CN101937481A - Transient simulation method of distributed power generation system based on automatic differentiation technology - Google Patents

Abstract

The invention discloses a transient simulation method of a distributed power generation system based on an automatic differentiation technology, which comprises the following steps: reading the basic information, topological connection, mathematical model expression and related parameters of a distributed power; stating a corresponding combinational function and independent variable, allocating memory for automatic differentiation and setting stimulation time to be zero; propelling a stimulation step forwardly for the stimulation time; calculating the differential coefficient information and function values of the corresponding combinational function through automatic differentiation; forming a Newton iterative format through combining the whole system equations, updating elements at corresponding positions of column vectors of a Jacobian matrix when iterative solving and the function values through the result obtained from automatic differentiation calculation; solving linear equations to obtain the column vector of variable increment of step k; updating the variable value; judging whether the stimulation time reaches the ceasing moment of stimulation, if yes, releasing the memory to finish stimulation; and otherwise, returning to step three. The method improves the calculation efficiency of programming and simultaneously keeps the maintainability and scalability of codes.

Description

Distributed generation system transient emulation method based on automatic differential technology

Technical field

The present invention relates to a kind of method that is used for the distributed generation system modeling and simulation of electric system.Particularly relate to a kind of distributed generation system transient emulation method based on automatic differential technology.

Background technology

In the performance history of distributed generation system simulation software, the model description problem that a right major issue of demand side is exactly the distributed power source control system, or perhaps the problem of implementation of control system model in simulation algorithm.Distributed power source has the advantages that kind is many, control strategy is various, described and be built in simulation algorithm according to a definite model integral body each distributed power source and control system thereof, the advantage of doing like this is that the efficient of emulation can be increased, but shortcoming is in the face of new distributed power source or new control system, the reprogramming of having to is realized model, since distributed power source and control strategy kind thereof are a lot, and be in the continuous development and change, the way of this built-in model is unpractical.Another kind of models treated mode adopts user-defined model exactly, according to the composed component of distributed power source and control system thereof, in the process of user's input element parameter, builds correlation model by Automatic Program.The advantage of this method is that program has versatility, and increasing new control system does not need simulated program is carried out any modification, and only needs the variation of input parameter.But this method also has weak point, the distributed power source The whole control system contains a large amount of basic links, is unit when carrying out simulation calculation with these basic links, and corresponding Jacobi matrix dimension is corresponding higher, and the modeling process more complicated in the program can reduce the simulation efficiency of program.

In order effectively to solve the problems referred to above of facing in the distributed generation system software development process, can between simulation software core algorithm and user, make up one flexibly, user-defined model interface easily, by the compositional modeling method of user-defined model the distributed power source control system is carried out modeling.The purpose of user-defined model compositional modeling method is suitably compromised with built-in modelling with based on the user self-defining method of primary element, and both user friendly input can effectively guarantee the efficient of simulation algorithm again; Both simplify the modeling process of simulation work, reduced the dimension of Jacobi matrix, had higher flexibility simultaneously.In the distributed generation system simulation software, user-defined model compositional modeling module is the interface module between software kernels simulation algorithm and the input of user-defined model parameter.At new distributed power source control system, same topology and the parameter that only needs input basic comprising element of user, user-defined model compositional modeling module will be carried out appropriate combination to the primary element of user input, offers the emulation kernel program after forming some functions.The input of compositional modeling module is primary element parameter and the topological connection relation that constitutes control system, and output then is composite function value under the step and relevant derivative when each emulation, and these derivatives will directly be filled in the relevant Jacobi matrix.

The composite function value that is formed primary element by the user-defined model interface is also uncomplicated, but forms relevant differential term automatically, can select diverse ways.Common methods comprises that manual programming, diff and numerical difference between grade.When using manual programming to calculate the analytical expression of derivative, computation process is comparatively complicated, and can't obtain the analytical expression of some differential term sometimes; Diff is fit to the calculating of problem on a small scale finds the solution, and is difficult to the higher derivative of computing function simultaneously, is unfavorable for the expansion of program; The realization of diff method is more convenient, adding improved sparse method of difference, to find the solution speed very fast relatively, thereby become one of method that is most widely used, but the shortcoming of diff method is to exist truncation error and round-off error, determines that simultaneously appropriate difference interval is also very difficult.

