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In the current electricity paradigm, the rapid elevation of demands in industrial sector and the process of restructuring are the main causes for the overuse of transmission systems. Hence, the evolution of novel technology is the ultimate need to avoid the damages in the available transmission systems. An appreciable volume of renewable energy sources is used to produce electric power, after the implementation of deregulation in power system. Even though, they are intended to improve the reliability of power system, the unpredictable outages of generators or transmission lines, an impulsive increase in demand and the sudden failures of vital equipment cause transmission congestion in one or some transmission lines. Generation rescheduling and load shedding can be used to alleviate congestion, but some cases require quite few improved methods. With the extensive application of Distributed Generation (DG), congestion management is also performed by the optimal placement of DGs. Therefore, this research employs a Line Flow Sensitivity Factor (LFSF) and Particle Swarm Optimization (PSO) for the determination of optimal location and size of multiple DG units, respectively. This proposed problem is formulated to minimize the total system losses and real power flow performance index. This approach is experimented in modified IEEE-30 bus test system. The results of N-1 contingency analysis with DG units prove the competence of this proposed approach, since the total numbers of congested lines get reduced from 15 to 2. Hence, the results show that the proposed approach is robust and simple in alleviating transmission congestion by the optimal placement and sizing of multiple DG units.

Transmission line congestion is one among the major key issues in deregulated power industry. Congestion occurs, when one or more constraints of the system get violated. These violations of restrictions can either be beyond the thermal or voltage limits or some indicated limits. In deregulated power systems, congestion can also occur due to commercial reasons and it has become a major concern. Fast, transparent and effective tools are necessary for congestion management. A comprehensive survey of congestion management methods based on their models is categorized and it is reported [

A congestion management method ensuring the voltage security is proposed for congestion management [

A congestion management strategy is proposed for combined operation of hydro and thermal generation companies [

An analytical approach is developed to address the optimal DG placement problem in distribution networks with different topologies [

Even though, the major conventional methods are listed in the above chapter as introduction and literature survey, this kind of approach is presented in only one literature [

This organization of this paper is given as follows. In chapter 2, the problem formulation, calculation of Performance Index (PI), contingency selection and optimal location of DGs are elaborated. A brief description about PSO is given in chapter 3. In chapter 4, the detailed simulation results and discussions are presented. Chapter 5 illustrates some of the conclusions of this work.

Allotment of DGs in order to relieve congestion using N-1 contingency measure certainly leaves some vital solutions against system security danger. A suitable location is identified for the allocation of DG, which could offer an enhanced performance almost in all the circumstances. The process of contingency ranking is performed by using the limits of voltages and power flow performance indices.

It is very obvious that various limit violations occur in power system frequently. But, for maintaining the system security, the most severe violations are monitored and evaluated promptly. The magnitude and impact of severity of these vigorous problems should be precisely assessed for enforcing the appropriate corrective measures in order to alleviate this danger. This process of assessment is known as contingency selection. Therefore, contingency analysis is performed in order to evaluate the impact of severe contingencies and to alert the system operator to take a necessary step against this critical contingencies. The violations in transmission line thermal limit, transformer capacity and poor voltages at system buses are listed as common limit violations. The common formula for real power flow performance index is given as Equation (1).

Since a variety of sound failures occurs during the operating period of power system and it creates a contingency group, which possibly guides to congestion or limit violations on some parameters. The normal state of power system can easily be recovered, if these dangerous contingencies are promptly acknowledged with comprehensive assessment and adaptation of appropriate corrective actions. The contingency selection is a way of categorizing significant contingencies and they are ranked based on the real power flow performance index values.

