Power System & LMP Fundamentals. Eugene Litvinov, Director Business Architecture & Technology Department

Transcription

1 Power System & LMP Fundamentals Eugene Litvinov, Director Business Architecture & Technology Department

2 What We Will Cover Electrical Network and Its Model Contingency Analysis Sensitivities LMP Calculation Marginal Loss Pricing Market System Major Components 2

3 Electrical Network and Its Model One-line diagram and bus/branch model Ohm s law Losses Kirchoff s law Power flow calculations (different model idealizations) Reference bus 3

4 One-Line Diagram and Bus/Branch Model Sub1 Line1 Line2 Line1 Sub1 Line2 L1 G1 Line3 Line4 L1 Line3 G1 Line4 Line1 Line2 Sub1 Line1 Sub1-1 Line2 + Sub1-2 G1 Line3 Line4 L1 Line3 G1 L1 Line4 4

5 Network Model Device any electrical device like line, transformer, breaker, etc. Node connection point of two or more devices in oneline model Bus connection point of two or more branches in the network model Branch physical or equivalent line connecting to buses Injection flow of power into bus generation Withdrawal flow of power from bus load Interface a set of branches that, when opened, split network into two separate islands 5

6 Bus/Branch Model Bus 1 Branch Branch 1-3 P 1 Injection 0 3 P 0 2 Withdrawal P 4 P 2 6

7 Interface MW 0 3 P 0 30 MW P 2 Positive Direction P 1 Interface -120 MW P 4 Interface contains lines: 0-2, 1-2, 1-3 The flow through an interface is the algebraic sum of the flows in the lines comprising interface: P = = -40 MW Negative sign means flow against positive direction. 7

8 External Interface Interface can be between two control areas (like NE and NY). It contains inter-ties only. Positive Direction CA1 CA2 8

9 Ohm s Law I U Voltage U I Current R Resistance R The current in the circuit: I = U/R U I R U = U 1 - U 2 U 1 U 2 I = (U 1 - U 2 ) / R 9

10 Power and Losses Power: P = U x I 1 P 12 2 P 12 U 1 U I 12 P = U I = U ( U U )/ R= ( U U U ) P U I U ( U U )/ R ( U U U ) R = 2 12 = = R P12 P12 P + P = P = I R loss 12 10

11 Kirchoff s Law All flows into the bus equal all flows out. In other words, the algebraic sum of all injections and withdrawals at the bus equals 0. Withdrawal is positive, injection is negative. 100 MW 35 MW 80 MW i 350 MW 55 MW 75 MW 515 MW = 0 11

12 Kirchoff s Law (cont.) This law is also true for any closed area of the network. 200 MW 150 MW 100 MW 100 MW 50 MW 150 MW Area 1 50 MW 100 MW 150 MW 350 MW MW 150 MW 12

13 Kirchoff s Law (cont.) This law is also true for the whole control area: sum of all generation, load and inter-tie flows equals 0. CA1 CA2 CA3 13

14 Powerflow Calculation Given: injections and withdrawals at every bus, branch parameters, network topology Find: power flows and currents in each branch and voltage at each bus High voltage electrical networks are three-phase alternate current circuits. The theory of power systems provides ways to perform calculations with one-line models for symmetric conditions. System losses is a sum of all branch losses in the system. 14

15 Bus/Branch Model in PowerWorld 15

16 Simple Two-Bus System I 1 U 1 U 2 I 12 R 1 I12 = ( U1 U2 ) R I I = 0 I = I ( U U ) = I R 1 ( U U ) = I R I 2 1 I2 = ( U1 U2 ) R I + I = 0 I = I I1 = ( U1 U2 ) R I = I = I The equations in the system are identical the system has infinite number of solutions. 16

17 Simple Two-Bus System (cont.) This means that we can arbitrarily choose voltage at one bus and calculate another voltage using only one of the equations. The bus where we specify voltage is called a Reference Bus. Power flow model always solves n-1 equations, where n-number of buses in the network. 17

18 AC Power Flow The model described above is a direct current (DC) model. The alternate current (AC) system is calculated using complex numbers. This means that any quantity is described by two components: real and imaginary or active and reactive. For example, power S=P+jQ, where S is MVA, P is active power in MW, and Q is reactive power in MVAR. 18

19 AC Power Flow (cont.) In addition to resistance R, each branch has reactance X. Instead of just resistance we use impedance Z = R + jx. Voltage has two components as well: U = U + ju. Both Ohm s law and Kirchoff s law hold true for AC case. 19

20 AC Power Flow Phase Angle Any complex number can be presented as a vector in Cartesian coordinates. U' + ju" U δ U Voltage magnitude, U" U δ - Voltage phase angle. U Phase angle at the reference bus is usually set to 0, so all other phase angles use it as a reference. The flow in any branch depends only on the difference of the voltages at the ends of the branch, so no matter which bus is a reference bus, the power flow is the same. δ U' U ref 20

21 AC Power Flow Losses in any branch also depend only on the difference of the voltages at the ends, so moving reference from one bus to another does not change system losses. As we saw, losses occur in each line that has a resistance generators have to cover all the losses in the network to supply required load. Thus, generators have to produce more power than just required by loads to keep system in balance. This means that in the system with losses the algebraic sum of all injections and withdrawals must be equal to system losses conservation of energy. 21

22 Reference, Slack and Swing Bus We introduced the concept of the angle reference bus as the reference for voltage vectors. In power flow calculations, besides the reference bus, we have to use slack or swing bus. Recall that when calculating power flow, one has to specify all nodal loads and generation. It is impossible to guess the total value of losses in the system before the power flows are calculated. Power system engineers resolve this problem by selecting a location in the network that would balance any difference between generation and load (generators have to supply losses in addition to the load) 22

