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APPLICATION SOFTWARE FOR REACTOR SIZING CALCULATION

Claudiu-Ionel NICOLA1, Marcel NICOLA1, Ion PĂTRU1, Maria Cristina NIȚU1, Viorica VOICU1, Sebastian POPESCU1

1National Institute for Research, Development and Testing in Electrical Engineering – ICMET Craiova

nicolaclaudiu@icmet.ro, marcel_nicola@yahoo.com, ipatru@icmet.ro, cristinanitu@icmet.ro programe@icmet.ro, tn.popescu@icmet.ro

Abstract: One of the primary goals of computer science, as interdisciplinary science is to develop methods for solving complicated research and computing problems by means of computational techniques. Currently, however, computer science has become an independent science, with its own methods and objects of research, which are based on mathematical regularities. Computer tools allow the problems to be solved both by analytical methods and simulation methods. Regardless of the method used, the solving of any problem includes several steps such as problem analysis, elaboration of the mathematical model of the problem and elaboration of the algorithm which enables the development of the application software. The paper presents a software application based on the LabVIEW programming environment which implements the mathematical model on calculating the size of reactors. The software is modular with a user friendly

interface and presents the general advantages of modern software.

Keywords: reactors, mathematical model, sizing, application software, LabVIEW

1. Introduction

One of the primary goals of computer science, as interdisciplinary science is to develop methods for solving complicated research and computing problems by means of computational techniques. Originally, computer science was developed as a branch of applied mathematics. The first issues addressed in the context of computer science were purely mathematical, and were solved by only carrying out a great amount of complex calculations. Currently, however, computer science has become an independent science, with its own methods and objects of research, which are based on mathematical regularities [1]. There are a considerable amount of software packages, (EPLAN, OrCAD, PSpice, AUTOCAD, CATIA, MathCAD, LabVIEW, MATLAB, SIMULINK), for the various types of CAD/CAM systems. Each package has its own capacity and particularity and is generally intended for certain markets and a specific group of users. For example, there is mechanical, electrical and architectural, CAD/CAM software, for users in the respective fields [2-10]. Computer tools allow the problems to be solved both by analytical methods and simulation methods. Regardless of the method used, the solving of any problem includes several steps, each of them with the same importance [11].

Problem analysis. This is the stage of researching the content of the problem: determining the set of initial data, the result to be achieved, the relations between the original data and the results. Additional restrictions on the data and results are also set during this stage.

Elaboration of the mathematical model of the problem. The initial data are represented by mathematical structures during this stage. The relations allowing the result to be obtained from the original data are defined using the mathematical language. Depending on the problem, these relations can be recurrent (creating a simulation model) or they can allow direct calculation of the result (analytical model). Also during this stage the problem is divided (if necessary) into sub-problems, and the mathematical models are elaborated separately for each of them.

Elaboration of the algorithm. In the case of problem solving by means of computational techniques, the algorithm contains the set of instructions necessary for solving the problem, defined by a default form (pseudocode, flowchart, etc.), as well as the sequence of their

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execution (the steps of the algorithm). If the problem was divided into sub-problems, in addition to defining sub-algorithms, the algorithm also determines the method and conditions of their call.

As a result of carrying out these steps the software application is implemented, solving the problems related to the sizing of the reactors. Further on, the article presents in Chapter 2 the general information relating to the mathematical simulation of reactors, and in Chapter 3 the proposed software implementation solution for calculating the size of reactors. Chapter 4 presents a practical example of using the developed software, and the conclusions and ideas for subsequent developments are presented in Chapter 5.