Automatic differential technology is a kind of accurate differential algorithm, compare with other differential methods (as: diff, diff), less to taking of CPU time and internal memory, and can obtain being equivalent to the derivative information of computing machine precision, and applying flexible, exploitation cost are little.Automatic differential technology obtains to use in fields such as electric power system tide calculating and sensitivity analysis at present.

Summary of the invention

Technical matters to be solved by this invention is, various at distributed power source control system kind, employing influences the problem of simulation efficiency based on the user-defined model of control system primary element, providing a kind of can combine automatic differential technology with this modeling method, utilize automatic differential technology can ask for the characteristics of corresponding composite function value and derivative information accurately and efficiently, effectively improve the counting yield of simulated program, keep the distributed generation system transient emulation method based on automatic differential technology of the maintainability and the extensibility of simulated program code simultaneously.

The technical solution adopted in the present invention is: a kind of distributed generation system transient emulation method based on automatic differential technology comprises the steps:

The first step: read the essential information of distributed power source, include power supply type and title; Topological connection relation, the input and output that include the distributed power source element are numbered; Mathematical model expression formula and correlation parameter; The composite function that statement is corresponding;

Second step: the statement independent variable is the automatic differential storage allocation, simulation time zero setting: t=0;

The 3rd step: simulation time is pushed ahead a simulation step length: t=t+ Δ T;

The 4th step: use automatic differential to calculate the derivative information and the functional value of corresponding composite function;

The 5th step: simultaneous total system equation forms Newton method iteration form F (x ^(k))+J ^(k)Δ x ^(k)=0, Jacobi matrix and functional value column vector relevant position element when the result who calculates with automatic differential upgrades iterative;

The 6th step: find the solution system of linear equations Ax=b, obtain the k variable increment column vector Δ x in step ^(k)

The 7th step: upgrade variate-value, according to the iteration convergence criterion || Δ x ^(k)||＜ξ judges whether convergence, and as iteration convergence, the calculating that goes on foot when then finishing this enters next step; Otherwise returned for the 4th step;

The 8th step: judge whether simulation time reaches emulation and end constantly, as reach emulation and end constantly, releasing memory then, emulation end; Otherwise returned for the 3rd step.

The implementation pattern that described use automatic differential of the 4th step calculates the derivative information of corresponding composite function is forward mode or reverse mode.

Distributed generation system transient emulation method based on automatic differential technology of the present invention, be to carry out modeling by the compositional modeling method of user-defined model, utilize automatic differential technology to ask for corresponding composite function value and derivative information accurately and efficiently, improve efficiency of programs, also kept the maintainability and the extensibility of code simultaneously.Compare with the User Defined modeling method based on the basic link of control system, the present invention has following characteristics:

1) adopts the compositional modeling method, avoided the embodiment of basic link in Jacobi matrix of big amount control system, reduced the Jacobi matrix dimension;

2) utilize automatic differential technology to calculate relevant position element in the Jacobi matrix accurately and efficiently, improved the transient emulation efficiency of programs;

3) automatic differential technology has kept the maintainability and the extensibility of program code;

4) automatic differential technology also is applicable to conventional control system component, and can handle the function by the program definition, can comprise structures such as branch, circulation and subroutine.

Description of drawings

Fig. 1 is the overall flow figure of the inventive method;

Fig. 2 is based on ohm superpotential modeling figure of the basic link of control system;

Fig. 3 is that automatic differential and compositional modeling method are at fuel cell Application in Modeling synoptic diagram.

Embodiment

Below in conjunction with embodiment and accompanying drawing the distributed generation system transient emulation method based on automatic differential technology of the present invention is made a detailed description.

As shown in Figure 1, the distributed generation system transient emulation method based on automatic differential technology of the present invention comprises the steps:

The first step: read the essential information of distributed power source, include power supply type and title; Topological connection relation includes the input and output numbering of distributed power source element, thereby the transient emulation program can be discerned this power supply and with which element links to each other; Mathematical model expression formula and correlation parameter, the composite function that statement is corresponding;

Second step: the statement independent variable is the automatic differential storage allocation, simulation time zero setting: t=0;

The 3rd step: simulation time is pushed ahead a simulation step length: t=t+ Δ T;

The 4th step: use automatic differential to calculate the derivative information and the functional value of corresponding composite function; The implementation pattern that uses automatic differential to calculate the derivative information of corresponding composite function can be forward mode or reverse mode.