23 Reference, Slack and Swing Bus (cont.) That location is called a slack or swing bus. This concept is very important in understanding sensitivities and LMP components later The reference bus and the slack bus do not have to be located at the same point of the network, however, in most cases, they are at the same location. That is why these names are being used interchangeably In the rest of this presentation, we will be using Reference Bus as a substitution for both reference and slack. Only when it is important, we will make a distinction between the two. 23

24 Slack Bus Total generation without slack: =

25 Slack Bus (cont.) Total generation without slack: =

26 Slack Bus. Some Observations When slack bus location changes, all the flows change too Losses also change with the change of the location of the slack bus Therefore: AC Power Flow is dependent on the location of the slack bus The higher the imbalance between calculated and guessed losses is, the higher the difference 26

27 AC Power Flow Power flow equations are highly non-linear. There are different methods to solve power flow, the most popular one is the Newton-Raphson method. For real time calculations, very often we use different idealizations of the model to speed up time for solution. One of the most popular methods is using DC model. 27

28 DC Model DC model is based on the linearization of the power flow equations around certain base point to avoid iterations. This allows solving large series of power flows within reasonable time frame. This model is also being used in the economic dispatch to make it possible to use linear programming technique. 28

29 Linearization Sinusoidal function of the flow is replaced with the linear function. In the quite wide range of normal conditions, the error of linearization is reasonably small. When the loading grows close to the limit, the errors are getting high. This is usually far above the thermal limit of the line. δ ij = δi δ j P ij UU i = X ij j sinδ ij U U i δi j J δ δ 29

30 DC Power Flow Model The following assumptions are made for DC idealization: All branch resistances are equal to zero. All voltage magnitudes are constant. The differences of phase angles between voltages at the ends of any branch are within normal loading range (where the errors are not very high). Under these assumptions, there are no losses in the system (no resistance); active power solution can be obtained without solving simultaneously for reactive power. 30

31 DC Power Flow Model (cont.) For DC model, only active power injections and withdrawals are given. The result of calculation is just voltage phase angles. This is a system of linear equations and can be solved very quickly without iterations. Very often this model is used for rough estimates of the system conditions and calculating multitude of different cases in a very short period of time. 31

32 Questions 32

33 Contingency Analysis Contingency model Limiting elements Thermal limits Stability limits Contingency analysis 33

34 Contingency Analysis (cont.) Contingency Analysis is a process of identifying the consequences of potential component outages (contingencies) in the system. Contingency could be a line, transformer, breaker, generator, etc. outage or their combination. Each contingency is described by the set of outaged components. 34

35 Contingency Analysis (cont.) The main goal of contingency analysis is to determine conditions violating operating limits. These limits include: branch overloads, abnormal voltages, interfaces, and voltage angle differences. Contingency analysis is done both in real time and in a study mode. 35

36 Contingency Analysis (cont.) The components that could be violated are called limiting (or monitored) elements they determine the constraints on system operating conditions. Transfer limits could be thermal and stability. A thermal limit is determined by the thermal rating of the limiting element the maximum amount of power that can flow through the element without burning it. 36

37 Transmission Line Thermal Ratings Normal Line Rating Can operate in this range forever Long-time Emergency Can operate in this range for several hours Duration changes with season Short-time Emergency Must reduce loading to LTE within 15 minutes Drastic Action Level Must reduce loading to LTE within five (5) minutes 37

38 Stability Limit Stability limit is determined by the consequences of dynamic (transient) processes in the system. Example is the stability of the synchronous generators that forces certain limitations on the power transfer due to the overload happening as a result of the short circuit at a substation. Stability limits are usually calculated in off-line studies that requires significant amount of time. There are new tools that may be used in the near future to calculate stability limits in real time. 38

39 Contingency Analysis The following steps are performed by most of the contingency analysis tools: Calculate base power flow (state estimator in real time). Check all limiting elements for violations Screen all the contingencies this is a process of simulating each contingency from the given set one by one by DC modelbased quick power flow analysis. Check each for potential violations. Run all suspicious contingencies through the full AC power flow analysis. Report violations in base case and under contingencies. 39

40 Contingency Analysis (branch R-S is open) 40

41 Contingency Analysis (branch P-Q is open) 41

42 Questions 42

43 Sensitivities Shift factors Loss factors 43

44 Sensitivities (cont.) Sensitivity is another way of linearization. It shows how a power flow variable (flow, voltage, phase angle, etc.) changes with the change of another value (injection, flow, etc.). Sensitivities are very widely being used in different industries for real-time control. 44

45 Sensitivities (cont.) The most-used sensitivities in electric network analysis are power transfer distribution factors (PTDF) and loss factors (LF). This is a fundamental security analysis tool. It can answer the questions: How will solution change for variations in inputs? How must inputs be changed to control the output? 45

46 Power Flow and Linear Analysis Inputs Outputs Answers Questions How do the voltages change with increased load? How will branch flows change with the requested transfer? Which generators affect the limiting element? How will system losses change with the requested transfer? 46

47 Power Transfer Distribution Factors PTDF determines a change in the power flow at each line when one (1) MW is transferred from one bus of the network to another. When one MW is transferred from one bus to another, it affects every single flow in the network! 47

48 PTDF s. Transfer P -> T. 48

49 PTDF s. Transfer P -> S. 49

50 Power Transfer Distribution Factors (cont.) In addition, depending on location of the two buses, the transfer causes different losses which are impossible to predict, so reference bus makes up for losses injecting additional MWs. That is why it is also called a slack (or swing) bus. This means that PTDFs are dependent on the selection of the reference bus. However, in the DC model, they are not dependent on the selection of the reference bus since there are no losses in DC network. 50

