Adaptive FPA Algorithm based OPF with Unified Power Flow Controller

In this work a novel modified flower pollination algorithm has been developed to solve the problem of single and multiobjective Optimal Power Flow operations for Unified power Flow Controller in Flexible Alternating Current Transmission Systems. In the proposed Adaptive Flower Pollination Algorithm the best initial solution can be chosen from the fittest and also the weights are adaptively adjusted to get better convergence characteristics. The nature of the objective functions is non-linear and difficult to get best possible solutions within the boundary conditions of total power demand. The weak nodes are determined in the system to locate the UPFC with Fuzzy approach considering input parameters as L-Index and voltage magnitudes. The projected method is validated using IEEE-30 and IEEE-57 bus systems for three objective functions, namely, system real power loss minimization, fuel cost minimization and the combination of total generating cost and system real power loss. Results of Fuzzy- Adaptive Flower Pollination Algorithm based OPF optimization for UPFC produced optimum results for the considered objectives of total fuel cost, real power loss and for the multiobjective.


Introduction
The power system is a largest man made system due to its wide geological coverage, a diversity of transactions among different utilities, and diversity in the layouts of electric power industries, size and the connected equipments.There is a necessity of advanced methods to optimally investigate, monitor and manage an assortment of aspects of such complicated system that take account of Unit Commitment (UC), Automatic Generation Control (AGC), state estimation, Economic Dispatch (ED) and Optimal Power Flow (OPF).The OPF is treated as the spinal column technique which was expansively researched since 1962 [1].
OPF is a static nonlinear problem that optimizes an objective function which suits a set of operational and physical constraints forced by apparatus restrictions as well as security needs.Numerous successful OPF techniques [2][3][4] have been projected to yield a best OPF solution.
Evolutionary algorithms with multiple objectives [5][6] have been examined to work out different OPF problems to defeat the shortfalls of orthodox methods.Diversified hybrid techniques were developed called hybrid EP with tabu search [7], firefly and particle swarm optimization [8] enroot for steadfastness ED problem for valve point fuel cost functions.
For the past twenty years, the ever-increasing developments in computational astuteness tools have been providing best solutions in the area of metaheuristics optimization techniques.Some of them are: Artificial Bee and Ant Colony and Bacterial Foraging algorithms [9][10][11], Cuckoo Search [12], Tabu Search [13], Harmony Search Algorithm [14], Black Hole Based Optimization [15], Improved GA [16][17] etc.
Flower Pollination Algorithm (FPA), is one of the latest optimization algorithms that intended to provide solutions for individual and combined objective optimization problems [18][19][20] introduced by X. S. Yang in the year 2012.This natural world inspired technique is developed from the distinctiveness of flowering plants with fascinating characteristics that lend a hand to travel around the viable groom in the neighbourhood and globally.In the recent times, it has gained increased attention to solve the OPF problem [21][22] to discover the most select settings of the controllable variables [23].
In the past three decades several research articles were published on OPF solution with FACTS devices.A decomposition scheme developed by Taranto et al. [24] to get to the bottom of OPF solution in the presence of FACTS.[25] Presented the FACTS modeling in OPF solution and discussed the task of that modeling.[26] published the OPF technique by placing the FACTS using Newton's method that led to an exceedingly dynamic solution.However, it has been identified that the solutions of OPF becomes a non-convex solution with series compensation that results, the traditional methods may struck at local optimum.To assuage the afore said complicatedness many advanced techniques have been projected by many researchers viz., [27] proposed with MDE, Hybrid DA-PSO in [28] to solve OPF problem by incorporating FACTS.
The main intention of this article is to put forward an Adaptive Flower Pollination Algorithm (AFPA) with UPFC for single and Multi-objective optimization problems.The modifications proposed in the Flower pollination algorithm to obtain AFPA are given in section-4.Here weak nodes are identified through fuzzy to identify the best location of UPFC.The three considered single and multi objectives are optimized using AFPA algorithm by controlling the shunt compensators, tap settings of the transformers along with UPFC series and shunt controllers.The L-Index is a voltage stability index is also considered as one of the constraints along with equality and inequality constraints to maintain the stability of the system while optimizing the considered objectives.The step by step procedure is represented in the block diagram given in Figure 1.

Fuzzy Approach To Find Weak Nodes
The proposed fuzzy approach uses L-index bus voltage profiles to identify the weak nodes in the system.

