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Economic Operation of Power Systems
Main Objective of ESI
 Main objectives of electricity Supply Industry (ESI)
i. Minimise cost (maximum efficiency)
ii. Reliability (Continuity of the supply)
iii. Security of Supply
iv. Sustainability
 A compromise is sought which must not jeopardise the safety
to personnel and equipment.
Actions Required
 Long-term load forecasts
 Network development
 Short-term load forecasts
 Power system operation and control
 Voltage regulator (AVR) – Control of Q and V
 Turbine Speed governors – Control of P and f
 Optimisation of power system operation
Load Characteristics
 In order to make the best utilisation of the power system
and available resources,
 knowledge on loading condition and characteristics of the
individual loads are essential.
 Loads may be characterised in regard to
Size (Watts to MW)
Symmetry (single or three-phase)
Load constancy (with respect to time, frequency, voltage)
Use cycle (regular or random)
 Symmetry between three phases can be achieved by
intentional distribution of single-phase loads
Load Curve
Load Factor
 Load curve is the plot of variation of load demand
with respect to time.
 Peak or maximum demand is defined as the
maximum load (occurring in the time under
 Load factor is defined as the ratio of average load
during a period to maximum load during the same
Load Factor
Average load
Load Factor 
Maximum load
Energy consumed during a period of time
Load Factor 
Maximum demand * Time under consideration
You can define daily Load factor or annual load factor of the plant
using this definition.
Diversity Factor
 Diversity factor applies to a group of loads whose individual
maximum demand do not all occur at the same time.
 Industrial, commercial and domestic loads
 The system maximum demand will always be less than the sum of
the maximum demand of all the loads.
 It is the parameter which provides the diversification in the load and
is used to decide the installed capacity of the power system.
 Diversity factor is the ratio of (sum of maximum demand of individual
consumers) to (maximum demand on system)
 Diversity factor is greater than unity.
Utilisation Factor
 Utilisation factor shows how well the plant is being used.
 Utilisation factor is the ratio of maximum demand to
installed capacity.
 Installed capacity or effective plant rating is the total rated
capacity of the plant.
 The difference between the maximum demand and the
effective plant rating is known as generating plant margin.
 Normally given as a percentage of the estimated maximum
Reserve Capacity
 To provide best reliability
 Failure of one generating unit should not affect the power
supply to consumers and / or power quality
 This means that additional generating capacity of at
least the value of the largest set operating must be
available instantaneously.
 Known as spinning reserve
 Hot standby
 Its output is available in a short time (about 30 minutes)
Demand Side Management (DSM)
Objective: encourage the consumer to use less
energy during peak hours so load curves lose
peak points.
How: Shift demand from peak times i.e. to
night time and or weekends.
Incentive: change of tariff or use Smart
metering to advise on best tariff rate and times.
Optimisation Method
• Economic Load Dispatch or Generation
• Minimising transmission losses
• Computers with optimal power-flow programs
are used
Optimisation of Power System Operation
 To optimise the performance of a power system, a system control
strategy is established on a daily, monthly and yearly basis.
 The result is the preparation of generation schedules, line usage, etc.
 Factors to be considered:
Fixed cost of supply e.g. interest, fixed salaries and depreciation
Variable cost of supply e.g. fuel
Transmission losses
Transportation of fuel
 Obviously, plant rating and stability limits must be observed.
Economic Dispatch
In this section of the lecture we will look at
how we can optimise generator loading so to
achieve ‘Economic Dispatch’
Variable Costs
 Although fixed element of the generation costs
affects the overall cost of production, it is not
normally considered when allocating generation
to meet demand.
 The allocation is based entirely on the variable
 This is obtained by considering fuel costs,
generation efficiency, maintenance cost etc.
Heat Rate Characteristics
 This is the thermal input – electrical output
characteristics of a turbine-generator set.
 The cost characteristics of thermal power stations
depend primarily on whether turbines used are
single or multiple valve units.
 Single valve units are preferred in the UK while
multiple valves are preferred in the USA.
Heat Rate Characteristics
 Maximum fuel efficiency occurs at the point
where the slope of the line from the origin to a
point on the curve is tangent to the curve e.g. 0.8
Economical Division
 For economical division of load between units, the incremental fuel
costs for all contributing turbine-generator sets should be the same.
 If two sets having different fuel costs are sharing a load, the total
cost can be reduced by transferring load from the set having higher
incremental cost to the set with the lower incremental fuel cost.
 This decreases the incremental cost of the former and increases that
of the latter.
 The limit is reached when the two incremental costs are equal and
the total cost is minimum.
Exercise 1
A power plant consists of two generators that have the following fuel costs (F1 and
F2) in £/hour:
F1  0.015P12  9.3P1  90.... for 0  p  100MW
F2  0.01P22  8.2 P2  80.... for 0 
 200MW
Where P1 and P2 are in MW.
The plant supplies a total load of 150 MW. By neglecting the losses:
1. Determine the power supplied by each generator if these generators are to be
operated in a mode of optimal dispatch.
2. The savings in fuel cost (in £/hour) when the plant is operated in the optimal
economic dispatch mode compared with equal load sharing.
Example 2
• Installed capacity of the generators is 150MW. The generator
supplied power to an industrial load having maximum demand
of 140MW. If the capacity utilization factor of the generator is
70%. Determine
a) Reverse Capacity in MW
b) Reverse margin in %
c) Provide your comment on adequancy of reserve margin.
d) Load factor in %
e) Annul energy in KWh
f) If load factor is to be improved by 10%, recommend one
method that can be used for this purpose.1
Example 3
The annual peak load on 30MV power system is 25MW. The
power station supply load having maximum demand of
10MW,8.5MW, 5MW and 4.5MW. The annul load factor is 45%.
a) Average Load?
b) Energy supply per year?
c) Diversity factor?
d) Capacity Factor?
References further reading
Weedy, B.M. and Cory B.J., “Electric Power
Systems”, Wiley publication.