Price Formation Education Session Day 1 Economic Dispatch

Transcription

1 Slide 1 Price Formation Education Session Day 1 Economic Dispatch Anthony Giacomoni Melissa Maxwell Laura Walter December 4, 2017

2 Slide 2 Disclaimer Slide This is not a committee meeting. This session is for educational purposes only, to help introduce and clarify different aspects of price formation. The material presented is not necessarily representative of any proposal PJM has or will present in the future. 2

3 Slide 3 Agenda Electricity Market Overview (status quo) Energy market offers Market clearing prices Uplift Unit commitment Economic dispatch Example of Economic Dispatch with Marginal Pricing Explanation of Fast-Start Pricing Questions 3

4 Slide 4 ELECTRICITY MARKET OVERVIEW General Concepts 4

5 Slide 5 Energy Supply Must Be Balanced against the Demand for Power 5 PJM is always balancing the grid the amount of electricity being consumed or lost must equal the amount generated. Because electricity is a speed-of-light product that cannot be stored, PJM must respond instantaneously to changes in demand and operating conditions across its territory. To keep the system in balance, PJM continuously monitors the electric system, reacting to changes in demand, equipment problems, weather conditions and other factors to maintain safe and reliable service while meeting customer needs for electricity when and where it s needed.

6 Slide 6 Energy Market Types Independent system operators (ISOs) and regional transmission organizations (RTOs) in the US have markets employing: Day-Ahead Energy Market Real-Time Energy Market Locational prices 6 The PJM Energy Market procures electricity to meet consumers demands both in real time and in the near term. It includes the sale or purchase of energy in PJM s Real-Time Energy Market (five minutes) and Day-Ahead Market (one day forward). The Day-Ahead Energy Market is the market for tomorrow s energy. The market closes at 10:30 a.m. EPT and results post by 1:30 p.m. EPT. The Real-Time Energy Market happens throughout the day with prices being calculated every five minutes. Locational prices in PJM called locational marginal prices or LMP.

7 Slide 7 Determining Price and Dispatch Unit Commitment Determines which units to turn on (committing) and when based on forecasted load and other requirements. Unit commitment is then fixed going into economic dispatch. Economic Dispatch Determines megawatt output for each resource that is online Locational Prices Determined by solving the economic dispatch Unit Commitment Economic Dispatch Locational Prices 7

8 Slide 8 The Stack and Determining Price 8 Supply offers are ordered from cheapest to most expensive. Then, in order to meet the system load at the lowest possible cost (subject to transmission and operational constraints), a shortterm determination of the optimal output of generation facilities is calculated. However, marginal pricing doesn t guarantee this outcome in pricing, which will be discussed later.

9 Slide 9 ELECTRICITY MARKET OVERVIEW Energy Market Offer 9

10 Slide 10 Components of an Energy Market Offer Three costs compose a resource s offer: Start-up cost ($/start) Incremental energy cost ($/MWh) No-load cost ($/hour) 10

11 Slide 11 What Is Start-up Cost? The start-up cost for a resource is: The cost to get a resource from shutdown to breaker close (i.e., megawatts greater than zero) Determined by various factors (e.g., start-fuel cost, startmaintenance cost) Incurred each time a resource starts up Included in commitment but not in dispatch 11 Start-up costs are defined as the unit costs to bring the boiler, turbine and generator from shutdown conditions to the point after breaker closure. Start-up costs include cost of start fuel, total fuel-related cost, performance factor, electrical costs (station service), start maintenance adder, and additional labor cost if required above normal station manning. Start-up costs can vary with the unit offline time being categorized in three unit temperature conditions: hot, intermediate and cold. Start-up cost is a dollar cost and is incurred once each time the unit operates regardless of the period of operation.

12 Slide 12 What Is Incremental Energy Cost? The incremental energy cost for a resource is: A variable operating cost: includes fuel, variable operating and maintenance cost, etc. Incurred for every megawatt-hour generated Included in commitment and dispatch Non-decreasing 12

13 Slide 13 Why Do We Need a Non-Decreasing Cost Curve? Non-decreasing incremental cost curves ensure that the total cost curve is convex. Why do we need convexity? Ensures that we can find an optimal solution! Otherwise we would not know if any solution we find is optimal. 13

14 Slide 14 What Is Convexity? Convexity refers to the curvature of a function. A function is convex if any straight line you draw across the function does not intersect the function in more than two places. Non-Convex Function more than two intersection points Convex Function only two intersection points 14