The sensitivity on the congested line with respect to power flow is different for all buses in the system. A Line Flow Sensitivity Factor (LFSF) with respect to active and reactive power is calculated for the overloaded lines by considering the change in power flow in a transmission line “k”, connected between the buses “i” and “j”. It can be written as,

Equation (8) can be rewritten as,

By neglecting P-V coupling, Equation (9) can be written as,

Then, this research effort has calculated the values of LFSFs for all the load buses for all contingencies of the most critical outage with the help of above equations. The calculated LFSF values are ranked. The load buses, which have larger negative LFSF values, are selected for DGs allocation, since they are the most influential on the congested line. Hence, this proposed sensitivity factor is fairly fast enough in calculating all the values of LFSFs. Now, the optimal location for the placement of DG unit is achieved. Hence, the effort is now focused towards the computation of optimal size of DG at these selected locations.

The optimal sizes of the DGs are determined from PSO. The objectives used in this PSO based optimization technique are to determine the optimal size of the DG units by minimizing the real power losses and the real power performance index. The objective function is defined as,

Subjected to,

The voltage magnitude and angle must be kept within standard limits at each bus

Thermal limit of transmission lines for the network must not be exceeded

Particle Swarm Optimization is one of the famous stochastic optimization techniques based on population and it is developed by Kennedy and Eberhart [

The locations and capacities of multiple DGs are determined by LFSF and PSO algorithm, respectively. The procedural steps involved in this research, which are listed in above steps, are illustrated in flowchart and is given in

The performance of PSO greatly depends on three parameters such as, cognitive parameter (C_{1}) and social parameter (C_{2}) and weight factors W_{min} and W_{max}. The balance among these factors determines the balance between local and global searching capability. The fitness framed in this research is addition of two components namely summation of total real power losses of the system and summation of real power performance index values of limit violated cases. These two objectives used in this optimization are considered with appropriate weights. The weight value assumed for first objective i.e. minimization of real power losses is 100 and for second objective i.e. minimization of real power performance index is 10. Hence, the proposed problem with different particle sizes is solved using PSO. The selected parameters are tabulated in

Social Factor C_{1} | Cognitive Factor C_{2} | Minimum Inertia Weight Factor W_{min} | Maximum Inertia Weight Factor W_{max} | Number of Particles | Weight for first objective W_{1} | Weight for second objective W_{2} |
---|---|---|---|---|---|---|

2 | 2 | 0.4 | 0.9 | 40 | 100 | 10 |

The simulation tests are carried out in modified IEEE 30 bus system to prove the robustness of this proposed ideology.

Initially, Newton Raphson load flow analysis is performed to determine whether the transmission line limit is violated or not. If there is a limit violation, it indicates line congestion. From the results of base case load flow analysis in modified IEEE 30 bus system, it is found that there is no congestion in all the transmission lines. Subsequently, N-1 contingency analysis is performed in order to find out the critical outage cases and the results are presented in

The PI values are computed as defined by Equation (1) for all the generators and line outage cases in order to prepare the critical contingency ranking in the system. All the calculated PI values are arranged in descending order and the top nine most critical outage cases along with their PI values are presented in

The congested lines due to outage of most critical case are 1 - 3, 3 - 4 and 4 - 6 with 48.10%, 39.01% and 25.37% violation, respectively. The usual practice used to relieve this transmission congestion is performing

Sl. No. | Outage of line/Generator | Congested lines | Limit (MVA) | Line flow (MVA) | % Violation |
---|---|---|---|---|---|

1 | 1 - 2 | 1 - 3 | 130 | 192.53 | 48.10 |

3 - 4 | 130 | 180.71 | 39.01 | ||

4 - 6 | 90 | 112.83 | 25.37 | ||

2 | 1 - 3 | 1 - 2 | 130 | 182.38 | 40.29 |

2 - 6 | 65 | 66.74 | 2.68 | ||

3 | 3 - 4 | 1 - 2 | 130 | 178.63 | 37.41 |

2 - 6 | 65 | 65.81 | 1.25 | ||

4 | 2 - 5 | 2 - 6 | 65 | 76.90 | 18.31 |

5 - 7 | 70 | 75.79 | 8.27 | ||

5 | 4 - 6 | 1 - 2 | 130 | 134.06 | 3.12 |

2 - 6 | 65 | 71.73 | 10.35 | ||

6 | 10 - 20 | 15 - 18 | 16 | 16.31 | 1.94 |

7 | 2 | 1 - 2 | 130 | 162.01 | 24.62 |

8 | 5 | 1 - 2 | 130 | 136.74 | 5.18 |

9 | 8 | 1 - 2 | 130 | 135.31 | 4.08 |

Sl. No. | Outage of line/Generator | Total number of congested lines | PI |
---|---|---|---|

