Stochastic Economic Dispatch for Power Stochastic Economic Dispatch for Power Grids with High Penetration of Wind Power Grids with High Penetration of Wind Power Ali Al Awami Awami Ali Al PhD Student PhD Student Department of Electrical Engineering Department of Electrical Engineering 1 1
Outline Outline � Overview Overview � � Why Is This Research Important? Why Is This Research Important? � � Different Economic Dispatch Algorithms Different Economic Dispatch Algorithms � � Statistical Characterization of Wind Power Output Statistical Characterization of Wind Power Output � � Simulation Results Simulation Results � – – Single Objective Single Objective – Multiple Objectives – Multiple Objectives � Conclusions Conclusions � 2 2
Overview Overview What Is Economic Dispatch (ED)? What Is Economic Dispatch (ED)? � � – Generation- -load balance, A MUST at all times load balance, A MUST at all times – Generation – ED is the process of allocating generation levels among ED is the process of allocating generation levels among – generating units in order to meet the load in the most generating units in order to meet the load in the most economical way economical way ED is a lot easier with traditional generating units ED is a lot easier with traditional generating units � � How do you run ED for a power system with high penetration How do you run ED for a power system with high penetration � � of wind power? of wind power? Remember: Remember: � � – Traditional generating units are very controllable. Wind Traditional generating units are very controllable. Wind – units are not. units are not. – Wind power is great, except for most Power System – Wind power is great, except for most Power System Engineers! Engineers! – Reason: it is highly unpredictable and uncontrollable Reason: it is highly unpredictable and uncontrollable – 3 3 � Limited bulk storage capabilities � – Limited bulk storage capabilities –
Overview Overview Stochastic dispatch for a power grid with wind and thermal Stochastic dispatch for a power grid with wind and thermal � � units is presented. units is presented. The formulation takes into account: The formulation takes into account: � � – Wind power uncertainty – Wind power uncertainty – – Imbalance charges Imbalance charges Simultaneous optimization of: Simultaneous optimization of: � � – Operating cost – Operating cost – Emissions – Emissions Multi- -objective particle swarm optimization (MO objective particle swarm optimization (MO- -PSO) is PSO) is Multi � � employed. employed. 4 4
Why is this important? Why is this important? � Power system operations: � Traditionally � deterministic � Now/Future � stochastic � Stochastic dispatch – An enabling tool for RES integration � The new cap-and-trade policies necessitates the inclusion of environmental objectives 5 5
Deterministic Dispatch – – Deterministic Dispatch Single Objective Single Objective This is the conventional way to do ED � Objective: Minimize the operating cost of the power system � subject to the generation-load balance constraint. For wind, schedule whatever you forecast . � 6 6
Deterministic Dispatch – – Deterministic Dispatch Single Objective Single Objective Minimize Deterministic combined OC d OC d ( P gi ,w i ) operating cost of TPs and WPs Output of i th TP P gi Subject to Scheduled output of i th WP w i w i = w fci Forecast output of i th WP w fci ≤ ≤ min max P P P System load including losses L gi gi gi * TP: Thermal Plant * TP: Thermal Plant m n ∑ ∑ * WP: Wind Plant * WP: Wind Plant = − P L w gi fci = = 1 1 i i 7 7
Stochastic Dispatch – – Stochastic Dispatch Single Objective Single Objective Objective: Minimize the expected value of the operating cost of � the power system subject to the generation-load balance constraint. � Takes into account the uncertainty associated with wind power output. 8 8
Stochastic Dispatch – – Stochastic Dispatch Single Objective Single Objective Minimize E [ OC s ( P gi ,w i )] Subject to ≤ ≤ 0 w w i ri ≤ ≤ min max P P P gi gi gi m n ∑ ∑ = + L P w gi i = = 1 1 i i 9 9
