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In a Power System, load is the most uncertain and extremely time varying unit. Hence it is important to determine the system’s supreme acceptable loadability limit called maximum loadability point to accommodate the sudden variation of load demand. Nowadays the enhancement of the maximum loadability point is essential to meet the rapid growth of load demand by improvising the system’s load utilization capacity. Flexible AC Transmission system devices (FACTS) with their speed and flexibility will play a key role in enhancing the controllability and power transfer capability of the system. Considering the theme of FACTS devices in the loadability limit enhancement, in this paper maximum loadability limit determination and its enhancement are prepared with the help of swarm intelligence based meta-heuristic Firefly Algorithm(FFA) by finding the optimal loading factor for each load and optimally placing the SVC (Shunt Compensation) and TCSC (Series Compensation) FACTS devices in the system. To illuminate the effectiveness of FACTS devices in the loadability enhancement, the line contingency scenario is also concerned in the study. The study of FACTS based maximum system load utilization acceptability point determination is demonstrated with the help of modified IEEE 30 bus, IEEE 57 Bus and IEEE 118 Bus test systems. The results of FACTS devices involvement in determining the maximum loading point enhance the load utilization point in normal state and also help to overcome the system violation in transmissionline contingency state. Also the firefly algorithm in determining the maximum loadability point provides better search capability with faster convergence rate compared to that of Particle swarm optimization (PSO) and Differential evolution algorithm.

In present days, the growing nations face the challenges of electrical power demand increasing in rocketing speed, mushrooming of ill-type load such as heaters, air conditioners and some type of motors, which have negative exponential load characteristics and sudden block out due to voltage collapse. The increasing power demand is not answered by expansion of power generating plant and transmission unit since it not only requires huge capital investment but also considers the socio-economic and environmental factors. The solution to the above problem is hidden in finding the answer of maximum loadabilty limit of the power system. The maximum loadability limit is the point where the system can able to accommodate the utmost total system loading value without violating system constraints such as voltage limit of the buses, real and reactive power limit of generator, transmission line power transfer limit. Since the control variables of the power system have a mixture of discrete and continuous variables, the maximum loadability limit determination problem has been formulated as a non- linear optimization problem. In the beginning stage of the maximum loadability point determination, mathematical iterative optimization techniques such as i) continuation power flow method (CPF); ii) sequential quadratic programming (SQP); iii) interior point method (IP); and iv) repetitive power flow solution have been utilized more. Most of the authors in their literature utilize the continuation power flow (CPF) technique proposed by Ajjarapu and Christy [

In early 2000, evolutionary/meta-heuristic computing techniques like Genetic Algorithm (GA), Particle Swarm Optimization (PSO) and Evolutionary Programming (EP) have emerged as very powerful general purpose solution tools for solving the complex power system problems. Basically, these meta-heuristics search techniques are capable of finding the optimum solution of a problem irrespective of the number of control variables and also effective in handling the mixture of continuous and discrete variables. Among the above mentioned meta-heuristic algorithm, the particle swarm optimization (PSO) technique [

The rise of load demand in the current electricity scenario may increase the stress of transmission system which in turn may lead to the chance of the transmission line outage. The Maximum loading point determination considering the above scenario is effectively handled with the inclusion of FACTS devices in the system. FACTS devices helps in controlling the real and reactive power flow of the transmission system and voltage support in the system [

In this paper, maximum loadability determination and its enhancement at normal and transmission line outage condition with the FACTS devices such as SVC and TCSC is experimented and the results are analyzed with the help of modified IEEE 30 Bus, IEEE 57 Bus and 118 Bus systems. Firefly Algorithm optimization tool is used to determine the maximum loading point by finding the optimal loading value of each load and also by finding the optimal placement and settings of TCSC and SVC in each Bus system without violating the system constraints.

Maximum loading value of the system is the boundary of the system load where all the system parameters such as Bus voltage, real and reactive power of the generator, power flow of the transmission line can be accommodated within their limits. The maximization of system load is achieved by optimizing the loading factor of each load. Hence the above is considered as an optimization problem and its mathematical problem formulation is described in below section

The main objective of our paper is to maximize the total real power load of the system without violating the system’s equality and inequality constraints such as power balance, voltage limit, generation real and reactive power limit and line flow limit. This can be mathematically formulated as below

where

^{th} bus in p.u,

^{th} bus in p.u.

