Load forecasting is vitally important for electric industry in the deregulated economy. This paper aims to face the power crisis and to achieve energy security in Jordan. Our participation is localized in the southern parts of Jordan including, Ma’an, Karak and Aqaba. The available statistical data about the load of southern part of Jordan are supplied by electricity Distribution Company. Mathematical and statistical methods attempted to forecast future demand by determining trends of past results and use the trends to extrapolate the curve demand in the future.
Long-Term Load Forecasting Peak Load Max Demand and Least Squares1. Introduction
In the absence of perspective planning, the state faces power crisis. The important factors which lead to power crisis are: 1) low utilization of existing energy sources; 2) low utilization of existing generating capacity; 3) faculty planning and defective execution of projects; 4) inadequate linking of transmission network; 5) absence of efficient and integrated operations of different power stations in a system; 6) political influences in decisions on locations of power stations due to lack of studies and researches.
Jordan suffers from the lack of the electrical energy due to the above mentioned factors especially the low utilization of existing energy sources, absence of long term planning of energy and no attentions or supports are given to the researchers and personnel of power stations.
Perspective planning of the system should be based on proper forecasting of the load of the system, availability of generating stations and their improvements, combination of resources, economic considerations, strengthening and coordinating various existing systems and above all the availability of the adequate finance and management skill for realizing the benefits of the perspective planning.
It is first necessary to find out the load requirements of the area where electricity is to be supplied. This depends on the population of area, density of population, standards of living, industrial development and the cost of energy; when we talk about these factors we talk about people’s energy security and country security which must be achieved. In the southern part of Jordan, the load consists mainly of domestic load like, lights, fan heaters, refrigerators, air conditioners, radio, television, electric cookers, electric water heaters and low power motors. Commercial load like lighting for big supermarket and street lighting. Industry load is excluded from this study because the maximum demand of industries in southern part of Jordan was taking into account the period of establishing these factories (and they have own substations and own tariff).
Load forecasting can be broadly divided into three categories: short-term forecasts which are usually from one hour to one week, medium forecasts which are usually from a week to a year, and long-term forecasts which are longer than a year [1] . Traditional studies for long-term load forecasting were based on regression method, which could not provide a true representation of power system behavior in a volatile electricity market. Many studies present traditional methods like neural networks, genetic algorithms, fuzzy rules, which support vector machines, wavelet networks and expert systems [2] [3] , while [4] - [6] introduce two approaches based on regression method and artificial neural network (ANN) for long-term load forecast by applying fuzzy sets to ANN for modeling long-term uncertainties and compare the enhanced forecasting results with those of traditional methods. There are also some researchers present artificial neural network (ANN) combined with linear regression [7] . In [8] , energy data of several past years were used to train an adaptive network based on fuzzy inference system (ANFIS). Also in [9] , a new hybrid forecast engine is proposed; the proposed engine has an iterative training mechanism composed of a novel stochastic search technique and Levenberg-Marquardt (LM) learning algorithm. Another method combined with artificial neural network supports vector machine (SVM). A novel dynamic architecture for artificial neural network (DAN2) method was used in load forecasting; the structure of DAN2 was automatic formed by training [10] .
In this paper, by using the max demand data which is recorded from 2005 to 2013 and employing the least squares regression, peak load demand for 2014-2023 is forecasted. The results are validated by using the real data of 2014.
2. Least Squares Method
Generally, load forecasting methods are mainly classified into two categories: classical approaches and non- classical techniques. Classical approaches are based on statistical methods and forecast future value of a variable by using a mathematical combination of the historic information but this way have week prediction result, least squares method is most power full techniques will be used in forecasting, load forecasting is of the most difficult problems in distribution system planning and analysis. However, not only historical load data of a distribution system play a very important role on peak load forecasting, but also the impacts of meteorological and demographic factors must be taken into consideration so least squares method is the best method to solve this kind of problem [11] .
Let D = demand of electrical power (kW or MW).
y = the year in which the demand is considered.
yo = base year.
Then the exponential growth of demand with time would be expressed as:
Where: a, b = constants.
In order to evaluate the constants a and b, based on actual demand data over a number of year, put.
then:
then:.
Let
then (1)
Equation (1) is an equation relating V and Y in a linear fashion.
Suppose that the demand for consecutive years are given as:. The plot of is shown in Figure 1.
Least squaresthe demand for consecutive years
Corresponding to various values of Yi’s there are Vi’s. All the Vi’s are randomly distributed as shown in the last figure. For an exponential growth,. In order to correctly assess the demand, the sum of the squares of the errors committed by such approximation should be minimzed [12] , i.e.
should be minimum. Conditions for s to be minimum are:
and
Then:
Also:
Thus, Equations (2) and (3) provide the conditions for the sum of the least squares of the deviation to be minimum.