15 Slide 15 Examples of Incremental Energy Cost 15

16 Slide 16 What Is No-Load Cost? The true cost for a resource may not always increase across the entire output range. No-load cost is the cost to operate a resource in the inefficient portion of its incremental energy offer curve. No-load cost is included in commitment but not dispatch. Generator Incremental Cost Curve 16 True generator cost may not be always increasing over the entire output range. No-load cost ($/hour) Cost associated with operating a unit in the low (inefficient) portion of its incremental energy offer curve because often a generator s incremental cost curves are not monotonically increasing. So to make an incremental energy offer curve monotonic, a minimum point is set to be its economic minimum. The no-load cost offer can then be used to recover a generators unrecovered costs. The no-load cost is incurred every hour the resource is online.

17 Slide 17 ELECTRICITY MARKET OVERVIEW Market Clearing Prices 17

18 Slide 18 Market Clearing Price In an ideal case, at the market clearing price, there are no incentives to deviate from equilibrium quantity. Equilibrium 18 In a market, prices perform a coordinating function. Producers and consumers react to prices by adjusting their output and consumption. At this market clearing price, producers are willing to supply the exact amount consumers would like to consume (i.e., supply = demand). There is no incentive to deviate from this price and quantity; no group can do better by trading among themselves outside the market.

19 Slide 19 What Is Locational Marginal Price? The locational marginal price (LMP) reflects the incremental cost of supplying the next megawatt of load at a particular location while satisfying all operational constraints. Total Production Cost Incremental energy cost Start-up cost No-load cost Costs Reflected in LMP Incremental energy cost 19 LMP is the cost of optimally supplying an increment of load at a particular location while satisfying all operational constraints. One can think of the LMP as the change in total production cost to deliver an increment of load at a location using the offers submitted to the market. The commitment cannot change in response to an increment in load. LMPs are produced as a result of economic dispatch with the commitment fixed.

20 Slide 20 LMPs and Market Clearing Do LMPs always provide an incentive for units to follow dispatch instruction? They do not incorporate start-up and no-load costs. Not all resources can set price. Uplift payments may be necessary to incent resources to follow dispatch instructions. 20 Inflexible units are not permitted to set price. When the cost of an inflexible unit that is needed to serve demand is precluded from setting price, the LMP does not accurately reflect the true incremental cost to serve load. This LMP limitation can suppress energy and reserve prices and inappropriately increase reliance on the capacity market.

21 Slide 21 ELECTRICITY MARKET OVERVIEW Uplift 21

22 Slide 22 What Is Uplift? Uplift = Make Whole Payments + Lost Opportunity Cost Make-whole payments: Occur when a resource s revenue cannot cover its total costs, including fixed costs like start-up cost and no-load cost. Lost opportunity cost: Occurs when a resource could have made more profit by not following RTO/ISO direction. 22 Currently, offline units that would have profited if they started up are not paid lost opportunity cost in most markets.

23 Slide 23 Example of Make-Whole Payment No recovery Startup cost ($/start) No-load cost ($/hour the resource is online) 23 In this example, the resource s incremental energy cost is equal to the LMP for the entire time the unit is online. In this case, the unit would need to be paid make-whole payments to cover the total cost of operation. Also, in this case, the unit might have an incentive to not follow PJM dispatch if make-whole payments were not available.

24 Slide 24 Example of Lost Opportunity Cost 24 In this example, the resource s incremental energy cost is less than the LMP for the entire time the unit is online. The unit has an incentive to generate more, but the ISO s direction is to stay at economic minimum. The resource has an incentive to not follow dispatch, so it is paid lost opportunity cost.

25 Slide 25 Uplift Drivers Uplift Drivers Unit Parameters Long lead time units Load, interchange and outages under or over forecast Reactive constraints 25

26 Slide 26 Uplift Is Undesirable Uplift payments are exclusive, non-transparent and difficult to hedge Exclusive Only received by some resources Non-transparent Out-of-market payments Difficult to Hedge Cannot be hedged in forward markets 26 Uplift costs are unavoidable as it is often due to restrictions and non-convexities based on the market framework. Uplift is non-transparent to the market. Only the market participant receiving uplift payments has visibility of those payments. From FERC - a failure to make the causes transparent and to price them into the energy and ancillary services markets can undermine the effectiveness of price signals and efficient system utilization, and mute investment signals. Volatile uplift charges may also create financial uncertainty for customers, depress liquidity and reduce market efficiency.