The 5th step: simultaneous total system equation forms Newton method iteration form F (x ^(k))+J ^(k)Δ x ^(k)=0, Jacobi matrix and functional value column vector relevant position element when the result who calculates with automatic differential upgrades iterative;

The 6th step: find the solution system of linear equations Ax=b, obtain the k variable increment column vector Δ x in step ^(k)

The 7th step: upgrade variate-value, according to the iteration convergence criterion || Δ x ^(k)||＜ξ judges whether convergence, and as iteration convergence, the calculating that goes on foot when then finishing this enters next step; Otherwise returned for the 4th step;

The 8th step: judge whether simulation time reaches emulation and end constantly, as reach emulation and end constantly, releasing memory then, emulation end; Otherwise returned for the 3rd step.

Below in conjunction with accompanying drawing, be example with Proton Exchange Membrane Fuel Cells (PEMFC), the distributed generation system transient emulation method based on automatic differential technology of the present invention is elaborated.

The first step:

Read the mathematical model expression formula of essential information, topological connection relation and the PEMFC of PEMFC.The output characteristics of Proton Exchange Membrane Fuel Cells (PEMFC) can be described with following expression:

Fuel cell output voltage V _FC=E _Nernst-V _Act-V _Ohm-V _Con, each voltage calculation expression is as follows in the formula,

Reversible open-circuit voltage

Activation overpotential

Each parameter can be calculated with following formula in the activation overpotential formula

ξ ₁＝-0.948

${\mathrm{\&xi;}}_2=0.00286+0.0002\ln A+(4.3\&times;{10}^{-5})\mathrm{<figure-callout\; id="2"\; label="ln\; C\; H"\; filenames="HSA00000245853800021.png"\; state="\{\{state\}\}">ln</figure-callout>}{C}_{H_{}}{{}_2}_{}$

ξ ₃＝7.6×10 ^-5

ξ ₄＝-1.93×10 ^-4

${\mathrm{<figure-callout\; id="2"\; label="C\; O"\; filenames="HSA00000245853800021.png"\; state="\{\{state\}\}">C</figure-callout>}}_{O_{}}=\frac{{\mathrm{<figure-callout\; id="2"\; label="p\; O"\; filenames="HSA00000245853800021.png"\; state="\{\{state\}\}">p</figure-callout>}}_{O_{}}}{5.08\&times;{10}^6\&times;e^{\frac{-498}{T}}}$

${\mathrm{<figure-callout\; id="2"\; label="C\; H"\; filenames="HSA00000245853800021.png"\; state="\{\{state\}\}">C</figure-callout>}}_{H_{}}=\frac{{\mathrm{<figure-callout\; id="2"\; label="p\; H"\; filenames="HSA00000245853800021.png"\; state="\{\{state\}\}">p</figure-callout>}}_{H_{}}}{1.09\&times;{10}^6\&times;e^{\frac{77}{T}}}$

Concentration overvoltage

Ohm superpotential V _Ohm=I _FC(R _M+ R _C)

$R_M=\frac{{\mathrm{\&rho;}}_M\&times;l}{A}$

${\mathrm{\&rho;}}_M=\frac{181.6[1+0.03\left(\frac{I_{\mathrm{FC}}}{A}\right)+0.062{\left(\frac{T}{303}\right)}^2{\left(\frac{I_{\mathrm{FC}}}{A}\right)}^{2.5}]}{[\mathrm{\&lambda;}-0.634-3\left(\frac{I_{\mathrm{FC}}}{A}\right)]\exp \left[4.18\left(\frac{T-303}{T}\right)\right]}$

In the formula, V _FCThe working voltage of expression fuel cell; I _FCThe running current of expression fuel cell; E _NernstThe reversible open-circuit voltage of expression battery; V _ActThe expression activation overpotential; V _ConThe indicated concentration superpotential; V _OhmExpression ohm superpotential;

With

The partial pressure of representing hydrogen and oxygen respectively; T represents the working temperature of battery;