Subject to the

1. Equality constraints of Power balance Equation

where

^{th} Generator Bus in p.u,

^{th} Load Bus in p.u,

^{th} Generator Bus in p.u,

^{th} Load Bus in p.u,

^{th} Bus in p.u,

^{th} Bus in p.u,

^{th} and j^{th} Bus in p.u,

^{th} and j^{th} Bus in p.u,

^{th} Bus in p.u,

^{th} Bus in p.u,

2. Inequality Constraints

where

^{th} transmission line in p.u,

^{th} Load,

FACTS devices have the flexible and rapid control capability of various system parameters in a power system network [

where

Firefly algorithm was developed by Xin-She Yang [

In the Equation (11) the second term gives the attractiveness of a firefly which varies with the light intensity/brightness seen by adjacent fireflies and the distance between themselves and _{0} = 0, it becomes a simple random walk. So, here the value of γ and β_{0} was selected by conducting trail and test me-

thod. The distance between any two fireflies i and j at

Third term is randomization with _{t} essentially control the randomness (or, to some extent, the diversity of solutions), we can tune this parameter during iterations so that it can vary with the iteration counter t. So a good way to express α_{t} is to use α_{t} = α_{0}δ_{t}, where δ_{t} is (0 < δ < 1) and δ is essentially a cooling factor. Here we use δ = 0.95 to 0.97 and α_{0} = 0.01 L where L is the scaling parameter depend on the problem. In this work, we use L as 10. Artificial diversification is also applied in the Firefly population to avoid premature convergence, which corresponds to a local optimum. In this work, random movement of firefly is used by simple mutation method like that of used in Genetic Algorithm. In this work, it is assumed that for a given firefly x, if the dimension O_{k} is selected, then the resulting dimension will be selected using the equation.

where

a_{k} and b_{k} are lower and upper bands of O_{k},

rand is a uniform random number chosen in the range of (0, 1).

Structure of Firefly Algorithm (FFA):

1. Initialize the objective function

2. Initialize a population of fireflies X (

3. The light absorption coefficient

4. While (t <= Max Generation)

5. For I = 1:n (all n fireflies)

6. For j = 1:i

7. Light Intensity

8. If (

9. Move firefly i towards j in all the dimensions as per the Equation (11)

10. Else

11. Move firefly i randomly by creating a new dimension as per the Equation (12)

12. End if

13. Evaluate newly created firefly Light Intensity and update the Light Intensity solutions

14. End for j

15. End for i

16. Rank the fireflies based on its Light Intensity

17. Extract the Local best firefly of each population

18. End While

19. Obtain the global best firefly from all the Local best firefly

Three standard IEEE Bus systems such as modified IEEE 30 Bus system, IEEE 57 Bus and IEEE 118 Bus system [

Strategy1: Determination of maximum loadability point using Firefly Algorithm and its result comparison with the other Meta-heuristic Algorithmic results.

Strategy2: FACTS devices Involvement in the Enhancement of maximum loadability point.

Strategy3: Maximum loadability point determination in Line Contingency.

The detailed study of these three strategies has been given below. The FFA Programs were developed and tested using the MATLAB 7.0 Software Packages with the support of MATPOWER simulation software package [

The total initial (Base case) real power load of 1.892 Per Unit,12.508 Per Unit and 42.42 Per Unit has been utilized in the modified IEEE-30 bus, IEEE-57 bus and IEEE-118 bus test system respectively. In this strategy, the maximum loading point is determined by finding the optimal incremental loading factor from each initial real power load using Firefly algorithm as mentioned in the section. Here the incremental load has been assumed to be at unity power factor. This strategic implementation result of modified IEEE-30 bus, IEEE-57 bus and IEEE- 118 bus test system have been recorded and emphasized in

In

To check the performance consistency of the FFA, higher order systems such as IEEE 57 Bus system having 42 loading factor and IEEE 118 Bus system having 99 loading factor has been used for implementation and the implemented results are recorded in

Algorithm | Maximum Loadability in p.u | Critical Voltage | Total Incremental System Load from Base Case in % | Optimal SVC Bus No. | Optimal TCSC Line | SVC in MW | in p.u |
---|---|---|---|---|---|---|---|

Base Case | 1.892 | 0.961 @ 8bus | - | - | - | - | |

DE [ | 2.6709 | Not Mentioned | 41.16807 | - | - | - | - |

DEPSO [ | 2.6974 | 0.9499 @ 8bus | 42.5687 | - | - | - | - |

FFA without FACTS | 2.7208 | 0.9501 @ 8bus | 43.8089 | - | - | - | - |

FFA with FACTS | 2.8461 | 0.9501 @ 8bus | 50.42957 | 1 | [1 3] | 14.0863 (Inductive Mode) | 0.073 (Capacitive Mode) |

Method | Worst | Mean | Best | Standard Deviation | No of Iteration |
---|---|---|---|---|---|

