Evaluation of Electric Power Losses on 33/11 kV Distribution Feeder Networks in Uyo Urban, Nigeria Using Loss Factor Approach

— No matter how carefully a power system is designed, grid inefficiencies or load losses would happen, causing power unbalance between distribution and major load centers. It is therefore fundamental to clearly determine and identify electric power system losses for network improvement because of their financial-economic value to distribution companies and consumers. In this work, relevant data including monthly loading, feeder route length, and cross-sectional area of four 11 kV feeders namely, Aka, Ibrahim Babangida, Udo Udoma, and Idongesit Nkanga secretariat-dedicated feeders were obtained from the Port Harcourt Electricity Distribution (PHED) company technical office, Uyo, Nigeria for four years (January 2018 to December 2021) for the 33/11 kV Akwa Ibom State Secretariat Injection Substation and distribution feeder circuits. Average load, maximum load, load factor, loss factor, power losses in the feeders and total power loss in the system were computed and the results which were shown graphically revealed grid inefficiencies and power imbalance or losses which increased slightly on a yearly basis. The losses are due to heat dissipation, lack of maintenance of the power system components, transformer overloading, copper losses, core losses, lengthy feeder routes, and location/aging of the transformers. Suggestions were made in order to reduce further losses in the network .


I. INTRODUCTION
Electricity is one of the greatest technological innovations of mankind. It has now become a part of our life and one cannot think of a world without electricity. Almost all devices at home and industries run because of electricity. Electrical energy is generally produced by conversion from other forms of energy. This often takes place at a remote location and the electricity generated is sent through transmission lines to distribution networks from where it is delivered to the consumers through a network of electrical equipment. The equipment and apparatus required for the generation, transmission and distribution of electrical energy forms the electric power system. Electric power system basically consists of generation, transmission and distribution systems, regulated either by a single entity or by a number of entities [1], [2].
No matter how carefully the power system is designed, technical losses (grid inefficiencies or load losses) would happen as a result of heat dissipation, resulting from current utilization in the power lines causing power unbalance between generation, distribution and major load centers. The more the power that flows through the power lines, the more the current that flows will be and consequently the power quality will decline. In addition, unusual operating problems like voltage being below the minimum or above the maximum acceptable level are encountered. Also, nontechnical losses which are losses due to human errors and social issues are equally unavoidable. These result in electrocution, poor quality of power and high cost of electricity. It is therefore necessary to evaluate and minimize power system losses to enhance network efficiency and highquality supply of electricity to end-users with reliability and economy [3].
In this paper, the loss factor and graphical approach is adopted in estimating electric power losses in 2 X15MVA 33/11 kV Akwa Ibom State Secretariat distribution feeder networks within the Port Harcourt Electricity Distribution (PHED) network in Uyo, Nigeria. This paper is organized as follows: Heading II, literature survey with focus on losses in power distribution systems, ways of minimizing them and research effort. The methodology adopted is explained in heading III which also explains the outlook of the 33/11 kV State Secretariat distribution networks and feeder circuits. The results and discussion from this case study network is presented in Section IV. Section V is conclusion while Acknowledgment makes up Section VI.

A. Losses in Power Distribution Systems and Ways of
Minimizing Them Losses in power system are broadly divided into two: technical and non-technical losses. Technical losses occur because the electrical equipment used in the power system by nature, have losses associated with them which cannot be totally eliminated. Generators and transformers have losses in their windings (due to winding resistance) as well as their core (due to eddy current and hysteresis). Transmission and distribution lines have losses due to the thermal effect of current flow in the conductors, as well as corona at higher voltages. Cables have resistive and dielectric losses; even fiscal meters also have associated losses [1]. Other causes of technical losses include inefficient equipment such as transformers, inadequate size of the conductor in the distribution lines, long distribution lines, low power factor, overloading of lines, transformers installed far from the load centers, bad workmanship [4]. Unbalanced loading is yet another factor responsible for losses in electric power distribution lines. If one of the phases is loaded more than others, the loss will be more than it would have been when the load is balanced [2].
Some of the ways to reduce technical losses include Use of proper jointing techniques and keeping the number of joints to a minimum, regular inspection of the connections, isolators, drop-out fuses, low tension switches, transformers, transformer bushing-stem and other distribution equipment. Proper selection of conductor size as well as a transformer in terms of efficiency, size and location is equally critical. It is important to; locate the distribution transformers near the load center and if possible, keep the number to a minimum, feed heavy consumers directly from the feeders, maintain the network components and replace those that are deteriorating, worn out or faulty. Finally, ensure proper load management and load balancing, use electronic meters which are accurate and tamper-proof and improve power factor by adding shunt capacitors [4].
Besides, non-technical losses otherwise known as commercial losses primarily relate to unidentified, misallocated and inaccurate energy flow. In essence, they represent the amount of energy that is delivered but not accounted for. It is important to separate non-technical losses from two cases: energy accounted for but not billed, or energy billed but the bills are not paid. In both cases, the entity consuming the energy is known. Non-technical losses occur due to energy theft, poorly estimated billing, defective metering equipment (either deliberately tampered with or not), unpaid bills etc. They are generally caused by actions external to the power system and cannot be empirically computed like the technical losses [1], [5]. Non-technical losses are losses due to human errors and social issues and are more difficult to measure because they are often unaccounted for by the operators and thus have no recorded information [6]. They can be reduced through proper enforcement of electricity regulatory laws, periodic and impromptu checks on consumers' homes, electronic tampering detection meter and use of prepaid meter [7].

