Optimizing and Scheduling of Super Large-scale Seawater Reverse

Osmosis Desalination System

Qiang Ding1, Zhiyuan Niu

1

1 Energy Utilization System and Automation Institute, Hangzhou Dianzi University, Zhejiang, China

Abstract—In order to realize optimizing and scheduling of

super large-scale seawater reverse osmosis(SWRO)

desalination system, an optimizing-scheduling system based on

General Algebraic Modeling System(GAMS) is developed

according to the forecast of water consumption. Firstly, water

consumption in each period of a day was forecasted based on

historical water consumption data. Secondly, an optimizing-

scheduling model with the minimum energy consumption cost

as the target was developed based on the process technological

requirements and period-based tariff policy of SWRO

desalination system. Finally, the optimizing solution was made

for the model by using GAMS software. It is indicated from

the scheduling example that the scheduling system can be used

to realize optimizing and scheduling successfully and obtain

obvious economic and social benefits.

Keywords-SWRO; water consumption forecasting; GAMS;

optimizing; scheduling

I. INTRODUCTION

With the increasing shortage of worldwide fresh water resources, seawater desalination technology has become an important way to solve global water crisis. Currently, main methods of seawater desalination include SWRO, MSF, MED, VC, etc

[1]. Among them, SWRO desalination

technology has developed rapidly since its emergence and now accounts for 44% of the total fresh water-production around the world

[2]. Theoretically, it is the most energy

saving desalination method. But at present, there is still a gap between technical economic index and social expected value, the SWRO desalination cost is still high

[3]. Energy

consumption cost accounts for a big proportion (about 40% of the cost of the whole system water) in the water-production cost of SWRO desalination system

[4]. Therefore,

reduction of energy consumption of SWRO desalination system becomes the focus of current study.

With regard to the reduction of energy consumption of SWRO desalination system, Merrilee and others

[5] have

conducted a study of pretreatment for seawater desalination. Energy consumption of water-production for desalination system can be reduced through improving preprocessing filtration membrane process and single membrane element water-production and flux. Busch and others

[6] have

conducted a study of energy recovery device in the SWRO system, energy consumption of water-production can be reduced through improving energy recovery of concentrated seawater.

The above studies focus on the optimization of the local equipment or system structure design of SWRO desalination

system, while the running state of the whole desalination system has not been discussed. With the gradual increment of water production of SWRO desalination system, desalination units in the plant increase gradually. In view of large scale and super-large scale seawater desalination system, it is necessary to optimize the operation of the desalination system, so as to reduce the system operating cost and improve economic and social benefits. Therefore, a scheduling model is proposed in the operation process according to the process characteristics of SWRO desalination system and the optimizing solution is obtained in this paper.

Optimizing-scheduling operation is carried out under the precondition of meeting the demand of urban water consumption. An optimizing-scheduling strategy based on the water consumption forecast is proposed in this paper. Firstly, ARMA (p, q) model is used to forecast the water consumption in each period of some day. Secondly, MIQLP model with minimum energy consumption cost as the target function is developed according to the forecasted water consumption and desalination system process characteristics, water supply plan of the water-production pool and start-stop plan of the desalting units are regarded as the decision variables. Finally the optimizing solution of the model is made by using Cplex solver of the GAMS software.

II. WATER CONSUMPTION FORECAST

Hourly water consumption on some day is forecasted based on historical hourly water consumption data. Currently, forecast methods include multi-factor regression analysis method, seasonal exponential smoothing method, autoregressive moving average method (ARMA (p, q))

[7-8].

ARMA (p, q) model is suitable for short-term forecast with high forecast precision, especially for non-stationary historical data, which can be processed and modeled through difference technique

[9].According to the observed water

consumption data of Liuheng Island, water consumption series is non-stationary series. Therefore, hourly water consumption on some day is forecasted based on ARMA (p, q) model.

