MA
Uploaded byMd Irshad Ahmad
PPT, PDF422 views

Power station practice (NEE-702) unit-4

The document discusses economic operation of power systems. It covers characteristics of steam and hydro plants, economic load scheduling of thermal plants with and without considering transmission losses, penalty factors and loss coefficients. It also discusses hydrothermal scheduling. The document provides information on retail electricity prices and factors contributing to prices like generation, transmission and distribution costs. It describes different generation technologies in terms of capital and operating costs. The concepts of economic dispatch formulation, incremental costs, lambda iteration method and inclusion of transmission losses in economic dispatch are explained.

Embed presentation

Downloaded 43 times
UNIT-IVUNIT-IV Economic Operation of PowerEconomic Operation of Power SystemsSystems • Md Irshad Ahmad • Irshad.ahmad@jit.edu.in • Electrical Engineering Department • Subject: : POWER STATION PRACTICE • (NEE /NEN–702)
ContentsContents • UNIT-IV:Economic Operation of Power Systems: • Characteristics of steam and hydro- plants,Constraints in operation • Economic load scheduling of thermal plants Neglecting and considering transmission Losses, • Penalty factor, loss coefficients, Incremental transmission loss. Hydrothermal Scheduling.
Retail Electricity PricesRetail Electricity Prices • There are many fixed and variable costs associated with power systems, which ultimately contribute to determining retail electricity prices. • The major variable operating cost is associated with generation, primarily due to fuel costs: – Roughly 30% to 50% of retail costs. • Retail prices also reflect the capital costs of building the generation, transmission, and distribution system as well as other 33
Power System EconomicPower System Economic OperationOperation • Different generation technologies vary in the: – capital costs necessary to build the generator – fuel costs to actually produce electric power • For example: – nuclear and hydro have high capital costs and low operating costs. – Natural gas generators have low capital costs, and (with gas available from fracking) moderate operating costs. 44
Economic Dispatch:Economic Dispatch: FormulationFormulation The goal of economic dispatch is to determine the generation dispatch that minimizes the instantaneous operating cost, subject to the constraint that total generation = total load + losses T 1 1 Minimize C ( ) Such that m i Gi i m Gi D Losses i C P P P P = = = + ∑ ∑ @ Initially we'll ignore generator limits and the losses 55
Unconstrained MinimizationUnconstrained Minimization This is a minimization problem with a single equality constraint For an unconstrained minimization a necessary (but not sufficient) condition for a minimum is the gradient of the function must be zero, The gradient generalizes the first derivative for multi-variable problems: 1 2 ( ) ( ) ( ) ( ) , , , nx x x  ∂ ∂ ∂ ∇  ∂ ∂ ∂  f x f x f x f x K@ ( )∇ =f x 0 66
Minimization with EqualityMinimization with Equality ConstraintConstraintWhen the minimization is constrained with an equality constraint we can solve the problem using the method of Lagrange Multipliers Key idea is to represent a constrained minimization problem as an unconstrained problem.That is, for the general problem minimize ( ) s.t. ( ) We define the Lagrangian L( , ) ( ) ( ) Then a necessary condition for a minimum is the L ( , ) 0 and L ( , ) 0 T = = + ∇ = ∇ =xλ f x g x 0 xλ f x λ g x xλ x λ 77
Economic Dispatch LagrangianEconomic Dispatch Lagrangian G 1 1 G For the economic dispatch we have a minimization constrained with a single equality constraint L( , ) ( ) ( ) (no losses) The necessary conditions for a minimum are L( , ) m m i Gi D Gi i i Gi C P P P dC P λ λ λ = = = + − ∂ = ∂ ∑ ∑P P 1 ( ) 0 (for 1 to ) 0 i Gi Gi m D Gi i P i m dP P P λ = − = = − =∑ 88
Economic Dispatch ExampleEconomic Dispatch Example 1 2 2 1 1 1 1 2 2 2 2 2 1 1 1 What is economic dispatch for a two generator system 500 MW and ( ) 1000 20 0.01 $/h ( ) 400 15 0.03 $/h Using the Lagrange multiplier method we know: ( ) 20 0.0 D G G G G G G G G G G P P P C P P P C P P P dC P dP λ = + = = + + = + + − = + 1 2 2 2 2 1 2 2 0 ( ) 15 0.06 0 500 0 G G G G G G P dC P P dP P P λ λ λ − = − = + − = − − = 99
Economic Dispatch Example,Economic Dispatch Example, cont’dcont’d 1 2 1 2 1 2 1 2 We therefore need to solve three linear equations 20 0.02 0 15 0.06 0 500 0 0.02 0 1 20 0 0.06 1 15 1 1 0 500 312.5 MW 187.5 MW 26.2 $/MW G G G G G G G G P P P P P P P P λ λ λ λ + − = + − = − − = − −         − = −      − − −             =      h          1010
Economic dispatch example,Economic dispatch example, cont’dcont’d • At the solution, both generators have the same marginal (or incremental) cost, and this common marginal cost is equal to λ. • Intuition behind solution: – If marginal costs of generators were different, then by decreasing production at higher marginal cost generator, and increasing production at lower marginal cost generator we could lower overall costs. – Generalizes to any number of generators. • If demand changes, then change in total costs can be estimated from λ. 1111
Economic dispatch example,Economic dispatch example, cont’dcont’d • Another way to solve the equations is to: – Rearrange the first two equations to solve for PG1 and PG2 in terms of λ, – Plug into third equation and solve for λ, – Use the solved value of λ to evaluate PG1 and PG2. • This works even when relationship between generation levels and λ is more complicated: – Equations are more complicated than linear 1212
Lambda-Iteration SolutionLambda-Iteration Solution MethodMethod • Discussion on previous page leads to “lambda-iteration” method: – this method requires a unique mapping from a value of lambda (marginal cost) to each generator’s MW output: – for any choice of lambda (common marginal cost), the generators collectively produce a total MW output, – the method then starts with values of lambda below and above the optimal value (corresponding to too little and too much total output), and then iteratively brackets the optimal• 1313 ( ).Gi P λ
Lambda-Iteration AlgorithmLambda-Iteration Algorithm L H 1 1 H L M H L H M 1 L M Pick and such that ( ) 0 ( ) 0 While Do ( )/2 If ( ) 0 Then Else End While m m L H Gi D Gi D i i m M Gi D i P P P P P P λ λ λ λ λ λ ε λ λ λ λ λ λ λ λ = = = − < − > − > = + − > = = ∑ ∑ ∑ 1414
Lambda-Iteration: GraphicalLambda-Iteration: Graphical ViewView In the graph shown below for each value of lambda there is a unique PGi for each generator. This relationship is the PGi(λ) function. 1515
