Load Flow Analysis: Load flow analysis is the basic tool for investigating these
requirements.
⎯ Static load flow equations
The load flow determines the voltage magnitude and angle
⎯ network model formulation
at each bus in a power system under balanced three-phase
⎯ solutions by Gauss-Siedal and Newton- steady-state conditions.
Raphson methods It also computes real and reactive power flows for all
Introduction equipment interconnecting the buses, as well as equipment
losses
A symmetrical steady state is the most important mode of
operation of a power system. Definition: Load flow (or power flow) is the solution for the normal
There are three major problems encountered in this mode of balanced three-phase steady-state operating conditions of an
operation as listed below in their hierarchical order electric power system.
1. Load flow problem
Conventional nodal or loop analysis (Circuit analysis) is not suitable
2. Optimal load scheduling problem
for power flow studies because the input data for loads are normally
3. Systems control problem
given in terms of power, not impedance. Also, generators are
Successful power system operation under normal balanced
considered to be power sources, not voltage or current sources.
three-phase steady-state conditions requires the following:
• Generation supplies the demand (load) plus losses. Therefore, the power flow problem is formulated as a set of
• Bus voltage magnitudes remain close to rated values. nonlinear algebraic equations i.e. power flow equations solved by
• Generators operate within specified real and reactive iterative techniques suitably by computer solutions.
power limits.
Necessity for Power Flow Studies
• Transmission lines and transformers are not overloaded
Power flow studies are undertaken to investigate various features of
the system i.e.:
, i. The line flows (MW and MVAr in the network branches. NB:
ii. The bus voltages and system voltage profile
✓ The data obtained from power flow studies are used for the
iii. The effect of change in configuration and incorporating new
studies of normal operating mode, contingency analysis,
circuits on system loading
outage security assessment, and optimal dispatching and
iv. The effect of temporary loss of transmission capacity and (or)
stability.
generation on system loading and accompanied effects.
✓ Note that, normally it is understood that a “contingency” is
v. The effect of in-phase and quadrative boost voltages on
the loss of a major transmission element or a large
system loading
generating unit.
vi. Economic system operation
✓ When a system can withstand any single major contingency,
vii. System loss minimization
it is now called “N-1 secure” according to the new
viii. Transformer tap setting for economic operation
terminology suggested by the National Electric Reliability
ix. Possible improvements to an existing system by change of
Council (NERC).
conductor sizes and system voltages.
✓ A “double contingency” is the loss of two transmission lines,
In general, load flow calculations are performed for, Power system or two generators, or a line and a generator. In this case, it
planning, system operation, maintenance and control. can be said that such a system is “N-2 secure.”
• Planning stage- determine when the specific power system Power flow methods
elements become underloaded or overloaded.
Before 1929, all power flow (or load flow) calculations were
• Operation stage- ensure that each generator runs at the
made by hand.
maximum operating point
In 1929, network calculators or network analyzers were
• Future expansion of power system - best operation and
employed to perform power flow calculations.
major expansion
The first successful digital method was developed by Ward
and Hale in 1956.
, Most of the early iterative methods were based on the Y-matrix of Contrary to the Gauss–Seidel algorithm, it needs a larger time per
the Gauss–Seidel method. It requires: iteration, but only a few iterations, and is significantly independent
of the network size.
• minimum computer storage
• only a small number of iterations for small networks Therefore, most of the power flow problems that could not be solved
by the Gauss–Seidel method (e.g., systems with negative
Unfortunately, as the size of the network is increased:
impedances) are solved with no difficulty by this method.
• the number of iterations required increases dramatically for
However, it was not computationally competitive on large systems
large systems.
because of the rapid increase of computer time and storage
• In some cases, the method does not provide a solution at all.
requirements with problem size.
Therefore, the slowly converging behaviour of the Gauss–Seidel
The development e.g. a very efficient sparsity-programmed ordered
method and its frequent failure to converge in ill-conditioned
elimination technique to solve the simultaneous equations, the
situations caused the development of the Z-matrix methods.
addition of automatic controls and adjustments, decoupling etc. have
Even though these methods have considerably better-converging enhanced the efficiency of the Newton–Raphson method, in terms of
characteristics, they need a significantly larger computer storage speed and storage requirements, and has made it the most widely
memory since the Z-matrix is full, contrary to the Y-matrix, which is used power flow method.
sparse.
Network Model Formulation
This difficulty encountered in load flow studies led to the
A power system comprises several buses which are interconnected
development of the Newton–Raphson method.
through transmission lines.
