Load Evaluation with Fast Decoupled-Newton Raphson Algorithms: Evidence from Port Harcourt Electricity

A R T I C L E I N F O A B S T R A C T Article history: Received: 06 June, 2020 Accepted: 11 September, 2020 Online: 20 October, 2020 The undulated power supply has dropped to its worst reliability index in most parts of the city despite the installations of distribution transformers to improve the power. In this work, examination of Port Harcourt Town Zone 4 (Z4), Rivers State power distribution system forcing on its operation, planning for future expansion of the system, and sharing of power between utilities was done. The objective was to unravel the problematic recurrent blackouts as a result high power loss, that is (IR) in the line; low voltage profile, poor cos∅ at the load end, excessive loading of feeder transformers, and conductors rating inadequacy at the receiving end of the 33KV Distribution part of the substation. A comprehensive study was carried out on the system with the formation of node admittance matrix. Programmable codes were written using MATLAB script to resolve the static power flow equations defined applying Fast decoupled-Newton Raphson calculation procedure centered on the advantages of time and PC memory space (PC-MS). Thus, the node voltage and the other variables like branch flows and phase angles were gotten, and network losses were reduced. However, the results obtained were compared with that gotten from Electrical Transient Analyzer Program (ETAP) application software. It was seen that the two results got were related. The general net power gotten was (129.741 MW, 83.818 MVAr) applying the Fast Decoupled-Newton-Raphson load flow technique in MATLAB programming environment after the addition of receptive power through the means of the capacitor bank to the affected nodes. The total net power that is real and reactive got employing ETAP programming were (125.765 MW, 92.782 MVAr). The overall line losses were enhanced by 0.246 reductions. That is from (4.75MW, 10.05MVAr) to (3.58MW, 7.57MVAr) of the entire real power losses.


Introduction
Generally, electrical power is transmitted from the sending end side to the receiving end substations. At the receiving side, the voltage is stepped down to a lesser value of the sending end value, most times accompanied by some technical and economic challenges. As a result of these challenges, electrical energy being the hub of modern technologies as well as the foundation of industrialization, has driven every nation to improve electrical power generation as well as enhancing the power transmission and distribution systems in order to make it efficient and meet-up with the growing power demand of the respective nations, thus massive upgrading. Despite the perceived upgrade to enhance the power wheeling capacity of the transmission line and its ancillary parts, low voltages are still felt in some areas and this has prompted the installation of distribution generators without adequate arrangement, accordingly causing the over-loading of the different feeders and some other issues. Thus, a few zones are under-used whereas certain transformers are over stacked. In this study, the combined Fast Decoupled -Newton Raphson method was utilized to study the Port Harcourt Zone 4 power network. The Port Harcourt Z4 substation includes 4-distribution transformers using a complete installed capacity/limit of approximately 164.9MVA with nine (9) serving feeders. However, the authority of the substation has attributed blame on poor power situation on ASTESJ ISSN: 2415-6698 The hypothesis is reasonable for dispersed processing of load flow problem. The studies can be performed in a very shorter period if calculations for various subsystems of an incorporated network are done simultaneously utilizing a few workstations. However, when distributed processing preparation is carried out continuously in actual time, information should be gathered from nearby points and only a generally little information base is to be updated locally at normal interims. The Reduction of transmission line information over long significant distances to the central workstation can be achieved [8,10].

Load Flow Analysis using ETAP Software Simulation
This product is a computer-based model that simulates a continuous real-time stable state power system process. It facilitates the calculation of system line losses, reactive and real power flow, and node voltage profiles [9][10][11]. ETAP software is used for designing and coordinating of relays in the distribution network [10,12]. To carry out a power flow study to analyze the performance of the electrical system during abnormal and normal working conditions, and giving the proof expected to upgrade or optimize circuit uses, create functional voltage profiles; identifies transformer tap settings, minimize MVAr, and MV losses. Besides, to help in developing equipment specification guidelines.

Analysis of the Load Flow Problem in Power System
Planning Studies According to [7,11,13], load flow or power flow is the movement of active and reactive power from generators to different load points of the system. This examination is an exceptionally basic instrument utilized by power system engineers for planning and deciding the steady-state activity of a power network. In [10,12,14] power system is presented as an electric circuit that comprises of generators, transformers, circuit breakers, lines, etc. to decide the different hub voltages, phase angles, dynamic and responsive power flows through the system [15]. The analysts or researchers in [14,16,17] said that the primary proof acquired from the load/power flow consists of voltage and phase angles at a given node number. The load flow problem equations are nonlinear and this requires an iterative technique to solve it.