A. Water Consumption Series Tranquilization

Water consumption series of each period is a non-stationary according to the historical hourly water consumption observation. ARMA (p, q) model requires a stationary time series, Water consumption series tranquilization can be realized through the difference. According to the Cramer decomposition theorem, non-stationary series {xt} can be decomposed into two parts: one part is the deterministic trend composition, and the other part is the stationary zero mean error composition

[10], i.e.:

This project is supported by National Key Technology R&D Program of China (grant no. 2009BAB47B06).

2013 10th IEEE International Conference on Control and Automation (ICCA)Hangzhou, China, June 12-14, 2013

978-1-4673-4708-2/13/$31.00 ©2013 IEEE 705

0

( )d

j

t j t

j

x t B a

(1)

In the equation, d<∞; j refer to the constant coefficients;

{at} refers to a zero mean white noise series; B refers to the delay operator.

B. White Noise Test

Whether there is significant difference between each autocorrelation coefficient and zero can be judged through the chi-square distribution of LB statistic

[11], so whether the

time series belongs to white noise series can be judged further. Null hypothesis and alternative hypothesis are as follows:

0 1 2H : = = = =0, 1m m

1H : at least there 0, s ,: 1i k m k m

Test statistic is LB (Ljung - Box) test statistic:

2

2

1

( 2) ( ) (m), m>0m

k

k

LB n nn k

(2)

If null hypothesis can't be rejected, then the series is white noise series.

In the equation, n refers to series observation periods, m

refers to a specified delay period, k refers to the autocorrelation coefficient.

C. Calculation of Autocorrelation Coefficient and Partial

Autocorrelation Coefficient

Autocorrelation coefficient (ACF) k and partial

autocorrelation coefficient (PACF) k of the samples can be obtained according to the values of observation value series:

1

2

1

( )( )

( )

n k

t t k

t

k n

t

t

x x x x

x x

0 k n (3)

k

k

D

D , 0 k n (4)

In the equation:

1 1

1 2

1 2

1

1

1

k

k

k k

D

(5)

1 1

1 2

1 2

1

1k

k k k

D

(6)

D. Model Identification

After calculating autocorrelation coefficient and partial autocorrelation coefficient of the samples, appropriate ARMA (p, q) model fitting observed series should be selected according to the properties of those coefficients, so as to estimate autocorrelation order p and moving average order q, i.e. model order estimation. The order of ARMA (p, q) model is estimated according to censored feature and trailing of correlation coefficient and partial autocorrelation coefficient

[12]. Censored feature refers to that ACF or PACF

will be zero after a certain order, while trailing refers to that ACF or PACF will not be zero after a certain order. Basic principle of order estimation is shown in Table I.

TABLE I. SELECTION PRINCIPLE OF MODEL ARMA(p, q)

Model ARMA(p, 0) ARMA(0, q) ARMA(p, q)

ACF

PACF

tailing

censored

censored

tailing

tailing

tailing

E. Estimation of the Value of Unknown Parameters in the

Model

The commonly used model parameters estimation methods include moment estimation, maximum likelihood estimation and least squares estimate

[13]. Moment estimation

is used to estimate the model parameters in this paper because the constraint of moment estimation on the model is less and it is convenient to solve through the computer programming.

1 1 2 2 1 1 2 2t t t p t p t t q t q ty y y y e e e (7)

Firstly, moment estimation of autoregressive parameters

vector is obtained as follows:

1

1 1 11

2 1 2 2

1 2

1

1

1

p

p

p p p p

(8)

And then the moment estimator of is obtained as follows:

2 2 2 2

1 2

2

1 1

(1 ), 0

( ), 1

a q

k

a k k q k q

kr

k q

(9)

The above equation is rewritten as follows by using Newton - Raphson algorithms:

22 2

0 1

1 1 1 2 1

( ) ( )

( ) ( )( ) ( )( )

( )

a a aq

a a a a q a q a

q a q a

r

r

r

(10)

706

Temporarily assume (1 )k a k k q and

0 a , (10) is as follows:

