This paper introduces a novel method for sitting and sizing the grid connected distributed generator (DG) for installation in distribution system at any input load condition, which is based on two port transmission equations, named as modified transmission parameters (MTP) method by considering the loss minimization as a constraint. If properly organized, with the help of various transmission parameters optimal DG allocation with minimum transmission losses, contribution of DG as well as the main supply source to each load, type of DG required to handle the existing power flow scenario, and operating power factor at which DG should operate can be easily investigated. Apart from this the author has also investigated the worst location for DG installation and referred to it as Consecutive Bus. The method has been tested on two test distribution systems with varying sizes and intricacy and the results have been compared with the two established methods reported earlier. Relative study presented has shown that the proposed method leads existing methods in terms of its simplicity, computational time, and handling less number of variables.
It is universally acknowledged that distributed generator (DG) is perched to become a key element in our future energy generation. DGs are generally defined as the generating plants serving a customer on-site or providing support to a distribution network, connected to the grid at distribution-level voltages [
The proposed method has been tested on two test distribution systems (IEEE 16-Bus [
The rest of the paper is organized as follows. Section
Consider a system with
Thus,
The columns of ILF matrix correspond to the generator bus numbers and its rows correspond to the load bus numbers. Higher the value of this factor lower will be the loss occurred across the path between respective generator and the load bus to which it will feed the power. Thus this matrix can directly give the proportion of power which should be supplied by each source present in the system to individual load so as to accomplish the total demand with maximum efficiency.
By rearranging (
So,
Now premultiplying the above matrix by diagonal matrix
It will give the power consumed in load which can also be obtained by subtraction of total transmission power losses from the total power supplied by generators; thus, we can say
Thus we can use the term of transmission power losses given by (
From (
From the matrix given above the power contributed by the generators placed at any particular location can be obtained which is actually similar to the
Thus the desired contribution of the DG is the summation of terms of power contribution of DG to each load and the local load at that bus, which will give the required capacity of DG which should be installed at that location
The capacity which we obtain will be a complex quantity giving both real as well as reactive power capacity of the DG. The capacity of the DG to be installed can also be used for calculation of power factor as explained in the next section.
Operating power factor of the DG to be installed can be obtained by using the equation
DG can be classified into four major types [ Type I: DG capable of injecting active power only, for example, photovoltaic, fuel cells, and so forth. Type II: DG capable of injecting reactive power only, for example, synchronous compensators such as gas turbines. Type III: DG capable of injecting both active and reactive power, for example, DG units that are based on synchronous machines and so forth. Type IV: DG capable of injecting active power but consuming reactive power, for example, induction generators that are used in wind farms and so forth.
So, if practically we will analyze the information given in [
From the complex equation (
As per the proposed method the DG to be installed will be of the following types. if the value of reactive power will be zero, operating power factor will be unity. if value of active power will be zero, operating power factor will be zero. if value of reactive power will be positive, if value of reactive power will be negative,
The proposed method suggests the optimal DG location, optimal DG capacity as well as power factor thereafter predicting the type of DG which should be installed at that location to achieve minimum losses. But if practically this is not possible, then with the available DG unit we can interconnect any other DG of other type, so as to achieve the required DG output in terms of reactive power output, power factor, and so forth.
For finding the optimal location, optimal capacity at that location, operating power factor, and type of the DG to be installed, following algorithm should be followed. For the given test system without DG run the load flow and find out the voltage at each bus as well as calculate the total losses. Select next bus as a DG location and consider the remaining buses (except original generator sources and the load bus on which DG is installed) as load buses. Now run the load flow for the case with DG installed at new position and find out the voltage at each bus. By using equation ( Now select all the next buses individually as DG location and repeat the steps from 2 to 4. Rank the buses in ascending order as per the amount of losses encountered at that location. Consider the top ranking bus as the best location for DG installation. Then calculate the optimal capacity of DG to be installed at optimal location from ( By using the complex power capacity of DG obtained in the above step calculate the operating power factor of the DG as per ( Then from the values of active as well as reactive power capacities obtained in step (8) and the calculated operating power factor from step (9) suggest the type of DG which should be installed on the candidate location obtained in step (7).
Figure
Flowchart for obtaining optimal location, optimal size at that location, operating power factor, and type of the new DG to be installed in the existing system to minimize the losses by MTP method.
In this paper two test systems are summarized, namely, the IEEE 16-Bus Test Radial Distribution System [
Comparative analysis of three methods of loss calculations for 16-bus system.