51 PTDF ΔP mn Δπ ij n Δπ mn k α ij ΔP k j ΔP ij ΔP ij i k α mn Line k m ΔP mn 51

52 AC PTDF with Slack Bus at S 52

53 AC PTDF with Slack Bus at Q 53

54 AC PTDF with Slack Bus at P 54

55 Shift Factors Shift Factors (SF) are the PTDFs when one of the points is always a reference bus. In other words, shift factor is the sensitivity of the line flows to the change in injections at the buses. SF shows how the flow in the branch will change if the injection at the bus changes by one (1) MW. Because the reference bus always makes up for the change in the injection (to keep balance), shift factor values are dependent on the location of the reference bus. This is true even for the DC model. By definition, the shift factor at the reference bus equals to zero (0). 55

56 Shift Factors X i MW X m MW S ik S mk 1 MW i ΔP k Line k m 1 MW

57 Shift Factors (cont.) 57

58 Linearization of the Line Flow Shift factors can be used to linearize flow in the line as a function of bus injections The shift factor will reflect the change of the line flow due to change in the injection In a linear model (DC model) we can use superposition to take into account the change in the line flow due to change in the injection at all buses 58

59 Linearization of the Line Flow (cont.) Assuming the injection change at node i being ΔP i the change in the line l flow would be: N Δ P = S ΔP l li i 1 This linear form of the line flow will be used later in the Economic Dispatch formulation The constraints must be linear in order to be able to use linear programming 59

60 Loss Factors Loss factor (LF) is the sensitivity of system losses to a change in the injection at the bus. In other words, a loss factor at the bus shows how system losses will change if the injection at the bus is changed by one (1) MW. Because the reference bus always makes up for this additional MW, the values of the loss factors are dependent on the selection of the reference bus. Loss factors are often used in linear analysis to estimate the effect of different transfers or transactions on system losses. By definition, the loss factor at the reference bus equals to zero (0). 60

61 Loss Factors (cont.) The value DF i =1-LF i is called delivery factor. The delivery factor shows how much power is going to reach the reference bus if additional one (1) MW is injected at the bus i. This means that if one injects additional MW of power at the bus i, only 1-LF i MW is going to reach the reference bus, the rest is lost in the network. The inverse of the delivery factor is called loss penalty factor. 61

62 Examples of the Sensitivities Shift factor of the line i-j to the bus k SF k =20%. If we change the injection at k by 10 MW, the flow on the line i-j will increase by two (2) MW. Shift factor of the line i-j to the bus k SF k = -20%. If we change the injection at k by 10 MW, the flow on the line i-j will decrease by two (2) MW. Loss factors at the bus k LF k =2%. If we change an injection at the bus k by 10 MW, system losses will change by 0.2 MW. 62

63 Questions 63

64 LMP Calculation Commercial network model Locations Node, zone, hub Economic dispatch formulation Shadow prices Location-based marginal price LMP components 64

65 Commercial Network Model Unlike bus/branch network model that is being used in advanced network applications, the objective of the commercial network model is to provide pricing locations for trading. Locations provide points in the system where participants submit offers and bids, markets settle, and LMPs are calculated. Location is not necessarily a physical point in the electrical network model. 65

66 Locations Node corresponds to a physical bus or collection of buses within the network Load zone aggregation of nodes. Zonal price is the load-weighted average of the prices of all nodes in the zone Hub representative selection of nodes to facilitate long term commercial energy trading. The hub price is a simple average of LMPs at all hub locations. External/proxy node location that serves as a proxy for trading between ISO New England (ISO-NE) area and its neighbors 66

67 Network Model Hierarchy SCADA One-line (Nodes) TP AC Bus/Branch (Buses) Linearization DC Bus/Branch (Buses) SCED Commercial (Private p-nodes) Agregation Commercial (Locations) SE RQM AC Power Flow (Buses) Settlements (MD/Locations) 67

68 NEPOOL Control Area and Pricing Hub Hub 68

69 Characteristics of a Hub Prices at the trading hub should move with prices in the target region. There should be very little intra-hub congestion. It should not be possible for the hub to be lost from service or disconnected from the rest of the system. Reasonable patterns of congestion should not cause the hub price to substantially diverge from the prices in the region. 69

70 Location-based Marginal Price (LMP) LMP is a cost of optimally supplying an increment of load at a particular location while satisfying all operational constraints. One can think of the LMP as a change of the total production cost to deliver additional increment of load to the location. LMPs are usually produced as a result of economic dispatch. LMPs can be calculated looking ahead ex-ante LMPs, or after the fact ex post LMPs. Ex-ante LMPs for generation locations are also called nodal dispatch rates (NDR). 70

71 Power System Normal Operation Control One of the most important power system control objectives is to keep the balance in the system. At any moment, the sum of all generation must meet all loads, losses and scheduled net interchange. There are three processes that achieve this goal under normal operations: automatic generation control (AGC), load following, and optimal/economic dispatch. 71

72 Load Following vs. AGC Load Load Following AGC Time 72

73 Balancing the System AGC is a fully automatic system that responds to comparatively small fluctuations of the load. Cycle 4 sec. Load following is the look ahead process of making sure that the ISO has enough capacity online to meet the load. Due to characteristics of the units, they cannot instantaneously respond to the ISO instructions they are limited by their response rates. If the load grows too fast, the operator may not have enough time to follow the load, so some units have to be started/committed in advance enough to be able to provide needed dispatch range. This process is also called resource adequacy analysis (RAA) in the ISO-NE. Response rate is the maximum speed at which the unit can move. It is measured in MW/min. 73

74 Economic Dispatch It is the least expensive way of supplying load in the system. Dispatching generators means changing their output to keep the system in balance. Economic dispatch is part of the load following control and is being run every five (5) min in ISO-NE to re-optimize the generation to meet load at minimum cost. The result of the dispatch is unit output levels desired dispatch points (DDP) in MW and LMPs at each generator node nodal dispatch rates. 74