Lambda-Iteration ExampleLambda-Iteration Example 1 1 1 2 2 2 3 3 3 1 2 3 Consider a three generator system with ( ) 15 0.02 $/MWh ( ) 20 0.01 $/MWh ( ) 18 0.025 $/MWh and with constraint 1000MW Rewriting generation as a function of , ( G G G G G G G G G Gi IC P P IC P P IC P P P P P P λ λ λ λ = + = = + = = + = + + = G1 G2 G3 ), we have 15 20 P ( ) P ( ) 0.02 0.01 18 P ( ) 0.025 λ λ λ λ λ λ λ − − = = − = 1616
Lambda-Iteration Example,Lambda-Iteration Example, cont’dcont’dm Gi i=1 m Gi i=1 1 H 1 Pick so P ( ) 1000 0 and P ( ) 1000 0 Try 20 then (20) 1000 15 20 18 1000 670 MW 0.02 0.01 0.025 Try 30 then (30) 1000 1230 MW L L H m L Gi i m Gi i P P λ λ λ λ λ λ λ λ = = − < − > = − = − − − + + − = − = − = ∑ ∑ ∑ ∑ 1717
Lambda-Iteration Example,Lambda-Iteration Example, cont’dcont’d 1 1 Pick convergence tolerance 0.05 $/MWh Then iterate since 0.05 ( )/ 2 25 Then since (25) 1000 280 we set 25 Since 25 20 0.05 (25 20)/ 2 22.5 (22.5) 1000 195 we set 2 H L M H L m H Gi i M m L Gi i P P ε λ λ λ λ λ λ λ λ = = = − > = + = − = = − > = + = − = − = ∑ ∑ 2.5 1818
Lambda-Iteration Example,Lambda-Iteration Example, cont’dcont’d H * * 1 2 3 Continue iterating until 0.05 The solution value of , , is 23.53 $/MWh Once is known we can calculate the 23.53 15 (23.5) 426 MW 0.02 23.53 20 (23.5) 353 MW 0.01 23.53 18 (23.5) 0.025 L Gi G G G P P P P λ λ λ λ λ − < − = = − = = − = 221 MW= 1919
Thirty Bus ED ExampleThirty Bus ED Example Case is economically dispatched (without considering the incremental impact of the system losses). 2020
Generator MW LimitsGenerator MW Limits Generators have limits on the minimum and maximum amount of power they can produce Typically the minimum limit is not zero. Because of varying system economics usually many generators in a system are operated at their maximum MW limits: Baseload generators are at their maximum limits except during the off-peak. 2121
Lambda-Iteration with GenLambda-Iteration with Gen LimitsLimits ,max ,max In the lambda-iteration method the limits are taken into account when calculating ( ) : if calculated production for then set ( ) if calculated production for Gi Gi Gi Gi Gi P P P P P λ λ > = ,min ,minthen set ( ) Gi Gi Gi Gi P P P Pλ < = 2222
Lambda-Iteration Gen LimitLambda-Iteration Gen Limit ExampleExample G1 G2 G3 1 2 3 1 In the previous three generator example assume the same cost characteristics but also with limits 0 P 300 MW 100 P 500 MW 200 P 600 MW With limits we get: (20) 1000 (20) (20) (20) 10 m Gi G G G i P P P P = ≤ ≤ ≤ ≤ ≤ ≤ − = + + −∑ 1 00 250 100 200 1000 450 MW (compared to 670MW) (30) 1000 300 500 480 1000 280 MW m Gi i P = = + + − = − − − = + + − =∑ 2323
Lambda-Iteration LimitLambda-Iteration Limit Example,cont’dExample,cont’dAgain we continue iterating until the convergence condition is satisfied. With limits the final solution of , is 24.43 $/MWh (compared to 23.53 $/MWh without limits). Maximum limits will always caus λ 1 2 3 e to either increase or remain the same. Final solution is: (24.43) 300 MW (at maximum limit) (24.43) 443 MW (24.43) 257 MW G G G P P P λ = = = 2424
Back of Envelope ValuesBack of Envelope Values $/MWhr = fuelcost * heatrate + variable O&M Typical incremental costs can be roughly approximated: – Typical heatrate for a coal plant is 10, modern combustion turbine is 10, combined cycle plant is 6 to 8, older combustion turbine 15. – Fuel costs ($/MBtu) are quite variable, with current values around 2 for coal, 3 to 5 for natural gas, 0.5 for nuclear, probably 10 for fuel oil. – Hydro costs tend to be quite low, but are fuel (water) constrained 2525
Inclusion of TransmissionInclusion of Transmission LossesLosses The losses on the transmission system are a function of the generation dispatch. In general, using generators closer to the load results in lower losses This impact on losses should be included when doing the economic dispatch Losses can be included by slightly rewriting the Lagrangian to include G 1 1 L( , ) ( ) ( ) m m i Gi D L G Gi i i C P P P P Pλ λ = =   = + + − ÷   ∑ ∑P 2626
Impact of Transmission LossesImpact of Transmission Losses G 1 1 G The inclusion of losses then impacts the necessary conditions for an optimal economic dispatch: L( , ) ( ) ( ) . The necessary conditions for a minimum are now: L( , ) m m i Gi D L G Gi i i C P P P P Pλ λ λ = =   = + + − ÷   ∂ ∂ ∑ ∑P P 1 ( ) ( ) 1 0 ( ) 0 i Gi L G Gi Gi Gi m D L G Gi i dC P P P P dP P P P P P λ =  ∂ = − − = ÷∂  + − =∑ 2727
Impact of Transmission LossesImpact of Transmission Losses th ( ) ( ) Solving for , we get: 1 0 ( )1 ( ) 1 Define the penalty factor for the generator (don't confuse with Lagrangian L!!!) 1 ( ) 1 i Gi L G Gi Gi i Gi GiL G Gi i i L G Gi dC P P P dP P dC P dPP P P L i L P P P λ λ λ  ∂ − − = ÷∂  =  ∂ − ÷∂  =  ∂ − ∂  ÷  The penalty factor at the slack bus is always unity! 2828
Impact of Transmission LossesImpact of Transmission Losses 1 1 1 2 2 2 The condition for optimal dispatch with losses is then ( ) ( ) ( ) 1 . So, if increasing increases ( ) 1 ( ) the losses then 0 1.0 This makes generator G G m m Gm i Gi L G Gi L G i Gi L IC P L IC P L IC P L P P P P P P L P λ= = = =  ∂ − ÷∂  ∂ > ⇒ > ∂ appear to be more expensive (i.e., it is penalized). Likewise 1.0 makes a generator appear less expensive. i i L < 2929
Calculation of Penalty FactorsCalculation of Penalty Factors Unfortunately, the analytic calculation of is somewhat involved. The problem is a small change in the generation at impacts the flows and hence the losses throughout the entire system. However, i Gi L P using a power flow you can approximate this function by making a small change to and then seeing how the losses change: ( ) ( ) 1 ( ) 1 Gi L G L G i L GGi Gi Gi P P P P P L P PP P P ∂ ∆ ≈ ≈ ∆∂ ∆ − ∆ 3030
Two Bus Penalty FactorTwo Bus Penalty Factor ExampleExample 2 2 2 2 ( ) ( ) 0.37 0.0387 0.037 10 0.9627 0.9643 L G L G G G P P P P MW P P MW L L ∂ ∆ − = − = = − ∂ ∆ = ≈ 3131
Thirty Bus ED ExampleThirty Bus ED Example Now consider losses. Because of the penalty factors the generator incremental costs are no longer identical. 3232
Area Supply CurveArea Supply Curve 0 100 200 300 400 Total AreaGeneration(MW) 0.00 2.50 5.00 7.50 10.00 The area supply curve shows the cost to produce the next MW of electricity, assuming area is economically dispatched Supply curve for thirty bus system 3333
Economic Dispatch - SummaryEconomic Dispatch - Summary Economic dispatch determines the best way to minimize the current generator operating costs. The lambda-iteration method is a good approach for solving the economic dispatch problem: – generator limits are easily handled, – penalty factors are used to consider the impact of losses. Economic dispatch is not concerned with determining which units to turn on/off (this is the unit commitment problem). Basic form of economic dispatch ignores the transmission system limitations. 3434