The oxygen concentration on expression cathod catalyst surface; ξ _{I (i=1...4)}The coefficient of expression activation overpotential, its value is decided by dynamics, thermodynamics and electrochemical theoretical balance; I _nExpression internal short-circuit electric current; R _MExpression dielectric film resistance; R _CExpression connects resistance; ρ _MThe resistivity of expression dielectric film; A represents the active area of battery; L represents the thickness of dielectric film; The superpotential coefficient of B indicated concentration, it is by fuel cell itself and running status decision; J _MaxThe expression maximum current density; J represents running current density, and its size is

With each variable substitution in the fuel cell output voltage expression formula, promptly obtain the corresponding composite function of fuel cell mode

$V_{\mathrm{FC}}=1.229-0.85\&times;{10}^{-3}(T-298.15)+4.308\&times;{10}^{-5}T[\ln \left(p_{H_2}\right)+\frac{1}{2}\ln \left(p_{O_2}\right)]$

$+{\mathrm{\&xi;}}_1+[0.00286+0.0002\ln A+(4.3\&times;{10}^{-5})\ln \left(\frac{{\mathrm{<figure-callout\; id="2"\; label="p\; H"\; filenames="HSA00000245853800021.png"\; state="\{\{state\}\}">p</figure-callout>}}_{H_{}}}{1.09\&times;{10}^6\&times;e^{\frac{77}{T}}}\right)]T$

$+{\mathrm{\&xi;}}_{3}T\ln \left(\frac{{\mathrm{<figure-callout\; id="2"\; label="p\; O"\; filenames="HSA00000245853800021.png"\; state="\{\{state\}\}">p</figure-callout>}}_{O_{}}}{5.08\&times;{10}^6{\&times;e}^{\frac{-498}{T}}}\right)+{\mathrm{\&xi;}}_{4}T\ln (I_{\mathrm{FC}}+I_n)+B\ln (1-\frac{J}{J_{\max }})$

$-I_{\mathrm{FC}}(\frac{181.6[1+0.03\left(\frac{I_{\mathrm{FC}}}{A}\right)+0.062{\left(\frac{T}{303}\right)}^2{\left(\frac{I_{\mathrm{FC}}}{A}\right)}^{2.5}]}{[\mathrm{\&lambda;}-0.634-3\left(\frac{I_{\mathrm{FC}}}{A}\right)]\exp \left[4.18\left(\frac{T-303}{T}\right)\right]}\&times;\frac{l}{A}+R_C)$

V _FC＝E _nernst-V _act-V _ohm-V _con

Second step:

The statement independent variable is T,

And I _FC, and be the automatic differential storage allocation, simulation time zero setting (t=0);

The 3rd step:

Simulation time is pushed ahead a simulation step length (t=t+ Δ T);

The 4th step:

Use automatic differential to calculate the derivative information and the functional value of corresponding composite function;

Because the detailed mathematic(al) representation of VFC is very complicated, thus in the invention only with reversible open-circuit voltage E _NernstExpression formula be the detailed process of example introduction based on automatic differential technology computing function value and derivative information.Independent variable T,

And I _FCUse x respectively ₁, x ₂, x ₃, x ₄Expression, reversible open-circuit voltage E _NernstCalculation expression then be rewritten into following form:

$y=f(x_1,x_2,x_3)=1.229-0.85\&times;{10}^{-3}(x_1-298.15)$

$+4.308\&times;{10}^{-5}{x}_1[\ln \left(x_2\right)+\frac{1}{2}\ln \left(x_3\right)]$

Utilizing chain rule computing function value and derivative information, only is that example provides computation process with the forward mode in the literary composition, as shown in table 1.