75 Economic Dispatch Formulation As any optimization problem, economic dispatch is formulated by specifying objective function and a set of constraints. In case of economic dispatch, the objective function is the total cost of producing electricity that has to be minimized. Each unit submits offer that specifies the incremental cost of producing energy. 75

76 Economic Dispatch Formulation (cont.) In general, this problem is non-linear and has to be solved by using OPF optimal power flow algorithm, but OPF software is not robust and quick enough to be used in real-time processes, so linearized version, utilizing linear programming (LP) technique, is used. 76

77 Economic Dispatch Formulation (cont.) ST.. N i= 1 gi i= 1 j= 1 N 1 N Min C P i L gi P P Loss = lj max ki gi k min max gi gi gi, Objective function total cost 0, S P T, k = 1,2,..., K, P P P, i = 1,2,..., N, System Balance Transmission Constraints Capacity Constraints Where Ski is a shift factor of branch k to the generator i, C is an incremental price of of energy at the generator i. i 77

78 Economic Dispatch Formulation (cont.) Unlike other constraints, the first constraint is an equality. It means that the balance in the system must be maintained at all times. Any optimal solution must satisfy this condition. All other constraints are limits on branch or interface flows that reflect reliability criteria in the system. This is the simplest form of presenting the formulation in real life it looks significantly more complicated. 78

79 Economic Dispatch Solution As a result of solving LP, the dispatch algorithm determines desired dispatch points for every dispatchable generator. These values are called primal variables. The prices are obtained using dual variables shadow prices. Each constraint has a corresponding shadow price, even the system balance one. Each shadow price reflects the effect of relaxing corresponding constraint by one (1) unit on the value of the objective function, which means the change of total cost. 79

80 Economic Dispatch Solution (cont.) The shadow price λ of the system balance constraint is one for the whole system (only one system balance equation). Each transmission constraint k has its own shadow price μ k. Some constraints may be binding. Binding constraint is the constraint that turns into equality for the optimal solution. For example, a particular branch has to be operated at its limit. 80

81 Economic Dispatch Solution (cont.) The shadow price of the binding constraint is non-zero, while the shadow price of the constraint that does not bind is zero (0). 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. 81

82 Economic Dispatch Solution (cont.) 250 P 1 Non-binding Constraint $1600 Load: P 1 +P 2 = 250 MW Cost: 5*P 1 +10*P 2 Binding Constraint P $1675 $1750 P2 200 P + P = P 2

83 Economic Dispatch Solution (cont.) 83

84 Economic Dispatch Solution (cont.) 84

85 Optimal Solution with Non-Binding Constraint 85

86 One of the Constraints Binds 86

87 Optimal Solution with Binding Constraint Binding Constraint 87

88 Binding Constraint 88

89 Binding Constraint Mechanical Analogy Non binding constraint Binding constraint 89

90 Economic Dispatch Two Unit Example 1 2 Transfer Limit = 150 MW P 12 P 2 P 2 max = 250 MW C 1 = $10/MWh SF 2 = 0 P 1 P 1 max = 250 MW C 1 = $5/MWh SF 1 = 1 P L TotalCost : C * P + C * P = 5* P + 10* P min s.t. P1+ P2 = P - System Balance L * P + 0* P = P 150 MW - Generic Constraint P1 250, P Capacity Constraints 90

91 Economic Dispatch Two Unit Example (cont.) P Total Cost = 5 * 200 = $1000 P Total Cost = 5 * * 50 = $1250 P P P 2

92 Economic Dispatch Two Unit Example (cont.) 5 $/MWh 10 $/MWh 150 MW P 2 =50 MW P 1 =150 MW 200 MW Total Cost: (5 * 150) + (10 * 50) = $1250 Let Transfer Limit increase by 1 MW. We can load Gen 1 up to 151 MW. We will need only 49 MW from Gen 2. Total Cost in this case will be (5 * 151) + (10 * 49) = $1245. The change in cost μ = $ $1250 = -$5 is a shadow price of the transmission constraint. 92

93 LMP Calculation LMP at any location is calculated based on the shadow prices out of LP solution. The following fundamental formula is used to calculate LMPs. For any node i: λ = λ LF λ+ S μ, i i ik k k= 1 where λ is a shadow price of the system balance constraint. K 93

94 LMP Calculation (cont.) While dispatched, all units will end up in one of three groups: At the maximum limit At the minimum limit Between minimum and maximum The maximum and minimum can be ramp rate constrained limit, regulation limit, etc. The third group of units is called Marginal Units these are the units that determine LMPs at ALL locations. 94

95 LMP Calculation Fundamental Properties The price at the location of each marginal unit is always equal to its offer price. n+1 Rule: for n binding constraints, there is at least n+1 marginal units. This does not include equality constraint. In the case of no congestion, there is only one marginal unit. 95

96 LMP Calculation Fundamental Properties (cont.) Any increment of load at a particular location will be delivered from the marginal units. An LMP at any location will be a linear combination of the LMPs (offer prices) at marginal locations. If there is no congestion (all μ k equal to zero) and no losses, the LMP will be the same at each location. LMPs at some locations can be higher than the highest offer price. Opening a branch can lower LMPs. LMP can be negative at some locations. 96

97 Base Case 97

98 The Price Can be Higher than the Highest Bid 98

99 The Difference Case 99

100 Prices Before Opening the Line 100

101 After Opening the Line 101

102 The Difference 102

103 LMP Components Energy Losses Congestion Each LMP can be split into three components. 103

104 LMP Components (cont.) λi = λ LFi λ + Si k μk, K k= 1 Congestion Component Loss Component Energy Component The energy component is the same for all locations and equals to the system balance shadow price. Congestion components equal zero for all locations if there are no binding constraints all μ k =0. The loss component is the marginal cost of additional losses caused by supplying an increment of load at the location. 104

