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This paper presents a technique for Medium Term Load Forecasting (MTLF) using Particle Swarm Optimization (PSO) algorithm based on Least Squares Regression Methods to forecast the electric loads of the Jordanian grid for year of 2015. Linear, quadratic and exponential forecast models have been examined to perform this study and compared with the Auto Regressive (AR) model. MTLF models were influenced by the weather which should be considered when predicting the future peak load demand in terms of months and weeks. The main contribution for this paper is the conduction of MTLF study for Jordan on weekly and monthly basis using real data obtained from National Electric Power Company NEPCO. This study is aimed to develop practical models and algorithm techniques for MTLF to be used by the operators of Jordan power grid. The results are compared with the actual peak load data to attain minimum percentage error. The value of the forecasted weekly and monthly peak loads obtained from these models is examined using Least Square Error (LSE). Actual reported data from NEPCO are used to analyze the performance of the proposed approach and the results are reported and compared with the results obtained from PSO algorithm and AR model.

MTLF is extremely important for energy suppliers and other participants in electric energy generation, transmission, distribution and markets. It helps make decisions, including decisions on purchasing and generating electric power system utilities. The main role of electric load forecasting in the electric system is to help the energy companies to plant the purchasing and generating of electric power needed. Load forecasting studies can be categorized based on forecasting period into three categories: short term load forecast (STLF) from one hour to a week, medium term load forecast (MTLF) from one week to a year and long term load forecast (LTLF) longer than one year [

The MTLF procedure for the models can be viewed in

Input variable selection, including: month type, peak load, average electrical de- mand, humidity and temperature data, and weather influences of previous time.

The monthly or weekly peak load demand data recorded from NEPCO for the years (2008-2014) taking into account external variables like holidays, weather and population growth.

It may be inevitable to have improperly recorded data and observation error.

Therefore the monthly and weekly reported data from NEPCO used to initialize the simulation results.

In this part, the peak load forecasting output is simulated using Matlab.

The stopping criterion is met when the parameters of PSO are achieving a global forecasting error within an efficient computation time. The convergence error must be less than 0.01% to make a sufficiently good fitness value.

The LSRM and PSO coefficients require calculations to prompt the desired forecasted load results.

As characteristics of load changes, error observations become more significant for the forecasting process. LSE is used to improve the accuracy of these models.

Regression analysis is widely used in the analysis of data for any design. Regression models one of the most commonly used statistical analysis techniques in any research [

where:

Regression analysis is the study of the action of the time series or process in the past and it is mathematical model, therefore the future behavior can be expected from it. In the forecasting process of medium term peak load, least squares regression methods are used by different relations between the input and output [

The medium term load forecasting of many business series such as, sales exports and production usually approximates a straight line. The simple linear regression method LRM model is designed to study the relationship between a pair of variables that appear in a data set. It is a model based on the linear relationship between the total demand y and month

where:

The least squares criterion is used to generate the line

By using the least square error approach [

where:

When

In this approach the parabolic function which is given in Equation (5) is used

After applying least square error we can find

When

In this method the exponential function is obtained through Equations (8)-(15) to get Equation (7).

By writing the equation in logarithmic form, the equation becomes:

The properties of algorithms give

This expresses

Therefore, if we find the best line using

After linearization,

When

A Particle swarm optimization PSO technique is used to find the optimal parameters for different forecasting methods. This algorithm is used to solve a wide class of complex optimization problems in engineering and science. Both linear and nonlinear models will be used in the system and the results will be obtained using PSO. Through the implementation of PSO all particles are kept as members of the population. The basic idea of the PSO is the mathematical modeling and simulation of the food searching activities of a swarm of birds in the multi- dimensional space where the optimal solution is sought. Each particle in the swarm is moved towards a point where it obtains optimal solution by the influence of its velocity. The velocity of a particle is affected by three factors; inertial momentum, cognitive and social [

where:

In this work, PSO is employed to minimize the LSE between the real values and prediction values. To evaluate the forecasting process for each model, LSE error can be used.