Security Constrained EDSecurity Constrained ED or Optimal Power Flowor Optimal Power Flow Transmission constraints often limit ability to use lower cost power. Such limits require deviations from what would otherwise be minimum cost dispatch in order to maintain system “security.” Need to solve or approximate power flow in order to consider transmission constraints. 3535
Security Constrained EDSecurity Constrained ED or Optimal Power Flowor Optimal Power Flow The goal of a security constrained ED or optimal power flow (OPF) is to determine the “best” way to instantaneously operate a power system, considering transmission limits. Usually “best” = minimizing operating cost, while keeping flows on transmission below limits. In three bus case the generation at bus 3 must be limited to avoid overloading the 3636
Security Constrained DispatchSecurity Constrained Dispatch Bus 2 Bus 1 Bus 3Home Area Scheduled Transactions 357 MW 179 MVR 194 MW 448 MW 19 MVR 232 MVR 179 MW 89 MVR 1.00 PU -22 MW 4 MVR 22 MW -4 MVR -142 MW 49 MVR 145 MW -37 MVR 124 MW -33 MVR -122 MW 41 MVR 1.00 PU 1.00 PU 0 MW 37 MVR100% 100% 100 MW OFF AGC AVR ON AGC ON AVR ON 100.0 MW Need to dispatch to keep line from bus 3 to bus 2 from overloading 3737
Multi-Area OperationMulti-Area Operation In multi-area system, “rules” have been established regarding transactions on tie-lines: – In Eastern interconnection, in principle, up to “nominal” thermal interconnection capacity, – In Western interconnection there are more complicated rules The actual power that flows through the entire network depends on the impedance of the transmission lines, and ultimately determine what are acceptable patterns of dispatch: Can result in need to “curtail” transactions that otherwise satisfy rules. Economically uncompensated flow through other areas is known as “parallel path” or “loop flows.” Since ERCOT is one area, all of the flows on AC lines are inside ERCOT and there is no uncompensated flow on AC lines. 3838
Power System EconomicPower System Economic OperationOperation • Fuel cost to generate a MWh can vary widely from technology to technology. • For some types of units, such as hydro, “fuel” costs are zero but the limit on total available water gives it an implicit value. • For thermal units it is much easier to characterize costs. • We will focus on minimizing the variable operating costs (primarily fuel costs) to meet demand. 3939
Power System EconomicPower System Economic OperationOperation • Power system loads are cyclical. • Therefore the installed generation capacity is usually much greater than the current load. • This means that there are typically many ways we could meet the current load. • Since different states have different mixes of generation, we will consider how generally to minimize the variable operating costs given an arbitrary, 4040
Thermal versus OtherThermal versus Other GenerationGenerationThe main types of generating units are thermal and hydro, with wind and solar rapidly growing. For hydro the fuel (water) is free but there may be many constraints on operation: – fixed amounts of water available, – reservoir levels must be managed and coordinated, – downstream flow rates for fish and navigation. Hydro optimization is typically longer term (many months or years). We will concentrate on dispatchable thermal units, looking at short-term 4141
Generator typesGenerator types Traditionally utilities have had three broad groups of generators: – “Baseload” units: large coal/nuclear; almost always on at max. – “Midload,” ‘intermediate,” or “cycling” units: smaller coal or gas that cycle on/off daily or weekly. – “Peaker” units: combustion turbines used only for several hours. during periods of high demand 4242
Block Diagram of Thermal UnitBlock Diagram of Thermal Unit •To optimize generation costs we need to develop cost relationships between net power out and operating costs. •Between 2-10% of power is used within the generating plant; this is known as the auxiliary 4343
Thermal generator Cost CurvesThermal generator Cost Curves Thermal generator costs are typically represented by one or other of the following four curves – input/output (I/O) curve – fuel-cost curve – heat-rate curve – incremental cost curve For reference - 1 Btu (British thermal unit) = 1054 J - 1 MBtu = 1x106 Btu - 1 MBtu = 0.29 MWh 4444
I/O CurveI/O Curve The IO curve plots fuel input (in MBtu/hr) versus net MW output. 4545
Fuel-cost CurveFuel-cost Curve The fuel-cost curve is the I/O curve multiplied by fuel cost. A typical cost for coal is $ 1.70/MBtu. 4646
Heat-rate CurveHeat-rate Curve • Plots the average number of MBtu/hr of fuel input needed per MW of output. • Heat-rate curve is the I/O curve divided by MW. Best heat-rate for most efficient coal units is around 9.0 4747
Incremental (Marginal) costIncremental (Marginal) cost CurveCurvePlots the incremental $/MWh as a function of MW. Found by differentiating the cost curve. 4848
Mathematical Formulation ofMathematical Formulation of CostsCostsGenerator cost curves are usually not smooth. However the curves can usually be adequately approximated using piece-wise smooth, functions. Two approximations predominate: – quadratic or cubic functions – piecewise linear functions We'll assume a quadratic approximation: 2 ( ) $/hr (fuel-cost) ( ) ( ) 2 $/MWh i Gi i i Gi i Gi i Gi i Gi i i Gi Gi C P P P dC P IC P P dP α β γ β γ = + + = = + 4949
Coal Usage ExampleCoal Usage Example •A 500 MW (net) generator is 35% efficient. It is being supplied with coal costing $1.70 per MBtu and with heat content 9000 Btu per pound. What is the coal usage in lbs/hr? What is the cost? At 35% efficiency required fuel input per hour is 500 MWh 1428 MWh 1 MBtu 4924 MBtu hr 0.35 hr 0.29 MWh hr 4924 MBtu 1 lb 547,111 lbs hr 0.009MBtu hr 4924 MBtu $1.70 Cost = 8370.8 $/hr or $16.74/MWh hr MBtu = × = × × = × = 5050
Wasting Coal ExampleWasting Coal Example •Assume a 100W lamp is left on by mistake for 8 hours, and that the electricity is supplied by the previous coal plant and that transmission/distribution losses are 20%. How much coal has he/she wasted? With 20% losses, a 100W load on for 8 hrs requires 1 kWh of energy. With 35% gen. efficiency this requires 1 kWh 1 MWh 1 MBtu 1 lb 1.09 lb 0.35 1000 kWh 0.29 MWh 0.009MBtu × × × = 5151
Incremental Cost ExampleIncremental Cost Example 2 1 1 1 1 2 2 2 2 2 1 1 1 1 1 1 2 2 2 2 2 2 For a two generator system assume ( ) 1000 20 0.01 $/hr ( ) 400 15 0.03 $/hr Then ( ) ( ) 20 0.02 $/MWh ( ) ( ) 15 0.06 $/MWh G G G G G G G G G G G G G G C P P P C P P P dC P IC P P dP dC P IC P P dP = + + = + + = = + = = + 5252
Incremental Cost Example,Incremental Cost Example, cont'dcont'd 1 2 2 1 2 2 1 2 If 250 MW and 150 MW Then (250) 1000 20 250 0.01 250 $ 6625/hr (150) 400 15 150 0.03 150 $6025/hr Then (250) 20 0.02 250 $ 25/MWh (150) 15 0.06 150 $ 24/MWh G GP P C C IC IC = = = + × + × = = + × + × = = + × = = + × = 5353
5454 THANK YOUTHANK YOU

