Ieee_conf_feb2018.docx

Power Loss Minimization in a Radial Distribution System with Distributed Generation Afroz Alam, Abhishek Gupta, Parth Bindal, Aiman Siddiqui, Mohammad Zaid Department of Electrical Engineering Z.H.C.E.T., Aligarh Muslim University Aligarh-202002, India [email protected]

Abstract- Optimal siting and sizing of distributed generation (DG) in a distribution system is a key for power loss minimization and voltage profile improvement of the system. In this paper, a mixedinteger nonlinear programming (MINLP) based optimization technique has been used to find the optimal locations and sizes of DGs to be placed in a distribution system for the reduction of power loss and improvement in voltage profile. The MINLP technique considered in this paper, utilizes the sequential quadratic programming (SQP) through ‘fmincon’ function available in the MATLAB optimization toolbox. The MINLP technique has been applied for the optimal placement of DGs in IEEE 33-bus and 69-bus distribution systems. For the purpose of load flow, a well-known technique, which comprises bus-injection to branch-current [BIBC] and branch-current to bus-voltage [BCBV] matrices, has been used. After the analysis of the results obtained for the two test systems, it can be concluded that MINLP is an effective approach for minimizing the distribution system losses and improving the voltage profile by optimally placing the DGs of suitable sizes at appropriate locations.

Keywords— Distribution system; generation; Voltage profile; MINLP; SQP

Distributed

I.INTRODUCTION Power distribution system suffers with a huge amount of power losses which needs to be minimized using various techniques. Distributed generation (DG) is one such solution, strategic placement of which can greatly improve the voltage profile and result in adequate loss reduction. Intense researches have been carried out in

recent years to explore various other aspects of power system like reliability, stability and protection. The term DG refers to small scale electric power generation (typically 1 kW–50 MW). Placement of DGs in distribution networks can reduce many problems to a great extent like power loss reduction, voltage profile improvement, on-peak operation cost minimization, increased security and reliability, reduced greenhouse gas emissions, grid reinforcement, relieved transmission and distribution congestion etc. DGs are mainly connected near the customer load to decrease the distribution losses and to improve voltage profile. In [4], it was shown that the region-wise placement of DGs produces better loss reduction in comparison to the other cases when time varying loads are considered. In [1], the authors have used symbiotic organisms search (SOS) algorithm with the objective to reduce active power loss only i.e. power losses associated with active component of current by optimal sizing and placement of DGs. A particle swarm optimization (PSO) based technique has been used in [2] to solve the same DG placement problem of [1] with additional consideration of loss sensitivity factor. The bus that has high sensitivity is used for DG placement. Improvement in bus voltage profile and branch currents using network reconfiguration is also an alternative as proposed by authors in [3]. Installing capacitor banks at load end delivers local reactive power support which improves voltage profile. In [7], authors have used feeder reconfiguration for the purpose of optimizing power losses with primary objective of determining appropriate sectionalizing switches. A loss minimum reconfiguration method based on Tabu search for open loop radial distribution system is proposed in [5]. The algorithm can take into reverse power flow caused by DG placement. This technique doesn’t require excess computation but to

improve the result and augmenting with a good convergence speed, simulated annealing can be used along with in form of a hybrid algorithm as used by author in [6]. Several techniques have been applied for optimal placement and sizing of DGs in distribution network such as analytical, numerical methods and heuristic methods. The DG placement problem is a complex combinatorial problem having nonlinear objective(s) as well as nonlinear constraints. In this paper, a mixedinteger nonlinear optimization (MINLP) technique has been used to find the optimal locations and sizes of DGs to be placed in the distribution system for the reduction of power loss and improvement in voltage profile. This paper uses a formulation, which takes advantages of the topological characteristics of distribution systems, and solves the distribution load flow directly. For the purpose of load flow, a well-known technique, which comprises of bus-injection to branch-current [BIBC] and branch-current to bus-voltage [BCBV] matrices, has been used. This technique has further been utilized in the formulation of the objective function which has been coded in MATLAB. The paper is organized as follows: The problem formulation is explained in Section II. Section III presents the load flow technique used for the two test distribution systems. The obtained results of the case studies are presented in Section IV and the final conclusions are drawn in Section V.