The AR model was developed by Box and Jenkins in 1970 to analyze historical data that had relations within it. In this study, the parameters were obtained from NEPCO. The AR process utilizes the least squares (LS) method, and it is an analogous way to fit a model by minimizing the sum of square errors for estimating parameters. The LSE uses the normal equations to implement the polynomial system. The parameters can be solved by Matlab. The purpose of this study was to implement the discounted least squares method with direct smoothing for estimating autoregressive model parameters [

The AR model structure is given by Equation (19)

The parameters of

Real peak loads are used in this study, so the electric peak loads in the years [2008-2014] have been founded for Jordan country. The data used are monthly and weekly peak loads recorded in the years [2008-2014]. This system of equation is solved using the proposed PSO algorithm to find the optimal coefficients for different forecasting models. Linear, quadratic, exponential and AR models are used in the system and the results obtained using PSO are compared with those of LSRM. A Matlab code was generated to execute the PSO Algorithm and LSRM Using the peak data of NEPCO grid. For PSO, all particles start at a random position in the range [0, 1] for each dimensions. The swarm size was limited to 250 particles. The selections of some parameters to carry out the procedures of the work successfully has great effect on the model, these parameters are maximum speed, inertia weight and acceleration constants. The most suitable values for maximum speed is set to be 2, _{1} and C_{2} are 2.

Key parameters of PSO algorithm used in this paper are presented in

Peak Loads of NEPCO recorded in the years [2008-2014] are used to estimate the coefficients of linear, quadratic and exponential models for MTLF. The inputs of these models are the number of weeks or months and the peak loads recorded in the years [2008-2014], whereas the output is the monthly or weekly peak loads predicted for the year 2015.

PSO and LSRM techniques are used to estimate models parameters. Horizon and the computed parameters are tabulated in

Since the forecasting in this work is carried out on monthly bases, monthly least square error is performed and calculated by Equation (21). The equation used is given by:

Parameter | Value |
---|---|

Population | 250 particles |

Stop criterion | 500 iterations |

Velocity | V_{max} = 2, V_{min} = 0 |

Acceleration constants | C_{1} = 2, C_{2} = 2 |

Inertia weight | w_{max} = 0.9, w_{min} = 0.4 |

Coefficients | Linear model | Quadratic model | Exponential model | |||
---|---|---|---|---|---|---|

LSRM | PSO | LSRM | PSO | LSRM | PSO | |

a | 1.9406 | 1.947 | 9.96 | 9.91 | 2654.3 | 2662.5 |

b | 2685.6 | 2695.82 | −121.43 | −121.58 | 1.0006 | 1.0008 |

c | - | - | 2978.2 | 2990.2 | - | - |

The monthly forecasted peak loads based on the parameters of linear, quadratic and exponential models and monthly least square error are shown in

It can be concluded from the tables that the results computed by PSO are more close to the peak load and have less error. In both approaches, the monthly peak load is increased continuously from January till December when using linear or exponential models. In quadratic model, the peak load is decreased continuously from January till June and increased from June till December. The forecasted monthly peak load using different models are shown in

It can be seen from the figure that the PSO and LSRM are close to each other. In each model the difference between LSRM and PSO is arranged from [

From

Month | Peak load (MW) | Linear model | Quadratic model | Exponential model | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

LSRM (MW) | PSO (MW) | Error (%) | LSRM (MW) | PSO (MW) | Error (%) | LSRM (MW) | PSO (MW) | Error (%) | |||||

Jan. | 3160 | 2687.54 | 2697.77 | 14.95 | 14.63 | 2866.73 | 2878.53 | 9.28 | 8.91 | 2655.89 | 2664.63 | 15.95 | 15.68 |

Feb. | 2950 | 2689.48 | 2699.71 | 8.83 | 8.48 | 2775.18 | 2786.68 | 5.93 | 5.54 | 2657.49 | 2666.76 | 9.92 | 9.60 |

Mar. | 2760 | 2691.42 | 2701.66 | 2.48 | 2.11 | 2703.55 | 2714.65 | 2.05 | 1.64 | 2659.08 | 2668.90 | 3.66 | 3.30 |

Apr. | 2670 | 2693.36 | 2703.61 | −0.87 | −1.26 | 2651.84 | 2662.44 | 0.68 | 0.28 | 2660.68 | 2671.03 | 0.35 | −0.04 |

May | 2690 | 2695.30 | 2705.56 | −0.20 | −0.58 | 2620.05 | 2630.05 | 2.60 | 2.23 | 2662.27 | 2673.17 | 1.03 | 0.63 |

Jun. | 2820 | 2697.24 | 2707.50 | 4.35 | 3.99 | 2608.18 | 2617.48 | 7.51 | 7.18 | 2663.87 | 2675.31 | 5.54 | 5.13 |