More Related Content

PPT
Ece4762011 lect16
bymiguelmena2013
 
PPTX
Economic load dispatch
byMd. Hasan Al Roktim
 
PPTX
Solution to ELD problem
byNaveena Navi
 
PPTX
Economic load dispatch
byVipin Pandey
 
PPTX
Economic dispatch
byHussain Ali
 
PPTX
Project on economic load dispatch
byayantudu
 
PDF
Solution of Combined Heat and Power Economic Dispatch Problem Using Different...
byArkadev Ghosh
 
PDF
ECONOMIC LOAD DISPATCH USING GENETIC ALGORITHM
byIJARIIT
 
Ece4762011 lect16
bymiguelmena2013
 
Economic load dispatch
byMd. Hasan Al Roktim
 
Solution to ELD problem
byNaveena Navi
 
Economic load dispatch
byVipin Pandey
 
Economic dispatch
byHussain Ali
 
Project on economic load dispatch
byayantudu
 
Solution of Combined Heat and Power Economic Dispatch Problem Using Different...
byArkadev Ghosh
 
ECONOMIC LOAD DISPATCH USING GENETIC ALGORITHM
byIJARIIT
 

What's hot

PPT
Lecture 16
byForward2025
 
PPTX
Economic load dispatch
byDeepak John
 
PDF
Economic Dispatch of Generated Power Using Modified Lambda-Iteration Method
byIOSR Journals
 
PPTX
ECONOMIC LOAD DISPATCH USING PARTICLE SWARM OPTIMIZATION
byMln Phaneendra
 
PPTX
Hydrothermal scheduling
byASHIRBAD BARIK
 
PPT
Cost of electricity generation
bySerajul Haque
 
PPTX
Optimal load scheduling
byMayank Sharma
 
PPT
Economic load dispatch
byvikram anand
 
PPTX
A presentation on economic load dispatch
bysouravsahoo28
 
PPT
Unit Commitment
byrohitdasari
 
PPTX
Optimization of power sytem
byshawon1981
 
PPTX
Economic operation of Power systems by Unit commitment
byPritesh Priyadarshi
 
PDF
A Case Study of Economic Load Dispatch for a Thermal Power Plant using Partic...
byInternational Journal of Science and Research (IJSR)
 
PDF
OPTIMAL ECONOMIC LOAD DISPATCH USING FUZZY LOGIC & GENETIC ALGORITHMS
byIAEME Publication
 
PPTX
Input output , heat rate characteristics and Incremental cost
byEklavya Sharma
 
PDF
Economic load dispatch
byMANGESHKULKARNI72
 
DOCX
Unit commitment
byAhmed M. Elkholy
 
PPTX
Economic Dispatch Research paper solution slides
byMuhammad Abdullah
 
Lecture 16
byForward2025
 
Economic load dispatch
byDeepak John
 
Economic Dispatch of Generated Power Using Modified Lambda-Iteration Method
byIOSR Journals
 
ECONOMIC LOAD DISPATCH USING PARTICLE SWARM OPTIMIZATION
byMln Phaneendra
 
Hydrothermal scheduling
byASHIRBAD BARIK
 
Cost of electricity generation
bySerajul Haque
 
Optimal load scheduling
byMayank Sharma
 
Economic load dispatch
byvikram anand
 
A presentation on economic load dispatch
bysouravsahoo28
 
Unit Commitment
byrohitdasari
 
Optimization of power sytem
byshawon1981
 
Economic operation of Power systems by Unit commitment
byPritesh Priyadarshi
 
A Case Study of Economic Load Dispatch for a Thermal Power Plant using Partic...
byInternational Journal of Science and Research (IJSR)
 
OPTIMAL ECONOMIC LOAD DISPATCH USING FUZZY LOGIC & GENETIC ALGORITHMS
byIAEME Publication
 
Input output , heat rate characteristics and Incremental cost
byEklavya Sharma
 
Economic load dispatch
byMANGESHKULKARNI72
 
Unit commitment
byAhmed M. Elkholy
 
Economic Dispatch Research paper solution slides
byMuhammad Abdullah
 

Similar to Power station practice (NEE-702) unit-4

PPT
Lecture_16.ppt
byKifle Godana
 
PPT
Economic Load Dispatch.ppt
bySuraj Dhungel
 
PPT
UNIT-4-PPT.ppt
byKarthik Kathan
 
PPTX
PSOC.pptx
bySrihari Datta
 
PPT
Lecture_15.ppt
byKifle Godana
 
PPT
electrical Economic Operation Of Power Systems
bykurmaiah86
 
PDF
2.Direct Method without TL Losshhhhhhhhhhhhhhhhhh.pdf
byblesslinthanushang
 
PDF
Economic_Load_Dispatch.pdf
byLucasMogaka
 
PDF
Economic_Load_Dispatch and loakd forecasting
bynptierpmsgmb
 
PDF
COMBINED ECONOMIC AND EMISSION DISPATCH WITH AND WITHOUT CONSIDERING TRANSMIS...
bycscpconf
 
PPTX
Unit 5 Economic Load Dispatch and Unit Commitment
bySANTOSH GADEKAR
 
PPT
Economic dispatch control ppt in unit 4
byssuser53fa43
 
PPTX
ECE476_2016_Lect17.pptx
byFeehaAreej
 
PPT
ECE4762011_Lect16.ppt
byMuhammadAniqueAslam1
 
PPT
Lecture_15.ppt
bySupravaGhoshPaul
 
PDF
Economic dipatch
byDoni Wahyudi
 
PDF
Farag1995
byPradip khatri
 
PDF
DFisher ETLS 747 Paper - Optimal Power Flow
byDan Fisher
 
PDF
Modified sub-gradient based combined objective technique and evolutionary pro...
byIJECEIAES
 
PDF
Optimal Power Generation in Energy-Deficient Scenarios Using Bagging Ensembles
byKashif Mehmood
 
Lecture_16.ppt
byKifle Godana
 
Economic Load Dispatch.ppt
bySuraj Dhungel
 
UNIT-4-PPT.ppt
byKarthik Kathan
 
PSOC.pptx
bySrihari Datta
 
Lecture_15.ppt
byKifle Godana
 
electrical Economic Operation Of Power Systems
bykurmaiah86
 
2.Direct Method without TL Losshhhhhhhhhhhhhhhhhh.pdf
byblesslinthanushang
 
Economic_Load_Dispatch.pdf
byLucasMogaka
 
Economic_Load_Dispatch and loakd forecasting
bynptierpmsgmb
 
COMBINED ECONOMIC AND EMISSION DISPATCH WITH AND WITHOUT CONSIDERING TRANSMIS...
bycscpconf
 
Unit 5 Economic Load Dispatch and Unit Commitment
bySANTOSH GADEKAR
 
Economic dispatch control ppt in unit 4
byssuser53fa43
 
ECE476_2016_Lect17.pptx
byFeehaAreej
 
ECE4762011_Lect16.ppt
byMuhammadAniqueAslam1
 
Lecture_15.ppt
bySupravaGhoshPaul
 
Economic dipatch
byDoni Wahyudi
 
Farag1995
byPradip khatri
 
DFisher ETLS 747 Paper - Optimal Power Flow
byDan Fisher
 
Modified sub-gradient based combined objective technique and evolutionary pro...
byIJECEIAES
 
Optimal Power Generation in Energy-Deficient Scenarios Using Bagging Ensembles
byKashif Mehmood
 

More from Md Irshad Ahmad

PPT
Power station practice (NEE-702) unit-3
byMd Irshad Ahmad
 
PPT
Power quality 5
byMd Irshad Ahmad
 
PPTX
Electrical measurement &amp; measuring instruments [emmi (nee-302) -unit-3]
byMd Irshad Ahmad
 
PPT
Power station practice (NEE-702) unit-2
byMd Irshad Ahmad
 
PPTX
Electrical measurement &amp; measuring instruments [emmi (nee-302) -unit-2]
byMd Irshad Ahmad
 
