Farm Electric Loads Optimization

CopyriKh! © IL\C 11th Triennial World CunKress. Tallilln . Estonia. L'SSR . 1' 1' 111

CONTROL SYSTEM APPROACH TO DEVELOPMENT

FARM ELECTRIC LOADS OPTIMIZATION E.

J.

Kokin

Departmellt of ElectriJi((ltiulI, Estolliall Agricultural Acar/I'III.\'. Tartu. Estollia. L'SSR

Abstract. The loss of electric energy, caused by the irregularity of the consumption, especially in case of agricultural farms, is quite essential . The possibility of diminishing it by finding the most suitable time of work for each of the technological processes and their parts is discussed . The optimum is achieved by shifting the movable zones of every process one step at a time and comparing the resulting graphs with the initial one . The shape coefficient of electric load graph is used as optimization criterion . The initial data for every process may be entered in computer by the operator or generated with the help of stochastic models . The resulting data may be used in an automatic control system or as a base for manual control of farm work. This method is also suitable for other fields beside agriculture . Keywords . Optimization; load modelling ; load regulation; automatic control; optimal control; smoothing .

INTRODUCTION

THE POSSIBILITIES OF LOAD OPTIMIZATION

The irregularity of electric energy consumption is especially high at agricultural dairy-farms, where the differences of installed power of consumers, which participate in making up the electric load diagram of the group, is conciderable enough (0.25 ... 100 kW) . The loss of active electric power, caused by this irregularity, may be determined as liP

= kZ ' k tine.pz $

stochastic systems ; farming;

Cl

The irregularity of electric loads ' graph may be diminished by switching off some consumers at one time and switching on additional ones at other, depending on the total load at given moment. If we take for granted , that the functioning of the systems and farm work organisation is flawless, then by switching some consumer or technological process entirely off at casual moment, we inevitably cause the disruption of technology. One possible way to overcome this is to set for every consumer or their group the time limits, in which the moments of their turning "off" or "on" could be shifted without serious consequences .

(1)

Here (2)

is the coefficient, which takes into account the parameters of the energy feeding line; ks is the shape coefficient of electric load line graph see also Eg. (12); Pa is active power and R is the active resistance of the cable or other line. The loss of reactive power 4Q may be mated just the same way .

The estimation of the best time of functioning for every piece of machinery and technological process is the task, which could be achieved only with the help of computer, because the number of possible solutions is very large. The other thing we should keep in mind is that the time sequence of consumers ' "on" and "off" states, which ensure the most smooth loads line graph, is also one of realizations of stochastic process, because the components from which it is made up are such processes themselvs .

power esti-

According to the results of our measurements, the shape coefficients of electric loads line graphs for different farms lays between 1 .025 and 1 . 301 . These values depend on the time of year, the size of the farm, the rate of consumption and some other factors. The corresponding loss of power changes from 5 . 1 % excess over the minimum loss to 69 . 3 % .

The total number of technological processes and groups of machinery with specific tecnological functions at the farm may be 25 ... 30 . All of them could be divided into 3 ... 5 differrent groups, depending on the time limits , set for them by the farm technology. There are a number of nonmovable processes, but others allow to shift a little the time of starting or stopping or both, to move the part of load, exceeding some level, or even the whole process to some other time of day or night .

The energy consumption by dairy-farms is highest in winter period and for various groups of farms the twenty-four hours ' mean value of active power is 22.8 ... 286.5 kW (Kokin, 1984) . So, the corresponding theoretical minimal loss of active power liP (when the k = 1.0) only for low-voltage input s

Into the first group we desided to put nonmovable processes , such as the milking, the lighting and others. Here also belongs a number of processes with automatic control - the ventilation of the cow-sheds, the cooling of milk and so on.

amounts up to 0 .61 ... 7 . 35 kW . Since the real shape coefficient reaches 1. 301, the power loss is 0.99 . .. 12.44 kW depending on the farm . If we also take into account the reactive power losses and total losses in high-voltage lines, then we may conclude, that the reduction of them is of considerable interest.

The processes of the last group,

287

such

as

ultra-

where v(j) ~ a.(j)w(j) . This AR - model with additional terms, describing deterministic sinusoidal trends, was suggested by Kashyap and Rao (1976) . In Eq. (3) w(j) is the sequence of independent values with zero mean . The a(j) factor is needed to take into account the systematic changes of load's standard variance and the term 'fI(j-l) describes the systematic changes of the mean of the load from step to step . The first term of the Eq. (3) is the sum of the function's values at some latest steps. For different processes the h, and At values are different .

violet treatment, manure transport and some others allow the shifting practically without limits to any desired time. The interesting possibilities from the point of view of the loads optimization are connected with the group of processes, which accumulate the product they are dealing with, such as water, forage, heat in the water, in the air or in some solid accumulator. All the rest of the processes may be put into intermediate groups.

the

Using the data obtained by the first or the second method and summing it up tuple by tuple for all processes, we can get the mean value of group's load at every step

THE LINE GRAPH MODELLING The creation of optimized graphs of dairy-farms ' electric loads is based on the initial data, entered into computer's memory with the help of some program package, capable of managing *.DIF files and Worksheets - Lotus 1-2-3 or others. The electric parameters of a large group of farms have been registered to obtain this data (Kokin, 1984).