Table 1 functional value and gradient calculation

Temporary variable substitution in will showing obtains corresponding derivative information calculations result

$\&dtri;f(x_1,x_2,x_3)=\{-0.85\&times;{10}^{-5}+4.308\&times;{10}^{-5}[\ln \left(x_2\right)+\frac{1}{2}\ln \left(x_3\right)\left]\right\}\&dtri;x_1$

$+(4.308\&times;{10}^{-5}{x}_1/x_2)\&dtri;x_2+(2.154\&times;{10}^{-5}{x}_1/x_3)\&dtri;x_3$

The 5th step: simultaneous total system equation forms Newton method iteration form F (x ^(k))+J ^(k)Δ x ^(k)=0, Jacobi matrix and functional value column vector relevant position element when the result who calculates with automatic differential upgrades iterative;

The 6th step: find the solution system of linear equations Ax=b, obtain the k variable increment column vector Δ x in step ^(k)

The 7th step: upgrade variate-value, according to the iteration convergence criterion || Δ x ^(k)||＜ξ judges whether convergence, and as iteration convergence, the calculating that goes on foot when then finishing this enters next step; Otherwise returned for the 4th step;

The 8th step: judge whether simulation time reaches emulation and end constantly, as reach emulation and end constantly, releasing memory then, emulation end; Otherwise returned for the 3rd step.

In the transient emulation process, will be when use is built fuel cell mode based on the user-defined model of primary element owing to containing a large amount of primary elements, make the Jacobi matrix dimension higher, influence the system emulation counting yield, Fig. 2 is that example has been introduced the basic link formation of control system with PEMFC ohm superpotential only.

As shown in Figure 3, when the compositional modeling method of utilizing the present invention to propose is carried out modeling, at first form the built-up pattern of fuel cell based on user-defined model, built-up pattern be input as T,

And I _FC, be output as V _FC, belong to the single output model of many inputs.Utilize automatic differential technology to calculate V on this basis _FCFunctional value and to T,

And I _FCDerivative information.

In the PEMFC model, its control system approximately contains 90 primary elements, and after utilizing built-up pattern to handle, only needs discrete component to express in simulated program, this greatly reduces the dimension of corresponding Jacobi matrix piece, will significantly improve the simulation efficiency of system.

Propose the influence of method in order to analyze the present invention, directly connect the example of ohmic load, tested respectively and adopted the present invention to propose method and based on computing time of the self-defined modeling method of control system primary element at PEMFC to the simulation calculation amount.The testing hardware platform configuration is Intel Pentium D 925 3GHz CPU, the PC of 1G RAM, software platform is University Of Tianjin's independently developed distributed generation system transient emulation program (Transient Simulator forDistributed Generation and Micro-grid, TSDG), this software uses the high-level programming language C++ that supports the operational character heavy duty to realize.PEMFC example simulation time is 1s, and step-length is 10us, and test result sees Table 2, is meant the control system resolving time computing time in the table, and unit is s.

The analysis of table 2 counting yield

From the test result of table 2 as can be seen, the iterations of two kinds of methods is equal substantially, but differs computing time bigger.Test result shows that the method that the present invention proposes has approximately improved 12 times based on the speed of the self-defined modeling method of primary element, and the transient emulation efficiency of programs greatly promotes.

Claims (2)

1. the distributed generation system transient emulation method based on automatic differential technology is characterized in that: comprise the steps:

The first step: read the essential information of distributed power source, include power supply type and title; Topological connection relation, the input and output that include the distributed power source element are numbered; Mathematical model expression formula and correlation parameter; The composite function that statement is corresponding;

Second step: the statement independent variable is the automatic differential storage allocation, simulation time zero setting: t=0;

The 3rd step: simulation time is pushed ahead a simulation step length: t=t+ Δ T;

The 4th step: use automatic differential to calculate the derivative information and the functional value of corresponding composite function;

The 5th step: simultaneous total system equation forms Newton method iteration form F (x ^(k))+J ^(k)Δ x ^(k)=0, Jacobi matrix and functional value column vector relevant position element when the result who calculates with automatic differential upgrades iterative;

The 6th step: find the solution system of linear equations Ax=b, obtain the k variable increment column vector Δ x in step ^(k)

The 7th step: upgrade variate-value, according to the iteration convergence criterion || Δ x ^(k)|| ξ judges whether convergence, and as iteration convergence, the calculating that goes on foot when then finishing this enters next step; Otherwise returned for the 4th step;

The 8th step: judge whether simulation time reaches emulation and end constantly, as reach emulation and end constantly, releasing memory then, emulation end; Otherwise returned for the 3rd step.

2. the distributed generation system transient emulation method based on automatic differential technology according to claim 1 is characterized in that, the implementation pattern that described use automatic differential of the 4th step calculates the derivative information of corresponding composite function is forward mode or reverse mode.

Images