N = number of buses. 2) Feeder capacity limits : |𝐼𝑘 | ≤ 𝐼𝑘 𝑚𝑎𝑥 , k ∈ {1,2,3, … … , 𝑙} (3) Where, 𝐼𝑘 𝑚𝑎𝑥 = maximum current capacity of branch k. 3) DG injection limits : 0 ≤ 𝑃𝐷𝐺 ≤ 𝑃𝐷𝐺 𝑚𝑎𝑥 (4) 0 ≤ 𝑄𝐷𝐺 ≤ 𝑄𝐷𝐺 𝑚𝑎𝑥 (5) Where, 𝑃𝐷𝐺 , 𝑄𝐷𝐺 , 𝑃𝐷𝐺 𝑚𝑎𝑥 and 𝑄𝐷𝐺 𝑚𝑎𝑥 are the active DG power injection, reactive DG power injection, maximum allowable active DG power injection and maximum allowable reactive DG power injection, respectively.

III. LOAD FLOW TECHNIQUE In this paper, the load flow methodology is adopted from [teng] which is based on two derived matrices, the bus-injection to branch-current matrix (BIBC) and the branch-current to bus-voltage matrix (BCBV). For a distribution network, complex load Si can be expressed as, Si = (Pi + j Qi) = 𝐼𝑖𝑟 (𝑉𝑖𝑘 ) + j𝐼𝑖𝑖 (𝑉𝑖𝑘 ) , i=1,2, …..N

and the corresponding equivalent current injection at kth iteration of solution is given by, 𝐼𝑖𝑘 = (

II. PROBLEM FORMULATION The objective of power loss minimization in a radial distribution system with distributed generation can be expressed as [9] Minimize L = ∑𝑙𝐾=1(𝐼𝐾 )2 𝑅𝐾 Where, L = total power loss l = number of feeder sections/branches 𝐼𝑘 = current flow in branch k 𝑅𝑘 = Resistance of branch k.

(1)

𝑃𝑖 +𝑗𝑄𝑖 ∗ 𝑉𝑖

)

(5)

Where 𝑉𝑖𝑘 and 𝐼𝑖𝑘 are the bus voltage and equivalent current injection of bus i at the kth iteration, respectively. 𝐼𝑖𝑟 And 𝐼𝑖𝑖 are the real and imaginary parts of the equivalent current injection of bus i at the kth iteration, respectively. The power injections can be converted to the equivalent current injections by Eq. (5), and the branch currents can then be written as functions of equivalent current injections using Kirchhoff’s Current Law. The relationship between the bus current injections and branch currents can be expressed as

The objective function (Eq. (1)) is subjected to the following constraints. 1) Bus voltage limits : 𝑉𝑚𝑖𝑛,𝑖 ≤ 𝑉𝑖 ≤ 𝑉𝑚𝑎𝑥,𝑖 , i ∈ {1,2, … 𝑁} Where, 𝑉𝑖 = voltage at bus i. 𝑉𝑚𝑖𝑛,𝑖 = lower voltage limit at bus i. 𝑉𝑚𝑎𝑥,𝑖 = upper voltage limit at bus i.

(4)

(2)

[B] = [BIBC][I]

(6)

Where, [B] is a column vector with element Bj is the current in jth bus. [I] is a column vector with element Ii is injection at ith bus. [BIBC] is the bus-injection to branch-current matrix. The relationship between branch currents and bus voltages can be expressed as

Vj = Vi - BiZij (7) [∆𝑉] = [BCBV][B] (8) where, ∆V is a column vector , Vj= V1 – Vi : j= 1,……….,N i=2,……..,N BCBV is the branch-current to bus-voltage matrix.[B] is column vector where Bi is current in ith branch. Combining (7) and (9), the relationship between bus current injections and bus voltages can be expressed as [∆V] = [BCBV][BIBC][I] = [DLF][I] (9) 705

buses and 32 branches. The line data and load data of this system are given in [10]. It has total active and reactive loads of 3.72 MW and 2.3 MVAr, respectively. Without installation of DG, the real and reactive power losses are 210.998 kW and ?? kVAr, respectively.