27 Slide 27 ELECTRICITY MARKET OVERVIEW Unit Commitment 27

28 Slide 28 What Is Unit Commitment? The least expensive way of supplying forecasted load in the system, often over an extended time period (e.g., 24 hours) Determines when to turn resources on and off Prices are not determined by solving the unit commitment, due to integer commitment variables. 28 Prices are not determined by solving the unit commitment due to the integer (0,1) commitment variables. Integer commitment variables are 0 or 1 depending on whether the resource is on or off.

29 Slide 29 Unit Commitment Formulation Objective Function Total Production Cost Cost + Start-up Cost + No-Load Cost System Balance Total Generation Total Load Losses = 0 Transmission Constraints The flow on each line must be below its operating limit. Resource Capacity Constraints The output of each resource must be within its operating range. Unit Commitment Constraints. 29

30 Slide 30 ELECTRICITY MARKET OVERVIEW Economic Dispatch 30

31 Slide 31 What Is Economic Dispatch? Holds the commitment from the unit commitment fixed Determines the least expensive way to supply load in the system Determines the output of all online units to keep the system in balance Prices are determined by solving the economic dispatch. 31

32 Slide 32 Economic Dispatch Formulation Similar to unit commitment formulation The difference: No integer variables, as the unit commitment is held fixed Start-up and no-load costs are not considered, as they become constants 32

33 Slide 33 Economic Dispatch Formulation Objective Function Total Production Cost Cost + Start-up Cost + No-Load Cost System Balance Total Generation Total Load Losses = 0 Transmission Constraints The flow on each line must be below its operating limit. Resource Capacity Constraints The output of each resource must be within its operating range. Integer variables are now fixed, so they do not affect the solution. Unit Commitment Constraints Economic dispatch only dispatches resources that are already online. 33

34 Slide 34 ECONOMIC DISPATCH EXAMPLE Marginal Pricing 34

35 Slide 35 When Is a Resource Marginal? A resource is marginal when it supplies the next megawatt of generation or demand reduction to meet load or to control a transmission constraint. System conditions heavily influence where that next megawatt is needed from the supply stack. Weather Interchange Accuracy of the load forecast 35

36 Slide 36 When Is a Resource Marginal? There will always be at least one marginal resource. System energy resource There are additional marginal resources for each binding transmission constraint (i.e., n+1 rule). In most cases, there are multiple marginal resources for a given time interval. 36 The number of marginal resources in a given five-minute pricing interval depends on the number of binding transmission constraints. When the system is unconstrained, there will only be one marginal resource. This resource is setting the system energy price, which we just said is the cost of the optimal dispatch to meet load absent congestion and losses. Each binding transmission constraint means an additional marginal resource. Given that PJM typically has congestion on the system due to either local transmission constraints or coordination on market-to-market flowgates, in most cases, there are multiple marginal resources for a given pricing interval.

37 Slide 37 Economic Dispatch Example I We assume no start-up or no-load cost. Each resource is completely flexible. 37 Let s assume for this example we have three resources and they have no start-up or no-load cost. Resource A has offered at $60/MWh and is available for 300 MW. Resource B has offered at $80/MWh and has 200 MW available. Resource C offered at $100/MWh and is available for 400 MW. All units are flexible and can start immediately with no restricting parameters.

38 Slide 38 Economic Dispatch Example I 175 MW 38 If load is 175 MW, then resource A is dispatched to 175 MW to meet load. Resource A is the marginal resource and sets price at $60/MWh.

39 Slide 39 Economic Dispatch Example I 300 MW 50 MW 39 When load increases to 350 MW, Resource A is now at full output and Resource B is brought online. The marginal resource is now Resource B as it would serve the next increment of load. The LMP is now $80/MWh and all resources online receive that price.

40 Slide 40 Economic Dispatch Example I 300 MW 100 MW 40 When load increases to 400 MW, Resource B is increased and remains the marginal resource. Resource B would serve the next increment of load. The LMP remains $80/MWh and all resources online receive that price.

41 Slide 41 Economic Dispatch Example I 300 MW 200 MW 50 MW 41 When load increases to 550 MW both Resource A and Resource B are at maximum output. Resource C is providing the last 50 MW and is marginal. LMP is set to $100/MWh and all resources receive that price.

42 Slide 42 LMP increases and load increases 42 At each level of MW of load needed, this shows that as load grows, LMP increases.

