Smart Grid for Sustainable Energy. 18. Synchronizing the Grid

Transcription

1 Smart Grid for Sustainable Energy EEL 4930/5934 Fall Synchronizing the Grid Sean Meyn, November 4, 2014

2 Synchronizing the Grid Outline 1 Recap 2 Primary Control Revisited once more 1 / 8

3 Recap

4 Recap Economic Dispatch Economic Dispatch problem min (V,S G S) N F i (P Gi ) i=1 subject to S G1 + + S GN = S Demand, S Gi = P Gi + jq Gi V min i V i V max i Real(V i I i,k) P T V i I i = P Gi P Di + j(q Gi Q Di ) P Gi P Di = V i Q Gi Q Di = V i N Y i,l V l cos(δ i δ l φ i,l ) l=1 N Y i,l V l sin(δ i δ l φ i,l ) l=1 Yecchhh!?? 2 / 8

5 Recap Economic Dispatch Economic Dispatch problem min (V,S G S) N F i (P Gi ) i=1 subject to S G1 + + S GN = S Demand, S Gi = P Gi + jq Gi V min i V i V max i Real(V i I i,k) P T V i I i = P Gi P Di + j(q Gi Q Di ) Idea: Introduce matrix variable W = VV (N N matrix, W i,k = V i V k ) V min i V i Vi max (Vi min ) 2 W i,i (V max V i Ii,k = V i (Vi Vk )Yi,k = (W i,i W i,k )Yi,k V i Ii = V i Yi,kV k k = k i ) 2 Y i,kw i,k 2 / 8

6 Recap Example: Multiple Solutions Nobody has a globally convergent algorithm For the two bus power system shown below, determine the voltage magnitude and angle at bus two. 3 / 8

7 Recap Example: Multiple Solutions Nobody has a globally convergent algorithm For the two bus power system shown below, determine the voltage magnitude and angle at bus two. Unknowns: Voltage and angle at second bus. 3 / 8

8 Recap Example: Multiple Solutions Nobody has a globally convergent algorithm For the two bus power system shown below, determine the voltage magnitude and angle at bus two. Unknowns: Voltage and angle at second bus. It turns out there are two solutions - one low-voltage and one high! 3 / 8

9 Recap Example: Multiple Solutions Nobody has a globally convergent algorithm For the two bus power system shown below, determine the voltage magnitude and angle at bus two. Unknowns: Voltage and angle at second bus. It turns out there are two solutions - one low-voltage and one high! V 2 =.855 pu, δ 2 = degrees, V 2 = pu, δ 2 = degrees. See ppt lecture at UT Austin 3 / 8

10 Recap Example: Multiple Solutions Newton-Raphson outcome 1 HV * 0.50 * LV Red region: NR converges to the high voltage solution, HV Green region: NR converges to the low voltage solution, LV 4/8

11 System frequency (Hz) (b) (a) (c) (d) (e) (a) No auxiliary control (b) Droop control on WF level (c) Droop control on WT level (d) Combined control, (e) Inertia control Time (secs) Operation and Control of Wind Farms in Non-Interconnected Power Systems Droop Primary Control

12 Primary Control Revisited once more Governors in the Grid We have seen, Power systems are interconnected across large distances. Most of North America east of the Rockies is one system, most of North America west of the Rockies is another. 5 / 8

13 Primary Control Revisited once more Governors in the Grid We have seen, Power systems are interconnected across large distances. Most of North America east of the Rockies is one system, most of North America west of the Rockies is another. Most of Texas is one interconnected system, and Quebec is another! 5 / 8

14 Primary Control Revisited once more Governors in the Grid We have seen, Power systems are interconnected across large distances. Most of North America east of the Rockies is one system, most of North America west of the Rockies is another. Most of Texas is one interconnected system, and Quebec is another! Each generator works together to stabilize the grid a seemingly impossible distributed control problem. 5 / 8

15 Primary Control Revisited once more Governors in the Grid We have seen, Power systems are interconnected across large distances. Most of North America east of the Rockies is one system, most of North America west of the Rockies is another. Most of Texas is one interconnected system, and Quebec is another! Each generator works together to stabilize the grid a seemingly impossible distributed control problem. So far, only steady state analysis in lecture. 5 / 8