PPTX
Electrical measurement & measuring instruments [emmi (nee-302) -unit-5]
byMd Irshad Ahmad
 
PPTX
Power quality 2
byMd Irshad Ahmad
 
PPTX
Power quality 4
byMd Irshad Ahmad
 
PPT
Academic Council Meet PPT- 19
byMd Irshad Ahmad
 
PPTX
Electrical measurement &amp; measuring instruments [emmi (nee-302) -unit-4]
byMd Irshad Ahmad
 
PPTX
Switchgear and protection 4
byMd Irshad Ahmad
 
PPTX
Switchgear and protection 5
byMd Irshad Ahmad
 
PPT
Power station practice (NEE- 702) unit-1
byMd Irshad Ahmad
 
PPTX
Power quality 3
byMd Irshad Ahmad
 
PPTX
Switchgear and protection 1
byMd Irshad Ahmad
 
PPTX
Switchgear and protection 2
byMd Irshad Ahmad
 
PPTX
Power quality 1
byMd Irshad Ahmad
 
PPTX
Switchgear and protection 3
byMd Irshad Ahmad
 
PPTX
ELECTRICAL MEASUREMENT & MEASURING INSTRUMENTS [Emmi- (NEE-302) -unit-1]
byMd Irshad Ahmad
 
PPT
Power station practice (NEE-702) unit-5
byMd Irshad Ahmad
 
Power station practice (NEE-702) unit-3
byMd Irshad Ahmad
 
Power quality 5
byMd Irshad Ahmad
 
Electrical measurement &amp; measuring instruments [emmi (nee-302) -unit-3]
byMd Irshad Ahmad
 
Power station practice (NEE-702) unit-2
byMd Irshad Ahmad
 
Electrical measurement &amp; measuring instruments [emmi (nee-302) -unit-2]
byMd Irshad Ahmad
 
Electrical measurement & measuring instruments [emmi (nee-302) -unit-5]
byMd Irshad Ahmad
 
Power quality 2
byMd Irshad Ahmad
 
Power quality 4
byMd Irshad Ahmad
 
Academic Council Meet PPT- 19
byMd Irshad Ahmad
 
Electrical measurement &amp; measuring instruments [emmi (nee-302) -unit-4]
byMd Irshad Ahmad
 
Switchgear and protection 4
byMd Irshad Ahmad
 
Switchgear and protection 5
byMd Irshad Ahmad
 
Power station practice (NEE- 702) unit-1
byMd Irshad Ahmad
 
Power quality 3
byMd Irshad Ahmad
 
Switchgear and protection 1
byMd Irshad Ahmad
 
Switchgear and protection 2
byMd Irshad Ahmad
 
Power quality 1
byMd Irshad Ahmad
 
Switchgear and protection 3
byMd Irshad Ahmad
 
ELECTRICAL MEASUREMENT & MEASURING INSTRUMENTS [Emmi- (NEE-302) -unit-1]
byMd Irshad Ahmad
 
Power station practice (NEE-702) unit-5
byMd Irshad Ahmad
 

Recently uploaded

PPTX
Chen,Usmani,Li - Optimizing PATH Weekend Operations - Presentation.pptx
byLeyanChen3
 
PDF
Presentation-on-Energy-Transition-in-Bangladesh-Employment-and-Skills.pdf
bysyedSajib8
 
PDF
ACI 318-2205_American Concrete Institute.pdf
byericaguilerasoto1
 
PPT
861828706-chapter-7 introductionto UrbanHydrology.ppt
byHussenMohammed18
 
PPTX
Natural Gas fundamentals and GRU for associated gas trap.pptx
byengineerhassan
 
PPTX
Importance of Asset Register in Maintenance Management
byMaintWiz Technologies Private Limited
 
PDF
Ground heat exchanger for rootzone cooling of crops in vertical aeroponics
byChristopherPascual13
 
PDF
FABRICATION AND CHARACTERIZATION OF CONDUCTING POLYMER COMPOSITE
byijoejnl
 
PPTX
Avoiding Pitfalls: The 7 Biggest Maintenance Mistakes Plant Managers Make
byMaintWiz Technologies Private Limited
 
PPTX
Design and Thermal Analysis of Plate Type Heat Exchanger
byKhageshKumarDansena
 
PPTX
Importance of Instrument Calibration — Improve Accuracy, Reliability & Mainte...
byMaintWiz Technologies Private Limited
 
PDF
CV_Rahul_ELV Project Engineer_8 Years Experience
byRahulSushruth
 
PPTX
Emerging Trends and Research Frontiers in Chemical Engineering for Green and ...
byChemical Engineering Dept. NIT Rourkela-769008, Odisha, India
 
PPTX
How to Create an Effective Monthly Maintenance Plan for Reliable Plant Operat...
byMaintWiz Technologies Private Limited
 
PPTX
TPM Metrics & Measurement: Drive Performance Excellence with TPM | MaintWiz
byMaintWiz Technologies Private Limited
 
PPT
new Introduction to PACS.ppt Picture Archieving and communication and medicine
byssuserf3d7af
 
PPTX
علي نفط.pptx هندسة النفط هندسة النفط والغاز
byengpe23e27
 
PPTX
UnrealGameplayAbilitySystemPresentation.pptx
byBenHowenstein
 
PPTX
MECCA Empire – Hotel Shuttle System for the 2026 FIFA World Cup
byay2432
 
PDF
Narrows Planning Collective Transportation Capstone.pdf
bycj2392
 
Chen,Usmani,Li - Optimizing PATH Weekend Operations - Presentation.pptx
byLeyanChen3
 
Presentation-on-Energy-Transition-in-Bangladesh-Employment-and-Skills.pdf
bysyedSajib8
 
ACI 318-2205_American Concrete Institute.pdf
byericaguilerasoto1
 
861828706-chapter-7 introductionto UrbanHydrology.ppt
byHussenMohammed18
 
Natural Gas fundamentals and GRU for associated gas trap.pptx
byengineerhassan
 
Importance of Asset Register in Maintenance Management
byMaintWiz Technologies Private Limited
 
Ground heat exchanger for rootzone cooling of crops in vertical aeroponics
byChristopherPascual13
 
FABRICATION AND CHARACTERIZATION OF CONDUCTING POLYMER COMPOSITE
byijoejnl
 
Avoiding Pitfalls: The 7 Biggest Maintenance Mistakes Plant Managers Make
byMaintWiz Technologies Private Limited
 
Design and Thermal Analysis of Plate Type Heat Exchanger
byKhageshKumarDansena
 
Importance of Instrument Calibration — Improve Accuracy, Reliability & Mainte...
byMaintWiz Technologies Private Limited
 
CV_Rahul_ELV Project Engineer_8 Years Experience
byRahulSushruth
 
Emerging Trends and Research Frontiers in Chemical Engineering for Green and ...
byChemical Engineering Dept. NIT Rourkela-769008, Odisha, India
 
How to Create an Effective Monthly Maintenance Plan for Reliable Plant Operat...
byMaintWiz Technologies Private Limited
 
TPM Metrics & Measurement: Drive Performance Excellence with TPM | MaintWiz
byMaintWiz Technologies Private Limited
 
new Introduction to PACS.ppt Picture Archieving and communication and medicine
byssuserf3d7af
 
