Load Flow Studies

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Topic Load
Flow Studies

• Presented By
• Arshdeep Kaur
• 
  Department of Electrical
  Engineering
• 
  GNDEC
  ,Ludhiana
• 
  

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What is a Load Flow Study???

• It is a steady-state analysis whose target is
  to determine the
• Voltages
• Currents
• Real and Reactive power flows in a system under
  a given load conditions
• A load flow study also known as power-flow
  study

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• A load flow study is done on a power system to
  ensure that
• Generation supplies the demand (load) plus
  losses.
• Bus voltage magnitudes remain close to rated
  values
• Generation operates within specified real and
  reactive power limits
• Transmission lines and transformers are not
  overloaded.

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A Load Flow Study Specifically Investigates the
Following

• Bus bar voltages
• Effect of rearranging circuits and incorporating
  new circuits on system loading.
• Effect of injecting in-phase and quadrature boost
  voltages on system loading.
• Optimum system running conditions and load
  distribution.
• Optimum system losses.
• Optimum rating and tap range of transformers.

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Power-flow Analysis Equations
The basic equation for power-flow analysis is
derived from the nodal analysis equations for the
power system. For example, for a 4-bus system

• where Yij are the elements of the bus admittance
  matrix,
• Vi are the bus voltages
• Ii are the currents injected at each
  node.
• The node equation at bus i can be written as

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Power-flow Analysis Equations

• Relationship between per-unit real and reactive
  power supplied to the system at bus i and the
  per-unit current injected into the system at that
  bus
• where Vi is the per-unit voltage at the bus
• Ii - complex conjugate of the
  per-unit current injected at the bus
• Pi and Qi are per-unit real and
  reactive powers.
• Therefore,

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Power-flow Analysis Equations
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The Load Flow Problem

• The starting point of a load flow problem is a
  single line diagram of the power system, from
  which input data for computer solutions can be
  obtained. Input data consist of bus data,
  transmission line data and transformer data.
• A bus is a node at which one or many lines, one
  or many loads and generators are connected.

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Formulation of load-flow study

• In a power system each node or bus is associated
  with 4 quantities, such as
• 1. Magnitude of voltage V
• 2. Phage angle of voltage d
• 3. Active power P
• 4. Reactive power Q
• In load flow problem two out of these 4
  quantities are specified and remaining 2 are
  required to be determined through the solution of
  equation.

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Bus Classification
Depending on the quantities that have been
specified, the buses are classified into 3
categories.
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• Each bus is categorized into one of the following
  bus types
• Swing bus / slack bus

Bus Defined To Defined Application
Slack bus V and d usually V1 1 d1 0o P and Q There is only one bus of this type in given power system This is numbered as one for convenience
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• 2.Load bus (P-Q bus)

Bus Defined To Defined Application
PQ bus Pi and Qi Vi and di It is pure load bus (no generator at the bus) These most common bus comprising almost 80 of all of the busses in power system.
It is required to specify only Pd and Qd at such
bus as at a load bus voltage can be allowed to
vary within the permissible values
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• 3. Generator bus (P-V bus)

Bus Defined To Defined Application
PV bus Pi and Vi Qi and di This bus always a generator connected to it. PV bus Comprise about 10 of all the buses in power system
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Methods for solving the load flow
problem.
The power flow equations are non-linear, thus
cannot be solved analytically. A numerical
iterative algorithm is required to solve such
equations

• There are 4 methods of solving the load flow
  problem.
• A) The Gauss Seidel Method
• B) The Newton Raphson Method
• C) Decoupled Newton Method
• D) Fast decoupled method

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A standard procedure follows

• 1.Create a bus admittance matrix Ybus for the
  power system
• 2.Make an initial estimate for the voltages (both
  magnitude and phase angle) at each bus in the
  system
• 3.Substitute in the power flow equations and
  determine the deviations from the solution.
• 4.Update the estimated voltages based on some
  commonly known numerical algorithms (e.g.,
  Newton-Raphson or Gauss-Seidel).
• 5.Repeat the above process until the deviations
  from the solution are minimal.

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Load Flow by Gauss-Seidel Method

• Gauss Seidel Method
• It is an iterative algorithm for solving a set of
  non linear algebraic
• equation. A power system is considered consisting
  of n number of
• buses .
• Let it be assumed that all the buses other than
  the slack bus are PQ buses
• The slack bus voltage is specified and for (n-1)
  PQ buses the bus voltage magnitude and angles are
  assumed .
• These values are then updated through an
  iterative process .

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algorithm

• Algorithm for system if only PQ buses are present
• Step 1 With the load profile known at each bus
  allocate PGi and QGi to all generating
  stations .With this step ,bus injection (
  PijQi)are known at all the buses than the slack
  bus
• Step 2 Formation of bus admittance matrix YBUS
• Step 3. Iterative computation of bus voltage
• A set of initial voltage values is assumed
  and flat voltage start i.e. all voltage are set
  equal to the (1-j0) Except the voltage of the
  slack bus. Bus voltage are calculated using
  equation

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• Where
•  
• And i2,3,4..n
  k1,2,3n also k?i
• Step 4 Computation of slack bus power
  Computation of all bus voltages in step 3 yields
  
• Si (Pi -jQi )
• Step 5.Computation of line flows Power flows on
  the various lines of the network are computed .