DE | 2.5813 | 2.6334 | 2.6709 | 0.0234 | 15 |

DE-PSO | 2.642 | 2.6759 | 2.6974 | 0.02149 | 12 |

FFA | 2.710249 | 2.7198 | 2.720865439 | 0.0031 | 15 |

compared with the DE and DEPSO algorithm results given in the literature [

In this strategy, the enhancement of system’s maximum load utilization is achieved by involving the FACTS devices such as TCSC and SVC united. The combined TCSC and SVC regulates the active and reactive power control and also the voltage magnitude control by means of shunt and series compensation. Hence the optimal placement and settings of FACTS devices such as TCSC and SVC along with the optimal loading factor for each load helps to increase the systems loadability limit. The above objective has been achieved using the FFA by solving the formulation mentioned in the section 2 along with the FACTS devices setting constraints. The FFA with FACTS devices strategy has been implemented using three test systems and the results are recorded in the fifth row of

In the modified IEEE 30 bus test system, the TCSC has been placed on the transmission line connected between bus no.1 and bus no.3 with the X_{TCSC} of 0. 073 p.u added to the line. Here TCSC operates in the capacitive mode that decrease the net reactance of the line in turn increases the real power capacity of the line. Similarly the SVC is connected to the bus no.1 with the size of 14.0863 MVAR. Here SVC operates in the inductive mode to control bus reactive power within the limits to increase power transfer capacity. The above combined TCSC and SVC placement in enhancement of load value is shown in

Algorithm | Maximum Loadability in p.u | Critical Voltage | Total Incremental System Load from Base Case in % | Optimal SVC Bus No. | Optimal TCSC Line | SVC in MVAR | X_{TCSC} in p.u |
---|---|---|---|---|---|---|---|

Base Case | 12.508 | 0.936 @ 31bus | - | - | - | - | |

PSO [ | 14.039 | Not Mentioned | 12.2401 | - | - | - | - |

HPSO [ | 14.062 | Not Mentioned | 12.4240 | - | - | - | - |

FFA without FACTS | 14.134 | 0.9221 @ 31bus | 12.9996 | - | - | - | - |

FFA with FACTS | 14.301 | 0.9340 @ 31bus | 14.3348 | 44 | [44 45] | 25.715 (Capacitive Mode) | 0.0045 (Inductive Mode) |

Method | Worst | Mean | Best | Standard Deviation | No of Iteration |
---|---|---|---|---|---|

PSO | 13.8 | 14.0296 | 14.039 | 0.0278 | 39 |

HPSO | 13.92 | 14.0555 | 14.062 | 0.0211 | 29 |

FFA | 14.04369 | 14.1218 | 14.13427 | 0.015 | 21 |

Method | Worst | Mean | Best | SD | No of Iteration |
---|---|---|---|---|---|

DE | 54.4993 | 56.2432 | 56.6212 | 0.6999 | 18 |

DE-PSO | 56.2189 | 56.4966 | 57.0156 | 0.27 | 15 |

FFA | 56.18822 | 57.2121 | 57.32037904 | 0.1935 | 22 |

Algorithm | Maximum Loadability in p.u | Critical Voltage | Total Incremental System Load from Base Case in % | Optimal SVC Bus No. | Optimal TCSC Line | SVC in MVAR | X_{TCSC} in p.u |
---|---|---|---|---|---|---|---|

Base Case | 42.42 | 0.946 @ 53bus | - | - | - | - | |

DE [ | 56.6212 | Not Mentioned | 33.4776 | - | - | - | - |

DEPSO [ | 57.076 | Not Mentioned | 34.5497 | - | - | - | - |

FFA without FACTS | 57.32 | 0.9397 @ 53bus | 35.1249 | - | - | - | - |

FFA with FACTS | 57.57 | 0.9412 @ 53bus | 35.7142 | 79 | [79 80] | 19.086 (Inductive Mode) | 0.03930 (Capacitive Mode) |

FFA without FACTS and base case. By comparing fourth and fifth row of

The Convergence Graph of FFA with FACTS and without FACTS has been shown in

In IEEE 57 Bus system, the SVC has been placed on the bus no.44 with the size of 25.715 MVAR. Here the SVC operates in capacitive mode it increases the voltage level of the Bus system which in turn increases the power flow capacity of transmission line. The above voltage level enhancement is shown in

The increase in the voltage level of the bus may affect the power flow controllability of the system in turn affects the loading capacity of the load. The power flow controllability of the system is maintained by the placement of TCSC at the transmission line connected between the bus no.44 and bus no.45.