L-index
A transmission system chosen with 'n' buses consists of 'g' generator buses, 'n-g' P-Q buses.L-Index [29] of the network is given by: Where, k = g +1,....,n.The Fki values of Y-bus matrix are complex in nature. i.e.

   
where,[YLG] and [YLL] are the sub parts of Y-bus.For the system to be stable, at any P-Q bus k the maximum value of Lk should be 1 [29].
The bus voltage profile and L-index values are expressed in fuzzy set notation.The severity index of each bus as an output are also divided into different categories.The fuzzy rules are used to evaluate the severity of each bus in the system.
The output membership functions to evaluate the severity of a week nodes are divided into five categories using fuzzy set notations: Very Less Severe (VLS), Less Severe (LS), Below Severe (BS), Above Severe (AS) and More Severe (MS).The severity index of each bus in the system is found using the formula Where, SIVP and SIVSI are the severity indexes of postcontingent voltage profile and voltage stability indexes, respectively.

Modeling of UPFC
UPFC is one of the sophisticated device from FACTS, can offer instant control of real, reactive power and voltage.The power injection model of the UPFC with two harmonized synchronous voltage sources shown in Figure 2.The voltage sources of UPFC are: ( ) ( ) With the help of equations ( 4) and ( 5) derived from the model, real and reactive power expressions can be obtained as: ( ) ( ) ( ) ) ( ) )

Formulation of OPF Problem
The solution of OPF focus at optimizing a preferred objective with the best promising amendment of the power network control parameters satisfying both equality and inequality constraints.OPF problem is formulated as: where, J is the objective function; x is dependent variable; g and h are equality and operating constraints; u is the control variable vector such as: 1. Generator voltages at PV buses.
2. Real power at PV buses excluding PG1 swing bus.
3. Tap settings of transformer.4. Shunt compensators.Optimal location of UPFC is calculated to optimize the particular objective function to improve the performance of the system where as thermal limits and voltage constraints should be satisfied.OPF problem formulation is given.After UPFC installation for the following objective functions:

Fuel cost function
The total fuel cost as objective function 'f1' by daunting the constraints is as follows: Where, NG=No. of generator units, PGi=Active power generation at i th unit, ai,bi and ci are the cost coefficients of i th generator and KP,KV,KQ,KS and KL are penalty factors for the limit violation.NL represents number of load buses, nl represent number of transmission lines and X lim is restrictive values reliant variable given as:

Power loss
The power loss minimization can be articulated as follows: ( ) ( ) Where Gij=Conductance belongs to i-j th line The amalgamation of objective function 1&2 is expressed as multi objective function.
( ) The optimization problem can be solved underneath the subsequent constraints:

Equality constraints
Nonlinear load flow equations that govern the power systems is given by, ( ) ( ) Where, , , ,

Flower Pollination Algorithm (FPA)
The following rules have been established for FPA technique to illustrate an ideal pollination process [30]: Rule I: Self-pollination is treated as neighborhood pollination, happened by the natural world through the air stream or precipitation.
Rule II: Cross-pollination is treated as a comprehensive pollination and the pollinators (birds or insects) that are moving from long distance carry the pollens which would be treated as Levy flights.
Rule III: Local pollination have been occurring in the midst of the plant flowers itself or from the same class flowers.
Rule IV: The above mentioned two processes could be constrained by a control probability function Pa∈ [0, 1].Because of the corporeal flower immediacy and the other characteristics airstream or precipitation, self pollination could have a momentous part on the whole pollination progression [31][32].
FPA optimization technique can be formulated from the afore mentioned rules, as follows: Let yi be the control vector of considered control variables that mentioned the i th flower.The cross-pollination is conceded out by producing arbitrary statistics L(λ) given below: The dot (*) in the above equation means element wise multiplication.The stride length L(λ) is haggard commencing a conformity Levy circulation; the equation was named a Levy flight which impersonates pollinator's deeds.Mantegna's approximation was used to engender Levy random numbers [33].
Self pollination has been carried out with the step length as homogeneously disseminate systematic number vector c1 exists among 0 to1 to organize the enormity of the elements metamorphosis of the upcoming flower generation.
Here, t = present iteration, yi t and yk t are the present pollen from the diverse flowers of the same class.It can be represented as, if y t+1 and y t are of same class, this homogeneously becomes a narrow random saunter.
The Levy flights can be changed to haphazard walks with a switching likelihood factor Pa as per the following rule: If Pa > rand (0,1) Do levy flights:

Adaptive Flower Pollination Algorithm (AFPA)
Most important aspects of FPA are the preliminary stage population and moving from self pollination to global pollination.It has a significant brunt on the computational encumber and the elucidation convergence.The following modifications were proposed to enhance the performance of the algorithm.