Bus numbers | Calculated loss at different DG location | Bus numbers | Calculated real loss at different DG location | ||||
---|---|---|---|---|---|---|---|
Location of DG | MTP |
ELF |
IA |
Priority list of buses | MTP |
ELF |
IA |
W/O DG | 515.4 + 607.7 |
511.43 | 511.43 | Bus 9 | 163.4 | 164.01 | 166.31 |
Bus 4 | 350.1 + 418.2 |
450.33 | 450.7 | Bus 12 | 249 | 196.84 | 200.93 |
Bus 5 | 298.4 + 336.5 |
456.57 | 456.86 | Bus 11 | 264.6 | 270.99 | 283.55 |
Bus 6 | 359.5 + 427.9 |
450.21 | 450.44 | Bus 8 | 290.4 | 228.57 | 233.17 |
Bus 7 | 356.5 + 423.2 |
455.05 | 455.32 | Bus 5 | 298.4 | 456.57 | 456.86 |
Bus 8 | 290.4 + 380.6 |
228.57 | 233.17 | Bus 10 | 341.3 | 335.61 | 350.77 |
Bus 9 | 163.4 + 212.7 |
164.01 | 166.31 | Bus 4 | 350.1 | 450.33 | 450.7 |
Bus 10 | 341.3 + 418.9 |
335.61 | 350.77 | Bus 14 | 351.1 | 491.93 | 493.16 |
Bus 11 | 264.6 + 296.7 |
270.99 | 283.55 | Bus 7 | 356.5 | 455.05 | 455.32 |
Bus 12 | 249.0 + 304.3 |
196.84 | 200.93 | Bus 6 | 359.5 | 450.21 | 450.44 |
Bus 13 | 368.5 + 452.4 |
483.53 | 483.7 | Bus 13 | 368.5 | 483.53 | 483.7 |
Bus 14 | 351.1 + 429.0 |
491.93 | 493.16 | Bus 15 | 378.1 | 477.74 | 477.86 |
Bus 15 | 378.1 + 445.1 |
477.74 | 477.86 | Bus 16 | 379.8 | 478.01 | 478.13 |
Bus 16 | 379.8 + 458.6 |
478.01 | 478.13 | W/O DG | 515.4 | 511.43 | 511.43 |
Comparative analysis of three methods of loss calculations for 33-bus system.
Bus numbers | Calculated loss at different DG location | Bus numbers | Calculated loss at different DG location | ||||
---|---|---|---|---|---|---|---|
Location of DG | Modified transmission parameters method | ELF | IA | Priority list of buses as per losses | Modified transmission parameters method | ELF | IA |
W/O DG | 212.5 + 142 |
211.2 | 211 | Bus 6 | 68.1 + 50.1 |
68.2 | 74.89 |
Bus 2 | 197.4 + 133.9 |
197.4 | 198.79 | Bus 26 | 70.9 + 55.4 |
69.48 | 76.18 |
Bus 3 | 144.7 + 107.0 |
141.05 | 146.78 | Bus 7 | 73.1 + 59.2 |
69.89 | 76.81 |
Bus 4 | 126.0 + 97.5 |
122.15 | 129 | Bus 27 | 72.1 + 55.9 |
71.04 | 77.7 |
Bus 5 | 108.1 + 88.4 |
104.33 | 111.64 | Bus 29 | 72.2 + 55.7 |
72.93 | 78.18 |
Bus 6 | 68.1 + 50.1 |
68.2 | 74.89 | Bus 28 | 72.5 + 55.0 |
73.22 | 79.27 |
Bus 7 | 73.1 + 59.2 |
69.89 | 76.81 | Bus 30 | 72.8 + 58.4 |
73.64 | 78.52 |
Bus 8 | 80.6 + 59.0 |
82.91 | 89.33 | Bus 8 | 80.6 + 59.0 |
82.91 | 89.33 |
Bus 9 | 92.0 + 65.0 |
88.89 | 95.03 | Bus 31 | 81.4 + 60.3 |
83.9 | 89.12 |
Bus 10 | 98.4 + 68.2 |
93.15 | 98.85 | Bus 32 | 85.4 + 63.9 |
87.64 | 92.92 |
Bus 11 | 99.5 + 68.4 |
93.95 | 99.58 | Bus 9 | 92.0 + 65.0 |
88.89 | 95.03 |
Bus 12 | 101.6 + 68.9 |
95.68 | 101.2 | Bus 33 | 92.2 + 71.8 |
92.9 | 98.44 |
Bus 13 | 109.2 + 74.2 |
102.1 | 107.32 | Bus 10 | 98.4 + 68.2 |
93.15 | 98.85 |
Bus 14 | 111.6 + 76.8 |
104.39 | 109.54 | Bus 11 | 99.5 + 68.4 |
93.95 | 99.58 |
Bus 15 | 115.9 + 80.0 |
107.88 | 113.1 | Bus 12 | 101.6 + 68.9 |
95.68 | 101.2 |
Bus 16 | 120.8 + 82.8 |
112.31 | 117.64 | Bus 13 | 109.2 + 74.2 |
102.1 | 107.32 |
Bus 17 | 129.3 + 91.4 |
119.65 | 125.19 | Bus 5 | 108.1 + 88.4 |
104.33 | 111.64 |
Bus 18 | 133.3 + 93.5 |
123.73 | 129.39 | Bus 14 | 111.6 + 76.8 |
104.39 | 109.54 |
Bus 19 | 204.1 + 138.0 |
204.63 | 205.25 | Bus 15 | 115.9 + 80.0 |
107.88 | 113.1 |
Bus 20 | 206.8 + 138.4 |
207.9 | 208.08 | Bus 16 | 120.8 + 82.8 |
112.31 | 117.64 |
Bus 21 | 206.9 + 138.5 |
208.06 | 208.21 | Bus 17 | 129.3 + 91.4 |
119.65 | 125.19 |
Bus 22 | 207.3 + 138.7 |
208.5 | 208.63 | Bus 4 | 126.0 + 97.5 |
122.15 | 129 |
Bus 23 | 157.8 + 114.7 |
154.92 | 159.31 | Bus 18 | 133.3 + 93.5 |
123.73 | 129.39 |
Bus 24 | 164.0 + 116.6 |
161.67 | 164.81 | Bus 3 | 144.7 + 107.0 |
141.05 | 146.78 |
Bus 25 | 171.3 + 120.0 |
169.38 | 171.94 | Bus 23 | 157.8 + 114.7 |
154.92 | 159.31 |
Bus 26 | 70.9 + 55.4 |
69.48 | 76.18 | Bus 24 | 164.0 + 116.6 |
161.67 | 164.81 |