For simplifying further, let
From Equation (1), we have:
And (5)
Thus Equations (4) and (5) would enable us to evaluate the constants a and b so as to minimize the error in load forecasting.
3. Distribution Electric System of Southern Governorates in Jordan
The distribution of electric system of southern governorates in Jordan cover four governorates Ma’an, Aqaba, Tafila and Karak. The total number of constructed substations and their accumulative capacity in the distribution areas lha1 belong to the company until the end of 2013 was (4531) with a capacity of 2542 MVA, at the end of 2013, the total length of medium and low voltage for both overhead and underground networks have been reached (11,650) km [13] , Figure 2 and Figure 3 represent the main substation in each governorate Karak, Ma’an, Tafila and Aqaba
i. Karak Forecasting
Referring to nine years load data, we found the Max demand of each years as shown in Table 1 by using this data in Figure 2, and applying the least squares to find the Max Demand for next ten years Table 2 and Table 3 shown the Max Demand for next ten years.
In the last column of Table 3, we found the value of forecasting for next ten years; then we put these values on the axis, then we have to generate the curve in Figure 4.
After we found the values of Max demand of next years, we will be able to predict the year for which you want the new plant, in next page Table 4 show this. Note here is that the pregnancy has exceeded the maximum allowable load before it is predictable.
ii. Tafila Forecasting
In appendix A found the table of last nine years, then we found the max demand of each years and plot in this Table 5. Then like us these values in the form of the curve in Figure 5 and Figure 6.
Then we use the least squares to find the Max Demand for next ten years. When use the least squares generate Table 6 and Table 7.
The main substation at Karak and Tafila governorate
The main substation at Ma’an and Aqaba governorate
Max demand of Karak governorate for nine years
City
2005
2006
2007
2008
2009
2010
2011
2012
2013
Karak
Karak
25.65
41.38
39.66
43.07
36.20
36.20
45.24
51.88
50.93
Qutraneh
16.86
17.15
18.34
19.31
22.19
22.19
18.70
19.96
20.18
karak total
48.32
58.53
58
59.3
71.02
71.02
76.66
84.04
84.38
Least squares co-officiant
Last Years
Max D
= D/10
Vi = ln
Yi
Yi^2
2005
48.32
4.832
1.57526
−4
−6.30104
16
2006
58.53
5.853
1.766954
−3
−5.30086
9
2007
58
5.8
1.757858
−2
−3.51572
4
2008
59.3
5.93
1.780024
−1
−1.78002
1
2009
71.02
7.102
1.960376
0
0
0
2010
71.02
7.102
1.960376
1
1.960376
1
2011
76.66
7.666
2.036795
2
4.07359
4
2012
84.04
8.404
2.128708
3
6.386123
9
2013
84.38
8.438
2.132745
4
8.530981
16
Max Demand for next ten years
Next Years
Sum of Vi
Sum of Yi
Sum of ViYi
a
b
Max D
2014
93.716134
2015
100.26608
2016
107.27381
2017
114.77132
2018
17.0990979
0
4.05342603
1.8999
0.067557
122.79285
2019
131.375
2020
140.55698
2021
150.3807
2022
160.89101
2023
172.1359
Total max demand for Karak governorate
Max demand of next years
Tafila total max demand
Karak forecasting for 10 years
Sub
Max D
85% - 90%
2014
2015
2016
2017
2018
2019
2020
2021
2022
2023
Karak
51.9
44.12 - 46.71
54.10
57.35
60.79
64.44
68.30
72.40
76.75
81.36
86.24
91.419
Qutraneh
23.14
19.67 - 20.83
21.65
22.15
22.65
23.17
23.69
24.24
24.79
25.35
25.93
26.523
karak total
75.04
63.79 - 67.54
93.716
100.27
107.27
114.77
122.79
131.38
140.56
150.38
160.89
172.14
Max demand of Tafila governorate for nine years
City
2005
2006
2007
2008
2009
2010
2011
2012
2013
Tafileh
Hasa
4.80
3.76
6.60
5.90
8.56
8.56
11.57
12.98
12.72
Rashedieh Tafileh
6.08
7.65
7.84
8.81
9.78
9.78
13.16
13.13
12.53
Tafileh Total
10.28
11.4
14.44
14.44
18.34
18.34
24.73
26.12
25.24
Least squares co-officiant
Last Years
Max D
= D/10
Vi = ln
Yi
Yi^2
2005
10.28
1.028
0.027615
−4
−0.11046
16
2006
11.4
1.14
0.131028
−3
−0.39308
9
2007
14.44
1.444
0.367417
−2
−0.73483
4
2008
14.44
1.444
0.367417
−1
−0.36742
1
2009
18.34
1.834
0.606499
0
0
0
2010
18.34
1.834
0.606499
1
0.606499
1
2011
24.73
2.473
0.905432
2
1.810864
4
2012
26.12
2.612
0.960116
3
2.880349
9
2013
25.24
2.524
0.925845
4
3.70338
16
In the last column of Table 7, we found the value of forecasting for next ten years, then we put these values on the axis, then we have to generate the curve in Figure 7.