Jul. | 2940 | 2699.18 | 2709.45 | 8.19 | 7.84 | 2616.23 | 2624.73 | 11.01 | 10.72 | 2665.47 | 2677.45 | 9.34 | 8.93 |

Aug. | 3180 | 2701.12 | 2711.40 | 15.06 | 14.74 | 2644.20 | 2651.8 | 16.85 | 16.61 | 2667.07 | 2679.59 | 16.13 | 15.74 |

Sep. | 3010 | 2703.07 | 2713.34 | 10.20 | 9.86 | 2692.09 | 2698.69 | 10.56 | 10.34 | 2668.67 | 2681.73 | 11.34 | 10.91 |

Oct. | 2587 | 2705.01 | 2715.29 | −4.56 | −4.96 | 2759.90 | 2765.4 | −6.68 | −6.90 | 2670.27 | 2683.88 | −3.22 | −3.74 |

Nov. | 2810 | 2706.95 | 2717.24 | 3.67 | 3.30 | 2847.63 | 2851.93 | −1.34 | −1.49 | 2671.87 | 2686.02 | 4.92 | 4.41 |

Dec. | 2890 | 2708.89 | 2719.18 | 6.27 | 5.91 | 2955.28 | 2958.28 | −2.26 | −2.36 | 2673.47 | 2688.17 | 7.49 | 6.98 |

Average error (%) | 6.64 | 6.47 | - | - | 6.40 | 6.18 | - | - | 7.41 | 7.09 |

Therefore the best represented model between the months and peak load in PSO is the quadratic regression model.

Weekly real peak demands recorded in the years [2008-2014] are used in this section. The data set is used to establish an over determined system of equations. This system of equations is LSRM and PSO technique. The weekly real peak loads are used to find the coefficients for linear, quadratic and exponential models. PSO and LSRM techniques are used to estimate models parameters for the same time horizon and the computed parameters are tabulated in

The forecasted loads based on the parameters of linear, quadratic and exponential models and weekly least square error are shown in

It can be concluded from the tables that the error computed by PSO are less than LSRM. In linear and exponential models, the weekly prediction load is increased from the first week till last week of the year 2015. In quadratic model, the weekly prediction load has vertex point [minimum peak value] occurs at week number 26. The peak load demand expected using LSRM and PSO shown in

Coefficients | Linear model | Quadratic model | Exponential model | |||
---|---|---|---|---|---|---|

LSRM | PSO | LSRM | PSO | LSRM | PSO | |

a | 0.8704 | 0.931 | 0.523 | 0.551 | 2524.8 | 2532.4 |

b | 2531 | 2652.3 | −26.8491 | −26.95 | 1.0003 | 1.0005 |

c | - | - | 2780.4 | 2794.6 | - | - |

Week | Peak load (MW) | Linear model | Quadratic model | Exponential model | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

LSRM (MW) | PSO (MW) | Error (%) | LSRM (MW) | PSO (MW) | Error (%) | LSRM (MW) | PSO (MW) | Error (%) | |||||

4 | 2830 | 2532.71 | 2654.16 | 10.50 | 6.21 | 2728.84 | 2742.90 | 3.57 | 3.08 | 2526.51 | 2534.93 | 10.72 | 10.43 |

8 | 2740 | 2537.94 | 2659.75 | 7.37 | 2.93 | 2599.13 | 2614.26 | 5.14 | 4.59 | 2531.62 | 2542.55 | 7.60 | 7.21 |

12 | 2530 | 2541.42 | 2663.47 | −0.45 | −5.28 | 2533.57 | 2550.54 | −0.14 | −0.81 | 2535.04 | 2547.64 | −0.20 | 0.70 |

16 | 2420 | 2544.90 | 2667.20 | −5.16 | −10.21 | 2484.75 | 2504.46 | −2.68 | −3.49 | 2538.45 | 2552.74 | −4.89 | 5.48 |

20 | 2520 | 2549.25 | 2671.85 | −1.16 | −6.03 | 2447.26 | 2471.64 | 2.89 | 1.92 | 2542.73 | 2559.12 | −0.90 | 1.55 |

24 | 2552 | 2552.73 | 2675.58 | −0.03 | −4.84 | 2436.10 | 2465.23 | 4.54 | 3.40 | 2546.16 | 2564.25 | 0.23 | 0.48 |