B. Methods of Determining Losses in a Power System and Research Efforts
Some of the methods for determining losses in a power system include; the Computation of IL 2 R, evaluation of line losses using B-loss co-efficient, differential loss method, the use of Dopazo formula, use of power system parameters, lossfactor approach and load-flow iterative techniques [3], [8]. The use of loss factor and load loss factor was also reported in [9], [10]. The energy flow models approach in the estimation of technical losses was captured in [11] while the use of estimated non-technical losses to compute technical losses was adopted in [12].
Reference [13] deployed the loss factor approach to compute the power losses on selected feeders in the 33/11 KV feeder circuits in the Port Harcourt electricity distribution network using data accessed from the substation. The feeders studied were Etinan, Obot-Akara, Onna, Eket and Ibesikpo 33/11 KV feeders. The losses in the feeders were traceable to poor maintenance of the power system components, transformer overloading, copper losses, core losses, deterioration/aging of the components, incessant illegal connections resulting in overloading of the feeders, and excessive feeder route length among others. Reference [2] computed the power losses in Ekpoma distribution network using data from the Power Holding Company of Nigeria, Ekpoma covering January 2008 to December 2012. The study found that besides factors such as unbalanced loading of transformers, aged transformer, inadequate size of conductors etc., technical losses arise predominantly from faults, reactance contributed and conductor resistances. Technical power losses in Abeokuta distribution network based on data accessed from the Ibadan Electricity Distribution Company (IBEDC), Ijeun District, Abeokuta Ogun State of Nigeria in respect of selected feeders domiciled in the Totoro, Kolobo, Abiola-Way, Ijeun-Titun, Ake-Road, GRA, Obantoko and Odeda areas of Ibadan for the period, 2012 to 2014 was equally investigated using the loss factor approach. The outcome of this study revealed that high technical losses are attributable to lengthy feeder spans and illegal connections which result in feeder overloading [14].

A. 2 X 15MVA 33/11 kV Akwa Ibom State Secretariat Injection Substation and Power Distribution Networks
The 2 X 15 MVA 33/11 kV State Secretariat distribution networks is an overhead radial network. The main substation power transformers are two rated 15 MVA each. The three phase secondary distribution transformers have their primary supplied at 11 kV while the secondary produce a rated voltage of 0.415 kV, phase to phase and 240 V, phase to ground. The three phases of the distribution transformer as well as the neutral are connected to the distribution lines suspended from concrete or wooden poles with insulators.
This distribution substation supplies four 11 kV feeders through its bus namely, Aka 11 kV feeder (Aka), 10 km; Idongesit Nkanga Secretariat 11 kV (dedicated) feeder (ID), 4km; Ibrahim Babangida 11 kV feeder (IBB), 8 km and Udo Udoma 11 kV feeder (UU), 7 km. The feeders have cross sectional area of 150 mm 2 with 2.82×10 -8 Ὠm as resistivity. The feeders are segregated into several three-phase sections connected through sectionalizing fuses or switches. Each feeder section has several single-phase laterals or branches connected to it through fuses, so that a fault on a branch can be cleared without interrupting the feeder. The feeders and laterals run as overhead lines/cables and supply distribution transformers which step down the voltage to the secondary distribution level (220 V single phase to 415 V 3-phase). These distribution transformers are installed on utility poles for overhead lines and on concrete pads at ground level. They are protected from overloads and faults by fuses or circuit breakers on the primary and/or the secondary side. From these distribution transformers, energy flows through secondary mains and service conductors directly to residential, commercial and light industrial consumer loads within the network [15].

B. Computation of Technical Losses
Data on the daily loading of the feeders which were used to calculate the monthly minimum, maximum and average loadings; feeder route length, cross sectional area of conductor, 150 mm 2 having a resistivity of 2.82×10 -8 Ὠm and line voltage between January 2018 to December 2021 were collected from PHED, Uyo technical Office, Uyo. The feeders are Aka 11 kV feeder (Aka), 10 km; Idongesit Nkanga Secretariat 11 kV dedicated feeder (ID), 4 km; Ibrahim Babangida 11 kV feeder (IBB), 8km and Udo Udoma 11 kV feeder (UU), 7 km. This study deployed the loss factor approach in computing electric power losses in these feeders. MATLAB (R2020a) was used for the computation.