Power Perturbation Technique for Study of Power Network Load Flow
Perturbation technique theory is a new power flow technique which goal is to try to improve the convergence rate by linearizing the load flow equation where more attention is given to the voltage values (V) and the phase angle (δ) in every recalculation step. This procedure is quicker, and it gives more precise results than the regular or normal Gauss-Seidal power flow computation method, having been tested on the IEEE 118-node, 30-node, 14-node, and 5-node systems [2,18,19]. Reduction of the computational challenges by decreasing the total equations, approximating the Jacobian matrix structure, and other different factors are the opinions of most developed existing algorithms.

Methodology of the Research
Among various power flow solution algorithms, power flow models depend more on the Newton-Raphson (NR) based algorithm. Various decoupled polar alternatives of the NR methodology have been tried for minimizing the storage capacity limit and calculation period associated with the load flow remedy. In this study, the tools needed for the study are line parameters, node information, MATLAB applications programming, a PC; MATLAB programming codes utilizing a Fast-decoupled load flow calculations approach. ETAP programming will be additionally utilized for examination, comparism, and result justification. The FDLF technique was utilized for the study being considered. The system was modeled and demonstrated using the Electrical Transient Analyzer Program (ETAP programming) for simulation purposes employing fast decoupled. The universal purpose NR method of power flow studies was used for solving initial values.

Power Flow Equations
Sample of Node of a Power System network is as shown in Figure 1  The capacitor, in this case, injects a specified power in the system, while the voltage is controlled. (1) Using Kirchhoff current law (kcl) from Figure 1(b) we obtain Ii = (yi0 + yi1 + yi2 +…yin) Vi -yi1 V1 -yi2 V2 -… -yinVn. (2) Substituting Ii from the above equation into 3 Equation 3 can be written as in Equation 5 And the polar representation The complex power at node I is given as Separating real and imaginary parts ( ) Equations 7 and 8 constitute a set of non-linear algebraic equations in terms of independent variables, voltage values in per unit, and phase angle in radians. Using the Taylor series approach in expanding Equations 7 and 8 with the initial estimate and neglecting all higher-order terms results in a set of equations as shown below: The diagonal and off-diagonal elements of J1 are The diagonal and off-diagonal of J4 are; ( )  The terms Pi (k) and Qi (k) in Equations 9 are the differences between the computed and scheduled quantities, called power mismatch or residual, expressed as in Equations 14 and 15.
The new estimates for node voltage are (17)

Formulation of Power Flow Equations
A complex unified system with several nodes interconnected through transmission lines can be described as a power system. The load flow issue includes the calculation of voltage values and phase angle at every node, real and reactive power flow in all subsystems in the network under predictable or consistent state condition. Formulation and calculation of node admittance matrix is the starting point in the solution of power flow which is formed from transmission line parameters. In this manner, a contextual analysis is taking from Port Harcourt Town (zone 4) on the 33KV Distribution System of active feeders with 165MVA as a complete installed limit of the Transformers. The breakdown of the distribution transformers added to the incoming substation is as shown in Table 1 while Figure 2 depicts the 33KV Distribution System of the substations used as the case study.

Line Parameters for Port Harcourt Town, 33KV Distribution Network
Consider the line Parameters of the 33KV Distribution System, the conductors are evenly sorted and are overhead lines. The spacing between FACT as in the case of the Nigerian 33KV distribution system is 88cm. (that is, D = 0.88m) and. Figure 3 is the phi representation of per phase Line. We compute the complex power demanded at the load side bearing in mind the percentage loading. Note that, the loading capacity is due to available power Per Unit Load Parameter at Each Feeder for Port Harcourt Town, 33KV Distribution Network UST Feeder (Node 1-2) for Port Harcourt Town, 33KV Distribution Network SD = 30MVA, Percentage loading =60%, Pf= cos = 0.8, Rf = sin = 0.6.
On 100 MVA base, the per unit values of the complex power demand, we have ) .
The complex power received from the grid network to the 33KV node is 165MVA at a power factor of 0.8, we have Srec = jB/2 jB/2 Z= r +jx (130+j100.8) MVA. Where 130MW is the real power and 100.8MVar is the reactive power demanded on the 33kV node.
The summary of the 33kV Distribution node network data under consideration are shown in Tables 2 and 3. It is much better to compute all other parameters using the per unit values. To realize its real values we multiply the per unit values by the base values assumed at the beginning.