Stochastic Dispatch – – Stochastic Dispatch Single Objective Single Objective The stochastic combined operating cost ( OC The stochastic combined operating cost ( OC s s ) can be formulated ) can be formulated � � as as Scheduled Actual wind power wind power M N N N ∑ ∑ ∑ ∑ = + + − + − [ ] ( ) ( ) [ ( )] [ ( )] E OC C P C w E C W w E C w W s i gi wi i pi i ac , i ri i i ac , = = = = 1 1 1 1 i i i i Operating cost Operating cost Imbalance cost due Imbalance cost due of TPs of WPs to over-generation to under-generation where where Penalty cost coeff. a for over-generation + + = 2 i C P b P c i gi i gi i 2 cpdf of wind power output Reserve cost coeff. = given the forecast level C d w for under-generation wi i i ∫ w − = − = ri [ ] ( )] ( ) ( | ) E C [ W w k w w f w w dw E k , pi pi i ac i p i i W fci w i ∫ w − = − = i [ ] ( )] ( ) ( | ) E C [ w W k w w f w w dw E k , ri ri i i ac ri i W fci 0 10 10
Perfect Scheduling – – Perfect Scheduling Single Objective Single Objective Objective: Minimize the operating cost of the power system � subject to the generation-load balance constraint. � Scheduled and actual wind power output ate identical w i = W i,ac � It is the theoretical lower bound 11 11
Perfect Scheduling – – Perfect Scheduling Single Objective Single Objective Minimize OC p ( P gi ,w i ) Subject to w i = W i,ac ≤ ≤ min max P P P gi gi gi M N ∑ ∑ = − P L w gi i = = 1 1 i i 12 12
Statistical characterization of WP Statistical characterization of WP output given the forecast - - output given the forecast ( | ) Find Find f w w W fci 1. Normalize 10 minute WP output, wi , for a year 2. Generate hour-ahead persistence forecast, wf ci 3. Re-arrange data based on forecast in an ascending order 4. Divide data according to forecast level into 25 bins 5. For each bin, find the pdf fits of the WP output, wi . Consider Weibull, Extreme Value, and Beta 6. Among the three pdf functions, pick the one that 13 13 best fits the bin data
Statistical characterization of WP Statistical characterization of WP output given the forecast output given the forecast 1 Actual wind power output 0.9 Wind power forecast 1. Normalize 10 minute WP Wind power output and forecast (pu) 0.8 output, wi , for a year 0.7 1 W i,ac 0.6 0.9 w fc 2. Generate hour-ahead 0.5 W in d p o w er o u tp u t an d fo recast (p u ) 0.8 persistence forecast, wf ci 0.4 0.3 0.7 0.2 0.6 3. Re-arrange data based on 0.1 forecast in an ascending 0.5 0 order 0 50 100 150 200 250 300 350 0.4 Time (Days) 0.3 1 T k T 4. Divide data according to Actual wind power output 0.2 0.9 Wind power forecast Wind power output and forecast (pu) forecast level into 25 bins t-T t t+k t+k+T 0.1 0.8 0.7 0 0 0.5 1 1.5 2 2.5 3 3.5 4 5. For each bin, find the pdf Time (hours) 0.6 fits of the WP output, wi . 0.5 Consider Weibull, Extreme 0.4 Value, and Beta 0.3 0.2 6. Among the three pdf 0.1 functions, pick the one that 0 best fits the bin data 0 1 2 3 4 5 6 7 14 14 Time (Days)
Statistical characterization of WP Statistical characterization of WP output given the forecast output given the forecast FC Actual FC Actual 1. Normalize 10 minute WP output, wi , for a year 0.52 0.34 0.00 0.41 0.44 0.52 . . 2. Generate hour-ahead persistence forecast, wf ci 0.44 0.30 . . 3. Re-arrange data based on 0.44 0.27 0.44 0.52 forecast in an ascending order 0.61 0.56 . . 0.61 0.66 . . 4. Divide data according to forecast level into 25 bins 0.61 0.73 0.52 0.34 5. For each bin, find the pdf . . . . fits of the WP output, wi . Consider Weibull, Extreme . . . . Value, and Beta . . 0.61 0.66 6. Among the three pdf . . . . functions, pick the one that best fits the bin data 15 15 . . 1.00 0.59
Statistical characterization of WP Statistical characterization of WP output given the forecast output given the forecast 1 Actual wind power output 1. Normalize 10 minute WP ) 0.9 Wind power forecast u st (p output, wi , for a year 0.8 ca re 0.7 fo d t an 0.6 2. Generate hour-ahead u tp 0.5 u persistence forecast, wf ci er o 0.4 w o 0.3 p d in 0.2 W 3. Re-arrange data based on 0.1 forecast in an ascending 0 order 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Number of data points x 10 4 4. Divide data according to forecast level into 25 bins 5. For each bin, find the pdf fits of the WP output, wi . Consider Weibull, Extreme Value, and Beta 6. Among the three pdf functions, pick the one that best fits the bin data 16 16
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