electricity transmission congestion and the dispatch of renewable power€¦ · ·...

Introduction PJM Model Estimation Conclusion

Electricity Transmission Congestion andthe Dispatch of Renewable Power

Claudia HitajUniversity of Maryland

USAEE North American ConferenceWashington, DC

October 12, 2011

C.Hitaj Transmission Congestion and Renewable Power


Overview

1 Motivation: Location of renewable plants in PJM Interconnection

2 Model: Connecting wind power plants to the grid at differentlocations

3 Estimation: Quantifying the impact of congestion on wind poweroutput



Transmission Congestion

Generator demand for a transmission line exceeds the line’s capacity

Higher electricity prices

Higher emissions?

Grid not built with renewables in mind

Timing problem: Plant first or line first?



PJM Interconnection

Source Generation capacity (MW) Proposed capacity (MW)Coal 76,968

29,916Natural Gas 50,729Nuclear 33,146Oil 11,212Hydro 8,030 403Wind 4,870 36,371Solar 15 3,460Total 167,362 70,150



Figure: Congestion in PJM (DOE 2006)



Transmission Line Coverage and Emissions

Table: Mean transmission line coverage and emission by fuel source

Fuel Line Emission (lbs/h) Annual CO2eq Year Obs.coverage PM SO2 emission (tons)

Coal 0.54 153.02 406.94 4,699,991 1973 90Oil & Other 0.47 47.82 62.55 562,389 1974 79Natural Gas 0.53 9.81 7.96 189,962 1994 113Waste 0.44 85.25 17.33 7,800 1991 31Nuclear 0.43 0.00 0.00 122 1979 17Hydro 0.78 0.00 0.00 0 1952 37Wind 0.20 0.00 0.00 0 2005 12



Modeling Effect of Congestion on Wind Plant Output

Modified IEEE 30 Bus Test System

6 generators, 30 buses, 21 loads

Solve optimal power flow (OPF) with Matlab package MATPOWER

Compare wind plant output at different locations in grid and forvarying load levels



Bus Data

Bus Load (MW) Bus Load (MW)Real Reactive Real Reactive

1 0 0 16 3.5 1.82 21.7 12.7 17 9 5.83 2.4 1.2 18 3.2 0.94 7.6 1.6 19 9.5 3.45 94.2 0 20 2.2 0.76 0 0 21 17.5 11.27 22.8 10.9 22 0 08 30 30 23 3.2 1.69 0 0 24 8.7 6.710 5.8 2 25 0 011 0 0 26 3.5 2.312 11.2 7.5 27 0 013 0 0 28 0 014 6.2 1.6 29 2.4 0.915 8.2 2.5 30 10.6 1.9



Generator Data

Area Bus Cost coefficients Pmin Pmax

c0 c1 c2 (MW) (MW)

11 0 2 0.02 0 802 0 1.75 0.0175 0 80

213 0 3 0.025 0 4023 0 3 0.025 0 30

322 0 1 0.0625 0 5027 0 3.25 0.00834 0 55

Polynomial cost function f i (P) = c i0 + c i1P + c i2P2 for each of the

i = 1, . . . , 6 generators.



Optimal Power Flow (OPF)

In the OPF, as described in Zimmerman et al. (2011), the objectivefunction is a summation of individual polynomial cost functions f iP and f iQof real and reactive power injections, respectively, for each generator:

minΘ,Vm,Pg ,Qg

ng∑i=1

f iP(P ig ) + f iQ(Q i

g )

subject to equality constraints, inequality constraints, and variable limits,where Θ and Vm are the nb × 1 vectors of voltage angles andmagnitudes, and Pg and Qg are the ng × 1 vectors of generator real andreactive power injections.



Constraints

1 Supply equals demand at each bus

2 Branch flow limits

3 Upper and lower limits on bus voltage magnitudes

4 Upper and lower limits on real and reactive power injections



Connecting a Wind Plant

As a zero marginal cost plant, will the wind plant always operate at fullcapacity?

Method

Model wind plant as zero-cost plant

Add wind plant to bus 26 at outer edge of grid

Add wind plant to bus 6 in center of grid

Compare wind plant output at different load levels

Result: The amount of power sold to the market depends on plantlocation within the electricity grid.



New Wind Plant at Outer Edge of Grid

Area Bus Cost coefficients Pmax P LMPc0 c1 c2 (MW) (MW) ($/MWh)

11 0 2 0.02 80 62.19 4.492 0 1.75 0.0175 80 79.86 4.55

213 0 3 0.025 40 36.83 4.8423 0 3 0.025 30 24.07 4.20

322 0 1 0.0625 50 28.83 4.6027 0 3.25 0.00834 55 39.89 3.9126 0 0 0 40 19.41 0.00

Objective function value is 907.88 $/h, compared with original 982.51$/h.



New Wind Plant in Center of Grid

Area Bus Cost coefficients Pmax P LMPc0 c1 c2 (MW) (MW) ($/MWh)

11 0 2 0.02 80 52.91 4.122 0 1.75 0.0175 80 69.13 4.176 0 0 0 40 40.00 4.20

213 0 3 0.025 40 24.75 4.2423 0 3 0.025 30 23.66 4.18

322 0 1 0.0625 50 26.18 4.2727 0 3.25 0.00834 55 52.57 4.13

Objective function value is 803.86 $/h, compared with 907.88 $/h forwind plant at outer edge of grid and 982.51 $/h for the originalconfiguration.



