Improvement of Power Factor. Technoeconomical Application in a Case Study at the Industrial Area of Kavala

Modern power systems are characterized by problems of increased losses and stability trends related to the availability of reactive power. The reactive power is a nonproductive one, necessary for the operation of the interconnected cargo and as well as the operation of distribution networks and transmission of electricity. The importance of reactive power is also shown by the great blackout "Great Northeast" in 2003 due to the loss of it. [1] The degree of reactive power consumption is expressed by the quantity cosφ, called power factor (PF). The power factor is the ratio of RMS power to the apparent one. The power factor is calculated as follow:


Introduction
Modern power systems are characterized by problems of increased losses and stability trends related to the availability of reactive power.The reactive power is a nonproductive one, necessary for the operation of the interconnected cargo and as well as the operation of distribution networks and transmission of electricity.The importance of reactive power is also shown by the great blackout "Great Northeast" in 2003 due to the loss of it.[1] The degree of reactive power consumption is expressed by the quantity cosφ, called power factor (PF).The power factor is the ratio of RMS power to the apparent one.The power factor is calculated as follow: where P is the active power (watt), U is the voltage (Volt), I is the current (A), φ is the phase difference between voltage and current, S is the apparent power (VA) and Q is the reactive power (VAR).
The most serious problem appears in systems with inductive engines and lighting -air conditioning and heating units.In order to solve these problems, kinds of compensation are used as following: 1. Individual compensation; 2. Central compensation.
In the central compensation is installed an array of capacitors in the entrance of the installation which is monitored by an electronic controller.The national electric generation, in order to encourage industrial users to optimize the power factor, has imposes penalties on their behalf.
In order to save energy and to optimize the cosφ, a range of actions is necessary such as, proper optimization of capacitors to be used, the procedure for the installation and more over the check if it is useful investment of this kind or not economically.
The pricing is divided into three main categories: 1. with low voltage, 2. with medium voltage, 3. with high voltage.
The main charges are G22 billing for domestic use and for industrial B1, B2, B1B and B2B one.The relations for the charge are: Billing G22.
According to the cosf there are the following cases: If cosφ <0.95, the xz is given by the following equation where XZ is the demand charge (kW) and KMZ is the recorded maximum demand (kW) If cosφ < 0.95, the xz is given by the following equation The billings B1, B2, B1B and B2B are given by the following equations, according to cosφ: -If cosφ <0.95 -If cosφ >0.95 0,87

Modeling process to improve the cosf
The reactive power is a critical point for the operation of power systems.For proper use of capacitors or range of capacitors, are used different algorithms for the proper choice.Some of these algorithms use the method of analytical hierarchy [2] and can be used models as shown in Fig. 1.

Fig. 1. Decision flowchart
In order to optimize the capacity of capacitors, the cosφ must be maximized, the losses of transfer lines must minimized and the gain of transfer line must maximized.According to this concept the capacitor C1 must calculated as follow [3]: where P L : power load; V L : the RMS voltage of the load; I s : the RMS value of the current; I sn : the value of current with harmonic h; R th : the resistance of the load.
In practice the choice of the capacity of each capacitor will be used, in order to improve cosφ, proceed as follows: 1. Convert mechanical power into electrical.

Economic analysis of the capacitor selection
The benefits from the improving of power factor is not only qualitative but mainly economically in the industry [4].Several economic methods have developed over time, in order to study the economic gain due to the improvement in the consumption of reactive power such as the relation ( 19) [1].
where B T : the total benefit of using capacitors; B 1 : the benefit of reducing the account; B 2 : the benefit of using the actual force; B 3 : the benefits of increasing portability force.
Another equation, used by the international literature, on the base of the minimization of reactive power using capacitors, is   where Qc the reactive power of capacitors; Cc Qc the cosφ of capacitors; ploss C the cost of line losses.The use of capacitors in an industrial application and the benefit due to this, is where Qc the cost of installation and r the cost of reactive power which is given by cos hours The annual cost of energy is where β the cost of electric energy.The implementation of any system in order to optimize the power factor requires expenditure of money.The total cost is the result of the total cost of each work as it is shown in relationship (24) 1 2  cost of materials (capacitors, electronic units, panel, relay, little u); 2 C  : cost of the assembly, design, installation.
Due to the high cost of the initial installation of the system improving the cosφ, the depreciation of the system must also take into account and is given by relationship (25).
where o c :amortization dose; i: interest rate; N: the number of doses