After we found the values of Max demand of next years, we will be able to predict the year for which you want the new plant, in next page Table 8 show this.
When we see to the Table 8, in 2017 the value of Demand is between 85% - 90%, in this range we must send to the authority concerned power plants that we want during the next 3 years we want a new Plant.
iii. Ma’an Forecasting.
In appendix A found the table of last nine years, then we found the max demand of each years and plot in this Table 9.
Then like us these values in the form of the curve in Figure 8.
Then we use the least squares to find the Max Demand for next ten years. When use the least squares generate Table 10 and Table 11.
In the last column of Table 11, found the value of forecasting for next ten years, then we put these values on the axis, then we have to generate the curve in Figure 7.
After we found the values of Max demand of next years, we predicted the year for which you want the new plant, in next page Table 12 show this.
When we see to Table 12, in 2017 the value of Demand is between 85% - 90%, in this range we must send to the authority concerned power plants that we want during the next 3 years we want a new Plant, then in end of 2019 the plant is Ready for operate and cover any increase above 100% in that year.
Max demand for next ten years
Next Years
Sum of Vi
Sum of Yi
Sum of ViYi
a
b
Max D
2014
31.914722
2015
36.101063
2016
40.836539
2017
46.19318
2018
4.8978694
0
7.39529519
0.544208
0.123255
52.252466
2019
59.106565
2020
66.859735
2021
75.62991
2022
85.550493
2023
96.772386
Tafila Forecasting for 10 years
Sub
Max Capacity
85% - 90%
2014
2015
2016
2017
2018
2019
2020
2021
2022
2023
Hasa
24.5
20.83 - 22.05
16.51
19.22
22.37
24.5
24.5
24.5
28.38
32.76
37.72
43.18
Rahadieh-Tafileh
29.44
25.02 - 26.50
15.30
16.81
18.47
21.69
27.75
34.60
38.48
42.87
47.82
53.29
Tafila total
53.94
45.86 - 48.55
31.9
36.09
40.84
46.19
52.25
59.10
66.86
75.63
85.54
96.47
Max demand of Ma'an governorate for nine years
City
2005
2006
2007
2008
2009
2010
2011
2012
2013
Ma’an
Ma’an
21.44
25.07
25.56
28.32
35.94
35.94
37.64
40.62
40.66
Rashadleh Quadiesieh
5.01
7.2
5.42
5.58
4.1
4.1
5.42
3.62
3.65
Ma’an Total
26.45
32.09
30.98
30.98
40.04
40.04
43.05
44.42
44.31
Least squares co-officiant
Last Years
Max D
= D/10
Vi = ln
Yi
Yi^2
2005
26.45
2.645
0.972671
−4
−3.89068
16
2006
32.09
3.209
1.165959
−3
−3.49788
9
2007
30.98
3.098
1.130757
−2
−2.26151
4
2008
30.98
3.098
1.130757
−1
−1.13076
1
2009
40.04
4.004
1.387294
0
0
0
2010
40.04
4.004
1.387294
1
1.387294
1
2011
43.05
4.305
1.459777
2
2.919554
4
2012
44.42
4.442
1.491105
3
4.473314
9
2013
44.31
4.431
1.488625
4
5.954501
16
Max Demand for next ten years
Next Years
Sum of Vi
Sum of Yi
Sum of ViYi
a
b
Max D
2014
50.492014
2015
53.921166
2016
57.583207
2017
61.493955
2018
11.6162154
0
3.94247393
1.290691
0.065708
65.670301
2019
70.130282
2020
74.893161
2021
79.97951
2022
85.411297
2023
91.211982
Tafila forecasting for 10 years
Substation
Max D
85% - 95%
2014
2015
2016
2017
2018
2019
2020
2021
2022
2023
Maan
38.95
33.11 - 35.1
38.95
38.95
38.95
38.95
38.95
38.95
41.34
43.9
46.63
49.55
Rahadieh- Quadiesieh
29.44
25.02 - 26.5
11.58
15.02
18.7
22.62
26.82
31.3
33.96
36.52
39.25
42.17
Total
68.39
58.13 - 61.6
50.53
53.97
57.65
61.57
65.77
70.25
75.03
80.14
85.6
91.43
Tafila max demand for next 10 years
iv. Aqapa Forecasting.