105 LMP Components (cont.) At the reference bus, loss factor LF ref = 0 and all shift factors S refk = 0. This means that both loss and congestion components are always zero at the reference bus. As the result, the price at the reference bus always equals to the energy component: λ ref =λ. 105

106 LMP and the Reference Bus LMPs will not change if we move the reference bus from one location to another. However, all three components are dependent on the selection of the reference bus (due to the dependency of the sensitivities on the location of the reference bus). 106

107 LMP Components The dependency of components on the selection of the reference bus proves that the value of each component by itself does not mean much only the differences have a meaning and are not dependent on the selection of the reference bus. The only reason we need LMP components is the need to use them for FTRs and split congestion cost from energy. 107

108 Two Unit Example LMP Components c c λ 1 = $5 / M Wh 2 $0 / M Wh λ 1 = $5 / M Wh λ 2 = $10 / M Wh μ = $5 150 MW 150 MW SF 1 = 1 c Ref 250 MW 100 MW SF = 2 0 λ2 = λ + λ2 = ( 5) = $10 / M Wh c λ1 = λ + λ1 = ( 5) = $5/ M Wh c λ 1 = $0 / MWh λ c 2 = $5/ MWh λ 1 = $5/ MWh λ 2 = $10 / MWh Ref 150 MW SF = 1 0 μ = $5 150 MW λ = λ = $10 / MWh 250 MW 100 MW SF = 2 1 c λ2 = λ + λ2 = 5 + ( 1) ( 5) = $10/ c λ1 = λ + λ1 = 5+ 0 ( 5) = $5/ MWh MWh λ = $5/ MWh 108

109 LMP Components λ i K = i + k= 1 λ(1 LF ) S μ, ik k Congestion Component Delivered Energy Component Grouping energy and loss components together can be considered as one component delivered energy component. This component is the marginal price of delivering an increment of load from the reference bus. In fact, the settlement process never needs energy and loss components separately. 109

110 LMP Components Settlement System wide, generators are being paid: λ P = ( λ LF λ + S μ ) P. i i i ik k i i i k System wide, loads pay: λ L = ( λ LF λ+ S μ ) L. i i i ik k i i i k Total revenue: λ ( P L) + λ LF ( P L) μ ( P L) S = i i i i i k i i ik i i k i = λ Loss + λ Loss μ T max marg k k k. 110

111 LMP Components Settlement (cont.) Loss revenue: Loss Re v = λ ( Loss Loss). marg Congestion revenue: Cong v T max Re = μk k. k Loss is a value based on the Revenue Quality Metering. 111

112 LMP Components Settlement (cont.) Both Loss and Congestion revenue depends on the selection of the reference bus. When moving the reference, total revenue stays the same, however the split into congestion and loss fund changes. This requires correct and consistent modeling of losses in the system. Under this condition, the dispatch and, therefore, μ k will be the same. This also means that no matter where you are located, both payment and credit will stay the same. 112

113 Revenue with the Slack at Bus T 113

114 Revenue with the Slack at Bus P 114

115 Revenue with the Slack at Bus S 115

116 Transmission Losses U 1 U 2 P G R P L P G P G = P L + Loss P L Transmission losses cause the power flow in the beginning of a transmission line to be different than the flow at the end. This is due to the dissipation of energy in the wires. In order to supply energy to the load, the generator has to supply more to cover load and transmission losses. 116

117 Transmission Losses (cont.) Based on the Ohm s law, the losses in the line A-B, π, are approximately proportional to the square of the power flow through the line: π a P AB 2, AB where a is a coefficient that depends on the voltage and resistance of the transmission line. 117

118 Transmission Losses Two Bus Example MW 100 MW 110 MW 100 MW Let a =.001. Then the losses in the line 1-2 will be x = 10 MW. Generator has to generate 110 MW in order to supply 100 MW of load. 10 MW are physical system losses. 118

119 Average Losses Average losses can be defined as the amount of losses per MW of transfer (power flow in the line): π av = π / P = a P AB AB AB AB For the above example, average losses will be x 100 = 0.1 MW. This means that every MW of load will cause an average 0.1 MW of losses.. 119

120 Marginal Losses Marginal losses are the rate system losses change with the change of flow. This is being expressed as a derivative: π m AB π AB = = 2 a PAB. P For the two bus example: π = 2 x x 100 = 0.2 AB 120

121 Average vs. Marginal Losses Comparing average and marginal losses, one can see that marginal losses are about twice as much as average. These two quantities describe different properties of the system: marginal effect on losses of increasing transmission loading vs. average amount of losses per MW of flow. Note that both average and marginal losses are dependent on the state of the system flow in the line A-B. 121

122 Two Bus Example Economic Dispatch MW P 1 max = 250 MW C 1 = $20/MWh Transfer Limit = 150 MW 100 MW 100 MW 0 MW P 2 max = 250 MW C 1 = $30/MWh This example is very easy to optimize. Since the flow in the line 1-2 is not higher than the transfer limit, all load can be supplied by the least expensive generator, so the system will be dispatched as shown above: generator 1 will be loaded up to 110 MW (supplying load and losses), and generator 2 will stay at zero. Total cost of production: 110 x 20 = $

123 Two Bus Example LMP Location-based Marginal Price (LMP) at a location is defined as a change in the total cost of production due to increment of load at this location. We can figure out the values of the LMPs in the two bus example by adding one MW of load at each bus and determining the corresponding change in the total production cost. 123