Bus 27 | 72.1 + 55.9 |
71.04 | 77.7 | Bus 25 | 171.3 + 120.0 |
169.38 | 171.94 |
Bus 28 | 72.5 + 55.0 |
73.22 | 79.27 | Bus 2 | 197.4 + 133.9 |
197.4 | 198.79 |
Bus 29 | 72.2 + 55.7 |
72.93 | 78.18 | Bus 19 | 204.1 + 138.0 |
204.63 | 205.25 |
Bus 30 | 72.8 + 58.4 |
73.64 | 78.52 | Bus 20 | 206.8 + 138.4 |
207.9 | 208.08 |
Bus 31 | 81.4 + 60.3 |
83.9 | 89.12 | Bus 21 | 206.9 + 138.5 |
208.06 | 208.21 |
Bus 32 | 85.4 + 63.9 |
87.64 | 92.92 | Bus 22 | 207.3 + 138.7 |
208.5 | 208.63 |
Bus 33 | 92.2 + 71.8 |
92.9 | 98.44 | W/O DG | 212.5 + 142 |
211.2 | 211 |
Comparative representation of loss calculation by three methods for 16-bus system.
Comparative table gives total losses calculated by MTP method, but comparison of only real losses is made against available results of, other two methods.
Figures
Active power contribution by each source as well as DG in 16-bus system to achieve minimum losses.
Reactive power contribution by each source as well as DG in 16-bus system to achieve minimum losses.
Comparative representation of loss calculation by three methods for 33-bus system.
For obtaining the optimal capacity, operating power factor, and type of the DG to be installed we can refer to Figures
Summarized results of both systems.
Test systems | Methods | Optimal location | Optimal size (MVA) | Operating power factor | Type | Base active loss, kw (W/O DG) | Reduced active loss (kw) |
---|---|---|---|---|---|---|---|
16-bus system | MTP | 9 | 13.634 | 0.88 | Type III | 515.4 | 190.4 |
IA | 9 | 13.0877 | 0.98 | Type I | 511.43 | 164.02 | |
ELF | 9 | 13.1551 | 0.98 | Type I | 511.43 | 164.01 | |
| |||||||
33-bus system | MTP | 6 | 3.2552 | 0.81 | Type III | 212.5 | 69 |
IA | 6 | 3.0247 | 0.85 | Type I | 211.2 | 68.28 | |
ELF | 6 | 3.1034 | 0.85 | Type I | 211.2 | 68.2 |
Active power Contribution by each source as well as DG in 33-bus system to achieve minimum losses.
Reactive power contribution by each source as well as DG in 33-bus system to achieve minimum losses.
Figures
In this paper in 16-bus system with a total load of 29.3 MVA and three substations handling approximately 10 MVA load each, buses number 4, 8, and 13 are the Consecutive Buses where the sizes of the DGs required are 14.375 MVA, 15.542 MVA, and 12.214 MVA each whereas in 33-bus system with a total load of 4.3566 MVA, bus number 2 is the Consecutive Bus at which the size required for the of DG is 4.6496 MVA. So here we can conclude that the Consecutive Bus may be considered as the worst location for DG installation.
This paper presents a novel method, that is, modified transmission parameters method of extracting the two port transmission equations for finding the optimal location, optimal size of that location, operating power factor, and the type of the DG to be installed in a primary distribution system to minimize the total losses of the system. The prominent feature of this method lies in its simplicity and ease of calculations as well as preciseness in achieving results. It avoids the time consuming and cumbersome iterative approach for handling the undemanding problem of designing the new DG to be installed in radial distribution system. Validity of the proposed method for designing DG to install in distribution system is tested and verified on two test distribution systems with varying sizes and complexity using already published Improved Analytical method and Exhaustive Load Flow solutions. Results show that locations, sizes, operating power factor, and type of distributed generators are decisive factors in minimizing total losses in the system and properly placed; pertinently chosen distributed generators can reduce losses appreciably. In this paper the worst location for DG allocation has been also located and referred as Consecutive Bus.