1 | 1 - 2 | 3 | 11.169 |

2 | 2 - 5 | 2 | 5.077 |

3 | 1 - 3 | 2 | 4.843 |

4 | 3 - 4 | 2 | 4.7 |

5 | 4 - 6 | 2 | 4.438 |

6 | 2 | 1 | 3.042 |

7 | 5 | 1 | 2.168 |

8 | 8 | 1 | 2.123 |

9 | 10 - 20 | 1 | 1.040 |

Sl. No. | Line 1 - 3 | Line 3 - 4 | Line 4 - 6 | |||
---|---|---|---|---|---|---|

Bus No. | LFSF | Bus No. | LFSF | Bus No. | LFSF | |

1 | 22 | −0.3698 | 22 | −0.1817 | 23 | −0.3965 |

2 | 23 | −0.3120 | 23 | −0.1486 | 22 | −0.3689 |

3 | 9 | −0.3052 | 7 | −0.1185 | 29 | −0.2428 |

4 | 7 | −0.2746 | 15 | −0.1035 | 19 | −0.2393 |

5 | 3 | −0.2720 | 21 | −0.0918 | 21 | −0.2392 |

Sl. No. | Bus No. | Optimal DG capacity in MW using PSO |
---|---|---|

1 | 22 | 36.7206 |

2 | 23 | 17.7379 |

rescheduling of generators. But in this work, the DGs are placed at the suitable locations of the load buses as corrective action for relieving congestion. To find the suitable location of DGs, LFSF (explained in Section 3.2) values are calculated for each of the overloaded lines for the most critical contingency and the top five preferred locations for each of the overloaded lines are given in

It can be observed that buses 22 and 23 have the highest negative values and they are selected as most suitable locations for the placement of DGs with respect to the overloaded lines 1 - 3, 3 - 4 and 4 - 6, respectively. Then, the optimal sizes of DGs are determined from PSO algorithm and the results are presented in

From

It is worthy to note that the total numbers of congested lines during various contingency cases get reduced from 15 to 2 by the placement of the DG units at their suitable locations. The congested lines due to N-1 contingency cases are almost alleviated by the optimal placement of multiple DG units except line 5 - 7 and 15 - 18 due to outage of line 2 - 5 and 10 - 20, respectively. Even though the congestion in these lines is not completely eliminated, the level of congestion in these lines is getting reduced from 8.27% and 1.94% to 7.77% and 1.81% for outage of line 2 - 5 and 10 - 20, respectively. The results of contingency analysis without and with the DG units are presented in

The comparison of results, with and without the multiple DG units are summarized and presented in

Sl. No. | Outage of line/Generator | Congested lines | Limit (MVA) | Line flow without DG units (MVA) | Line flow with DG units (MVA) | % Violation |
---|---|---|---|---|---|---|