I

Pa )

P~bij

(4)

1.=1

The sum of all tuples of array gives us value of group ' s energy consumption

Before entering it into computer, we first of all have to choose the step of discretization At. Usually, At = const = 0.5 hours. After that the values of mean of the maximum power ' s share b . = 0 . .. 1 .0 , which participate in the load graph

k

11' a

~

the

mean

k

AtP . ~

"\

L

)

At " \

L

OJ

j =1

P

(5)

OJ

j=1

~)

On the first stage of modelling we can calculate also the mean value of group ' s load for the twenty four hours period

forming with some probability, for example 95% , are entered for every given process m . . The farm ~

group's means of maximum power Pi of every process are also entered. Here i ~ 1.. . n is the total number of technological processes m ; j 1. . . 48 is the number of discretization steps. The lenght of newly formed graph in this case does not exceede the twenty-four hours period .

W Pmean T a

and the mean values of group's energy for every process

Wm~

Autumn

Winter

At At

1 2

P1 b 11

P b

P b

P b

1

12

2 2

21 22

At _ P, b , )<_, P b 2 2)<-1 k Atk

Pb 1

1k

Pb 2

zk

mn

mn-1

2

Pn-1 b 71-1,1

Pb

P

Pb

P

b n-1 n-1. 2

n n

n1

b n-1 n-1.k

Pb n

n

nk P nj

Fig. 1. Basic structure of data arrays Here

This method could be used also for the prognostication of farm electric loads. In this case the load of technological process on the j step of discretization could be found with the help of auto-regressive model of the form k

y(j)

I

(7)

Pib i j

P. n)

I

2

is the

(8)

Pib i j

mean value

in which the processes

of the group ' s load,

with the numbers

n, to n 2

( n , ~ 1, n 2 :S n ) are participating at the step This part of a new graph will stay constant.

j

.

To this base graph we sum up the graph of one of the movable processes (by finding their sum on every step) and calculate the mean of effective power of these processes

1

Aty(j-n + 'fI(j-l) + v(j),

k

After all recalculations by the Eq . (3) to Eq. (7) are completed, it is possible to begin the creation of new and optimized load graph. First of all we sum up loads of all nonmovable processes, separately for every step of discretization

n2

b Pb n-1 n-1)<-1 n n.k-1

P

I

For further calculations beside the data arrays we described above some additional parameters of the farm and the processes are needed. In dialogue regime the operator enters the desirable time limits for shifting the movable parts of processes, marks down the time of day, when the energy system demands to minimize the load, and enters some other data. The number of processes, which don't exist at given farm, are excluded from the maximum standard list and do not take part in calculations. All changes are entered through the Worksheet . The main program is in Turbo Pascal .

Summer Sprt..ng

m

At

consumption

j=1

~)

1

(6)

L

j =1

After some recalculations this data is present in computer's memory in a form of two-dimensional array, every vector of which is a load graph of some technological process . If we have such a data for every time of a year, then for all groups of farms individually we get a three-dimensional arrays, shown on Fig. 1. The b . . factor enables to simplify the data input for a given real farm.

m

k

At " \ T Paj

(3)

t=1

288

From all of these we choose one, that is nearest to 1. 0 . The corresponding graph will have the best possible smoothness and we take this as the base for future summing up with next technological process graphs .

(9)

Then we find the mean value of twenty load for the same processes

four

The sequence, in which the processes are choosen for calculations, may be given by the operator. In alternative case all possible combinations are calculated one after another.

hours

After all graphs of all processes are summed up, we get the optimized graph of loads of given farm. We may obtain hard copy of this and all other graphs, too . Then all calculations may be repeated for next realization of the optimized graph.

(10)

For movable process the number and the length of movable parts and the limits of shifting are determined. This gives us the possibility to find the total number of steps the movable parts of the process may be shifted to . We then create a new graph , which differs from the latest one only by the position of one of movable parts, which is shifted for one step . So we get as many grphs, as there are possible positions for all movable parts and their combinations . All these grphs are one by one summed up with the latest base graph . Figure 2 shows movable parts of one step in each The total number as

H=

P

all possible positions of two one process, if there are only direction to move these parts to . of combinations may be calculated

rl [

~:A,

AT

T

Fig. 3. Optimization of the load graph . + 1 ] .

(11)

1.=1

where AT, is the length of a

time

period,

Besides the graphic information we get also the list of the best time of work for every process . This data could be used for automatic control system or manual control of machinery .

where

the movable part of a process may be situated and A, is the length of the movable part . Both A, and AT, should be equal to integer number of steps AT. The total number of movable parts different processes .

1

I

~

I

I -'- _I

ffiNCLUSION

may vary for

Suggested method then makes possible, through the load graph modelling on personal computer (IBM PC AT or compatible), to obtain the time sequences of the turning "on" and "off" of machinery , which ensure m1n1mUm loss and irregularity of farm energy consumption . If we want reliable results for a given farm or some other consumers group, we need to know it ' s energy consumption parameters . But if we want to simulate some load graphic for nonexisting system, then the initial data may be just any sequence of variable values with parameters, we think will be adequate .

9 8 7 6

I I

I

I

I

a

5 4 3 2 1

I

I I I I AT 2 =

REFERENCES

3At

Kashyap, R.L. , and A. R. Rao (1976) .

[)yrIt;rmic Stochastic Hodels from Empirical Data. Harcourt,

Fig . 2 . Possible positions of movable parts of a process .

London . E.I1. (1984) . I1CCJ1e)lj:)BaH>1e 3Jl9IIX 4lePw. C6 . w::ry
KOKHH,

3cotO>
The level of load Po' which stays behind after the

TapTy.

shifting of movable part , is taken equal to the load highest value on the border of the movable zone and stays constant . Figure 3 shows also the position of movable parts Ai' A2 and the length of zones AT i

,

AT2 ' where the movable

parts may

be

shifted . For all new graphs we calculate it with

P,. obtain the k=P/P s • ..

p.

and

comparing

shape coefficient values (12)

289

CTp .

27-34.

148.