The convergence graph of FFA with FACTS and without FACTS has been shown in

In the IEEE 118 Bus system, the SVC has been placed on the bus no. 79 and TCSC has been placed on the

transmission line connected between the bus no.79 and bus no.80. Here the SVC operates in inductive mode and TCSC operates in capacitive mode. Each load value of the system using FFA with FACTS has been compared with the base case and FFA without FACTS and it is shown in

The Convergence Graph of FFA with FACTS and without FACTS has been shown in

In a power system, the contingencies may be due to the outage of transmission lines or generators. Since in a practical power system, the possibility of transmission line outage is very high compared to that of generator outage hence it is necessary to calculate the maximum loadability point at a transmission line contingency. Considering the above subject matter, system’s maximum loadability point is determined by creating a transmission line outage for each test systems in this strategy.

Consider a transmission line connected between bus no.19 and bus no. 20 in modified IEEE 30 Bus system has been assumed to be tripped. The tripped transmission line outage decreases the voltage level to 0.9492 p.u and 0.9384 p.u at bus no. 18 and bus no. 19 respectively. The decreased voltages violate the system since the minimum system bus voltage limit is 0.95 p.u. FFA based optimal placement of SVC on bus no.15 with the size of 17.4309 MW and TCSC operates in the inductive mode with the X_{TCSC} of 0.0123 p.u added to the transmission line connected between bus no. 15 and bus no.18 provide the solutions to determine the maximum loadability point by limiting all the bus voltage within the limits of 0.95 and 1.05 p.u. The above is illustrated in the comparison voltage graph between base case and FFA with FACTS in the contingency state shown in

In IEEE 57 Bus system, a transmission line between bus no.9 and bus no.12 has been assumed to be tripped. The above line outage increases the reactive power of generator bus no. 9 to 17.4693 MVAR in the base case. Here the system gets violated since the reactive power maximum limit of generator bus no. 9 is 9MVAR.The FFA based optimal placement of SVC on bus no 24 and TCSC on the transmission line connected between bus no 24 and bus no 26 provide the solution to determine the maximum loadability point by limiting the generator bus no. 9 reactive power to 8.4413 MVAR and also the other system control variables within the limit. Here the SVC operates in capacitive mode with the size of 58.5261 MVAR and TCSC operates in inductive mode with the X_{TCSC} of 0.0084 p.u added to the line. The maximum loading point of 14.1135 p.u is obtained at the assumed line outage and it is recorded in the second row of

the base case line outage and the FFA with FACTS based line outage is shown in

Similar like modified IEEE 30 Bus system and IEEE 57 system, a transmission line between bus no. 69 and bus no. 75 has been assumed to be tripped in IEEE 118 Bus system. The tripped transmission line outage causes the system violation since the reactive power of the bus no.32 is increased to 17.5 MVAR compared to the maximum limit of 17 MVAR at bus no. 32. This reactive power violation has been brought into control by optimally placing the SVC at bus no.17 with the size of 29.4520MVAR and TCSC operates in the inductive mode with the

The loading value of each bus in the three test system using FFA based optimal placement of FACTS devices in the contingency state has given in

FFA With SVC and TCSC at a Line Contingency State | Transmission Line Outage [Sending Receiving End Bus] | Maximum Loadability in p.u | Critical Voltage in p.u @ bus | Optimal SVC Bus No. | Optimal TCSC Line | SVC in MVAR | X_{TCSC} in p.u |
---|---|---|---|---|---|---|---|

IEEE 30 Bus System | [18 19] | 2.714 | 0.9501 @ 8 | 15 | [15 18] | 17.4309 | 0.0123 |

IEEE 57 Bus System | [9 12] | 14.11 | 0.9758 @ 1 | 24 | [24 26] | 58.5261 | 0.0084 |

IEEE 118 Bus System | [69 75] | 54.512 | 0.9392 @ 53 | 17 | [17 113] | 29.4520 | 0.0080 |

In this work, maximum loadability point determination using Firefly Algorithm is implemented in modified IEEE 30 Bus system, IEEE 57 Bus System and IEEE 118 Bus system. The results of Firefly algorithm provides better maximum loading point compared to the other evolutionary algorithm. It is evident from the convergence characteristics that the FFA provides better balance between the exploration and exploitation process at the faster convergence rate. The FACTS devices involvement of TCSC and SVC in determining the maximum loading point enhances the load utilization point in normal state and also helps to overcome the system violation in transmission line contingency state. Overall, the firefly algorithm in determining the maximum loadability point and its enhancement with the help of FACTS provides better search capability and also enriches the system load utilization capacity by maintaining the system security level.

S. Rajasekaran,Dr. S. Muralidharan, (2016) Firefly Algorithm in Determining Maximum Load Utilization Point and Its Enhancement through Optimal Placement of FACTS Device. Circuits and Systems,07,3081-3094. doi: 10.4236/cs.2016.710262