علي نفط.pptx هندسة النفط هندسة النفط والغاز
byengpe23e27
 
UnrealGameplayAbilitySystemPresentation.pptx
byBenHowenstein
 
MECCA Empire – Hotel Shuttle System for the 2026 FIFA World Cup
byay2432
 
Narrows Planning Collective Transportation Capstone.pdf
bycj2392
 

Power station practice (NEE-702) unit-4

  • 1.
    UNIT-IVUNIT-IV Economic Operation ofPowerEconomic Operation of Power SystemsSystems • Md Irshad Ahmad • Irshad.ahmad@jit.edu.in • Electrical Engineering Department • Subject: : POWER STATION PRACTICE • (NEE /NEN–702)
  • 2.
    ContentsContents • UNIT-IV:Economic Operationof Power Systems: • Characteristics of steam and hydro- plants,Constraints in operation • Economic load scheduling of thermal plants Neglecting and considering transmission Losses, • Penalty factor, loss coefficients, Incremental transmission loss. Hydrothermal Scheduling.
  • 3.
    Retail Electricity PricesRetailElectricity Prices • There are many fixed and variable costs associated with power systems, which ultimately contribute to determining retail electricity prices. • The major variable operating cost is associated with generation, primarily due to fuel costs: – Roughly 30% to 50% of retail costs. • Retail prices also reflect the capital costs of building the generation, transmission, and distribution system as well as other 33
  • 4.
    Power System EconomicPowerSystem Economic OperationOperation • Different generation technologies vary in the: – capital costs necessary to build the generator – fuel costs to actually produce electric power • For example: – nuclear and hydro have high capital costs and low operating costs. – Natural gas generators have low capital costs, and (with gas available from fracking) moderate operating costs. 44
  • 5.
    Economic Dispatch:Economic Dispatch: FormulationFormulation Thegoal of economic dispatch is to determine the generation dispatch that minimizes the instantaneous operating cost, subject to the constraint that total generation = total load + losses T 1 1 Minimize C ( ) Such that m i Gi i m Gi D Losses i C P P P P = = = + ∑ ∑ @ Initially we'll ignore generator limits and the losses 55
  • 6.
    Unconstrained MinimizationUnconstrained Minimization Thisis a minimization problem with a single equality constraint For an unconstrained minimization a necessary (but not sufficient) condition for a minimum is the gradient of the function must be zero, The gradient generalizes the first derivative for multi-variable problems: 1 2 ( ) ( ) ( ) ( ) , , , nx x x  ∂ ∂ ∂ ∇  ∂ ∂ ∂  f x f x f x f x K@ ( )∇ =f x 0 66
  • 7.
    Minimization with EqualityMinimizationwith Equality ConstraintConstraintWhen the minimization is constrained with an equality constraint we can solve the problem using the method of Lagrange Multipliers Key idea is to represent a constrained minimization problem as an unconstrained problem.That is, for the general problem minimize ( ) s.t. ( ) We define the Lagrangian L( , ) ( ) ( ) Then a necessary condition for a minimum is the L ( , ) 0 and L ( , ) 0 T = = + ∇ = ∇ =xλ f x g x 0 xλ f x λ g x xλ x λ 77
  • 8.
    Economic Dispatch LagrangianEconomicDispatch Lagrangian G 1 1 G For the economic dispatch we have a minimization constrained with a single equality constraint L( , ) ( ) ( ) (no losses) The necessary conditions for a minimum are L( , ) m m i Gi D Gi i i Gi C P P P dC P λ λ λ = = = + − ∂ = ∂ ∑ ∑P P 1 ( ) 0 (for 1 to ) 0 i Gi Gi m D Gi i P i m dP P P λ = − = = − =∑ 88
  • 9.
    Economic Dispatch ExampleEconomicDispatch Example 1 2 2 1 1 1 1 2 2 2 2 2 1 1 1 What is economic dispatch for a two generator system 500 MW and ( ) 1000 20 0.01 $/h ( ) 400 15 0.03 $/h Using the Lagrange multiplier method we know: ( ) 20 0.0 D G G G G G G G G G G P P P C P P P C P P P dC P dP λ = + = = + + = + + − = + 1 2 2 2 2 1 2 2 0 ( ) 15 0.06 0 500 0 G G G G G G P dC P P dP P P λ λ λ − = − = + − = − − = 99
  • 10.
    Economic Dispatch Example,EconomicDispatch Example, cont’dcont’d 1 2 1 2 1 2 1 2 We therefore need to solve three linear equations 20 0.02 0 15 0.06 0 500 0 0.02 0 1 20 0 0.06 1 15 1 1 0 500 312.5 MW 187.5 MW 26.2 $/MW G G G G G G G G P P P P P P P P λ λ λ λ + − = + − = − − = − −         − = −      − − −             =      h          1010
  • 11.
    Economic dispatch example,Economicdispatch example, cont’dcont’d • At the solution, both generators have the same marginal (or incremental) cost, and this common marginal cost is equal to λ. • Intuition behind solution: – If marginal costs of generators were different, then by decreasing production at higher marginal cost generator, and increasing production at lower marginal cost generator we could lower overall costs. – Generalizes to any number of generators. • If demand changes, then change in total costs can be estimated from λ. 1111
  • 12.
    Economic dispatch example,Economicdispatch example, cont’dcont’d • Another way to solve the equations is to: – Rearrange the first two equations to solve for PG1 and PG2 in terms of λ, – Plug into third equation and solve for λ, – Use the solved value of λ to evaluate PG1 and PG2. • This works even when relationship between generation levels and λ is more complicated: – Equations are more complicated than linear 1212
  • 13.
    Lambda-Iteration SolutionLambda-Iteration Solution MethodMethod •Discussion on previous page leads to “lambda-iteration” method: – this method requires a unique mapping from a value of lambda (marginal cost) to each generator’s MW output: – for any choice of lambda (common marginal cost), the generators collectively produce a total MW output, – the method then starts with values of lambda below and above the optimal value (corresponding to too little and too much total output), and then iteratively brackets the optimal• 1313 ( ).Gi P λ
  • 14.
    Lambda-Iteration AlgorithmLambda-Iteration Algorithm LH 1 1 H L M H L H M 1 L M Pick and such that ( ) 0 ( ) 0 While Do ( )/2 If ( ) 0 Then Else End While m m L H Gi D Gi D i i m M Gi D i P P P P P P λ λ λ λ λ λ ε λ λ λ λ λ λ λ λ = = = − < − > − > = + − > = = ∑ ∑ ∑ 1414
  • 15.
    Lambda-Iteration: GraphicalLambda-Iteration: Graphical ViewView Inthe graph shown below for each value of lambda there is a unique PGi for each generator. This relationship is the PGi(λ) function. 1515
  • 16.
    Lambda-Iteration ExampleLambda-Iteration Example 11 1 2 2 2 3 3 3 1 2 3 Consider a three generator system with ( ) 15 0.02 $/MWh ( ) 20 0.01 $/MWh ( ) 18 0.025 $/MWh and with constraint 1000MW Rewriting generation as a function of , ( G G G G G G G G G Gi IC P P IC P P IC P P P P P P λ λ λ λ = + = = + = = + = + + = G1 G2 G3 ), we have 15 20 P ( ) P ( ) 0.02 0.01 18 P ( ) 0.025 λ λ λ λ λ λ λ − − = = − = 1616
  • 17.
