Linear Structured approach for optimal

power flow using bacterial foraging technique

Guided By: Shashank Khandelwal(07BEE149)

Mr. J Belwin Edward Rohit Kala (07BEE135)

Load FlowLoad flow solution is a solution of the

network under steady state condition subjected to certain inequality constraints under which the system operates.

The load flow solution gives the bus voltages and phase angles, hence the power injection at all the buses and power flow through interconnecting transmission lines.

Goal of Power FlowTo obtain complete voltage angle and

magnitude information for each bus in a power system for specified load and generator real power and voltage conditions.

To plan the future expansion of power systems as well as in determining the best operation of existing systems.

What is optimal power flow?

• The OPF optimizes a power system operating objective function such as operating cost of thermal resources, transmission losses etc. while satisfying a set of system operating constraints.

• Optimization is a procedure of finding and comparing feasible solutions until no better solution can be found.

• Optimal power flow (OPF) is a static nonlinear programming problem which optimizes a certain objective function while satisfying a set of physical and operational constraints imposed by equipment limitations and security requirements.

Goal of optimal power flow

The primary goal of a generic OPF is to minimize the costs of meeting the load demand for a power system while maintaining the security of the system.

The objective can be the minimization of losses or cost of operation or emission losses, maximization efficiency or reliability etc.

The standard OPF problem The standard OPF problem can be written in the following form : Min. ( )𝐹 𝑥Subject to: h( ) = 0 𝑥and ( ) ≥ 0𝑔 𝑥 where, 𝐹( ) 𝑥is the objective function, h( ) 𝑥is the equality constraints and 𝑔( ) 𝑥is the inequality constraints.

OPF FORMULATION FOR GENERATION COSTMINIMIZATION

• OBJECTIVE FUNCTION F(x) = ∑ [ai(Pgi)2 + bi(Pgi) 𝑚𝑖𝑛

+ ci]

𝑃𝑔𝑖 𝑚𝑖𝑛 < < 𝑃𝑔𝑖 𝑃𝑔𝑖 𝑚𝑎𝑥 where,

i=1,2,3…………..ng • Pgi is the

generated active power at bus i. ai , bi , ci are

the unit costs curve for ith generator.

EQUALITY CONSTRAINTS While minimizing the cost function, it is necessary to make sure that the generation still supplies the load demands (Pd ) plus losses in transmission lines [36]. Usually the power flow equations are used as equality constraints: The power flow equation of the network g(V, Φ) = 0 where, Pi (V, Φ )− Pi net g (V,Φ) = Qi V, Φ )− Qi net Pm( V, Φ) − Pm net

INEQUALITY CONSTRAINTS

The inequality constraints of the OPF reflect the limits on physical device in the power systems as well as the limits created to ensure system security. Qgi min ≤ Qgi ≤ Qgi max Vi min ≤Vi ≤ Vi max Φi min ≤Φi ≤ Φi max MVAij ≤ MVAij max

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Lineared Structure of IEEE14 bus

Mathematical Model

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Bacterial Foraging

112/04/1113

Moving track of E. Coli:

Bacterial Foraging Algorithm

112/04/1114

Bacterium:PositionStep Sizes for Each DimensionHealth Status

Bacterial Foraging Algorithm(2)

112/04/1115

Parameters:EliminationReproductionLifetimeMaximum Swim LengthSelection Rate (for Elimination)Step Size (for Moving)Attraction and Repellent between cells to

cells. (x4)

Advantages of bacterial foraging algorithm for solving opf over conventional methods

The algorithms work with a population of string, searching many peaks in parallel, as opposed to a single point.

They work directly with strings of characters representing the parameters set not the parameters themselves.

They use probabilistic transition rules instead of deterministic rules.

Cont…They use objective function information

instead of derivatives or others auxiliary knowledge.

They have the potential to find solutions in many different areas of the search space simultaneously.

 

Problems with optimal power flow in India

• For optimal scheduling of generator it is necessary that the generation should always be more than the demand so that the optimal scheduling can be done to give the over all minimum generation cost. This case is not true with India as generation is rarely more than demand.

• Non availability of the generator cost coefficient (a,b,d) required for evaluating fuel cost and used to predict the optimal scheduling of the generator.

References A Power Flow Method Suitable for Solving OPF

Problems Using Genetic Algorithms-:Mirko Todorovski and Dragoslav Rajicic,IEEE.

J.A.Monioh,R.J Koessler,M.S Bond,B.Slott,D.Sun.A papalexopou “Challenges to Optimal Power Flow.”IEEE trans.Power systems.Feb.1997

W.F Tinney and J.W Walker “Direct Solution of Sparse Network Equations by Optimally Ordered Triangular Factorization,”Proc IEEE 1801-1809.1967

A.G Bakirtzis.P.N Biskas,C.F Zoumas and V.Peridis.”Optimal power flow by enhanced Genetic Algorithm,”IEEE trans Power Systems.May 2002.