Optimal Tuning of Unified Power Flow Controller Parameters Using Firefly Algorithm

Optimal parameter values of UPFC device is obtained by minimizing the multi-objective function with adequate equality & inequality limitations. The objective function consists of over-all transmission line loss, complete voltage deviation, the entire cost of true power generation & branch loading.

2.1 Objective function

$\mathrm{F}=\mathrm{V}_{1} * \mathrm{TTPC}+\mathrm{V}_{2} * \mathrm{TTL}_{loss}+\mathrm{V}_{3} * \mathrm{VD}+\mathrm{V}_{4} * \mathrm{BL}$             (1)

$\mathrm{V}_{1}+\mathrm{V}_{2}+\mathrm{V}_{3}+\mathrm{V}_{4}=1$        (2)

where, V₁, V₂, V₃, V₄ are the weighting factors in this work equal importance is given to all the objectives so V₁+V₂+V₃+V₄ = 0.25.

2.1.1 Total true power generation cost (TTPC):

This objective considering the quadratic function, the function follows as

TTPC=$ \sum_{i=1}^{n g}\left[a_{i}+b_{i} P_{G_{i}}+c_{i} P_{\mathrm{Gi}}^{2}\right]$            (3)

where, Ng is the number of PV buses.

a, b & c are cost quantities of a true power generation plants.

2.1.2 Total transmission line loss (TTL):

It can be conveyed as:

$\mathrm{TTL}=\left(\sum_{i=1}^{n t l} \operatorname{real}\left(S_{i j}^{\mathrm{k}}+S_{\mathrm{ji}}^{\mathrm{k}}\right)\right)$          (4)

where, ntl is number of inter linked lines, $S_{j i}^{k}$ is compound power flow in line k, from bus j.

2.1.3 Voltage deviation (VD):

The Voltage Deviation (VD) is one of the main intents to improve the power system performance, it can be shown as:

$V D=\left(\sum_{k=1}^{N b u s}\left|V_{k}-V_{k}^{\mathrm{ref}}\right|^{2}\right)$            (5)

Vk is voltage at bus k, Vk^ref is specified voltage at bus k.

2.1.4 Branch loading (BL):

It can be given as: 

$B L=\sum_{\mathrm{k}=1}^{\mathrm{nl}}\left(\frac{\mathrm{S}_{\mathrm{k}}}{\mathrm{S}_{\mathrm{k}}^{\mathrm{max}}}\right)^{2}$                 (6)

S_k is complex power in line k & Sk^max is maximum compound power in line k.

2.2 Constraints

$\sum_{i=1}^{N} P_{G i}=\sum_{i=1}^{N} P_{D i}+P_{L}$        (7)

$\sum_{i=1}^{N} Q_{G i}=\sum_{i=1}^{N} Q_{D i}+Q_{L}$     (8)

$V_{G i} \min _{\leq} V_{G i} \leq V_{G i} \max$       (9)

$P_{G i} \min _{\leq} P_{G i} \leq P_{G i} \max$       (10)

i=1, 2, 3... N & N is number of true power generation buses

$Q_{G i} \min \leq Q_{G i} \leq Q_{G i} \max$      (11)

2.2.1 UPFC limits

$V_{v r}^{\min } \leq V_{v r} \leq V_{v r}^{\max }$      (12)

$V_{c r}^{\min } \leq V_{c r} \leq V_{c r}^{\max }$      (13)

In this work, the main objective is to identify the best parameter settings for UPFC device.

To identify the usefulness of the planned firefly Algorithm optimal parameter setting of UPFC, IEEE 14 & IEEE 30 bus system are engaged as case studies. MATLAB R2009 environment with Windows 7 Home Basic operating system consists of an i3 processor and 4 GB RAM laptop has been used to do the simulation. Simulation results of firefly algorithm established OPF without& with UPFC have been tabulated. In these study, 50 fireflies with 20 generations have been considered.

4.1 For 14 bus system

IEEE 14 bus system involves of five generator buses out of that first bus is considered as a swing bus and second, third, sixth and eighth buses are taken as generator buses & remaining all buses are PQ buses. All these buses are interconnected with twenty transmission lines. Simulations were done on MATLAB environment and the obtained results are presented in Tables. Table 1 indicates the input parameters of FA. Table 2 specifies the generator characteristics of IEEE 14 bus system. Table 3 specifies the UPFC parameters for different conditions. Table 4 designates various objectives in objective function consisting without and with UPFC using Firefly Algorithm. Table 5 presents the voltage profile comparison with GA & FA. Table 6 shows the optimized generator values of the generator using GA & FA. From these results, it is witnessed that FA is superior to GA. Figure 1 and Figure 2 presents the voltage magnitude and phase angles comparison with and without UPFC.

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Figure 1. Comparison of bus voltages for 14bus system using FA-OPF without and with UPFC

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Figure 2. Comparison of phase angles for 14 bus system using FA-OPF without and with UPFC

Table 1. Input parameters of Firefly Algorithm

Table 2. Generator characteristics of IEEE 14 bus system

Table 3. Comparison of UPFC parameters in IEEE 14 bus system

Table 4. Comparison of different objectives using FA -OPF in IEEE 14 bus system

Table 5. Comparison of voltage profile of IEEE 14 bus system

Table 6. Comparison of the real power generation of generator busses in various methods

4.2 For 30 bus system

IEEE 30 bus system has six generator buses, in which first is slack bus and second, fifth, eighth, eleventh and thirteen buses are PV buses, remaining buses are PQ buses. These buses are connected by forty-one lines. Simulations are performed on MATLAB environment and the results have been tabulated. Table 7 represents the generator characteristics of 30 bus system. Table 8 shows the size of the UPFC for different conditions. Table 9 indicates various objectives of the minimization function. It shows the without and with UPFC objectives using Firefly Algorithm.

Table 7. Generator characteristics of IEEE 30 bus system

Table 8. Comparison of UPFC parameters in IEEE 30 bus system

Table 9. Comparison of different objectives using FA -OPF in IEEE 30 BUSSYSTEM

Table 10. Comparison of Voltage deviation of IEEE 30 bus system

Table 11. Comparison of the Real power generation of Generator busses in various methods

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Figure 3. Voltage profile comparison for IEEE 30 bus system without and with UPFC

Table 10 presents the comparison of Voltage deviation considering FA & GA. Table 11 shows power generation of generator buses using GA & FA. From these tables, it is observed that FA is superior to GA. Figure 3 shows that after incorporating UPFC in FAOPF voltage, profile has been enhanced.