124 Two Bus Example LMP at Bus 1 If one (1) MW of load was added at bus 1, there would be no need to transfer any additional energy over transmission line this one (1) MW can be supplied by the cheapest generator 1 at the price of $20/MWh. Additional cost of producing one (1) MW will be $20 total cost will be $2220. The change in total cost of production will also be $20, so the LMP at bus 1 will be $20/MWh. 124

125 Two Bus Example LMP at Bus 2 $20/MWh Transfer Limit = 150 MW MW $24/MWh C 2 = $30/MWh 0 MW MW C 1 = $20/MWh 101 MW Let us add 1 MW of load at bus 2. The flow in the line will become 101 MW, so the losses will be x = 10.2 MW. Generator 1 will have to produce = MW. Total cost will be x 20 = $2224. LMP at bus 2 will be equal to the change in total cost: = $24/MWh. 125

126 Two Bus Example LMP As we can see, even in the non-congested case, LMPs are different at different locations. This is due to the marginal effect of losses an increment of load at any location causes additional losses that require more energy to be produced by the generators. Note that we have not mentioned any LMP components so far. Have we used loss factors? Have we used marginal loses? The market can be settled using calculated LMPs. 126

127 Two Bus Example Settlement For the last example, generator will be credited: 20 x 110 = $2200. The load will pay 24 x 100 = $2400. ISO will be left with $200 surplus. The surplus comes from the marginal pricing this is inherent to location based marginal pricing. 127

128 Marginal Pricing Loads implicitly pay for physical losses just due to the fact that generation is higher than load by the amount of physical losses, so this is coming out of the surplus. The surplus of money has nothing to do with payment for losses it is the result of marginal pricing. If we accept the principles of marginal pricing, the surplus is inevitable, both with respect to congestion and losses. 128

129 Who Paid Extra Money? Looking at the LMPs, it is impossible to tell which part is payment for marginal losses and which is payment for energy LMP is the price of energy at a location. As soon as we want to split LMPs into components in order to separate energy and marginal loss money, we have to arbitrarily define a reference (slack) bus. Depending on the location of the reference bus, the values of energy revenue and marginal losses revenue will change, even though the total will not. 129

130 Reference Bus Energy component of the LMP is a price of energy at the reference bus it is the same for all locations in the system. Moving reference bus from one location to another will preserve all the LMPs. This means that the energy component will change and marginal loss component will have to change as well to preserve the value of LMP at each location. Loss factors are used to split LMP into energy and marginal loss components. 130

131 Loss Factors Loss factor is a sensitivity of system losses to the change in injection at a location. There are as many loss factors as locations in the network. The values of loss factors are dependent on the location of the slack bus because it is the slack bus that has to balance the increment of injection by consuming additional increment of load to keep the system balance. 131

132 Loss Factors Example LF Transfer Limit = 150 MW LF 2 =0 1 = MW 100 MW Ref 100 MW 0 MW With the reference bus at bus 2, the loss factors will be 0 at 2, and at 1. Note that loss factor at the reference bus is always zero there is no change in power flow (and, therefore, transmission losses) if we balance the increment of injection at the same bus. The change in injection at bus 1 will cause the increase in the transmission flow and, therefore, system losses. 132

133 Loss Factors Example (cont.) LF 1 =0 1 2 Ref 110 MW Transfer Limit = 150 MW 100 MW LF 2 = MW 0 MW With the reference bus at bus 1, the loss factors will be 0 at 1, and 0.2 at 2. The change in injection at bus 2 will decrease the flow in the transmission line and, therefore, system losses this is why the value of the loss factor is negative. It can be interpreted this way: if 1 MW of generation is added at bus 2, the system losses will drop by 0.2 MW. 133

134 LMP Components In the system without congestion, an LMP can be split into two components: energy component and marginal loss component. As we discussed, the term energy component is not very reflective of the meaning it is the price of energy at the reference bus. L LMP at bus i: λ = λ LF λ = λ+ λ. i i i Loss component at bus i: λ L = LF λ. i i 134

135 LMP Components Two Bus Example 1. Reference Bus 2 Energy component: $24/MWh LMP at 2: $24 + $0 = $24/MWh LMP at 1: $24 - $0.167 x 24 = $24 - $4 = $20/MWh Was generator penalized for marginal losses? 2. Reference Bus 1 Energy component: $20/MWh LMP at 2: $20 (-0.2) x 20 = $20 + $4 = $24/MWh LMP at 1: $20 + $0 = $20/MWh Did load pay for marginal losses? Note that in both cases load paid the same amount and generator was credited the same amount. 135

136 Pre-SMD, No Congestion $24/MWh Transfer Limit = 150 MW $24/MWh MW C 2 = $30/MWh 0 MW 110 MW C 1 = $20/MWh 100 MW In this case, generator 1 s offer is modified by its bus penalty factor: C 1 = 1.2 x 20 = $24/MWh. The optimal solution will be delivering all the load (and corresponding losses) from generator 1 because its effective offer ($24/MWh) is lower than $30/MWh of generator 2 (penalty factor at 2 equals 1). This will set the ECP to $24/MWh at all locations. 136

137 Pre-SMD, No Congestion Settlement G1 is being credited: 110 x 24 = $2640. G2 is being credited: 0 x 24 = $0. Load pays ECP: 100 x 24 = $2400. Load pays for physical losses: 10 x 24 = $240. Load is charged: $ $240 = $

138 SMD, No Congestion $20/MWh $24/MWh MW C 1 = $20/MWh Transfer Limit = 150 MW 100 MW 100 MW C 2 = $30/MWh 0 MW The optimal solution produces prices as shown. Generators and the load will be paid or pay their location s respective LMPs. The difference in the LMPs is due to marginal losses. 138

