms, the system can be converged and vibrates near a steady-state value when the simulation step length is 1.73ms, and when the step length is 1.74ms, the system gradually diverges from the beginning of calculation, and the simulation result is consistent with the theoretical maximum simulation step length.
When the inverter starts to operate, the reference active power of each inverter is 20kW, the power is reduced to 15kW when the reference active power is 2 seconds, the power is restored to 20kW when the reference active power is 3 seconds, the simulation results of active comparison under the approximate limit step length of three algorithms of the simulation method are shown in figure 4, it can be seen from waveform comparison that the precision cannot be guaranteed when the trapezoidal method is approximate to the limit step length, large oscillation exists under the step length of 1.7ms in the variational method, and the convergence performance is superior to that of other three situations when the step length of 1.5 ms. The total time consumption ratio of 100 simulations of 5 seconds using each simulation algorithm is shown in table 1. Since the variational method allows simulation calculation with a larger step size, the improvement in simulation efficiency is significant.
TABLE 1
When the operation is started, the reference active power of each inverter is 20kw, the power is reduced to 15kw when the operation is started for 2 seconds, the power is restored to 20kW when the operation is started for 3 seconds, fig. 5 is an active power comparison graph output by the inverters in different trigger modes, fig. 6 is a voltage comparison graph output by the inverters in different trigger modes, and as can be known from fig. 5, when the steady trigger mode is adopted, because the current reference value is updated to be the instantaneous current value which is still the last steady value, the difference is substituted into a modulation wave calculation formula, large fluctuation can be caused, and the simulation is not allowed. The precision and convergence rate of the fixed-step triggering are not as good as those of the event triggering, and the event triggering can basically achieve the effect consistent with the original method.
Fig. 7 is a structural diagram of the improved IEEE-33 node active power distribution network test system in the embodiment. Wherein: the distributed photovoltaic power generation system is connected to load nodes 8, 13, 25, 33 in the system. The total load of the system is 5084.26+j2547.32kV I. The simulation step length is 10 mus, when in normal operation,the initial environmental condition of the photovoltaic power generation system is 1000W/m 2 And 25 ℃ and all run at unity power factor. Line parameters: c PV ＝10 -4 F，L Two oost ＝50mH，C Two oost ＝5mF，L f =5mH. The controller parameters are as follows: k is a radical of p1 ＝k p2 ＝1.5，k i1 ＝k i2 =30. The total simulation time is 5s, and when the system runs to 2.5s, all photovoltaic irradiance is reduced to 800W/m 2 And is recovered to 1000W/m in 3s 2 。
As shown in fig. 8 to 10, the simulation method respectively adopts simulation results of simulation by an improved variational method based on event triggering, a variational method without triggering a lock value, and a trapezoidal integration method, and compares the per unit values of the active power, the reactive power, and the effective value of the node voltage of the node 8. The precision of the basic variational method is approximate to that of the trapezoidal method, and when the bus voltage is calculated by the improved variational method, an error of about 0.1 percent exists, the error magnitude is small, and the precision requirement is basically met. The simulation time for each algorithm is shown in table 2. The simulation time consumption mainly comprises distributed photovoltaic calculation and load flow calculation, and the improvement variation is reduced by about 29% in comparison with a trapezoidal method in the aspect of photovoltaic calculation time from the table 2, so that certain advantages are achieved.
TABLE 2
The invention provides an improved variational iteration simulation method, provides a numerical stability verification method, an error calculation method and an event triggering method, compares the method with a traditional numerical integration algorithm, and combines a variational iteration method in the mathematical field with distributed photovoltaic in an active power distribution network, thereby establishing a simulation algorithm combining the variational method with the traditional numerical integration method, utilizing the approximate analytic characteristic of the variational method, and improving the efficiency of simulation calculation; and (3) carrying out numerical stability analysis on the mathematical model established by the variational method by using a state space theory, thereby obtaining the maximum simulation step length allowed by the simulation method as the basis of simulation design.
The simulation method provided by the invention is improved by aiming at the problem that the expression is updated once per step length in the existing variation simulation method, an improved form based on event triggering is provided, and the simulation efficiency of the system is further improved. The algorithm iteration format is simple to construct and has high universality, the simulation method has the precision close to that of the traditional simulation algorithm, the allowed step length is larger, the simulation speed is higher, and the method has a certain application prospect in a modern active power distribution network accessed by a high-density distributed power supply.
Reference to "one embodiment," "an example," "a specific example," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
The foregoing shows and describes the general principles, essential features, and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed.
Claims (5)
1. An improved variation iteration simulation method based on event triggering is characterized by comprising the following steps:
step one, according to relevant steps calculated by a variational iterative method, a mathematical model of a variational form is established for a two-stage photovoltaic power station, and then the step two is carried out;
step two, calculating a state space expression corresponding to the model, performing numerical stability analysis on the system according to a state space stability discrimination theory, comparing the maximum simulation step length allowed by the system with a trapezoidal method and an improved Eulerian method, and then entering step three;
step three, fixing the step length and updating partial high-order analytic expressions, performing numerical stability analysis and error transmission on the method, expanding the maximum equivalent step length of the variational method, and then entering step four;
and step four, based on an event trigger correlation theory, taking the norm of the error vector as a trigger discrimination condition to obtain an error threshold, improving the original variation iteration method, and further improving the operation efficiency of the simulation system.