Looking for the best initial condition
The earliest alteration is, opening from a nearer or fittest solution by concurrently inspecting the conflicting guess.With this modification, the initial best solution can be chosen from the fittest (either from opposite guess).The probability theory reveals that, the probability of two contradictory solutions which belongs to the identical feasible class has an opportunity of 50% that one is well again than the further.Therefore, beginning from the fittest of the two such as either presumption or contradictory presumption will be the impending to encompass an initial position more rapidly to the most advantageous way out.To achieve this, A contradictory vector to be required [34].
Let y be a present solution and the contradictory solution vector Y can be obtained by it apparatus as: Where [ai, bi] are upper and lower limits of yi.Quasi-oppositional point: The elucidation point is distinct from the preceding conflicting position and it has been demonstrated to furnish improved solution than the regular conflicting vector [35].Let

Moving from local to global pollination process
Another amendment proposed based on the methods proposed in reference [36].It is based on the combining of equations ( 29) and ( 30) by means of scalar dynamic auto adjusted weights w1 and w2 which may vary based on the generation counter 't'.The weight variations are obtained as follows: F =Average of the fitness functions of the present population.As a final point, accumulate an arbitrary scale factor γ(considered 0.15here) and a Gaussian distribution vector (ε2=N(0,1))as an alternative of a uniform distribution to self random walks, the modified equation is: This amendment moves the use of the probability.Switch Pa and Levy flights and Brownian motion have been merged into a solitary random walk expression.

Simulation results and discussion
The proposed technique was validated on IEEE-30 and IEEE-57 bus system in MATLAB programming environment.

Case 1: Testing on IEEE-30 Bus System
The considered test system has six generators inter related with 41 lines with a load demand of 283.4 MW and 126.2 MVAR [37].The shunt VAR suppliers are provided at buses 10, 12, 15, 17, 20, 21, 23, 24 and 29 [38].Upon identifying the weak buses on the system using Fuzzy by considering L-Indices and voltage magnitudes and consequent results of top weak nodes are tabulated in Table 2.The bus 27 has utmost severity and treated as feeble node in the system as given in Table  UPFC results of the network for minimization of fuel cost and power loss were shown in Table 3 and Table 5 respectively.It is found that, total generating cost in proposed scheme is reduced to 798.01 $/h with respect to FPA yielding 800.15$/h and AFPA yielding 799.15$/h.Figure 3 shows the comparison of above results.It is also noted that, the L-Index is decreased to 0.1209 with respect to FPA yielding 0.1350 and AFPA yielding 0.1338 that gives enhanced voltage stability and the resultant graphical representations is as shown in Figure 4.The variations of voltage magnitudes of FPA and AFPA and AFPA with UPFC are shown in Figure 5.     4, It is apparent that the system real power loss in proposed scheme has been reduced to 5.91MW where it is 7.12 MW and 6.95 MW in FPA and AFPA respectively.The proposed method results obtained for the multi-objective function are tabulated in Table 6.From the Table 6, it is evident that the projected AFPA method with UPFC is also provided an optimum solution for multi-objective function.

Case 2: Testing on IEEE-57 bus system
The IEEE-57 bus system has 80 transmission lines together with 17 tap changing transformers, 7 generators The bus 57 has utmost severity treated as weakest node and the line between 56-42 is preferred for the most favourable location of UPFC.The AFPA-OPF results of the system with UPFC are given in subsequent tables.

Conclusion
Standard test networks IEEE-30 & IEEE-57 bus systems were selected to check the efficacy of the projected method for the considered single and multi objective functions.Fuzzy approach has been used to find the location of UPFC in the considered test system that effectively eliminated the masking effect in contingency ranking of the other proposed methods.
The proposed method i.e AFPA with UPFC was very effective in eliminating the drawbacks of FPA and AFPA while finding the best possible control settings of the control variables.The proposed method reduced the fuel cost from 802.9$/h to 798.01$/h i.e 4.89$/h compared to existing literature and the power loss has been reduced to 83% of FPA where as in the case of multi-objective function the reduction in the weighted sum from 800.23 to 798.01 with respect to FPA.Here, in addition to proposed objectives, the inclusion of UPFC in the projected technique enhanced the stability margin and reduces voltage deviation too.This research work may also be extended by placing multiple facts devices in optimal places for single and multi objective optimization problems and also be extended to support the system under contingency conditions which gains lot of attention especially for planning and operation of the complex power systems.
generation number.F(t) = Fitness value at generation t.

Figure 3 .
Figure 3. Fuel cost for different OPF techniques

Figure 4 .
Figure 4. Bus voltages for different OPF techniques

Figure 5 .
Figure 5. L-indices for different OPF techniques

Table 1 .
Decision matrix to find weak nodes of the system

Table 2 .
Weak nodes of the system

Table 4 .
Fuel cost comparison for different techniques

Table 5 .
OPF Results with Power loss as an objective

Table 10 .
OPF results for multi-objective function (f3)From the Table7, 8 & 9, it is evident that proposed AFPA technique with UPFC is very efficient to acquire optimum solution for single and multi-objective function.