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Firefly algorithm is the new intelligent algorithm used for all complex engineering optimization problems. Power system has many complex optimization problems one of which is the optimal power flow (OPF). Basically, it is minimizing optimization problem and subjected to many complex objective functions and constraints. Hence, firefly algorithm is used to solve OPF in this paper. The aim of the firefly is to optimize the control variables, namely generated real power, voltage magnitude and tap setting of transformers. Flexible AC Transmission system (FACTS) devices may used in the power system to improve the quality of the power supply and to reduce the cost of the generation. FACTS devices are classified into series, shunt, shunt-series and series-series connected devices. Unified power flow controller (UPFC) is shunt-series type device that posses all capabilities to control real, reactive powers, voltage and reactance of the connected line in the power system. Hence, UPFC is included in the considered IEEE 30 bus for the OPF solution.

In power engineering bus voltage, real, reactive power flow needs to calculate for proper operation and planning. This information may derive from power flow analysis, and that does not include economic operation. “Optimal Power Flow” (OPF) was introduced in 1968 [

OPF problem may have multi-objectives and become non-linear and constrained optimization problem. Traditionally, OPF problem has been solved for various types of objectives are converted into one objective problem [

OPF is the minimization problem to find the optimal fuel cost and subjected to equality constraints, and inequality constraints. The Objective function is given by the Equations (1) and (2). Generating cost is the fuel cost for the thermal power plant obeys quadratic function given in $/Hr [

Subject to

Equality Constraints (3) and (4)

Inequality Constraints (5)-(9)

_{G} (5)

_{G} (6)

_{B} (7)

_{T} (8)

_{br }(9)

where,

C_{t} = Total generation cost; α, β, γ = Cost coefficients of the generator;

P_{Gi}, Q_{Gi} = Active and Reactive power generation ith generator;

P_{D}, Q_{D} = Active and Reactive power Demand; P_{L}, Q_{L} = Active and Reactive power Loss;

V_{i} = Voltage at ith bus; t_{i} = Transformer tap position; MVA_{i} = MVA flow in ith branch;

NB = Number of buses; NG = Number of generators; NT = Number of transformers;

Nbr =Number of branches;

This constraint minimization of generating cost is achieved by tuning the set of control variables. The set of control variables are generator real power, voltage, transformer tap position and UPFC location and power injection. Considered Firefly algorithm explores the solution space bounded by equality and inequality constraint and find better values for all these control variables. Loss minimization and generating cost minimization combined and the objective problem become multi- objective optimization problem.

The existing transmission system is laid for AC transmission and has a limitation of power transfer due to thermal constraint and its impedance. To increase the power transfer capability of the transmission system requires the new installation and huge money and time. To solve this bottleneck problem, FACTS devices are introduced which are power electronic devices. By connecting this FACTS device, an impedance of the transmission line may alter and loss thereby temperature of the transmission line. This gives new way for using the existing transmission infrastructure but with enhanced power transfer capability. Based on the connection of these FACTS devices, they are classified as series, parallel, and hybrid FACTS devices. UPFC is one hybrid FACTS device having parallel and series connection [

It consists of two power electronic converters. These converters are connected back to back to the common DC link. This power electronic converter has three arm bridge thyristors controlled by the control unit. DC link is the capacitor used to store the DC voltage needed for the converter. The first converter is connected in parallel to the transmission line at the sending end. The second converter is connected in series with the transmission line and the injection effect the receiving end bus. UPFC converters are designed to work in medium voltage hence insertion transformers are required to connect high voltage transmission line as shown in

control the converter one (shunt converter) control signals VVR and ӨVR are used and for converter two (series converter) control signals VCR and ӨCR are used. These control signals are derived from the control unit that which takes the feedback signals of transmission line voltage, current and reference values of control variables.