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• Algorithm modification when PV buses are also
  present
• At PV buses
• P and V are specified and Q and d are
  unknowns to be determined . Therefore the values
  of Q and d are to be updated in every GS
  iteration. Let 2,3,..m are PV buses and
  remaining m1,..n are PQ buses
• Step1 Qi is calculated for each bus using
  equation
• Revised value Qi is obtained in each
  iteration is calculated by following equation

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• Step2 Revised value of d is obtained using
  equation
• di(r1) Vi(r1)
• Step3 Q at this bus should be within range
• if set and
  treat bus i as a PQ bus. Compute
• if set and
  treat bus i as a PQ bus. Compute
•  
• Disadvantages
• It convergence much slower and may be sometimes
  fail to do so.

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Load flow by Newton-Raphson Power Flow

• It is a powerful method of solving non linear
  algebraic equations.
• Its works faster and is sure to convergence in
  most of the cases as compared to GS method .
• Algorithm
• Step 1. With voltage and angle at the slack bus
  fixed. Assume V and d at all PQ buses and d at
  all PV buses .use flat voltage start

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• Step 2. Compute ?Pi (for PV and PQ buses) and
  ?Qi (for all the PQ buses) from equation
• If all the values are less than tolerance , stop
  the iteration, calculate Pi and Qi
• Step 3. If the convergence criterion is not
  satisfied, evaluate elements of the jocobian.
• Step 4. Solve equation f0 -J0 ?x0 for
  corrections of voltage angles and magnitudes.
• Step 5. Update voltage angles and magnitude by
  adding the corresponding changes to previous
  values and return to step 2.

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Newton-Raphson Power Flow

• Advantages
• fast convergence as long as initial guess is
  close to solution
• large region of convergence.
• Disadvantages
• each iteration takes much longer than a
  Gauss-Seidel iteration
• more complicated
• Newton-Raphson algorithm is very common in power
  flow analysis the only drawback is large
  requirement of computer memory

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Decoupled Newton Method

• Decoupled load flow method is very similar to
  Newton method but achieved after some assumption
  for the sake of simplification .There is weak
  interaction between P-V and q-d.,
• This assumption gives faster computation with
  reasonable accuracy
• 
  
• 
  (1)

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(2) (3)
Eqs 2 and 3 can be constructed and solved
simultaneously with each other at each iteration,
updating the H and L in each iteration using eqs
A better approach is to conduct each iteration by
first solving eqs 2 for and the updated delta
in constructing and then solve eqs 3 for
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Advantage And Disadvantage

• The main advantage of DLF is its reduced memory
  requirement in storing jocobian elements .
• Storage of jocobian and matrix triangularisation
  is saved by factor 4, that is an overall saving
  of 30-40
• Computation time per iteration is less
• However the decoupled load flow takes more number
  of iteration to converge because of approximation
  made.

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Fast decoupled method

• In this method some assumption are made to
  make the computation process faster with
  reasonable accuracy.
• The assumption are
• 1 .There is weak physical interaction between MW
  and MVAR flows in power system therefore MW-d and
  MVAR- V calculation can be decoupled
• 2. Angle differences( di- dk) across transmission
  lines are small under normal loading condition
  i.e

0
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e

• For a transmission line reactance is very high
  as compared to resistance
• i.e can be
  ignored.

• Importance
• In Fast decoupled load flow method converges into
  two to five iteration
• The method is more reliable
• The speed of iteration of FDLF fast
• In FDLF the storage requirement are 60 of the NR
  method and slightly more than the decoupled NR
  method

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Comparison Of Load Flow Methods
PARAMETERS OF COMPARISION GAUSS SIEDEL METHOD NEWTON RAPSON METHOD FAST DECOUPLED LOAD FLOW
Coordinate Rectangular Coordinates Polar Coordinates Polar Coordinates
Arithmetic operation Less in no. to complete one iteration Elements of jocobian to be calculated in each iteration Less than Newton Raphson
Time Less time /iteration, increases with the number of buses. Time Per Iteration Is 7 Times Of GS And Increases With number Of Buses Less Time As Compared To NR And GS Method
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PARAMETERS OF COMPARISION GAUSS SIEDEL METHOD NEWTON RAPSON METHOD FAST DECOUPLED LOAD FLOW
Convergence Linear convergence Quadratic convergence Geometric convergence
No of iteration Large no., increases with number Of buses Very less for large system and is practically constant Only 2or5 iteration for practical accuracy
Slack bus selection Choice of slack bus affect convergence adversely Sensitivity to this minimal Moderate
Accuracy Less accurate More accurate Moderate
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PARAMETERS OF COMPARISION GAUSS SIEDEL METHOD NEWTON RAPSON METHOD FAST DECOUPLED LOAD FLOW
Memory Less memory because of sparsity of matrix Large memory even with compact storage scheme Only 60 of memory when compared to NR
Usage Small size system Large system, ill conditioned problem, optimal load flow studies Optimization studies multiple load flow studies
Programming logic Easy Very difficult Moderate
Reliability Reliable only for small system Reliable for large system More reliable than NR method
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Conclusion

• Load-flow studies are important for planning
  future expansion of power systems as well as in
  determining the best operation of existing
  systems.
• Load flow studies also provide the information
  about the line and transformer load through the
  system.
• We have formulated the algorithm and designed the
  MATLAB programs for bus admittance matrix,
  converting polar form to rectangular form,
  Gauss-Siedel method and Newton Raphson method for
  analyzing the load flow bus systems.

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Thank you