Said Ali El-Quliti 1) and Mohammed Reda Kabli 2)  

1) Professor, 2) Assistant Professor,

Department of Industrial Engineering,

King AbdulAziz University, Jeddah, Saudi Arabia.

Economic Scheduling the Construction of Electric Transmission/ Distribution

Substations in Jeddah City with Parametric Results

1. INTRODUCTION

• Subject: Scheduling the construction of electric transmission/ distribution substations.

• Scope: The electricity field in Jeddah City; for a long-term time horizon (10 years).

• Main Goal: minimizing the total cost and determining the installation time.

Specific objectives

1. Forecasting the needed number of substations.

2. Formulate a dynamic programming model for scheduling the electric transmission/ distribution substations in Jeddah city.

3. Develop parametric results to study the effect of changing parameters on the obtained optimum solution.

2. LITERATURE REVIEW

"Eighth Development Plan 2005 – 2009", Ministry of Planning, Kingdom of Saudi Arabia, 2004.

The population forecast in Jeddah city is expected to increase with an increasing rate of 2.2% a year.

In a previous paper,

A study to forecast the number of substations needed for the 10 years (2006 – 2015) is determined, and also the optimum scheduling of these substations.

Said Ali Hassan ElQuliti, Ibrahim A. El-Darrab, and Mohammed Abdu Al-Ameer, "A Dynamic Programming Model for Scheduling the Electric Transmission/Distribution Substations in Jeddah City", WSEAS Intern. Conferences, Univ. of Cambridge, Cambridge, United Kingdom, 2009.

Parols A.G. et al, found that an essential

element of electric utility resource planning is forecasting of the future load demand.

Parols A.G., Esmaeil O., Muthusami J, Patton A. and Atiya A.F., “Development of an Intelligent Long-Term Electric Load Forecasting System”, Intelligent Systems Applications to Power Systems, Proceedings, ISAP International Conference, pp. 288 – 292, 1996.

F.-C. Lu, and Y.-Y. Hsu

Investigate the reactive power/voltage control in a distribution substation. An approach based on dynamic programming is presented to reach the desired schedule.

F.-C. Lu, Y.-Y. Hsu, " Reactive power/voltage control in a distribution substation using dynamic programming", IEE Proceedings, Generation, Transmission and Distribution, Volume 142, Issue 6, pp. 639-645, November 1995.

Yixin Yn et al, Use dynamic programming

for the optimal planning of substation locations which satisfy the load demands and minimize the investment and operating cost.

Yixin Yn, Chengshan Wang, Shaoyun Ge, Jun Xiao, Xuefei Yan, Chunhua Huang "Models and Methods for Urban Distribution Planning", School of Electrical and Automation Engineering, Tianjin University, Perth, WA, Australia, 2000.

3 .DATA COLLECTION

The single national company for generation, transmission and distribution of electricity all over Saudi Arabia. (Now it is divided into several Companies).

SAUDI ELECTRICITY COMPANY

Time Series Data of the annual total electricity consumption in Jeddah city 32 years (1979-2010) were collected.

FORECASTING OF THE ELECTRIC LOAD

Forecasting

• The number of required substations to be

built (from 2011 to 2020) is forecasted

depending on results for forecasting annual

total consumption of electricity .

• The forecasting is done using Multiple

Regression Analysis (Causal Methods) and

Artificial Neural Networks (ANN).

4. THE DYNAMIC PROGRAMMING MODEL

THE MODEL

Decision variables: the number of transmission/distribution substations to build in each year (stage).

The states: the number of substations still required in remaining years.

The objective function: minimize the total cost of building (investment cost) and operating the substations in the coming ten years.

The constraints: the number of required substations, budget to maintain both the building and operating costs.

4.1 Recursive Relationship in Dynamic Programming

• Identifies the optimal policy for stage n, given the optimal policy for stage n + 1.

Stage 1 2 3 4 5 6 7 8 9 10

1212

1111

1010

1313

22

11

00

33

002525 2222 17172020 1414

1515

99

88

77

1111

66

55

44

77

22

33

11

44

66

55

1919

2121

1616

1818

1313

1010

88

99

Network formulation for the problem

Required Substations:3 1 3 3 2 2 2 3 3 3

Budget Constraints:Constructed number ≤ 3 substation/year

Stage 1 2 3 4 5 6 7 8 9 10

Possible branches Branch of minimum total cost to the end node Branch on the optimum path