2. Reactors. Mathematical modeling

Reactors are used for: balancing the reactive - capacitive power in electrical networks, limiting short-circuit currents in the power system or limiting the operate current in induction motors, filtering harmonics from AC curves or DC smoothing in rectifier power grids, protection of electrical networks against earth faults, protection of high-voltage lines against surges. The concept of reactors or inductors is assigned to the elements of an electric circuit or of a power system which under electromagnetic quasi-stationary conditions are considered as having only one inductance, i.e. an inductance reactance. Their introduction into the power system is aimed at generating a voltage drop when an alternating current or a current varying in time passes through it, i.e. achieving an exchange of reactive power to the system [12]. The AC voltage drop generated by the reactor, assuming that the winding resistance is neglected and under quasi-stationary conditions is denoted by the relation:

ILf2bU (1)

The voltage drop is proportional to virtual current I and frequency f, if it is assumed that the inductance L of the coil is constant. The reactive power of the coil is:

Lf2

2b

UQ

(2)

The stages of the reactor sizing:

calculation of reactor pre-sizing

Determination of the inductance of the solenoid:

HLkh

1

4

2md2w0L

(3)

where: - μ0 = 4π · 10-7 [H / m], the vacuum permeability; - w – the number of turns which fill the entire space of the winding; - dm = ½ (dE + di) [m] – average diameter of the winding; - dE [m] – outer diameter of the winding; - di [m] – inner diameter of the winding; - h [m] – height of the coil (size in the axial direction of the winding); - kL - a coefficient which depends on the geometry of the winding and is specified in

nomograms from [12, 13] according to ratios: h/dm and b/dm; - b = ½ (dE - di) [m] – is the thickness of the winding (size in radial direction).

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Given the horizontal size of the uninsulated conductor no, vertical size of the uninsulated conductor nv and the thickness of the insulation Δiz summed for both sides of the conductor, the following parameters can be determined:

- horizontal size of the insulated conductor – ino;

]mm[iznoino (4)

- vertical size of the insulated conductor – inv;

]mm[iznvinv (5)

Determining the number of turns on the flat coil “n” by the formula:

]flat/turns[izno

bn

(6)

Determining the number of flat coils Ng by the formula:

]flat[

kvinv1R

Rkv2RNg

(7)

where ΔR is the thickness of the reactor and ΔR1 is the thickness of the winding. Determining the inductance of the equivalent coil Lc is based on the formula:

]H[Ln2

ino

1ko

inv

kv

invino

kv1ko1

2

2g

invinoNLc

(8)

where: - N – the number of paralleled conductors; - kv – distance between vertical flat coils; - g – section of elementary turns; - ko – width of cooling ducts; - ko1 = Δiz +ko/n; - Ln – inductance of the coil to which an increase is applied.

heat exchange

The heat exchange [14] by radiation plays a greater part in cooling the windings of dry reactors compared to a winding located in an oil tank. The amount of heat radiated per unit time by the unit area is denoted by the relationship [15]:

)4amb

T4T(121015,5grad (9)

where T is the absolute temperature of the winding surface, and Tamb is the absolute ambient temperature (both expressed in Kelvin). In simplified form, the calculation of the quantity of heat transmitted by convection by the unit surface per unit time is denoted by the formula:

)ambtt(conconq (10)

where t and tamb are the temperature of the cooled surface and the ambient temperature, in °C and αcon is the convection efficiency. The following analytical expression of the function αcon =f (hbob, Δ, ϑ) will result from the

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combination of the previous relations:

4bobh

4con

(11)

where the values of the quantities are expressed as : ϑ [°C], hbob. [m]. and Δ [cm].

the permissible current density in the windings

The permissible current densities, calculated according to the relation (12) combined with (11) with radial thickness b = 0,010; 0,015; 0,020; 0,025 and 0,030 m, for copper cylindrical windings with class insulation A (ci = 115,7; ϑ = 60°C), F (ci = 130,5; ϑ = 100°C) and H (ci = 139,7033; ϑ = 125°C), and for aluminum cylindrical windings with class insulation A (ci = 183,2; ϑ = 60°C), F (ci = 205,74; ϑ = 100°C) and H (ci = 219,834; ϑ = 125°C).

bsk1010ic

conj

(12)

calculation of losses under stationary regime

The determination of losses under rated load is based on the relation:

[Watt]2jM

)]20(1[20sk2IRskP

(13)

where: - ks – coefficient of additional losses;

- 20 – resistivity of the material at 20°C: for copper 20 = 1/58·10-6 [Ω·m] and for aluminum