Table 1: Results for 33- Bus system Optimal Power loss Power loss DG size (without DG) (with DG) (MW) (kW) (kW) 1.0536 210.998 72.951 1.0913 0.8018

The results obtained for the 33-Bus distribution system are shown in Table 1. From this table, it can be observed that the optimal locations of three DGs are at buses 13, 24 and 30, respectively. The corresponding optimal sizes of DGs are 0.8018 MW, 1.0913 MW and 1.0536 respectively. For this optimal sizes of DGs, placed at the optimal locations in the system, the power loss of the system is reduced to 72.951 kW. The total reduction in power loss is found to be 65.42%. The voltage profile of the system with and without the DG placement is shown in Fig. 2.

30 24 13

And the solution for distribution load flow can be obtained by solving (11) iteratively 𝐼𝑖𝑘 = 𝐼𝑖𝑟 (𝑉𝑖𝑘 ) + j𝐼𝑖𝑖 (𝑉𝑖𝑘 ) = ( [∆Vk+1] = [DLF][Ik] [Vk+1] = [V0]+[∆Vk+1]

𝑃𝑖 +𝑗𝑄𝑖 𝑉𝑖

)∗

For the purpose of optimal placement of DGs in the 33-Bus distribution system for minimizing the power loss, MINLP optimization technique has been used. The MINLP technique considered in this paper, utilizes the sequential quadratic programming (SQP) through ‘fmincon’ function available in the MATLAB optimization toolbox.

(10a) (10b) (10c)

For IEEE 69-Bus system For large network system, 69-Bus radial distribution Results for 33-Bus system for Optimal DG placement.

system consisting of 68 branches, the single line diagram of IEEE 69-Bus system is as shown in Fig. 3.

IV. CASE STUDIES IEEE 33-Bus system The single line diagram of IEEE 33-Bus radial distribution system is shown in Fig. 1. It consists of 33

Fig. 2 Voltage profile with and without DG placement in 33-Bus distribution system

The line data and load data are given in [10] with rated voltage of 12.66 kV. The 69-bus radial distribution system has total active and reactive loads of 3.80 MW and 2.69 MVAr, respectively with same voltage and base MVA rating. Without installation of DG, the total real power losses are 224.7 kW.

After the DG placement, the losses were reduced to 69.53 kW. The location and size of DG placed are tabulated along with comparison of power losses for both the cases. The total reduction in power loss is found to be 69.05%. The voltage profile before and after the DG placement is shown in Fig. 4.

V. CONCLUSION In this paper, an attempt is made to determine the optimal location and size of DG units in the radial distribution system with the help of fmincon optimization technique. ‘fmincon’ applies to most smooth objective functions with smooth constraints. Power loss reduction and voltage profile improvement are taken into main consideration while placing DG units. Proposed method is applied on both IEEE 33bus and IEEE 69-bus systems. Results of the work validate the effectiveness of this approach. Such methodic approach can easily be applied to distribution systems incorporating complexities like tie line/switches, addition of more buses or alternation in number of feeders. Such optimization technique results in a faster, more accurate solution to a

Fig.3 The schematic diagram of 69-Bus Distribution System

Optimal DG Location

Optimal DG size (MW)

12 25 53 61

0.4584 0.2543 0.3302 1.6866

Power Losses (before DG installation) (kW)

Power losses (After DG installation) (kW)

224.7

69.53

Results for 69-Bus system for Optimal DG placement. Fig.4 Voltage profile with and without DG placement in 69-Bus distribution system.

constrained minimization problem. The optimization technique would itself determine the optimal location and size of DG to be placed to minimize the power losses without the requirement of analysis of load flow results being done. Thus it will reduce the complexity and increase the efficiency of the work. Successive implementation of this technique leads to future work expansion and planning.

REFERENCE [1] M. P. Lalitha and P. S. Babu and B. Adivesh, ” SOS algorithm for DG placement for loss minimization considering reverse power flow in the distribution systems”, 2016 International Conference on Advanced Communication Control and Computing Technologies (ICACCCT), vol. , no., pp. 443-448, 2016. [2] Sarfaraz and A. Bansal and S. Singh, ” Optimal allocation and sizing of distributed generation for power loss reduction”, International Conference Workshop on Electronics Telecommunication Engineering