2 2 2

00 1

10 1 1 2 1

0

0

0

0

q

q q

qq

r

r

r

(11)

The left of the above equations on assumed as

0 1( , , , )( 0,1,2, , )qk kf f k q , and then:

0 00 0

0

1 1

0

, ,

q

q q

q q

q

f ff

f ff F

f ff

(12)

It is easy to see that:

0 1 0 1 0 1

1 2 0 1 1 2 10

0 0

2 2 2

0

q q q

q q q

q q

F

(13)

According to the Newton-Raphson iteration principle [14]

,

if the i step iterative value is ( )i , then the i+1 step ( 1)i

must satisfy:

( ) ( )[ ( 1) ( )] 0f i F i i i (14)

i.e. 1( 1) ( ) ( ) ( )i i F i f i (15)

As long as the initial value (0) is given, iteration

operation can be made according to (14); repeat the iteration

until the difference between 2

( )a m and ( )m , ( 1)a m

and ( 1)m is less than the scheduled precision, and then

stop iteration, the ultimate ( )m is regarded as the

approximate solution for (11), then the approximate solution

for (9) is 2 2

0 ( )a m

0

( ) (1 )

( )

kk

mk q

m

(16)

k is just the moment estimation of model moving

average parameter for ARMA(p, q).

F. Test of Model Significance

Model significance test is mainly used to test the validity of the model. Whether a model is significantly effective basically depends on whether extracted information is sufficient, a good fitting model can extract almost all the

sample information of the observed series. In other words, fitting residual series should be white noise series, such a model is called the significantly effective model, the test method is the same with the above mentioned white noise test method.

III. OPTIMIZING-SCHEDULING MODEL OF SEAWATER

DESALINATION

Optimizing-scheduling model is developed for a 100

thousand tons of SWRO desalination plant located in

Liuheng Island in Zhejiang Province. It is currently the

largest SWRO desalination plant in China. The plant is

divided into four stages, there are eight desalination units.

Fresh water produced by the desalination units is stored in

four water-production pools temporarily, and then the fresh

water is transported to the municipal water supply network

according to the demand. Water-production and water-

supply of seawater desalination plant for Liuheng Island is

shown in Figure 1.

Un

it 1#

Stage 1

Un

it 2#

Un

it 3#

Un

it 4#

Water

-pool

1#

Municipal pipe network

Water

-pool

2#

Un

it 5#

Un

it 6#

Un

it 7#

Un

it 8#

Water

-pool

3#

Water

-pool

4#

Stage 2 Stage 3 Stage 4

Fig. 1. Seawater desalination plant product-supply diagram of Liuheng

Island

A. Model Optimization Objective

The main objective of seawater desalination optimizing

and scheduling is the reduction of energy consumption of

desalination cost based on the precondition of satisfying the

demand of municipal water supply. Through the description

and demand analysis of actual scheduling problems in the

water-production and water-supply, the target function

expression of mathematical model shown in (17) is

proposed as follows:

1

1 1 1 1 1 1

= ( , ) ( , ) ( , ) ( , )K I J I J K

k k k k k

k i j i j k

minF E S i j P i j S i j S i j

(17)

1( , ) ( , )k kP i j C Q i j (18)

In (17) and (18):

k=1,2,3…K represents a time period of the day

i=1,2,3..I represents the serial number of the water pool

j=1,2,3…J represents the unit number of the water pool

707

minF represents the daily objective function of energy consumption of water consumption for SWRO desalination system

Ek represents the tariff at period k

S(i, j)k represents the start-stop condition of unit j of water pool i at the period of i, which is assumed to be 0 and 1, 0 means stop, 1 means start

P(i, j)k represents the energy consumption of unit j of water pool i at period k

represents the factor of start-stop cost from start to stop, or from stop to start of the desalination unit

C1 represents the correlation coefficient of energy consumption and water production

Q(i, j)k represents the water production of unit j of water pool i at period k

B. Model Constraint Conditions

Mathematical model of water-production and water- supply of seawater desalination mainly includes the following constraint conditions:

1) Constraints of total water production

1

( ) , 1,2...I

k k

i

Q Qp i k K

(19)

kQ represents the total amount of planning water-

supply at k period, ( )kQp i represents the amount of

planning water-supply at k period for water pool i.