Mathematical Model of Fast Decoupled Power Flow Method
In a power network, the net infused active and receptive power at an ith node are mathematically represented by: (26) where Vi and Vj, represent voltage levels at the ith and jth nodes separately; Gij+ jBij is the ijth component of the Y-node; and "n" the entire number of nodes. The linearized power flow Eqns. (26) and (27) We compute the complex power demanded at the load side bearing in mind the percentage loading. Note that, the loading capacity depends on the available power.
(29)  The suffix "i" represents the ith node, Q-shunts,i; and Pshunts,i are the reactive and real powers, because of lumped shunts at the ith node. It ought to be noticed that the order for the Jacobians   (33) Thus, by utilizing an abridged fast decoupled load flow technique, the voltage values and change in phase angle can be determined.

Fast Decoupled Power Flow for Radial Distribution System
In the Radial Distribution network, the massive R-X ratio constitutes problems in the convergence of the normal ordinary load flow calculation. Hence, for excellent convergence, some modifications in the load flow methods are applied. The model can be represented by a radial interconnection of networks of the fundamental structure depicted in Figure 4. The dotted lines from the co-generator, shunt capacitor, and load to the ground are to demonstrate that these components might be interconnected in floated delta-design since a given branch might be two-phase or single-phase as situation demands.
One of the key ideas driving our techniques is that the current and voltage at one node can be expressed as an element of the current and voltage on the other node. If we let the equation be: The branch update function [I] is given beneath as: Where Wk is a vector containing the real and imaginary parts of the voltages and current flows at node k. The factor gk is controlled by the sub-laterals joined at node k like as the models for distribution lines, switches, loads, transformers, co-generators, and shunt capacitors. From Vk we can calculate the flows as a result of the loads, co-generators shunt and, capacitors, given Ik + 1 and the currents Ij taken into sub-laterals branching out from node k, applying KCL at node k to the calculate current [I] given by Eq. 36: Where Ak is the set of nodes adjacent to node k on sub-laterals. (39) So that by applying this formulation or definition we get the converged values easily and faster than the other normal techniques.

a. Formulation for Fast Decoupled Power Flow Method
The stepwise calculation procedure to solve the power flow issue by applying the Fast Decoupled Power Flow Method is as given in [3] and as summarized thus: Creation of the node admittance Y as indicated by the lines given by the IEEE standard node test system, identification of all kinds of nodes according to the IEEE standard and setting all node initial value of u p. 0 1 , Creation of the matrices B1 and B11 Where B1 and B11 are the imaginary part of the node admittance matrix of Ynode, Calculating the value P and Q mismatches, Check the convergence status, Calculation of real and reactive power at every node, and checking if MVAr of generator nodes are within the cutoff points, Update of the voltage magnitude V and the voltage angle  at every node. The current can then be determined from the calculated Y node using Eqn. (36) Line compensators are introduced in the network because of line losses and other line limitations to reduce losses. In the system under study, shunt capacitors are applied over an inductive load to give part of the reactive VARs required by the load to keep the voltage within the anticipated range. They can also be applied through capacitive loads and in light load situations to consume some amount of the main (leading) VARs for accomplishing voltage regulation. Capacitors are connected either directly to a node or through the tertiary winding of the primary transformer and are installed along the line as to limit mishaps in form of losses, voltage drop, also improves loading power factor. The shunt capacitor banks introduce reactive power into the system and compensate for line losses. To avoid much harmonic in line FACTS devices suffice.
Implementation of the Fast-Decoupled Load Flow in MATLAB. The program is implemented in the MATLAB programming language and is run in MATLAB Software development environment. The software modules files (M-files) results are as presented in appendices A1 to A3:

Results and Analysis
The results obtained are shown in Figs 5, 6, A1 to A3, and Tables 4 to 9 using the Fast decoupled-N-R procedures inserted in ETAP programming. The outcomes of the studied power flow and its parameters determined utilizing MATLAB program are represented in Figs Table 4.  Table 4 shows the summary of reactive power injected into the feeders to improve the voltage profile and the net power received, using ETAP.
Injection of Reactive Power into the Feeder (via Capacitor Bank) using MATLAB In the new input node data, we have injected reactive power via the capacitor bank. The results are as in Table 5. The values of the reactive power injected were as follows: Node-2 @ 20 MVar, Node-3 @ 30MVar, Node-5 @ 20MVar and Node-7 @ 22MVar. (Check along QGi) From the voltage profile, the network required more power injection and some tap setting. In Table 7, M means the bus voltage is marginal while C mean critical.

Discussion
Power flow is a significant and fundamental device for the study of any power system and also applied in the operation, arranging for future development/upgrade of power systems. It will help in deciding the best mode of operation of the existing networks. The results of the voltage values in nodes, 2, 3, 5, and 7 were not within the acceptable range because its node voltage was critical while node 6 is marginal and is within the required range. The steady-state MW and MVAr delivered to the slack node is not equal to the sum of the load (Power) demanded at each node. The transmitted/injected power and the power expected/net power at the load point were not equal, due to power losses on each feeder.