43 Slide 43 Economic Dispatch Example II What happens if we introduce inflexibility to the resources? Minimum output the resource can produce when online 200 MW 100 MW 100 MW 43 These are the same resources, but now they have minimum output levels that they cannot go below: P and J have to be on at a minimum of 100 MW. If M is called on, it must be on at a minimum of 200 MW.

44 Slide 44 Economic Dispatch Example II 200 MW 175 MW 100 MW 44 At 175 MW, A is marginal and sets the price at $60/MWh.

45 Slide 45 Economic Dispatch Example II 250 MW 200 MW 100 MW 45 At 350 MW, Resource B must be called on, but at the minimum of 100 MW. So we must back down Resource A to 250 MW. The marginal resource is A, and the price is set at $60/MWh. At this LMP, Resource B is operating at a loss and must be made whole through uplift.

46 Slide 46 Economic Dispatch Example II 300 MW 200 MW 100 MW 46 At 400 MW, Now Resource A is at maximum output at 300MW and Resource B has met the minimum output at 100MW. Resource B would serve the next increment of load and is the marginal resource. LMP is set at $80/MWh and both Resource A and Resource B receive that price.

47 Slide 47 Economic Dispatch Example II 250 MW 200 MW 100 MW 47 At 550 MW, A and B together can only get to 500 MW, so C must be called on and has a minimum of 200 MW. So both P and J are backed down, and the marginal resource is A, resulting in a $60 LMP. All resources receive $60/MWh and both B and C must receive make whole payments to cover their costs.

48 Slide 48 $/MWh $120 Price Formation Curve $110 $100 $90 Completely flexible $80 $70 $60 $50 Parameter restrictions $ Provided for informational purposes only 48 MW of Load

49 Slide 49 $/MWh $120 Price Formation Curve Using Resources A, B & C Production Cost ($) $120,000 $110 $100 Resource Dispatch A B C $100,000 $90 $80,000 $80 $70 $60 $50 LMP Production Cost Available Dispatched Marginal Resource $60,000 $40,000 $20,000 $40 $ Provided for informational purposes only 49 MW of Load When load is less than 300 MW, Resource A is online and marginal. The increasing production cost is resource A producing more MW at $60/MWh. LMP is $60/MWh.

50 Slide 50 $/MWh $120 Price Formation Curve Using Resources A, B & C Production Cost ($) $120,000 $110 $100 $90 Resource Dispatch A B C $100,000 $80,000 $80 $60,000 $70 $60 $50 LMP Production Cost Available Dispatched Marginal Resource $40,000 $20,000 $40 $ MW of 50 Load When load is between 300 MW and 400 MW Both Resource A and B are online. We see a jump in production cost because Resource B is on at min. Resource A is still marginal. Even though production costs increase, LMP does not change and remains at $60/MWh.

51 Slide 51 $/MWh $120 Price Formation Curve Using Resources A, B & C Production Cost ($) $120,000 $110 $100 Resource Dispatch A B C $100,000 $90 $80,000 $80 $60,000 $70 $60 $50 LMP Production Cost Available Dispatched Marginal Resource $40,000 $20,000 $40 $ MW of Load Between 400 MW and 500 MW of load, both Resources A and B remain on, but once Resource A is at maximum, Resource B becomes marginal. LMP increases to $80/MWh.

52 Slide 52 $/MWh $120 Price Formation Curve Using Resources A, B & C Production Cost ($) $120,000 $110 $100 Resource Dispatch A B C $100,000 $90 $80,000 $80 $60,000 $70 $60 $50 LMP Production Cost Available Dispatched Marginal Resource $40,000 $20,000 $40 $ MW of Load When load is between 500 MW and 600 MW Resources A, B and C are all on. Resource A is marginal as it needed to be backed down to accommodate Resource B and C minimum output. Production costs jump as Resource C comes online. LMP drops to $60/MWh. Resource B and Resource C will need out-of-market payments

53 Slide 53 $/MWh $120 $110 $100 $90 Price Formation Curve Using Resources A, B & C Resource Dispatch A B C Production Cost ($) $120,000 $100,000 $80,000 $80 $70 $60 $50 LMP Production Cost Available Dispatched Marginal Resource $60,000 $40,000 $20,000 $40 $ MW of Load 53 When load is between 600 MW and 700 MW, all three resources remain online. Resource A is at max. Resource B is marginal. Resource C is at min. LMP increases to $80/MWh but does not cover the cost of Resource C operating at minimum output. Resource C will need out-of-market payments to cover the cost of operation.