28 | 2690 | 2556.21 | 2679.30 | 4.97 | 0.40 | 2441.68 | 2476.44 | 9.32 | 7.94 | 2549.59 | 2569.38 | 5.22 | 5.22 |

32 | 2810 | 2560.57 | 2683.95 | 8.88 | 4.49 | 2472.18 | 2515.26 | 12.02 | 10.49 | 2553.89 | 2575.81 | 9.11 | 8.33 |

36 | 2900 | 2563.18 | 2686.75 | 11.61 | 7.35 | 2503.03 | 2551.77 | 13.69 | 12.01 | 2556.47 | 2579.67 | 11.85 | 11.05 |

40 | 3010 | 2564.92 | 2688.61 | 14.79 | 10.68 | 2528.83 | 2581.62 | 15.99 | 14.23 | 2558.19 | 2582.25 | 15.01 | 14.21 |

44 | 2540 | 2569.27 | 2693.26 | −1.15 | −6.03 | 2611.63 | 2675.54 | −2.82 | −5.34 | 2562.50 | 2588.72 | −0.89 | 1.92 |

48 | 2660 | 2571.88 | 2696.06 | 3.31 | −1.36 | 2673.87 | 2745.11 | −0.52 | −3.20 | 2565.09 | 2592.60 | 3.57 | 2.53 |

52 | 2820 | 2576.23 | 2700.71 | 8.64 | 4.23 | 2798.51 | 2883.10 | 0.76 | −2.24 | 2569.41 | 2599.09 | 8.89 | 7.83 |

Average error (%) | 6.62 | 5.49 | - | - | 6.36 | 5.12 | - | - | 6.71 | 6.46 |

From

From

Weather is the most important independent variable for MTLF. In this section, MTLF models used weather influence to predict the future peak load demand in terms of month and week. Various weather variables could be considered for MTLF. Temperature is the most commonly used for load predictors. The result of the previous section shows that there is a high positive correlation between temperature and peak load during summer and there is a negative correlation between temperature and peak load during winter. For these positive and negative correlations, LSRM used to predict the peak load in the hot and cold days. Because the relation between temperature and peak load is very complicated in nature and cannot be analyzed with ordinary mathematical models, the quadratic model used for data obtained in summer and winter seasons.

Peak loads of NEPCO are used to estimate the coefficients of quadratic model for MTLF in summer and winter season. Summer season extends from June till September; winter season extends from December till March. Long studies investigated that the changing of the temperature affects the peak load. The researches focused on the effect of the higher and lower temperatures on electricity

consumption using peak load data and temperature influence. The studies indicate that the impact of a one-degree in temperature higher than 25˚C, the peak load predicted will increase by 8 MW and a one-degree in temperature lower than 15˚C, the peak load predicted will increase by 6 MW [

The inputs of this model is the number of months per each season and the peak loads recorded in the years [2008-2014], whereas the output is the monthly peak loads predicted for the year 2015 after taking the temperature effect by each season. PSO and LSRM techniques are used to estimate quadratic model parameters for winter and summer season. The quadratic parameters are tabulated in

It can be concluded from the table that in summer season, the peak load is increased continuously from June till August and decreased from August till

Coefficients | Summer | Winter | ||
---|---|---|---|---|

LSRM | PSO | LSRM | PSO | |

a | 1.439 | 1.428 | −55.07 | −56.07 |

b | 93.82 | 93.71 | 447.28 | 446.21 |

c | 2536.2 | 2532 | 2144 | 2142 |

Month | Peak load (MW) | Quadratic MODEL | Error (%) | ||
---|---|---|---|---|---|

LSRM | PSO | ||||

Jan. | 3160 | 3118 | 3095.7 | 1.33 | 2.03 |

Feb. | 2950 | 3019.65 | 2989.3 | −2.36 | −1.33 |

Mar. | 2760 | 2845.16 | 2800 | −3.09 | −1.45 |

Apr. | 2670 | 2631.46 | 2627.14 | 1.44 | 1.61 |

May | 2690 | 2729.6 | 2725.13 | −1.85 | −1.68 |

Jun. | 2820 | 2830.61 | 2825.98 | −0.38 | −0.21 |

Jul. | 2940 | 2950.5 | 2945.68 | −0.36 | −0.19 |

Aug. | 3180 | 3260 | 3116 | −2.52 | 2.01 |

Sep. | 3010 | 3150.92 | 3145.67 | −4.68 | −4.51 |

Oct. | 2587 | 2536.21 | 2532.14 | 1.96 | 2.12 |

Nov. | 2810 | 2818.28 | 2810.14 | −0.29 | 0.00 |

Dec. | 2890 | 3008.21 | 2994 | −4.09 | −3.60 |

Average error (%) | 2.02 | 1.73 |

September, while in winter season the peak load is increased continuously from December till January and decreased continuously from January till March. The forecasted monthly peak load using quadratic model and PSO algorithm based on temperature effect is shown in

