USING THE COMPUTER PROGRAM FOR DEVELOPMENT OF THE ENERGY SYSTEM

Tinatin Mshvidobadze

Gori (Georgia) University

Phone:+995 55118379

Email: tinikomshvidobadze@gmail.com

Abstract

The paper describes the structure of the energy system to optimize with ensuring economic efficiency of the capital investments. Where is shown in a mathematical model creation. Based on this model is solved the following tasks by a computer program "MATLAB": problem of maximization of electric capacities, problem of maximization of electric power, problem of minimization of investments, problems of minimization of exploitation expenses. The models can also be used in any other country's energetic power system.

Introduction

The power system is a complex system and for analysis this complex systems it is advisable to use a mathematical model,where complex can be set for different types of power stations to achieve the optimal structure.

For this purpose, a mathematical model was constructed, which enables us to resolve the specific conditions for possibility of using the maximum capacity, power generation and maximizing capital investments to minimize problems.

Mathematical model to determine the optimal structure of the energy system

Constructed mathematical model consists of East and West sections of Georgia. In addition, each of this two section contains equals power and energy balance for three typical periods of the year: the period of shallow water, off-season, high water. Specifics Georgia lies in the fact that hydroelectric resources dramatically decreases during the winter period (reduced by 10-times, 15-times), also during the fall and spring in the rivers of Republic is changing the water debit in different ways.

Because power stations work in the regime of variable load and cost per unit during the change of fuel and load changes nonlinearly, by reducing the equality’s to linear type the following approach is adopted:

At the three periods of work (shallow water, off-season, high water), for each i power station in the power system of Georgia the specificity is provided for of the station (thermo-station, season at its, regulating his)[1].

Taking this into consideration, for the period of high-water there was established basic and maneuver capacity one power balance equalities of the eastern part of the Georgian power system:

⁽¹⁾

Where - is the capacity of basic use,

P_m - is the capacity of maneuver use,

- is the power of basic use,

W_m – power of maneuver able use.

Accordingly, and are basic capacities, which are transmitted from the east part of the power system to its western part and vice versa by the means of power transmission lines, which unite these regions of the Republic.

At the same time, and are maneuver able capacities of transmission, – is duration of high water period.

and correspondingly are the duration of transmission of basic power and correspondingly are the duration of transmission of basic power and .

П –is the coefficient of losses in the transmision line.

Analogous equalities of the equalities of high-water period were established for western Georgia. The same equalities are established for off-season and shallow water periods.

Then for each two regions there is established equality of balance according to the used quantity of organic fuel[2].

In the particular, the equality of balance of the used amount of gas has the following form:

(2)

where, – is total expenditure of gas,

– reserve of gas in the region.

– specific expenditure of gas at i station at the time of working in j regime.

A mathematical model contains also limitations for capacity of each station and power lines of Energy Systems.

Eastern and western regions of Georgia are connected with the high voltage power lines. The Energy Systems model includes a various electricity interconnection and the transfer values of capacity. Including some unknown is consistent with energy interconnection and transmission capacities from the west to the eastern region, and vice versa, and the rest of the existing optimal loading and loading of power lines, which should be taken in a perspective period.

Also, some unknown is consistent with the basic energy flow and transfer capacities, while the rest of maneuvering energy flow and transmitted maneuvering capacities. In addition, each group of drawn from the indicated unknowns contain some unknowns in connection with periods of the flood, between seasons and low-flow.

To determine of mathematical model equation constraints

As it was said above, on the basis of constructed mathematical model there may be solved different optimization problems[3]. For examples I took power stations of eight types:

1. Small hydro power stations.

2. River bed hydro power stations,

3. Derivation hydro power stations.

4. Hydro power stations with water reservoir.

5. Thermo-stations working on coal.

6. Thermo-stations working on black oil.

7. Thermo-stations working on gas.

8. Wind power stations.

Define equalities of model constraints:

1. Investments constraints:

Where is specific investment for i type power-station of 1 kW established power. - is the capacity of i type power station .

- is the fund received from the state budget for the development of the system during the calculated period.

Where is specific investment for i type power-station of 1 kW established power. - is the capacity of i type power station.