Load flow study for such a system necessitates proceeding
systematically by first formulating the network model of the system.
requirements.
⎯ Static load flow equations
The load flow determines the voltage magnitude and angle
⎯ network model formulation
at each bus in a power system under balanced three-phase
⎯ solutions by Gauss-Siedal and Newton- steady-state conditions.
Raphson methods It also computes real and reactive power flows for all
Introduction equipment interconnecting the buses, as well as equipment
losses
A symmetrical steady state is the most important mode of
operation of a power system. Definition: Load flow (or power flow) is the solution for the normal
There are three major problems encountered in this mode of balanced three-phase steady-state operating conditions of an
operation as listed below in their hierarchical order electric power system.
1. Load flow problem
Conventional nodal or loop analysis (Circuit analysis) is not suitable
2. Optimal load scheduling problem
for power flow studies because the input data for loads are normally
3. Systems control problem
given in terms of power, not impedance. Also, generators are
Successful power system operation under normal balanced
considered to be power sources, not voltage or current sources.
three-phase steady-state conditions requires the following:
• Generation supplies the demand (load) plus losses. Therefore, the power flow problem is formulated as a set of
• Bus voltage magnitudes remain close to rated values. nonlinear algebraic equations i.e. power flow equations solved by
• Generators operate within specified real and reactive iterative techniques suitably by computer solutions.
power limits.
Necessity for Power Flow Studies
• Transmission lines and transformers are not overloaded
Power flow studies are undertaken to investigate various features of
the system i.e.:
, i. The line flows (MW and MVAr in the network branches. NB:
ii. The bus voltages and system voltage profile
✓ The data obtained from power flow studies are used for the
iii. The effect of change in configuration and incorporating new
studies of normal operating mode, contingency analysis,
circuits on system loading
outage security assessment, and optimal dispatching and
iv. The effect of temporary loss of transmission capacity and (or)
stability.
generation on system loading and accompanied effects.
✓ Note that, normally it is understood that a “contingency” is
v. The effect of in-phase and quadrative boost voltages on
the loss of a major transmission element or a large
system loading
generating unit.
vi. Economic system operation
✓ When a system can withstand any single major contingency,
vii. System loss minimization
it is now called “N-1 secure” according to the new
viii. Transformer tap setting for economic operation
terminology suggested by the National Electric Reliability
ix. Possible improvements to an existing system by change of
Council (NERC).
conductor sizes and system voltages.
✓ A “double contingency” is the loss of two transmission lines,
In general, load flow calculations are performed for, Power system or two generators, or a line and a generator. In this case, it
planning, system operation, maintenance and control. can be said that such a system is “N-2 secure.”
• Planning stage- determine when the specific power system Power flow methods
elements become underloaded or overloaded.
Before 1929, all power flow (or load flow) calculations were
• Operation stage- ensure that each generator runs at the
made by hand.
maximum operating point
In 1929, network calculators or network analyzers were
• Future expansion of power system - best operation and
employed to perform power flow calculations.
major expansion
The first successful digital method was developed by Ward
and Hale in 1956.
, Most of the early iterative methods were based on the Y-matrix of Contrary to the Gauss–Seidel algorithm, it needs a larger time per
the Gauss–Seidel method. It requires: iteration, but only a few iterations, and is significantly independent
of the network size.
• minimum computer storage
• only a small number of iterations for small networks Therefore, most of the power flow problems that could not be solved
by the Gauss–Seidel method (e.g., systems with negative
Unfortunately, as the size of the network is increased:
impedances) are solved with no difficulty by this method.
• the number of iterations required increases dramatically for
However, it was not computationally competitive on large systems
large systems.
because of the rapid increase of computer time and storage
• In some cases, the method does not provide a solution at all.
requirements with problem size.
Therefore, the slowly converging behaviour of the Gauss–Seidel
The development e.g. a very efficient sparsity-programmed ordered
method and its frequent failure to converge in ill-conditioned
elimination technique to solve the simultaneous equations, the
situations caused the development of the Z-matrix methods.
addition of automatic controls and adjustments, decoupling etc. have
Even though these methods have considerably better-converging enhanced the efficiency of the Newton–Raphson method, in terms of
characteristics, they need a significantly larger computer storage speed and storage requirements, and has made it the most widely
memory since the Z-matrix is full, contrary to the Y-matrix, which is used power flow method.
sparse.
Network Model Formulation
This difficulty encountered in load flow studies led to the
A power system comprises several buses which are interconnected
development of the Newton–Raphson method.
through transmission lines.
Load flow study for such a system necessitates proceeding
systematically by first formulating the network model of the system.