139 SMD, No Congestion Settlement Energy component is $24/MWh. Loss component at 1 is -$4/MWh. Loss component at 2 is $0/MWh. G1 is being credited: 110 x 20 = $2200. G2 is being credited: 0 x 24 = $0. Load is being charged: 100 x 24 = $

140 Pre-SMD with Congestion $24/MWh $24/MWh MW C 1 = $20/MWh Transfer Limit = 100 MW 100 MW 120 MW C 2 = $30/MWh 20 MW The load is 120 MW, while the transmission capacity is only 100 MW. The optimal dispatch will load G1 to 110 MW (including covering losses) and G2 to 20 MW. G2 will be constrained for transmission producing 20 MW and is not allowed to set the ECP. G1 will set the ECP at $24/MWh. 140

141 Pre-SMD with Congestion Settlement G1 is being credited: 110 x 24 = $2640. G2 is being credited 20 x 24 = $480. G2 is also being credited an uplift for being constrained for transmission: 20 x 6 = $120, so G2 is credited $600 overall. The load is being charged 120 x 24 = $2880. The load also pays for physical losses: 10 x 24 = $240. Load is also charged for uplift: $120, so, altogether, it is being charged $

142 SMD with Congestion $20/MWh Transfer Limit = 100 MW MW $30/MWh C 2 = $30/MWh 20 MW 110 MW C 1 = $20/MWh 120 MW The binding transmission constraint causes price separation. Both generators become marginal and set the prices at their respective locations. The price at 1 will be $20/MWh. The price at 2 will be $30/MWh. 142

143 SMD with Congestion Settlement G1 is being credited: 110 x 20 = $2200. G2 is being credited: 20 x 30 = $600. The load is charged: 120 x 30= $

144 SMD with Congestion LMP Components Let us assume that the reference bus is at 2. Then the energy component of the price will be equal to the price at 2: $30/MWh. The loss and congestion components are both equal to zero at this location. The loss component at bus 1 will be: x 30 = -$5/MWh. Then the congestion component will be: = -$5/MWh. So the price at 1 can be decomposed as follows: $20/MWh = $30/MWh - $5/MWh - $5/MWh. 144

145 SMD with Congestion Settlement with FTR Let us assume that the load at 2 bought 100 MW FTR between 1 and 2 at the auction. Let us also assume that the load paid $1.40/MW, so it spent $140 at the FTR auction. Then the load will be credited an FTR payment 100 x [0-(-5)]= $500. So, overall, the load will pay: $ $500 + $140 = $3240. This is the same amount it would pay pre-smd. 145

146 SMD vs. Pre-SMD No Congestion Congestion Pre-SMD SMD Pre-SMD SMD Gen Gen Total Gen Load (w/ftr) (3240) Total (440) 146

147 Modeling Losses in the Lossless System LP methodology uses DC network model to calculate LMPs. In the DC model, there are no losses in the transmission lines, but sum of all generation is greater than sum of all loads by the amount of losses. This brings up an issue: if there are no losses in the network, where to put losses to keep the balance? 147

148 Losses in the DC Model In a traditional approach, slack bus always makes up for losses, which means that all system losses are withdrawn at one bus. This may significantly distort the power flow in the network and, as a result, change LMPs. The slack bus that has been selected as a reference for shift factors determines the location of the losses in the network. 148

149 Two Bus LP Formulation 1 Transfer Limit = 150 MW 2 P 2 $10/MWh P 12 P 1 $5/MWh L 1 =50MW L 2 =250MW LP1: Min 5P + 10P S.T. 1 2 P1+ P2 L1 L2 Loss = 0; Loss = lf1( P1 L1) + lf2( P2 L2); sf ( P L ) + sf ( P L )

150 Two Bus LP Formulation with Distributed Losses LP2: Min 5P + 10P 1 2 S.T. P1+ P2 L1 L2 Loss = 0; Loss = lf1( P1 L1) + lf2( P2 L2); sf ( P L d Loss) + sf ( P L d Loss)

151 Distributed Slack The reference for shift and loss factors does not have to be located at a particular physical bus. If we select a distributed slack, we assign participating factors for each bus to cover imbalance in the system. 151

152 Distributed Slack Example S ik x 1-x ΔP k 1 MW i Line k 152

153 Distributed Slack Example (cont.) Let us use distributed bus with the load-weighted participating factors. Let us distribute losses among all load buses as well. 153

154 Distributed Slack Loss distribution factors: d d = = ; = = To convert loss sensitivities to refer to a distributed slack: lf lf (1/ /60) = = ; 1 (1/ /60) 0 (1/ /60) = = (1/ /60) 154

155 Distributed Slack (cont.) To convert shift factors to refer to the same distributed slack: sf sf 1 2 = 0 1/6 0 5/6 ( 1) = 5/6; = 1 1/6 0 5/6 ( 1) = 1/6. The LP2 solution will be: Case 5 D Generation Load LMP LMP_Energy LMP_Loss LMP_Congestion Bus Bus Loss Lambda Tau Mu

156 Distributed Slack (cont.) The results can be presented as follows: 205MW $5/MWh $10/MWh 1 Transfer Limit = 150 MW MW 126 MW L 1 =50 MW 5 MW 26MW L 2 =250 MW $9.17/MWh Distributed Slack Loss=31 MW 156

157 LMP with Distributed Slack When distributed slack participating factors are selected the same as loss distribution factors: d λ + d λ = λ This means that the energy component will be the weighted average of all load locational prices. For the two bus example: λ = 1/ / 6 10 = $ / MWh. 157

158 5 Bus Model E Transfer Limit = 240 MW D Sundance $40/MWh EcoMax=200 Brighton X ED =2.97% $20/MWh EcoMax=600 A XEA =0.64% X AD =3.04% 400 MW Alta X AB =2.81% B X BC =1.08% C X CD =2.97% $14/MWh Park City EcoMax=110 $15/MWh EcoMax= MW 300 MW Solitude $30/MWh EcoMax=