2) Constraints of water supply of the water pool

min max( ) , 1,2... ; 1,2...S k SQ Qp i Q k K i I

(20)

minSQ represents the minimum amount of water-supply

for the water pool,maxSQ represents the maximum

amount of water-supply for the water pool.

3) Constraints of water production of the unit

min max

, , ,k

Q i j Q i j Q i j (21)

min

,Q i j represents the minimum water production of

the unit, max

,Q i j represents the maximum water

production of the unit.

4) Liquid level constraints of the water-production pool

, 1 ,

1

( , ) ( , ) ( )

1, 2... ; 1, 2...

J

i k i k k k p k

j

V V Q i j S i j Q i

i I k K

(22)

, , 1, 2... ; 1, 2...i kV V i I k K Lmax (23)

, , 1, 2... ; 1, 2...i kV V i I k K Lmin (24)

,i kV represents the surplus water capacity from period

k for water pool i, VLmax represents the maximum water

capacity of the water pool, VLmin represents the

minimum water capacity of the water pool.

5) Start-stop time constraints

, min ,

on on

i j i jT T (25)

, min ,

off off

i j i jT T (26)

,

on

i jT represents the running time of unit j of water pool i,

min ,

on

i jT represents the minimum running time of unit j of

water pool i, ,

off

i jT represents the outage time of unit j of

water poor i, min ,

off

i jT represents the minimum outage time of

unit j of water pool i.

6) Start-stop constraint of the unit During the scheduling cycle, the start-stop times of the

unit has the following constraint:

, , +1 , , max

=1

| - |K

i j k i j k s

k

M M N (27)

NS, max represents the maximum start-stop times of the

desalination unit.

7) Continuous running time constraint of the unit During the scheduling cycle, the continuous running time

of the unit has the following constraint:

, , max

=1

K

i j k r

k

M N (28)

Nr, max represents the maximum continuous running time

of the desalination unit.

IV. GAMS SOLUTION MODEL

GAMS, which is a modeling tool used to solve large-scale complicated mathematical programming problem, is applicable to solve various linear programming, nonlinear programming, mixed integer programming, mixed integer nonlinear programming and mixed integer quadratic constraint programming problems. It is widely used in the study of some important fields, such as the forecast of air pollution index, rainfall. Seawater desalination optimizing-scheduling mathematical model is a mixed integer quadratic constraint programming(MIQCP) including binary variables and continuous variables. Therefore, it is suitable to use GAMS in the solution.

In the model solution, GAMS should be called in the main program of seawater desalination optimizing-scheduling software. Firstly, the forecasted water consumption and scheduling parameters will be updated to GAMS template. Then GAMS process (GAMS. exe) will be started up in the main program to obtain the scheduling results. The call process is shown in Figure 2:

708

GAMS

templateGAMS data file

GAMS

Update

real

time

data

Seawater desalination optimizing-scheduling system

Link

data

file

Start

GAMS

process

Optimizing-

scheduling results

Call

results

Fig. 2. Call process of GAMS

Specific call process includes the following steps:

Step 1: Update the forecasted water consumption, scheduling parameters shown in Table II and the tariff schedule shown in Table III to GAMS template.

Step 2: Call GAMS in the model calculation.

Step 3: Read the solution data which is outputted from GAMS.