It can be observed from

From

The historical and weather data for the period [2008-2014] are used for estimation the models parameters for winter and summer seasons. Data for the year

2015 are used for testing LSRM and PSO models. The inputs of this model is the number of weeks per each season, whereas the output is weekly peak loads predicted for the year 2015 after taking the temperature effect by each season. The quadratic parameters are tabulated in

The weekly forecasted peak load using quadratic model and PSO algorithm based on temperature effect is shown in

From

It can be concluded from the table that in summer season, the peak load is increased continuously from the 22^{nd} week till the 35^{th} week and decreased from the 36^{th} week till the 39^{th} week (the weeks representing summer semester), while in winter season the peak load is increased continuously from the 48^{th} week till the 3^{rd} week and decreased continuously from the 4^{th} week till the 12^{th} week (the weeks representing the winter semester). The weekly least square error depends on the temperature effect is shown in

From

Coefficients | Summer | Winter | ||
---|---|---|---|---|

LSRM | PSO | LSRM | PSO | |

a | 0.343 | 0.3326 | −1.95 | −1.8028 |

b | 10.8 | 10.787 | 58.189 | 56.175 |

c | 2412.8 | 2410.3 | 2317.2 | 2313 |

Week | Peak load (MW) | Quadratic model | Error (%) | ||
---|---|---|---|---|---|

LSRM | PSO | ||||

4 | 2830 | 2817.29 | 2816.02 | 0.45 | 0.49 |

8 | 2740 | 2697.22 | 2715.67 | 1.56 | 0.89 |

12 | 2530 | 2553.18 | 2590.65 | −0.92 | −2.40 |

16 | 2420 | 2448.29 | 2445.67 | −1.17 | −1.06 |

20 | 2520 | 2521.15 | 2517.90 | −0.05 | 0.08 |

24 | 2552 | 2591.79 | 2587.66 | −1.56 | −1.40 |

28 | 2690 | 2689.41 | 2684.06 | 0.02 | 0.22 |

32 | 2810 | 2870.86 | 2863.52 | −2.17 | −1.90 |

36 | 2900 | 2949.57 | 2940.79 | −1.71 | −1.41 |

40 | 3010 | 3005.47 | 2995.62 | 0.15 | 0.48 |

44 | 2540 | 2559.40 | 2548.84 | −0.76 | −0.35 |

48 | 2660 | 2657.91 | 2647.05 | 0.08 | 0.49 |

52 | 2820 | 2762.11 | 2756.63 | 2.05 | 2.25 |

Average error (%) | 2.20 | 1.55 |

average error point of view it is found that PSO method has produced better estimation than the LSRM.

In this paper, the autoregressive data were generated with order equal 13. Therefore, AR (13) was investigated and the forecasts of this model were started from the month [84 - 95] for monthly prediction and from the week [313 - 364] for weekly prediction (The months and weeks which are represented the year 2015. A Matlab code was used to generate the data and check the AR property. The results were evaluated by LSE to compare computing peak loads and accuracy of the two forecast basis, respectively.

Monthly real peak demands recorded in the years [2008-2014] are used to implement AR model and the real data for 2015 is used to test this model. The monthly AR model parameters which are estimated using variants of the least- squares method are given by the following equation.