2. The improved variational iterative simulation method based on event triggering according to claim 1, wherein in the first step, in the modeling of the two-stage photovoltaic power station, a mathematical model of the two-stage photovoltaic power station comprising a photovoltaic array, a boost chopper circuit and a grid-connected inverter is established according to related steps calculated by a variational iterative method, and the specific operation comprises the following steps:
s11, introducing a variational iteration method to solve a general form of a differential equation in the two-stage photovoltaic power station, wherein the form is as follows:
ly (t) + Ny (t) = f (t) formula (1)
Wherein y (t) is a function to be solved, and L and N are respectively a linear operator and a nonlinear operator. According to the VIM principle, the corresponding correction functional of this equation is:
wherein n is the number of iterations, λ (τ) is the Lagrangian, is a undetermined function,
denotes y n (τ) a limiting variation for which a variation operation result is 0;
s12: mathematical modeling is respectively carried out on a photovoltaic array, a boost chopper and a grid-connected inverter in a two-stage photovoltaic power station, and algebraic-differential equation (D-Es) models corresponding to all parts are as follows:
a photovoltaic array:
wherein u is PV 、i PV Respectively photovoltaic voltage, current i Two oost, L Chopping input current for boosting, C PV Is a photovoltaic equivalent capacitance;
a step-up chopper:
wherein u is Two oost To output a voltage, i Two oost For output current, D is chopping duty cycle, L Two oost 、C Two oost Respectively an inductance, a capacitance u in the chopper M For photovoltaic maximum power point corresponding to voltage, k p1 、k i1 The controller parameters of the two oost circuit;
grid-connected inverter (single-ring PQ control, when park conversion is performed, the d axis is taken to be consistent with one phase):
u Boost i Boost ＝u id i d +u iq i q formula (14)
Wherein u is mdq 、u idq 、u sdq 、i dq Dq components, k, of the modulated wave voltage, inverter output voltage, grid-connected point voltage, current, respectively 0 Is the modulation ratio. k is a radical of formula p2 、k i2 Is the controller parameter of the inverter circuit. When the SPWM modulation mode is adopted, k 0 Get
If u is Two oost Is 800V, U A C 380V, then m =2.227;
s13: all differential equations in the expressions (3) to (13) are solved by using a variation iteration method, the variation iteration format is calculated by taking the expression (8) as an example, and the correction functional is as follows according to the expression (2):
considering algebraIn alternate solution of differential equations, u is calculated sd 、u id 、L f All are known quantities, so the quantities are combined into a parameter one, and the variational operation is carried out on the formula (15):
according to the variation principle, as the iteration proceeds, the left side of equation (16) gradually approaches 0, and then for the right side, there is a constraint condition:
and lambda = -1, an iterative format of id can be obtained by substituting formula (15), an initial function is substituted, and an approximate analytical solution can be obtained by iteration. The same can be said of the variant iteration formats corresponding to the equations (4) - (11).
3. The improved variation iterative simulation method based on event triggering according to claim 1, wherein in the second step, based on a state space theory, a state space expression corresponding to the grid-connected inverter is calculated, and the numerical stability of the state space expression is analyzed, and the specific steps include:
s21, listing a mathematical model corresponding to the grid-connected inverter after the variational iteration is applied, wherein the inverter adopts PQ single-ring control, and the variational iteration method adopts a second-order expression, and the model is as follows:
wherein, the subscript contains 0 to indicate that the variable is the updated initial value;
s22: the simulation calculation is carried out on a single simulation step length by adopting alternative solution, because u in the control system md1 、u md2 The integral equation has no coupling of state quantity, and can be discretized by directly adopting an Eulerian method, and other variables are adoptedUsing variational format, take i d 、i q 、u md1 、u mq1 As state variables, the state space expression of the system can be obtained after arrangement:
where Δ t is the simulation step size, and C is a constant matrix related to parameters such as inverter input and output. And m is the ratio of the output voltage of the inverter to the modulation voltage. According to the state space theory, when the spectrum radius of the state matrix is less than 1, the system can be stable, so that whether the system can be stable can be calculated under the condition that each parameter in the matrix is known. Thus, the state iteration matrix can be used for the determination of the maximum simulation step size when the remaining pending parameters are known.
4. The improved variational iterative simulation method based on event triggering according to claim 1, wherein in the third step, an analytic expression is updated by a fixed step length, so that a certain simulation speed is increased, according to the following formula:
and acquiring a state space expression corresponding to the fixed step length update. By the method, the equivalent step length can be enlarged to n delta t. For the improved form of numerical stability, the spectral radius of the state matrix one' can be used for numerical stability discrimination.
5. The improved variational iterative simulation method based on event triggering as claimed in claim 1, wherein said step four is based on the event triggering correlation theory, and locks i when the system state quantity satisfies a certain condition dq So as to omit the calculation of the secondary expression in the simulation calculation time step, and the specific operation steps comprise:
s41: the state space expression corresponding to equation (19) is simplified as follows:
y(k+1)＝Ay(k)+C 1 formula (21)
And assume its steady state value of y ∞ Deviation e between the state quantity and the steady state value 0 The state matrix after locking is one 1 Then the new state space expression is:
y ∞ +e(k+1)＝A 1 [y ∞ +e(k)]+C 2 formula (22)
Remember one 1 = one + Δ one, which can be modified by substituting equation (26), i.e.:
the left side and the right side simultaneously eliminate the steady-state component, and the iterative expression of the obtained error is as follows:
e(k+1)＝A 1 e(k)+ΔAy ∞ +C 2 -C 1 ＝A 1 e(k)+C 3 formula (24);
and S42, converting the error iteration format of the formula (24) into a continuous form for solving, wherein according to the conversion relation between the discrete form and the continuous form:
taking norm to obtain inequality constraint:
solving the differential inequality can obtain the condition of event triggering, namely the constraint condition of the error norm is as follows:
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| CN111900718A (en) * | 2020-06-17 | 2020-11-06 | 东南大学 | Active power distribution network dynamic simulation method based on multi-stage optimization catch-up variational iteration method |
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