- is the fund received from the state budget for the development of the system during the calculated period.

2. Constraints of exploitation expenditures:

Where - is specific exploitation expenditures during the use of 1 kW of established capacity during the year, taking into consideration closing expenses on organic fuel for power stations of i type[4].

- is the fund received for system functioning.

3. Constraints on capacity:

Where is the magnitude of total capacity which shall be attained in the system until the end of calculated period.

4. Constraints on power:

Where -is average annual quantity of hours during the use of i type power stations’ capacity. value -is basically defined depending on the type of the power station. is taken the number 2500 of hours considering a specific data in Georgia.

-is annual production of that should give a guarantee the end of the calculation period.

5. Constraints on peak capacity:

From this consideration, for to cover the peak and maneuver parts of load a fourth type is selected, i.e. hydro-power stations with water reservoir:

where -is magnitude of peak capacity, additional guarantee of which shall be given by system in the end of calculation period.

As to wind power stations, they do not guarantee power output; that is why the power produced by them is basically used for storage of organic fuel and water at hydro-power stations with water reservoir[5].

6. Constraints of ecological damage in hydro power stations with water reservoir.

Where , K-is average value of dependence of water reservoir’s surface area on established capacity of the Georgian hydro power station. S-is maximal value of the water reservoir’s surface area. In our case km² and kW/km² kW=1.111·10³ mw. is obtained.

7. Constraints of economical damage in thermal electrical stations:

Where - is a set points harmful substances of emissions into the atmosphere.

- is the maximum value of harmful substances of the emissions.

8.Constraints of total capacities established for wind power stations:

Constraints of such form is explained by the fact that power stations of such types occupy large area but they still have small capacity. In the model we received kW.

Ultimately the mathematical model is derived:

(3)

On the basis of this model problems of the following types may be solved by means of the computer system ”MATLAB”: problem of maximization of electric capacities, problem of maximization of electric power, problem of minimization of investments, problems of minimization of exploitation expenses.

results

By means of the computer program "MATLAB" in solved problems: of maximization of electric capacities, of maximization of electric power, of minimization of investments, problems of minimization and of exploitation expenses was accepted the following meanings of the capacity:

Table.1. Capacity values for each power station.

№	Type of power station	P - Capacity values(mw.)
		Maximization of electric capacities	Maximization of electric power	Minimization of investments	Minimization of exploitation expenses
1	Small hydro power stations	100	100	70	70
2	River bed hydro power stations	300	300	250	250
3	Derivation hydro power stations	400	400	350	350
4	Hydro power stations with water reservoir	200	200	150	150
5	Thermo-stations working on coal	450	450	450	450
6	Thermo-stations working on black oil	812	812	800	800
7	Thermo-stations working on gas	600	600	600	600
8	Wind power stations	200	200	150	150

CONCLUSIONS

The paper describes the structure of the energy system to optimize with ensuring economic efficiency of the capital investments. By means of the computer system ”MATLAB” solved problem of maximization of electric capacities, problem of maximization of electric power, problem of minimization of investments, problems of minimization of exploitation expenses and was adopted the optimal values of capacity for the various types power stations. The models can also be used in any other country's energetic power system.

REFERENCES:

1. MSHVIDOBADZE, Tinatin I., Computer systems to optimize the energy structure -Tbilisi: "Universal". 2012, 27-38pp. ISBN 978-9941-17-677-7.

2. BARAMASHVILI A., GOMELAURI A., JANIKASHVILI M. A mathematical model of energy equipment on the example of Georgia. Tbilisi: Technical University “the problems of automatic control” . 2007.16-17.04.

3. ARZAMASTSEV D., LIPETS A ., MIZIN A., . “Optimization models Development of the energetic systems”. 2012, M .: Higher. school, Vol 3. №12. p 272.

4. MAKAROV A.,

Recent long-term strategy of energy development. "Economical and Mathematical Methods". 2011 ,Vol. 23. №1. pp.25-37.

5. DALE V., KRISHAN Z., NAZGLE O., Mathematical models of optimization of network power systems. "Electricity." 2013, Vol. 17. №9. pp. 1-6.