In appendix A found the table of last nine years, then we found the max demand of each years and plot in this Table 13.
Then like us these values in the form of the curve in Figure 9 and Figure 10.
Then we use the least squares to find the Max Demand for next ten years. When use the least squares generate Table 14 and Table 15.
In the last column of Table 15, we found the value of forecasting for next ten years, then we put these values
Ma’an total max demand
Next ten years forecasting of Ma’an
Total max demand
Max demand of Aqaba governorate for nine years
City
2005
2006
2007
2008
2009
2010
2011
2012
2013
Aqaba
Industrial East
1.08
27.28
30.16
38.32
47.68
47.68
26.64
23.00
27.28
A2
50.07
35.73
37.08
33.62
30.03
30.03
42.44
33.27
51.65
Thermal
8.52
9.46
11.79
14.83
22.72
22.72
21.73
23.73
17.71
Guweira
13.05
13.07
15.25
14.78
15.95
15.95
16.22
15.46
17.48
Aqaba Total
72.73
85.47
95.03
95.03
117.23
117.23
119.93
116.47
131.49
Least squares co-officiant
Last Years
Max D
= D/10
Vi = ln
Yi
Yi^2
2005
72.73
7.273
1.984169
−4
−7.93668
16
2006
85.47
8.547
2.14558
−3
−6.43674
9
2007
95.03
9.503
2.251608
−2
−4.50322
4
2008
95.03
9.503
2.251608
−1
−2.25161
1
2009
117.23
11.723
2.461553
0
0
0
2010
117.23
11.723
2.461553
1
2.461553
1
2011
119.93
11.993
2.484323
2
4.968646
4
2012
116.47
11.647
2.455049
3
7.365146
9
2013
131.49
13.149
2.576346
4
10.30538
16
Max demand for next ten years
Next Years
Sum of Vi
Sum of Yi
Sim of ViYi
a
b
Max D
2014
144.73949
2015
154.64678
2016
165.23221
2017
176.5422
2018
21.0717872
0
3.97248867
2.34131
0.066208
188.62635
2019
201.53765
2020
215.33272
2021
230.07205
2022
245.82027
2023
262.64644
on the axis, then we have to generate the curve in Figure 11.
After we found the values of Max demand of next years, we predicted the year for which you want the new plant, in next page Table 16 and Table 17 show this.
When we see to Table 16 and Table 17, not found any value of Demand is between 85% - 90%, for ten years we not need a new plant for Al-Aqapa city.
4. Conclusion
This paper presents long-term load forecasting of Southern Governorates of Jordan Distribution Electric System
Next ten years forecasting of Aqab
Aqaba forecasting for 10 years
Sub
Max D
2014
2015
2016
2017
2018
2019
2020
2021
2022
2023
Industrial Estat
150.4
35.23
43.18
51.13
59.08
67.03
74.98
82.93
90.88
98.83
106.78
A2
131.56
55.38
60
64.18
68.35
72.53
76.71
80.88
85.06
89.23
93.41
Thermal
73.6
21.16
24.64
28.07
31.53
34.98
38.44
41.89
45.35
48.8
52.256
Guweira
15.52
32.97
26.83
21.85
17.58
14.09
11.41
9.63
8.68
8.96
10.204
aqapa Total
371.08
144.74
154.65
165.23
176.54
188.63
201.54
215.33
230.07
245.82
262.65
Total max demand of southerner governorates of Jordan distribution electric system forecast 2014-2023
City
Max of Sub
2014
2015
2016
2017
2018
2019
2020
2021
2022
2023
Aqapa
371.08
144.74
154.65
165.23
176.54
188.63
201.54
215.33
230.07
245.82
262.65
Karak
75.04
93.716
100.27
107.27
114.77
122.79
131.38
140.56
150.38
160.89
172.14
Tafila
53.94
31.92
36.1
40.84
46.19
52.25
59.11
66.86
75.63
85.55
96.77
Maan
68.39
50.53
53.97
57.65
61.57
65.77
70.25
75.03
80.14
85.6
91.43
Total
568.45
320.906
344.99
370.99
399.07
429.44
462.28
497.78
536.22
577.86
622.99
based on least squares method by finding the Max Capacity of all Substations for each city and finding total Max capacity for that substations, and total Max Demand of South area. In 2020, the Max Demand of south between 85% - 90% from Max capacity in this year, to cover the expectoration for upcoming load we recommend to build new plant for the South Jordan to be ready to operate in end of 202. Also the max demand will be at Aqapa 262.65 MW and total max demand at all Southern Governorates will equal 622.99 MW. The forecast in Aqapa calculated based on all proposed upcoming industrial projects. Under this scenario, the forecasted peak load in 10years’ time is 262.65 MW.
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