TABLE II. SCHEDULING PARAMETERS

Stage

Level of water-pool/ m3h

-1

min max

Supply of water-pool/ m3h

-1

min max

Energy consumption/kWh unit 1# unit 2#

Production of unit/m3h

-1

min max

1

2

3

4

320

320

320

320

1600

1600

1600

1600

100

100

100

100

800

800

800

800

993

1242

993

1242

967

1738

967

1738

380

470

470

470

460

570

570

570

TABLE III. TARIFF SCHEDULE OF LIUHENG ISLAND

Time 1-8 9-11 12-13 14-19 20-21 22 23-24

Tariff

/ yuan·(kW·h)-1

0.270 0.687 0.270 0.687 0.890 0.687 0.270

V. EXAMPLE ANALYSIS OF SCHEDULING

Forecast water consumption of 24 periods on May 22

using hourly water consumption data in Liuheng seawater

desalination plant from May 1, 2011 to May 21, 2011. The

curve of forecasted water consumption is shown in Figure 3.

Fig. 3. Forecasted and actual water consumption

It is indicated from Figure 3 that the hourly water

consumption which is based on ARMA model has high

forecasting precision. The average absolute percentage error

of forecasting result is24

=1

-1=3.62%

24

t t

MAPE

t t

y FE

y , which

can meet the requirement of the forecasting precision and

can be used for optimizing and scheduling of seawater

desalination system. ty in the equation refers to the actual

value at t period, while Ft refers to the forecasted value at t

period.

According to the forecasted water consumption, water-

production and water-supply will be optimized and

scheduled by optimizing-scheduling system. Water

production and water pool capacity at each period can be

obtained, as shown in Figure 4 and Figure 5:

Fig. 4. Water production after scheduling

709

Fig. 5. Water pool capacity after scheduling

The actual water-production and water-supply is made

based on human experience when water-production and

water-supply is not scheduled. At night, water pool will be

fully stored with water, while in the day time, water-

production will be made according to the change status of

liquid level of water pool. Water-production and water pool

capacity at each period is shown in Figure 6 and Figure 7

respectively.

Fig. 6. Water-production capability before scheduling

Fig. 7. Water pool capacity before scheduling

Compare the water production and water pool capacity before and after scheduling, the following conclusions can be drawn based on the analysis:

(1) During the period of 0-8, water production is large. During the period of 9-24, peak-valley price is not taken into account before scheduling, while water-production will be made reasonably considering the peak-valley price after scheduling. Under the condition of meeting the demand of

water supply, water production is small in the period with high tariff, while it is large in the period with low tariff.

(2) Liquid level of water pool is the maximum in the period of 7 before scheduling, and then it gradually reduces to the minimum level. After scheduling, it is the maximum in 6-7 period and 15-17 period, which can make a preparation for water consumption at peak period; while the tariff at period of 9-11 is at a high level, water production is small, but water-supply capacity is large. Therefore, the liquid level at the period of 11 is the minimum. After scheduling, water-storage and water-supply of the water pool can be made reasonably.

In the example, daily water production capacity is 42960 tons, cost of energy consumption is 49,107 yuan/day before scheduling, while it is 44,834 yuan/day after scheduling. Compared to that before scheduling, 10% can be saved for the cost of energy consumption for each ton of water.

VI. CONCLUSION

A study of optimizing and scheduling of super-large scale SWRO desalination system according to the process characteristics is conducted in this paper. ARMA water consumption forecasting method based on the historical data is proposed. Seawater desalination optimizing-scheduling model is developed based on the obtained forecasted water consumption, and the optimizing solution was made for the model by using GAMS software. Through the scheduling case analysis, we can conclude that after optimizing and scheduling, the cost of energy consumption for the seawater desalination system is reduced significantly and the economic benefit of desalination can be improved greatly. Therefore, based on the design of optimizing-scheduling system, a feasible solution to reduce energy consumption cost for the super-large scale SWRO desalination system is proposed in this paper. At the same time, necessary support is offered for further promotion of SWRO desalination technology.

ACKNOWLEDGMENT

We are grateful to all those who have lent us hands in the course of our writing this paper. Without their help, it would be much harder for us to finish our study and this paper.

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