Case study in the industrial area of Kavala
Kavala is the capital of the prefecture and geographically is located in North Eastern Greece (Fig. 2).The population growth is the result of the industrial development.The majority of the city residents are employed in service sector output.Here there is the only company in Greece where oil and desulphurise are extracted (Kavala Oil AE).Beyond the deposit of black gold, in Thassos/Kavala there is the only Phosphate Fertilizer Manufacturing in Greece.Dozens of other units in the industrial district, with major units of marble and glass, offer thousands of jobs (most famous are the ASCO SA and KRE.KA.SA).
In this paper, are presented two industrial enterprises (company A and company B) of Kavala in combination of loads (resistive, inductive and capacitive).The accounts of the electricity and the power factor for a year are used in the studied companies.Then, an estimation is done based on relationships (5), ( 6) and (7), of the capacitors array used to offset the cosφ.Moreover, a prediction of the power factor is taking into account and the cost of installations of the capacitor's arrays is calculated and performance analysis of financial results is obtained.

Company A
The first undertaking study presents the curves of the energy consumed during one year (Fig. 3) and the variation of cosφ is presented.(Fig. 4).As it shown in Fig. 4, the values of cosφ have a range between 0.6 and 1.This variation leads to absorption of reactive power and consequently the economic burden.The company is a craft wood one and is carried out from 2008.The Company operates a working one system of shift 8 hours.
The company (tables 1 and 2) is characterized by annual working time (H) 7260, 123200 kW average load, reactive power before the improvement 216000 kVAR, total installation of capacitors 120 kVAR, total cost of power before the improvement 23687 €, total cost of power after the improvement 22628 € and total profit of 1059 €

Fig. 4. The cosφ of company A in one year
A vital function of management of a company is the planning for the future.So for any future development and decision, a key tool it is used.To make the prediction, relationships (26), ( 27) and (28) are used: where X is cosφ and Y is the number of days.Applying relations ( 26) and ( 27) in the relationship Y1=0,7535-0,00527Xi are produced.
Using this one, the value of power factor for a future month can be predicted and estimated.Choosing the invoice of 15 months and 30 months the values of power factor will be 0.6745 and 0.5954 respectively.Observing the values derived from the model prediction, the values of power factor are much less than the unit and are: 15 0.6745 Y  30 0.5954 Y  .The big divergence that appears in the power factor from 1, requires the use of capacitor's array and according to relationships (9), ( 10) and ( 11) must be placed in case study A capacitor of about 120 KVar.
The total cost of installing the array of capacitors is as follows: .Using the relationship (25) with the rate of 4.5% the extinction of installation of capacitor arrays will be in 23 months while, if they are placed in the first year, the results would be those in Table 2 the first year would have saved 1059 €.Note: total profit from their accounts 1059,00 €

Company B
The first undertaking study presents the curves of the energy consumed during one year (Fig. 5) and the variation of cosφ is presented.(Fig. 6).Company B (Table 3 and  Table. 4) is a small one with a working system of one unit of 8 hours, annual working time (H) 7260, 63200 kW average load, reactive power before the improvement 94400 kVAR, total installation of capacitors 100 kVAR, total cost of power before the improvement 8277 €, total power cost improvement after 6892 € and total gain of 1385 €.

Conclusions
The electrical networks consume active and reactive power caused by the magnetic fields of motors and power transformers, impedance of the transmission and distribution lines, coils, fluorescent lighting and all inductive circuits.The main reasons for making the decision to install capacitor arrays for improving the power factor of a load, for the best technoeconomical solution, are mainly the cost of excessive consumption of reactive power, the decrease of energy and power losses, the increase of the available power at the substation, the best planning of a new substation in the network, the increase or regulation of the voltage scales, the facilitating to start of large motors at the edge very charged distribution lines.The placement of capacitor's arrays in the two companies in Kavala, showed a reduction in the consumption of reactive power, power factor improvement, energy and money saving and reducing emissions.The depreciation of the capacitor array installation takes place in a relatively short period of about two years.

Fig. 5 .Fig. 6 .
Fig. 5.The consumption of energy of company B during a year

Table 1 .
Recording power consumption of company A ΩΧΒ is the reactive power and ΩΧΒΑ is the active power

Table 2 .
Recording power consumption of the company A by placing capacitors

Table 3 .
Power consumption of the company B

Table 4 .
Recording power consumption of the company B by placing capacitors