20 = 1 / 36,2·10-6 [Ω·m];

- – temperature coefficient of electrical resistance for copper = 428·10-5 [1/°C], and for

aluminum = 408·10-5 [1/°C];

- – reference temperature: for insulation classes A, E and B: = 75°C and for insulation

classes F and H: = 115°C; - M – mass of active winding conductor [kg];

- – material density = 8,9·103 [kg/m3]; - j – current density.

short-time rated current operation

The operation of the reactor under short-time rated current Isc is adequate if the following inequality is met:

2T1T (14)

]C[310t2scja1T (15)

where: - T1 is the temperature rating determined by calculation; - T2 is the standard rating of the maximum permissible average temperature [17].

- [°C] – maximum admissible initial temperature a rated winding according to insulation class;

- a – coefficient given in the table [12], according to parameter ½ ( + T2); - jsc – the short-term nominal current density; - t – the duration of the short-term nominal current in seconds according to international

standards.

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3. Application software for reactor sizing calculation

A development environment is a set of programs allowing the programmer to write programs and combines all the steps necessary for creating a program, such as source code editing, documentation compiling, debugging, testing and generating, in a single application software, which typically provides a user-friendly graphical interface. The main elements of a development environment are the source code editor and the debugger. The development environments call on compilers or parsers, which can be provided in the same package as the environment itself, or can be installed separately by the programmer. The facilities present in more sophisticated development environments include: source code scanners, version control systems, graphical interface designers, or software engineering tools. LabVIEW is a graphical programming language that uses icons instead of lines of text to create applications. In contrast to text-based programming languages, where instructions determine the program execution, LabVIEW uses dataflow programming, where the flow of data determines the execution [18]. The programming language used in LabVIEW, also referred to as G, is a dataflow programming language. Execution is determined by the structure of a graphical block diagram on which the programmer connects different function-nodes by drawing wires. These wires propagate variables and any node can execute as soon as all its input data become available. Since this might be the case for multiple nodes simultaneously, G is inherently capable of parallel execution. Multi-processing and multi-threading hardware is automatically exploited by the built-in scheduler, which multiplexes multiple OS threads over the nodes ready for execution [20]. The software automatically creates the report to an excel file with the calculated quantities necessary for calculation of reactor sizing and plots with certain parameters which are inserted automatically by the software from a set of charts whereby they are selected (see Figure 1). Figure 2 shows the block diagram of the software application. LabVIEW MathScript RT Module adds math-oriented, textual programming to LabVIEW. The MathScript Node offers an intuitive means of combining graphical and textual code within LabVIEW, both of which are currently used in a number of science, engineering and technology programs and industries for simulation and analysis [19].

Fig. 1. The block diagram part for the Excel report

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Fig. 2. The block diagram for calculation of reactor sizing of the software application

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4. Example of calculation

The reactor with the ratings: line voltage Ul=20 kV, single phase reactive power Q=140 kVAr, phase voltage Uf=11,547 kV, frequency : f=50 Hz, single phase inductance Xn=952 ohm, impedance L=3,03 H, phase rated current In=12,1 A. The figures 3-7 present the interfaces of the software application corresponding to the calculation steps for the reactor sizing according to the mathematical model in section 2.

Fig. 3. Software interface – step 1

Fig. 4. Software interface – step 2

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Fig. 5. Software interface – step 3

Fig. 6. Software interface – step 4

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Fig. 7. Software interface – step 5

4. Conclusions

This article presents the application software which implements the mathematical model on reactor sizing calculation. The software is modular with a user friendly interface and presents the general advantages of modern software. Among them it suffices to mention the automatic generation of a report in Excel format and the possibility of creating a record of the calculated models. The developed software is a useful tool for the designing activity of expert engineers by decreasing the duration of calculation and by excluding altogether miscalculations in mathematical relations. In the future, the research will be broadened in order to achieve complementary modules for other elements and physical processes that are suitable to be modeled.

Acknowledgments

The paper was developed with funds from the Ministry of Education and Scientific Research as part of the NUCLEU Program: PN 16 15 02 07.

References

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