The Firefly optimization technique is used by Yang. X. S in 2008 [

Step 1: Read bus data and line data

Step 2: Select the control variables

Step 3: Create the initial population

Step 4: Find the light intensity or objective of each firefly

Step 5: For the all firefly find the attractive with other firefly based on the light intensity

Step 6: Find distance between the fireflies to move towards brighter one

Step 7: Move the less intensity firefly towards the brighter firefly

Step 8: Repeat the steps 4 to 7 until convergence criterion satisfied

Step 9: Maximum iteration is considered as the convergence and iteration stopped after maximum iteration

Step10: After the convergence print the results

Step11: Stop

The following are the steps used in the implementation of Firefly Algorithm for Optimal Power Flow is explained as follows. Flowchart for Firefly Algorithm is shown in

The fireflies characteristics are the following three rules are given below [

1) Fireflies are assumed to be unisex which attracts another one without considering its sex.

2) Less light intensity Firefly move towards brighter Firefly, this attractiveness is inversely proportional to the

distance between them. If the brighter Firefly could not found, then the firefly moves in the random direction.

3) Brightness of Firefly also subjected to the nature environment, based on this environment the brightness is affected.

Test case IEEE 30 bus considered to validates the developed algorithm; the parameters considered to evaluate the performance are reactive power, voltage and losses. MATLAB environment is used to develop and implement the program. The IEEE 30 bus system has six generator bus, 24 load bus and 41 transmission lines [

For the economical operation, generating cost has to be minimized as far as possible. This obeys the quadratic cost function. The coefficient of the cost function is given in

The optimal allocation of UPFC in buses and Lines are represented in

S. No | Bus No | Min Real Power (MW) | Max Real Power (MW) | Alpha ($/hr) | Beta ($/Mwhr) | Gamma ($/Mw2hr) |
---|---|---|---|---|---|---|

1 | 1 | 50 | 200 | 0.0038 | 2 | 0 |

2 | 2 | 20 | 80 | 0.0175 | 1.75 | 0 |

3 | 5 | 15 | 50 | 0.0625 | 1 | 0 |

4 | 8 | 10 | 35 | 0.0083 | 3.25 | 0 |

5 | 11 | 10 | 30 | 0.025 | 3 | 0 |

6 | 13 | 12 | 40 | 0.025 | 3 | 0 |

S. No. | Sending end Bus | Receiving end Bus | Shunt MVAr | Series MVAr |
---|---|---|---|---|

1 | 6 | 7 | 4.0736 | 25.2553 |

UPFC has shunt and series power injection; Firefly algorithm optimizes the location and value of reactive power injection. STATCOM has shunt power injection and support voltage control there by losses in the transmission line. UPFC has shunt and series power injection and superior to STATCOM. The best location of UPFC is given in the table that is connected between the buses 6 and 7. The corresponding reactive power injection is also given in

S.No | Parameter | Pmin (MW) | Pmax (MW) | Base Case without FACTS device [ | FFA with STATCOM [ | FFA with UPFC |
---|---|---|---|---|---|---|

1 | PG1 (MW) | 50 | 200 | 229.687 | 151.314 | 150.289 |

2 | PG2 (MW) | 20 | 80 | 20 | 42.5989 | 41.857 |

3 | PG5 (MW) | 15 | 50 | 15 | 24.0831 | 23.471 |

4 | PG8 (MW) | 10 | 35 | 10 | 31.9497 | 30.543 |

5 | PG11 (MW) | 10 | 30 | 10 | 24.9827 | 23.481 |

6 | PG13 (MW) | 12 | 40 | 12 | 19.5219 | 18.402 |

7 | Total Generation, MW | --- | --- | 296.687 | 294.45 | 288.05 |

8 | Total Demand, MW | --- | --- | 283.4 | ||

9 | Real Power Loss, MW | --- | --- | 13.29 | 11.05 | 4.65 |

10 | Generating Cost ($/Hr) | --- | --- | 833.70 | 826.120 | 803.15 |

Firefly Algorithm is implemented to solve OPF with UPFC. The implemented FACTS devices UPFC results are compared to STATCOM, and it is clear that the UPFC outperforms well. Firefly algorithm is used for the both FACTS device to prove the performance of the UPFC. The losses and prime objective of cost minimization of OPF problem are minimized very well when UPFC is included in the system. Voltage profile of all the generator and load buses is within the limit and satisfies constraints that are required for the practical implementation of the developed algorithm.

T. Hariharan,K. Mohana Sundaram, (2016) Optimal Power Flow Using Firefly Algorithm with Unified Power Flow Controller. Circuits and Systems,07,1934-1942. doi: 10.4236/cs.2016.78168