Generator Output at Different Load Levels



Regression Equation

How much curtailment of wind power is caused by congestion?

Wt = β1St + β2Ct + β3Lt + εt

where Wt is wind generation (MW), St is wind speed (mph), Ct iscongestion cost ($), and Lt is load (MW) for each hourt ∈ {0, 1, . . . , 8760} in the year 2009.



Regression Output

Dependent variable: OLSWind generationWind speed (IL) 48.00***

(77.67)Wind speed (Western PA) 26.97***

(34.63)Wind speed (Eastern PA) 2.264**

(2.60)Congestion cost -0.0551***

(-5.47)Load -0.00167***

(-13.98)R-squared 0.818Number of hours 8301



Estimated CO2 Emissions Due to Curtailed Wind Power

Curtailed wind power = W C =8760∑t=0

(Wt(Ct = 0)−Wt) = 96, 953.85 MWh

CO2 emissions =8760∑t=0

et ·W Ct = 90, 450 tons

where et is the CO2 emissions rate in tons/MWh of the marginal unit(monthly average for peak and off-peak hours). At a carbon price of$20/ton, the environmental cost of the CO2 emissions amounts to $1.81million.The CO2 emissions justify investment in 0.9 miles of a 230 kVtransmission line or 0.42 miles of a 500 kV line.



Conclusion

Wind plant output depends on plant location within the grid.

Wind plants are more severely affected by congestion thanconventional plants.

Wind curtailment reached an estimated 97 GWh in PJM in 2009.

Curtailment led to an additional 90,450 tons of CO2 in 2009.

The environmental cost of wind curtailment is estimated at $1.81million, justifying investment in 0.9 miles of a 230 kV transmissionline.



References

DOE (2006). 2006 Congestion Study. US Department of Energy,http://nietc.anl.gov/congestionstudy.

DOE (2009). National Electric Transmission Congestion Study. US Departmentof Energy, http://congestion09.anl.gov.

NCDC (2011). Hourly Surface Data. National Climatic Data Center, NationalOceanic and Atmospheric Administration (NOAA), www.ncdc.noaa.gov.

PJM (2010). CO2 Emissions Report. PJM Interconnection,http://www.pjm.com/documents/%7E/media/documents/reports/co2-emissions-report.ashx

PJM (2011a). Wind Generation. PJM Interconnection,http://www.pjm.com/markets-and-operations/ops-analysis.aspx.

PJM (2011b). Historical Metered Load. PJM Interconnection,http://www.pjm.com/markets-and-operations/ops-analysis/historical-load-data.aspx.

PJM (2011c). Energy Information Agency (EIA) 411 Reports. PJMInterconnection, http://www.pjm.com/documents/reports/eia-reports.aspx.

PJM (2011d). Real Time Transmission Constraints. PJM Interconnection,http://www.pjm.com/markets-and-operations/energy/real-time.aspx.




The IEEE 30 Bus Test System is based on Alsac and Stott (1974) with branchparameters rounded to nearest 0.01, shunt values divided by 100 and shunt on bus 10moved to bus 5. Generator locations, costs and limits and bus areas were taken fromFerrero et al. (1997). The optimal power flow was solved using the Matlab packageMATPOWER developed by Zimmerman et al. (2011).

Alsac, O., and B. Stott (1974). Optimal Load Flow with Steady State Security.IEEE Transactions on Power Apparatus and Systems 93(3): 745-751

Ferrero, R.W., S.M. Shahidehpour, and V.C. Ramesh (1997). Transactionanalysis in deregulated power systems using game theory. IEEE Transactions onPower Systems 12(3): 1340-1347.

Zimmerman, R.D., C.E. Murillo-Sanchez, and R.J. Thomas (2011).MATPOWER Steady-State Operations, Planning and Analysis Tools for PowerSystems Research and Education. IEEE Transactions on Power Systems 26(1):12-19.



Equality and Inequality Constraints

The equality constraints are the full set of 2 · nb nonlinear real andreactive power balance equations.

Pb(Θ,Vm) + Pd = CgPg (1)

Qb(Θ,Vm) + Qd = CgQg (2)

The sparse nb × ng generator connection matrix Cg can be defined suchthat its (i , j)th element is 1 if generator j is located at bus i and 0otherwise.The inequality constraints consist of two sets of nl branch flow limits, onefor the from end and one for the to branch:

|Ff (Θ,Vm)| ≤ Fmax (3)

|Ft(Θ,Vm)| ≤ Fmax (4)

The flows F (Θ,Vm) can be flows of apparent power S(Θ,Vm) in MVA,real power P(Θ,Vm) in MW, or current I (Θ,Vm) in A.



Variable Limits

The variable limits include an equality constraint on any reference busangle and upper and lower limits on all bus voltage magnitudes and realand reactive power injections:

θrefi ≤ θi ≤ θrefi , i ∈ Iref (5)

ν i,minm ≤ ν im ≤ ν i,max

m , i = 1, . . . , nb (6)

pi,ming ≤ pig ≤ pi,max

g , i = 1, . . . , ng (7)

qi,ming ≤ qig ≤ qi,max

g , i = 1, . . . , ng (8)


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