54 Slide 54 $/MWh $120 $110 $100 $90 $80 $70 $60 $50 Price Formation Curve Using Resources A, B & C Resource Dispatch LMP Production Cost Available Dispatched Marginal Resource A B C Production Cost ($) $120,000 $100,000 $80,000 $60,000 $40,000 $20,000 $40 $ MW of Load When load is greater than 700 MW, Resources A and B are at maximum. Resource C is marginal and setting LMP at $100/MWh.

55 Slide 55 FAST-START PRICING 55

56 Slide 56 Session Objectives Review motivation for the FERC fast-start pricing Notice of Proposed Rule Making (NOPR) Review PJM s current special-pricing treatment Review other ISO/RTO special-pricing treatments for faststart resources 56

57 Slide 57 What Is a Fast-Start Resource? Fast-start resources can start up quickly and typically have shorter minimum run times than other resources. Definitions of fast-start resources vary across ISOs/RTOs 57

58 Slide 58 History of the FERC Fast-Start NOPR Context: Operating characteristics of fast-start resources prevent them from setting price. Requested Action: In 2016, the FERC asked RTOs/ISOs to improve price formation by: Enabling fast-start resources to set price more often Motivation Fast-start pricing can improve performance incentives for all resources during tight system conditions. Reflecting the cost of fast-start deployment through transparent price signals 58

59 Slide 59 PJM Combustion Turbine Special-Pricing Treatment Combustion turbines are usually offered as inflexible (i.e., block-loaded, where economic minimum = economic maximum). This means they cannot set price naturally For block-loaded combustion turbines that are eligible to set price, relax their economic minimum by a specific factor (currently 0.8) The wider the relaxed dispatchable range, the better chance a resource has to set price. But with a wider dispatchable range, the dispatch solution may be far below its economic minimum. 59

60 Slide 60 History of PJM Combustion Turbine Special-Pricing Treatment Special-pricing treatment was implemented over 12 years ago to allow block-loaded combustion turbine resources to set price. Relaxation factor was set to 0.9 until last year, when it was decreased to

61 Slide 61 PJM Block-Loaded Combustion Turbines As of October 2017 Approximately 180 combustion turbines offered into the Day-Ahead and Real-Time Markets as block-loaded Represents approximately 10,000 MW of capacity (based on economic maximums) 61

62 Slide 62 Shortcomings of Current Methodology Combustion turbines are generally unable to set price even though they are committed and dispatched economically. Relaxing economic minimum values in the dispatch solution distorts the system energy balance and can lead to inefficient system dispatch. Distortions must be managed by regulation at potentially higher cost than a balanced energy dispatch. 62

63 Slide 63 How Do Other ISOs/RTOs Treat Fast-Start Resources? Each ISO/RTO considers start-up and no-load costs in its commitment process for fast-start resources. However, treatment of fast-start resource start-up and no-load costs varies among ISOs/RTOs in the dispatch and pricing processes. 63

64 Slide 64 CAISO Fast-Start Resources Special pricing treatment for committed Constrained Output Generators Resource must elect constrained output generator status (currently, this option is rarely used) For a committed constrained output generator: Day-Ahead Market: Economic minimum is relaxed to 0 in the dispatch and pricing processes. Real-Time Market: Economic minimum is relaxed to 0 only in the pricing process. 64 Special pricing treatment: Resource with an operating range no greater than the higher of 3 MW or 5% of its economic maximum that registers, on an annual basis, its economic minimum as economic maximum less 0.01 MW ([economic minimum = economic maximum] 0.01 MW)

65 Slide 65 CAISO Fast-Start Resources Committed constrained output generator s submitted energy offer is replaced by a calculated energy bid: For dispatch range between 0 and economic minimum: Calculated energy bid = minimum load cost/economic minimum For the 0.01 MW between economic minimum and economic maximum: Calculated energy bid = max{submitted bid price, minimum load cost/economic minimum} 65

66 Slide 66 ISO New England Fast-Start Resources Special pricing treatment for fast-start resources in real time Resources with start-up times that do not exceed 30 minutes Separate dispatch and pricing runs Dispatch run: no changes are made to resource offers. Pricing run: fast-start resource economic minimums are relaxed to 0. Start-up costs are amortized over economic maximum and minimum run time and added into energy offers. No-load costs are amortized over economic maximum and added into energy offers for all online hours. Lost opportunity cost paid when dispatch signals are not profit maximizing 66