The monthly forecasted loads based on the parameters of AR model and monthly least square error are shown in

It can be concluded from the table that the error computed by AR model is high compared with other techniques. In February, March and May the AR model gives good results, otherwise the results gives unacceptable prediction of peak load data. By using Equation (19) in Matlab, The monthly forecasted peak load using AR model can be shown in

From

From

Month | Peak load (MW) | AR (MW) | Error (%) |
---|---|---|---|

Jan. | 3160 | 2592.40 | 17.96 |

Feb. | 2950 | 2858.26 | 3.11 |

Mar. | 2760 | 2695.13 | 2.35 |

Apr. | 2670 | 2852.50 | −6.84 |

May | 2690 | 2758.84 | −2.56 |

Jun. | 2820 | 2442.88 | 13.37 |

Jul. | 2940 | 2645.44 | 10.02 |

Aug. | 3180 | 2784.94 | 12.42 |

Sep. | 3010 | 2811.21 | 6.60 |

Oct. | 2587 | 2957.33 | −14.32 |

Nov. | 2810 | 2666.22 | 5.12 |

Dec. | 2890 | 2547.89 | 11.84 |

Average error (%) | 8.88 |

Weekly real peak demands recorded in the years [2008-2014] are used in this section. The data set is used to establish AR model. The weekly AR model parameters which are estimated using variants of the least-squares method are given by the following equation.

The weekly forecasted loads using AR model and weekly least square error are shown in

It can be seen from the table that the results computed by AR have the least accuracy compared with LSRM and PSO. In AR model, the weekly prediction load has maximum value in the week number 6 for the year 2015, but it still has a big difference compared with real value shown in many weeks for this year. By using Equation (19) in Matlab, The weekly forecasted peak load using AR model can be shown in

From

Week | Peak load (MW) | AR (MW) | Error (%) |
---|---|---|---|

4 | 2830 | 2659.93 | 6.01 |

8 | 2740 | 2692.87 | 1.72 |

12 | 2530 | 2691.63 | −6.39 |

16 | 2420 | 2686.27 | −11.00 |

20 | 2520 | 2686.21 | −6.60 |

24 | 2552 | 2684.31 | −5.18 |

28 | 2690 | 2684.72 | 0.20 |

32 | 2810 | 2683.94 | 4.49 |

36 | 2900 | 2683.42 | 7.47 |

40 | 3010 | 2683.23 | 10.86 |

44 | 2540 | 2682.58 | −5.61 |

48 | 2660 | 2682.15 | −0.83 |

52 | 2820 | 2681.49 | 4.91 |

Average error (%) | 8.12 |

From

The particle swarm optimization PSO, least square regressive LSR and auto regressive AR methods are presented as MTLF techniques for Jordan electric power systems. This paper has presented approaches used for MTLF of electric loads: LSRM and PSO algorithm. The prediction is made either weekly or monthly based on historical peak load data and weather influence. Least square error (LSE) is introduced to evaluate the performance of the two models then compared these models with AR model and the educated guess assumptions currently used in NEPCO. The comparison between LSRM, PSO and AR models is made by using an average error and depicted by using tables and figures. A PSO algorithm is presented for optimal parameter estimation of MTLF in power system. The solution is implemented and tested using actual recorded data obtained from NEPCO. Real peak load data from NEPCO are used to validate the performance of these approaches; three different models for LSRM and PSO algorithm based on the peak load data and weather influence are used; the quadratic model provides the least errors for both monthly and weekly peak load compared with the linear and exponential models. The forecasted peak load resulted by using the PSO algorithm has been compared with that obtained with LSRM and AR models. From average error point of view, it is found that LSRM and PSO algorithm have produced better estimation than the AR model and current prediction assumptions used in NEPCO. The results are shown the average error for each model used. Two cases were obtained; forecasting depends on peak load data and forecasting depends on peak load data influenced by the weather

Forecasting type | Forecasting depends on peak load | Forecasting depends on peak load adjusted considering weather effects | Forecasting by using AR model | ||||||
---|---|---|---|---|---|---|---|---|---|

Linear model | Quadratic model | Exponential model | Quadratic model | ||||||

LSRM | PSO | LSRM | PSO | LSRM | PSO | LSRM | PSO | ||

Monthly | 6.64 | 6.47 | 6.40 | 6.18 | 7.41 | 7.09 | 2.02 | 1.73 | 8.88 |

Weekly | 6.62 | 5.49 | 6.36 | 5.12 | 6.71 | 6.46 | 2.20 | 1.55 | 8.12 |

effects. The average error for LSRM and PSO for the three models and forecasting using AR model are represented in

Hattab, M., Ma’itah, M., Sweidan, T., Rifai, M. and Momani, M. (2017) Medium Term Load Forecasting for Jordan Electric Power System Using Particle Swarm Optimization Algorithm Based on Least Square Regression Methods. Jour- nal of Power and Energy Engineering, 5, 75-96. https://doi.org/10.4236/jpee.2017.52005