1 | 1-2 | 1 - 3 | 130 | 192.53 | 125.36 | Alleviated |

3 - 4 | 130 | 180.71 | 118.73 | Alleviated | ||

4 - 6 | 90 | 112.83 | 75.39 | Alleviated | ||

2 | 1-3 | 1 - 2 | 130 | 182.38 | 120.69 | Alleviated |

2 - 6 | 65 | 66.74 | 42.61 | Alleviated | ||

3 | 3-4 | 1 - 2 | 130 | 178.63 | 118.05 | Alleviated |

2 - 6 | 65 | 65.81 | 41.72 | Alleviated | ||

4 | 2-5 | 2 - 6 | 65 | 76.90 | 56.54 | Alleviated |

5 - 7 | 70 | 75.79 | 75.44 | 7.77 | ||

5 | 4-6 | 1 - 2 | 130 | 134.06 | 90.86 | Alleviated |

2 - 6 | 65 | 71.73 | 46.05 | Alleviated | ||

6 | 10-20 | 15 - 18 | 16 | 16.31 | 16.29 | 1.81 |

7 | 2 | 1 - 2 | 130 | 162.01 | 122.993 | Alleviated |

8 | 5 | 1 - 2 | 130 | 136.74 | 98.129 | Alleviated |

9 | 8 | 1 - 2 | 130 | 135.31 | 96.525 | Alleviated |

Cases Factors | Before DG placement | After DG placement using PSO | Reduction | % Reduction |
---|---|---|---|---|

Base case P_{loss} (MW) | 9.482 | 5.914 | 3.568 | 37.63 |

Base case Q_{loss} (MVAR) | −9.897 | −26.354 | 16.457 | 166.28 |

Total Number of congested lines during various contingencies | 15 | 2 | 13 | 86.66 |

PI value for the outage of line 2 - 5 | 5.077 | 2.389 | 2.688 | 52.94 |

PI value for the outage of line 10 - 20 | 1.040 | 1.037 | 0.003 | 0.29 |

The placement of DG units in identified optimal locations results a notable reductions in real, reactive power losses and total number of congested lines with a percentage of 37.63%, 166.28%, 86.66%, respectively. The real power performance index values for outage of line 2 - 5 and line 10 - 20 get reduced with a percentage of 52.94% and 0.29%, respectively.

The reduction in real power losses after DG placement is shown in

To validate the sturdiness of this proposed approach in reaching the optimal or near optimal solution, 25 independent and continuous runs are performed with the same level of maximum iteration, i.e., 50 iterations with two different particle sizes i.e. 20 and 40. The results are compared with the statistical investigation and they are given in

The comparative plot between total fitness value and number of run with 20 and 40 particles is shown in

Congestion in transmission network is effectively relieved by the optimal placement and sizing of multiple DG units. It is obvious that inappropriate size and incorrect location of DG units induce higher power losses and

Sl. No. | Number of Particles | Total Fitness Value | Calculation Time in (Hours) | |||
---|---|---|---|---|---|---|

Best | Worst | Mean | Standard Deviation | |||

1 | 20 | 621.5341 | 661.8594 | 632.7218 | 11.8301 | 4.67 |

2 | 40 | 621.1392 | 660.0684 | 627.7925 | 10.2189 | 8.92 |

horrible voltage troubles. Therefore, this research employs LFSF to determine the most favorable sites of DG units and PSO for choosing the best size of DGs. The objective of this investigation is minimization of real power losses and real power performance index. The pragmatism of the projected method is tested in modified IEEE 30 bus test system. The results of N-1 contingency analysis with DGs prove the competence of this proposed approach, since the total numbers of congested lines get reduced from 15 to 2. Even though, this approach claims for its simplicity, still there are 2 congested lines for some critical cases. To overcome this bottleneck, modern approaches like demand side management and FACTS devices may be added additionally along with this proposed method to relieve the congestion completely. This method of congestion relief by PSO demonstrates competent, sturdy and straightforward, since it has considered the minimization of performance index as objective. In order to prove the usefulness of this proposed approach, statistical study is also carried out and the results are given. Comparatively, this method of relieving congestion is superior, since it employs renewable energy sources, which help for the reduction of environmental pollution.

The authors of this manuscript express their heartfelt gratitude to the Management of Kamaraj College of Engineering & Technology, Thiagarajar College of Engineering and the authorities of Anna University Regional Campus Madurai for aiding the essential amenities to complete this research.

Karuppasamy Muthulakshmi,Rajamanickam Manickaraj Sasiraja,Velu Suresh Kumar, (2016) The Phenomenal Alleviation of Transmission Congestion by Optimally Placed Multiple Distributed Generators Using PSO. Circuits and Systems,07,1677-1688. doi: 10.4236/cs.2016.78145