159 5 Bus Model: Distributed Slack Alta ParkCity Solitude Sundance Brighton Loss Ge ne ration Bus Name Bus No Bus Gen Bus Load Bus Loss Net Injectio D W Lf@W SF@W LMP LMPE LMP Loss LMPC A B C D E LHS RHS Shadow Price Energy Balance Loss Balance Constraint ED obj Distributed slack with the following weights is selected: W B =0.3, W C =0.3, W D =0.4

160 5 Bus Model: Distributed Slack (cont.) $20/MWh E Transfer Limit = 240 MW $33.87/MWh D Sundance Brighton 463 MW $23.07/MWh Alta 110 MW A 223 MW 240 MW Park City 100 MW Distributed Slack $28.58/MWh 246 MW 300 MW B 187 MW $31.12/MWh 7 MW 7 MW 61 MW 300 MW C 9 MW $30/MWh 23 MW 19 MW Solitude 349 MW 0 MW 400 MW λ = = $31.12 / MWh 160

161 Loss Model with Loss Distribution With the appropriate and consistent loss distribution, the selection of the slack bus/market reference is not important. Under this design, with the change of the slack bus, LMPs do not change. Moreover, the congestion component and the sum of energy and loss components stay the same. Loss component of the LMP is never used by itself in settlements. Even for analysis, only differences of components between locations make sense to look at. 161

162 External Transactions External transaction (ET) is a purchase by a participant of energy external to the control area or a sale of energy by a Participant that is external to the control area in the day-ahead energy market and/or real-time energy market or a through transaction scheduled by a non-participant in the real-time energy market. Each ET is associated with two locations (not necessarily different). ET always uses proxy node as one of the locations. 162

163 External Transactions (cont.) Types: Fixed and Dispatchable Up-to congestion (in DAM only) Direction: Import and export Wheel-through (in RTM only) ETs imports and exports look to SPD just like generation or load respectively. 163

164 Proxy Node Proxy node is a node outside of the control area that provides a proxy pricing location for the entities willing to perform trades between different markets or control areas. The proxy node reflects the price of bringing in, moving energy out or through control area. The price at this node only reflects constraints internal to the control area of the market. 164

165 Proxy Node (cont.) Border Control Area External Pricing Location P T Neigboring CA Network Model 165

166 LMP at the Proxy Node The LMP at the proxy node is calculated the same way as any other internal to the market location. The only difference is the calculation of the loss component losses in the parts of tie lines outside of the control area must be excluded. This is achieved by modifying loss factors at the proxy nodes so that they do not include the effect of losses in the neighboring area. 166

167 Seams Issues with External Node Pricing Scheduling ETs and calculating prices at the proxy bus is one of the major sources of seams issues. While calculating price at external proxy node, SPD does not take into account offer and bid prices and constraints in the neighboring markets. This produces inconsistent prices across the border. 167

168 Seams Issues with External Node Pricing (cont.) The resolution to that seams issue could be: Large RTO with a single dispatch, network model, and market Coordinated Markets, where LMPs are coordinated Super RTO clearing inter-control area transactions There are different possible approaches to coordinate prices from very simple approximations to a rigorous decomposition. 168

169 Questions 169

170 Market System Architecture and Major Components Unit Commitment (UC) Simultaneous feasibility test Security constrained UC Security constrained economic dispatch LMP calculator State estimator Settlements 170

171 Major Business Streams in the ISO Capability Map Capturing Data Planning Forecasting Market-Facing Capabilities Scheduling Dispatching Operating Auctions Settlement Billing Publishing Information Monitoring Compliance Serving Customers Managing Disputes Analyzing Markets Supporting Capabilities Managing the Enterprise Information Technology Managing Change 171

172 SMD System Architecture Operations Market Assessment and Performance Monitoring MUI Settlements Publishing MUI FTRs Billing Accounting 172

173 Market Operations MOI Supply Offers and Demand Bids Day Ahead Scheduling Unit Schedules Hour Ahead Scheduling MOI Unit Schedules Archiving (Analysis System) Hourly Targets MOI Resource Adequacy Assessment Real Time Scheduling & Dispatch 5-min Targets MOI 173

174 Operations. Major Components FTR Unit Commitment SCUC SCED SFT SCED Real Time Contingency Analysis State Estimator RT LMP Calculator Network Model SCADA EMS FTR - Financial Transmission Rights SCED - Securuity Constrained Economic Dispatch SFT - Simultaneous Feasibility Test SCUC - Security Constrained Unit Commitment EMS - Energy Management System 174

175 Unit Commitment Unit Commitment is the process of optimizing the total production cost over comparatively long period of time, for example 24 hours. The result of this process is units start/stop schedules. Unlike economic dispatch, this problem cannot be solved by one LP solution, even in the linearized form. In general, UC is a mixed integer programming problem. 175

176 Simultaneous Feasibility Test (SFT) SFT, in effect, is a contingency analysis process as described earlier. The objective of SFT is to determine violations in all postcontingency states and produce generic constraints to feed into economic dispatch or FTR auction. Generic constraint is a transmission constraint that is linearized for the unit outputs using shift factors in post contingent states. 176

177 Security Constrained Unit Commitment (SCUC) SCUC is a combination of UC, economic dispatch and SFT. For each hourly schedule produced by UC, economic dispatch determines unit dispatch points to meet hourly load. Each set of dispatch points is then tested by SFT for violations. If any violations are found, new generic constraints are generated and are fed into dispatch or UC. This process ensures that the set of schedules produced by UC satisfies reliability criteria. 177