1212

1111

1010

1313

22

11

00

33

002525 2222 17172020 1414

1515

99

88

77

1111

66

55

44

77

22

33

11

44

66

55

2083.22 1948.22

1794.63 1620.04

1477.17

1525.67

1198.62

1257.52

1309.41

1375.74

947.06

1010.09

1065.34

1135.88

731.88

664.44

791.02

933.93

347.51

419.68

482.93

563.69

635.86

699.44

138.00

224.40

301.61

369.63

0.00

1919

2121

1616

1818

1313

1010

88

99

1885.09

1842.73 1671.49

1716.81

1422.11

993.34

866.49

1198.91

)(* inn Sf

inS

Solution of the problem The optimal Solution: 3 1 3 3 3 3 0 3 3 3

Required Substations:3 1 3 3 2 2 2 3 3 3

PARAMETRIC RESULTS

6.1 Control Parameters Affecting the Solution

1. The substation building cost (investment cost).

2. The percentage of yearly increase in the substation building cost.

3. The percentage of discount for buying more than one substation.

4. Initial value of the operating cost (in the 1st. Year).

5. The percentage of yearly increase in the operating cost..Initial Value (1st. Year of the plan) Parameter50 million Saudi Riyals 17% 25% 33 million Saudi Riyals 47% 5

The Same Optimal SolutionThe optimal Solution: (3, 1, 3, 3, 3, 3, 0, 3, 3, 3)

The Same Optimal Solution

Range Initial Value Parameter19.4 – 51.5 million Saudi Riyals 50 million Saudi Riyals 1

1. The substation building cost.

Total Optimum Values for different initial building cost.

The Total Optimal Value (TOV):

The optimal Solution: (3, 1, 3, 3, 3, 3, 0, 3, 3, 3)

Range Initial Value Parameter0 - 7% 7% 2

2. The percentage of yearly increase in the substation building cost.

The optimal Solution: (3, 1, 3, 3, 3, 3, 0, 3, 3, 3)

(TOV )for different increases in substation building cost .

Range Initial Value

Parameter

5 % or more 5% 3

3. The percentage of discount for buying more than one substation.

The optimal Solution: (3, 1, 3, 3, 3, 3, 0, 3, 3, 3)

(TOV )for different discounts for substation's cost.

(TOV )for different initial operation cost.

4. Initial value of the operating cost.

The optimal Solution: (3, 1, 3, 3, 3, 3, 0, 3, 3, 3)

Range Initial Value Parameter2.95 – 7.7 million Saudi rials 3 million Saudi Riyals 4

(TOV )for different % yearly increase in operation cost.

5. The percentage of yearly increase in the operating cost.

The optimal Solution: (3, 1, 3, 3, 3, 3, 0, 3, 3, 3)

Range Initial Value

Parameter

6% – 25% 7% 5

6.3 Changes in the Optimal Solution

If changes in parameters are outside the range, a new optimal solution appears:

Optimal Solution (3, 1, 3, 3, 2, 2, 2, 3, 3, 3)

(TOV )for different substation building cost.

1. For substation building cost < 19.3 million Saudi Riyals:

2. When there is no discount for buying more than one substation.

(TOV )for different initial operating cost.

Initial operating cost

Optimal Solution (3, 1, 3, 3, 2, 2, 2, 3, 3, 3)

(TOV )with different substation building cost .

A New Optimal Solution

(3, 1, 3, 3, 3, 3, 3, 3, 3, 0)1. Substation building cost: )51 – 53.5( million Saudi Riyals.

(TOV )with different initial operation cost.

Optimal Solution: (3, 1, 3, 3, 3, 3, 3, 3, 3, 0)

7. CONCLUSIONS

1. The ability of NN’s to forecast within an error range of about 2 % only.

2. Mean annual electricity consumption increase (2011 – 2020) = 3.49%.

3. A backward model of dynamic programming approaches can be used.

4. The solution procedure starts at the last year (stage n = 10) and then move backward to the initial stage (first year).

CONCLUSIONS (Cont’d.)

5. The optimal solution is (3,1,3,3,3,3,0,3,3,3) in the years

(2010 – 2020) with total cost of SR. 2,083,220,000.

6. There are many parameters affecting the optimal

solution:

- Initial value of the substation building cost.

- Percentage of yearly increase in the substation building cost.

- Percentage of discount for buying more than one substation.

- Initial value of the operation cost.

- Percentage of yearly increase in the operation cost.

7. The parametric results gives the decision for different

changes in the problem data.

8. POINTS FOR FUTURE RESEARCHES

1. To prove analytically the parametric results.

2. To analyze the sudden changes in the optimal values.

3. To study the time value of money.

4. To study the parametric results for simultaneous

changes in different parameters.

5. To use the shortest route and other techniques.

6. To generalize the method for other regions in the kingdom.

7. To build a decision support system for such problems.