    Lambda-Iteration Example,Lambda-Iteration Example, cont’dcont’dm Gi i=1 m Gi i=1 1 H 1 Pickso P ( ) 1000 0 and P ( ) 1000 0 Try 20 then (20) 1000 15 20 18 1000 670 MW 0.02 0.01 0.025 Try 30 then (30) 1000 1230 MW L L H m L Gi i m Gi i P P λ λ λ λ λ λ λ λ = = − < − > = − = − − − + + − = − = − = ∑ ∑ ∑ ∑ 1717
  • 18.
    Lambda-Iteration Example,Lambda-Iteration Example, cont’dcont’d 1 1 Pickconvergence tolerance 0.05 $/MWh Then iterate since 0.05 ( )/ 2 25 Then since (25) 1000 280 we set 25 Since 25 20 0.05 (25 20)/ 2 22.5 (22.5) 1000 195 we set 2 H L M H L m H Gi i M m L Gi i P P ε λ λ λ λ λ λ λ λ = = = − > = + = − = = − > = + = − = − = ∑ ∑ 2.5 1818
  • 19.
    Lambda-Iteration Example,Lambda-Iteration Example, cont’dcont’d H * * 1 2 3 Continueiterating until 0.05 The solution value of , , is 23.53 $/MWh Once is known we can calculate the 23.53 15 (23.5) 426 MW 0.02 23.53 20 (23.5) 353 MW 0.01 23.53 18 (23.5) 0.025 L Gi G G G P P P P λ λ λ λ λ − < − = = − = = − = 221 MW= 1919
  • 20.
    Thirty Bus EDExampleThirty Bus ED Example Case is economically dispatched (without considering the incremental impact of the system losses). 2020
  • 21.
    Generator MW LimitsGeneratorMW Limits Generators have limits on the minimum and maximum amount of power they can produce Typically the minimum limit is not zero. Because of varying system economics usually many generators in a system are operated at their maximum MW limits: Baseload generators are at their maximum limits except during the off-peak. 2121
  • 22.
    Lambda-Iteration with GenLambda-Iterationwith Gen LimitsLimits ,max ,max In the lambda-iteration method the limits are taken into account when calculating ( ) : if calculated production for then set ( ) if calculated production for Gi Gi Gi Gi Gi P P P P P λ λ > = ,min ,minthen set ( ) Gi Gi Gi Gi P P P Pλ < = 2222
  • 23.
    Lambda-Iteration Gen LimitLambda-IterationGen Limit ExampleExample G1 G2 G3 1 2 3 1 In the previous three generator example assume the same cost characteristics but also with limits 0 P 300 MW 100 P 500 MW 200 P 600 MW With limits we get: (20) 1000 (20) (20) (20) 10 m Gi G G G i P P P P = ≤ ≤ ≤ ≤ ≤ ≤ − = + + −∑ 1 00 250 100 200 1000 450 MW (compared to 670MW) (30) 1000 300 500 480 1000 280 MW m Gi i P = = + + − = − − − = + + − =∑ 2323
  • 24.
    Lambda-Iteration LimitLambda-Iteration Limit Example,cont’dExample,cont’dAgainwe continue iterating until the convergence condition is satisfied. With limits the final solution of , is 24.43 $/MWh (compared to 23.53 $/MWh without limits). Maximum limits will always caus λ 1 2 3 e to either increase or remain the same. Final solution is: (24.43) 300 MW (at maximum limit) (24.43) 443 MW (24.43) 257 MW G G G P P P λ = = = 2424
  • 25.
    Back of EnvelopeValuesBack of Envelope Values $/MWhr = fuelcost * heatrate + variable O&M Typical incremental costs can be roughly approximated: – Typical heatrate for a coal plant is 10, modern combustion turbine is 10, combined cycle plant is 6 to 8, older combustion turbine 15. – Fuel costs ($/MBtu) are quite variable, with current values around 2 for coal, 3 to 5 for natural gas, 0.5 for nuclear, probably 10 for fuel oil. – Hydro costs tend to be quite low, but are fuel (water) constrained 2525
  • 26.
    Inclusion of TransmissionInclusionof Transmission LossesLosses The losses on the transmission system are a function of the generation dispatch. In general, using generators closer to the load results in lower losses This impact on losses should be included when doing the economic dispatch Losses can be included by slightly rewriting the Lagrangian to include G 1 1 L( , ) ( ) ( ) m m i Gi D L G Gi i i C P P P P Pλ λ = =   = + + − ÷   ∑ ∑P 2626
  • 27.
    Impact of TransmissionLossesImpact of Transmission Losses G 1 1 G The inclusion of losses then impacts the necessary conditions for an optimal economic dispatch: L( , ) ( ) ( ) . The necessary conditions for a minimum are now: L( , ) m m i Gi D L G Gi i i C P P P P Pλ λ λ = =   = + + − ÷   ∂ ∂ ∑ ∑P P 1 ( ) ( ) 1 0 ( ) 0 i Gi L G Gi Gi Gi m D L G Gi i dC P P P P dP P P P P P λ =  ∂ = − − = ÷∂  + − =∑ 2727
  • 28.
    Impact of TransmissionLossesImpact of Transmission Losses th ( ) ( ) Solving for , we get: 1 0 ( )1 ( ) 1 Define the penalty factor for the generator (don't confuse with Lagrangian L!!!) 1 ( ) 1 i Gi L G Gi Gi i Gi GiL G Gi i i L G Gi dC P P P dP P dC P dPP P P L i L P P P λ λ λ  ∂ − − = ÷∂  =  ∂ − ÷∂  =  ∂ − ∂  ÷  The penalty factor at the slack bus is always unity! 2828
  • 29.
    Impact of TransmissionLossesImpact of Transmission Losses 1 1 1 2 2 2 The condition for optimal dispatch with losses is then ( ) ( ) ( ) 1 . So, if increasing increases ( ) 1 ( ) the losses then 0 1.0 This makes generator G G m m Gm i Gi L G Gi L G i Gi L IC P L IC P L IC P L P P P P P P L P λ= = = =  ∂ − ÷∂  ∂ > ⇒ > ∂ appear to be more expensive (i.e., it is penalized). Likewise 1.0 makes a generator appear less expensive. i i L < 2929
  • 30.
    Calculation of PenaltyFactorsCalculation of Penalty Factors Unfortunately, the analytic calculation of is somewhat involved. The problem is a small change in the generation at impacts the flows and hence the losses throughout the entire system. However, i Gi L P using a power flow you can approximate this function by making a small change to and then seeing how the losses change: ( ) ( ) 1 ( ) 1 Gi L G L G i L GGi Gi Gi P P P P P L P PP P P ∂ ∆ ≈ ≈ ∆∂ ∆ − ∆ 3030
  • 31.
    Two Bus PenaltyFactorTwo Bus Penalty Factor ExampleExample 2 2 2 2 ( ) ( ) 0.37 0.0387 0.037 10 0.9627 0.9643 L G L G G G P P P P MW P P MW L L ∂ ∆ − = − = = − ∂ ∆ = ≈ 3131
  • 32.
    Thirty Bus EDExampleThirty Bus ED Example Now consider losses. Because of the penalty factors the generator incremental costs are no longer identical. 3232
  • 33.
    Area Supply CurveAreaSupply Curve 0 100 200 300 400 Total AreaGeneration(MW) 0.00 2.50 5.00 7.50 10.00 The area supply curve shows the cost to produce the next MW of electricity, assuming area is economically dispatched Supply curve for thirty bus system 3333
  • 34.
    Economic Dispatch -SummaryEconomic Dispatch - Summary Economic dispatch determines the best way to minimize the current generator operating costs. The lambda-iteration method is a good approach for solving the economic dispatch problem: – generator limits are easily handled, – penalty factors are used to consider the impact of losses. Economic dispatch is not concerned with determining which units to turn on/off (this is the unit commitment problem). Basic form of economic dispatch ignores the transmission system limitations. 3434
  • 35.
    Security Constrained EDSecurityConstrained ED or Optimal Power Flowor Optimal Power Flow Transmission constraints often limit ability to use lower cost power. Such limits require deviations from what would otherwise be minimum cost dispatch in order to maintain system “security.” Need to solve or approximate power flow in order to consider transmission constraints. 3535