67 Slide 67 MISO Fast-Start Resources Special pricing treatment for one-hour fast-start resources Separate runs for dispatch and pricing: Committed one-hour resources are qualified for special pricing treatment. Not-committed one-hour resources: If they can relieve transmission, energy or reserve constraint violations, qualified for special pricing treatment Otherwise, not qualified (output fixed at 0 MW in pricing) Slow-start resources not qualified for special pricing treatment 67

68 Slide 68 MISO Fast-Start Resources In pricing run, qualified one-hour fast-start resources are allowed to be partially committed (integer relaxation). Economic minimums are relaxed to 0 MW. Commitment costs are amortized over economic maximum and added to energy offers for both qualified committed and not-committed resources. 68

69 Slide 69 NYISO Fast-Start Resources Special pricing treatment for block-loaded resources (mostly gas-turbines) Separate runs for dispatch and pricing 69

70 Slide 70 NYISO Fast-Start Resources Dispatch run: Determines dispatch signals sent to resources Committed block-loaded resources output fixed at economic maximum Not-committed (offline) resources: 10-minute resources with capacity less than or equal to 80 MW economic minimum relaxed to 0 MW All other resources output fixed at 0 MW 70

71 Slide 71 NYISO Fast-Start Resources Pricing run determines energy and reserve prices Committed block-loaded resources: Economic minimums are relaxed to zero may set price. Commitment costs (start-up and no-load) are not considered. Not-committed 10-min. resources with capacity not exceeding 80 MW are qualified for price setting. Economic minimums are relaxed to zero may set price. Commitment costs are amortized over economic maximum and added into energy offers. 71

72 Slide 72 ISO/RTO Fast-Start Pricing Summary PJM CAISO ISO-NE MISO NYISO Separate Pricing and Dispatch Runs Economic Minimum Relaxation Includes Start-up and No-Load Costs 72

73 Slide 73 APPENDIX Duality 73

74 Slide 74 Economic Dispatch Solution As a result of solving the economic dispatch, the dispatch algorithm determines desired dispatch points for every dispatchable generator. The desired dispatch points are called primal variables. To calculate the prices, the dual is formulated. The prices are obtained by solving for the dual variables (shadow prices). 74

75 Slide 75 What Is Duality Theory? For any linear program (LP), a dual can be formulated using a defined set of rules. Let represent our primal variables and our dual variables. Each constraint in the primal has a corresponding dual variable (shadow price). Each shadow price reflects the effect of relaxing the corresponding constraint by one unit on the value of the objective function (change in total production cost). 75

76 Slide 76 Duality Theory Primal (Dispatch) : : Dual (Pricing) Dual Variables For example, the dual variable reflects the change in the primal objective function value from relaxing (increasing) by one unit. 76

77 Slide 77 Calculate Desired Dispatch Points Duality Theory for Separate Pricing and Dispatch Runs Primal Dispatch Relax Unit Commitment Integer Variables Primal Pricing : : Dual Dispatch : : Dual Pricing Calculate Prices 77

78 Slide 78 Economic Dispatch Formulation Objective Function Total Cost is the incremental cost is the start-up cost is the no-load cost of resource. Transmission Constraints k 2 K System Balance s.t. Integer Variables are now fixed, so will not impact the solution. Resource Capacity Constraints 2 N Unit Commitment Constraints 2 Economic dispatch only includes online resources. 78

79 Slide 79 Economic Dispatch Solution and Duality The shadow price of the system balance constraint is one for the whole system (only one system balance equation). Each transmission constraint has its own shadow price. Some constraints may be binding. A binding constraint is a constraint that turns into an equality at the optimal solution. For example, a particular line has to be operated at its limit. 79

80 Slide 80 Economic Dispatch Solution and Duality (cont.) The shadow price of a binding constraint is non-zero, while the shadow price of a constraint that does not bind is zero. The system balance constraint always binds, so its shadow price is never zero. This means that there is always a price to support system balance. If there are no binding transmission constraints, there is no congestion in the system. 80

81 Slide 81 Binding Constraint Example Let the flow on line 1,, be 5 MW at the optimal solution, and let line 1 have a limit,, of 10 MW: Increasing the limit of by 1 MW will not change the optimal solution Shadow price ( ) of the line 1 flow constraint will be 0 If the flow on line 1,, is 10 MW at the optimal solution, then increasing the limit by 1 MW will allow an additional MW to flow across the line further reducing total system costs Shadow price ( of the line 1 flow constraint will be non-zero 81