1) Mathematical analysis of losses in a power transformer
Load factor and load loss factor technique was employed in calculating the technical losses of the power transformer.
Loss Factor (Lf) is the ratio of average power consumed during a designated period to maximum demand occurring in the same period.
Loss factor can be defined as (1).
Load Loss Factor ( 1 ) describes the average electrical energy losses for electricity distributed during a designated period. The average energy losses or load loss factor during a designated period is given by (2).
Loss factor and load loss factor are related to each other by the expression, Where K is the co-efficient of loading, given in (4).
The total power loss WTLoss in kW, in the power transformer is expressed as (5) and (6).
and where, = Full load copper loss max = Maximum KVA demand in a period = KVA rating of the transformer WnL = No-load losses.

2) Mathematical analysis of line losses in a distribution feeder
The load losses in a distribution feeder are typically computed under peak demand condition. Basically, when current passes through line of feeders, feeder load loss results due to imperfection of the conductors of the lines [14]. Equation (9) gives the Line Losses in feeders.
The maximum current (IL) in Amperes (A) drawn from the feeder is given as (13).
Distribution feeder resistance, R in Ohms (Ω) of the distribution line is shown in (14).
where, P is Maximum monthly loading on the feeders in MW V is line voltage in kV; r is resistivity in Ω-m R is distribution feeder resistance in ohms (Ω) P (loss) is the power loss in the feeder in MW A is cross sectional area of conductor in mm 2 L is route length of the feeders in km IL is current drawn from feeder in Ampere f is power factor.
Therefore, the total power loss in the system is given in (16).
Noteworthy is the fact that many transformers work off constant voltage mains and consequently the WTLoss component of the total loss can be assumed to be constant [16].

C. Non-Technical Losses
These losses which are caused by factors external to the power system can neither be empirically computed nor quantified. It can be reduced through proper enforcement of electricity regulatory laws, periodic and impromptu checks on consumers' homes, electronic tampering detection meter and use of prepaid meter [7].

A. Results
Computation was carried out based on the flow diagram presented in Fig. 2 and the algorithm developed.

B. Discussion
The computation of technical power losses on selected 11 kV feeders of the 33/11 kV Akwa Ibom State secretariat injection substation and power distribution networks has been performed in this paper using load factor and loss factor method. Monthly minimum, maximum and average loading of all selected feeders have been presented in Table I, Table  III, Table V and Table VII while the computed load factor, loss factor and power losses of all feeders for the period under review are presented in Table II, Table IV, Table VI and  Table VIII. Average maximum loading (MW) on the four feeders from 2018 to 2021 is shown in Table IX while total average power loss of 0.05561MW in the four feeders for the four years under review is shown in Table X. The relationship between feeder route length, average maximum loading and average power losses is expressed in Table XI.
The average power losses on the feeders increase very slightly on a yearly basis. From January 2018 to December 2021, the average power losses on the selected feeders are 0.00947 MW, 0.01086 MW, 0.01456 MW and 0.02072 MW for 2018, 2019, 2020 and 2021 respectively as shown in Table  X. The maximum average power losses as shown in Fig. 4 occur on Aka feeder for the four years period while the minimum average power losses occur on Idongesit Nkanga Secretariat dedicated feeder which has a very short feeder length of 4 km. Clearly, the high average power losses on Aka feeder were due to its long route (10 km), the nature of the connected load, overhead construction and illegal connections resulting in overloading of the feeder.

V. CONCLUSION
The primary aim of all power systems is to maintain a continuous power balance between production and consumption with all voltages, both in magnitude and angle, remaining within specified limits. Again, the purpose of distribution system is to take electric power from transmission system and deliver it to consumer load centers. Unfortunately, an appreciable portion of the power generated is lost in the distribution process. This paper adopts a unique mathematical and graphical approach in determining electric power losses in 2 X15MVA 33/11 kV Akwa Ibom State Secretariat distribution networks and feeder circuits within the Port Harcourt Electricity Distribution (PHED) network in Uyo, Nigeria. There is dare need for electricity to be protected for efficient power delivery to consumers. Planned Preventive and corrective maintenance needs to be carried out regularly to minimize power losses in the distribution system. Again, overused transformers should be replaced while overloaded ones should be upgraded. Generally, concerted efforts should be made to expand power infrastructures such as the installation of an additional distribution substation near Aka feeder circuit to cater for new consumers and to prevent overloading and unnecessary losses in the power distribution system.