  • 36.
    Security Constrained EDSecurityConstrained ED or Optimal Power Flowor Optimal Power Flow The goal of a security constrained ED or optimal power flow (OPF) is to determine the “best” way to instantaneously operate a power system, considering transmission limits. Usually “best” = minimizing operating cost, while keeping flows on transmission below limits. In three bus case the generation at bus 3 must be limited to avoid overloading the 3636
  • 37.
    Security Constrained DispatchSecurityConstrained Dispatch Bus 2 Bus 1 Bus 3Home Area Scheduled Transactions 357 MW 179 MVR 194 MW 448 MW 19 MVR 232 MVR 179 MW 89 MVR 1.00 PU -22 MW 4 MVR 22 MW -4 MVR -142 MW 49 MVR 145 MW -37 MVR 124 MW -33 MVR -122 MW 41 MVR 1.00 PU 1.00 PU 0 MW 37 MVR100% 100% 100 MW OFF AGC AVR ON AGC ON AVR ON 100.0 MW Need to dispatch to keep line from bus 3 to bus 2 from overloading 3737
  • 38.
    Multi-Area OperationMulti-Area Operation Inmulti-area system, “rules” have been established regarding transactions on tie-lines: – In Eastern interconnection, in principle, up to “nominal” thermal interconnection capacity, – In Western interconnection there are more complicated rules The actual power that flows through the entire network depends on the impedance of the transmission lines, and ultimately determine what are acceptable patterns of dispatch: Can result in need to “curtail” transactions that otherwise satisfy rules. Economically uncompensated flow through other areas is known as “parallel path” or “loop flows.” Since ERCOT is one area, all of the flows on AC lines are inside ERCOT and there is no uncompensated flow on AC lines. 3838
  • 39.
    Power System EconomicPowerSystem Economic OperationOperation • Fuel cost to generate a MWh can vary widely from technology to technology. • For some types of units, such as hydro, “fuel” costs are zero but the limit on total available water gives it an implicit value. • For thermal units it is much easier to characterize costs. • We will focus on minimizing the variable operating costs (primarily fuel costs) to meet demand. 3939
  • 40.
    Power System EconomicPowerSystem Economic OperationOperation • Power system loads are cyclical. • Therefore the installed generation capacity is usually much greater than the current load. • This means that there are typically many ways we could meet the current load. • Since different states have different mixes of generation, we will consider how generally to minimize the variable operating costs given an arbitrary, 4040
  • 41.
    Thermal versus OtherThermalversus Other GenerationGenerationThe main types of generating units are thermal and hydro, with wind and solar rapidly growing. For hydro the fuel (water) is free but there may be many constraints on operation: – fixed amounts of water available, – reservoir levels must be managed and coordinated, – downstream flow rates for fish and navigation. Hydro optimization is typically longer term (many months or years). We will concentrate on dispatchable thermal units, looking at short-term 4141
  • 42.
    Generator typesGenerator types Traditionallyutilities have had three broad groups of generators: – “Baseload” units: large coal/nuclear; almost always on at max. – “Midload,” ‘intermediate,” or “cycling” units: smaller coal or gas that cycle on/off daily or weekly. – “Peaker” units: combustion turbines used only for several hours. during periods of high demand 4242
  • 43.
    Block Diagram ofThermal UnitBlock Diagram of Thermal Unit •To optimize generation costs we need to develop cost relationships between net power out and operating costs. •Between 2-10% of power is used within the generating plant; this is known as the auxiliary 4343
  • 44.
    Thermal generator CostCurvesThermal generator Cost Curves Thermal generator costs are typically represented by one or other of the following four curves – input/output (I/O) curve – fuel-cost curve – heat-rate curve – incremental cost curve For reference - 1 Btu (British thermal unit) = 1054 J - 1 MBtu = 1x106 Btu - 1 MBtu = 0.29 MWh 4444
  • 45.
    I/O CurveI/O Curve TheIO curve plots fuel input (in MBtu/hr) versus net MW output. 4545
  • 46.
    Fuel-cost CurveFuel-cost Curve Thefuel-cost curve is the I/O curve multiplied by fuel cost. A typical cost for coal is $ 1.70/MBtu. 4646
  • 47.
    Heat-rate CurveHeat-rate Curve •Plots the average number of MBtu/hr of fuel input needed per MW of output. • Heat-rate curve is the I/O curve divided by MW. Best heat-rate for most efficient coal units is around 9.0 4747
  • 48.
    Incremental (Marginal) costIncremental(Marginal) cost CurveCurvePlots the incremental $/MWh as a function of MW. Found by differentiating the cost curve. 4848
  • 49.
    Mathematical Formulation ofMathematicalFormulation of CostsCostsGenerator cost curves are usually not smooth. However the curves can usually be adequately approximated using piece-wise smooth, functions. Two approximations predominate: – quadratic or cubic functions – piecewise linear functions We'll assume a quadratic approximation: 2 ( ) $/hr (fuel-cost) ( ) ( ) 2 $/MWh i Gi i i Gi i Gi i Gi i Gi i i Gi Gi C P P P dC P IC P P dP α β γ β γ = + + = = + 4949
  • 50.
    Coal Usage ExampleCoalUsage Example •A 500 MW (net) generator is 35% efficient. It is being supplied with coal costing $1.70 per MBtu and with heat content 9000 Btu per pound. What is the coal usage in lbs/hr? What is the cost? At 35% efficiency required fuel input per hour is 500 MWh 1428 MWh 1 MBtu 4924 MBtu hr 0.35 hr 0.29 MWh hr 4924 MBtu 1 lb 547,111 lbs hr 0.009MBtu hr 4924 MBtu $1.70 Cost = 8370.8 $/hr or $16.74/MWh hr MBtu = × = × × = × = 5050
  • 51.
    Wasting Coal ExampleWastingCoal Example •Assume a 100W lamp is left on by mistake for 8 hours, and that the electricity is supplied by the previous coal plant and that transmission/distribution losses are 20%. How much coal has he/she wasted? With 20% losses, a 100W load on for 8 hrs requires 1 kWh of energy. With 35% gen. efficiency this requires 1 kWh 1 MWh 1 MBtu 1 lb 1.09 lb 0.35 1000 kWh 0.29 MWh 0.009MBtu × × × = 5151
  • 52.
    Incremental Cost ExampleIncrementalCost Example 2 1 1 1 1 2 2 2 2 2 1 1 1 1 1 1 2 2 2 2 2 2 For a two generator system assume ( ) 1000 20 0.01 $/hr ( ) 400 15 0.03 $/hr Then ( ) ( ) 20 0.02 $/MWh ( ) ( ) 15 0.06 $/MWh G G G G G G G G G G G G G G C P P P C P P P dC P IC P P dP dC P IC P P dP = + + = + + = = + = = + 5252
  • 53.
    Incremental Cost Example,IncrementalCost Example, cont'dcont'd 1 2 2 1 2 2 1 2 If 250 MW and 150 MW Then (250) 1000 20 250 0.01 250 $ 6625/hr (150) 400 15 150 0.03 150 $6025/hr Then (250) 20 0.02 250 $ 25/MWh (150) 15 0.06 150 $ 24/MWh G GP P C C IC IC = = = + × + × = = + × + × = = + × = = + × = 5353
  • 54.