16 Primary Control Revisited once more Governors in the Grid Generated power Generator A Generator B Frequency Generator A will make much larger power adjustments in response to a change in system frequency (ω 1 or ω 2 ). The droop characteristic (the slope) determines the share of primary control delivered by the generator 6 / 8

17 Primary Control Revisited once more Governors in the Grid Generated power Generator A Generator B Frequency Generator A will make much larger power adjustments in response to a change in system frequency (ω 1 or ω 2 ). The droop characteristic (the slope) determines the share of primary control delivered by the generator NERC demands that all droop curves be set to 5%, and never more than 6%. 6 / 8

18 Primary Control Revisited once more Governors in the Grid Need for Secondary Control A disturbance in Agra spreads instantly to Mumbai and Calcutta: en.wikipedia.org/wiki/2012_india_blackouts Relay problem near the Taj Mahal Frequency A Kanpur, Uttar Pradesh B IIT Mumbai, Maharashtra C Kharagpur, West Bengal D New Delhi, Delhi Delhi-Kolkata Hwy and AH 4,535 km, 66 hours secs Two features to notice: Steady-state frequency is below nominal Synchronization 7 / 8

19 Primary Control Revisited once more 36 º 32 º 28 º 24 º 23.5 º 20 º 16 º 12 º 8 º 68 º 72 º 76 º 80 º 84 º 88 º 92 º 96 º Gandhinagar Diu Daman & Diu Dadra & Nagar Haveli Mumbai Panaji Silvasaa Pondicherry (Mahe) Kavarati Jaipur Bangalore Thiruvananthapuram Srinagar Chandigarh Bhopal Shimla Dehradun New Delhi Hyderabad Lucknow Raipur Chennai Pondicherry (Puducherry) Pondicherry (Karaikal) Patna Ranchi Pondicherry (Yanam) Gangtok Bhubaneshwar National Capital State Capital Union Territory Capital Mi Km Kolkata Guwahati Shillong Agartala Aizwal Itanagar Kohima Imphal Port Blair Governors in the Grid Need for Secondary Control Synchronization sometimes fails: en.wikipedia.org/wiki/2012_india_blackouts 50.2 Frequency July 30, 2012 Blackout 50 Mumbai Kanpur Gujarat Lakshadweep Islands Rajasthan States and Union Territories Jammu & Kashmir Map of India Haryana Goa Karnataka Himachal Pradesh Punjab Tamil Nadu Uttaranchal Uttar Pradesh Madhya Pradesh Maharashtra Kerala Andhra Pradesh Chhattisgarh Orissa Bihar Sikkim JharkhandWest Bengal Meghalaya Tripura Arunachal Pradesh Assam Andaman & Nicobar Islands Nagaland Manipur Mizoram 8 / 8

20 Primary Control Revisited once more 36 º 32 º 28 º 24 º 23.5 º 20 º 16 º 12 º 8 º 68 º 72 º 76 º 80 º 84 º 88 º 92 º 96 º Gandhinagar Diu Daman & Diu Dadra & Nagar Haveli Mumbai Panaji Silvasaa Pondicherry (Mahe) Kavarati Jaipur Bangalore Thiruvananthapuram Srinagar Chandigarh Bhopal Shimla Dehradun New Delhi Hyderabad Lucknow Raipur Chennai Pondicherry (Puducherry) Pondicherry (Karaikal) Patna Ranchi Pondicherry (Yanam) Gangtok Bhubaneshwar National Capital State Capital Union Territory Capital Mi Km Kolkata Guwahati Shillong Agartala Aizwal Itanagar Kohima Imphal Port Blair Governors in the Grid Need for Secondary Control Synchronization sometimes fails: en.wikipedia.org/wiki/2012_india_blackouts 50.2 Frequency July 30, 2012 Blackout 50 Mumbai Kanpur Gujarat Lakshadweep Islands Rajasthan States and Union Territories Jammu & Kashmir Map of India Haryana Goa Karnataka Himachal Pradesh Punjab Tamil Nadu Uttaranchal Uttar Pradesh Madhya Pradesh Maharashtra Kerala Andhra Pradesh Chhattisgarh Orissa Bihar Sikkim JharkhandWest Bengal Meghalaya Tripura Arunachal Pradesh Assam Andaman & Nicobar Islands Nagaland Manipur Mizoram Need for responsive regulation. 8 / 8

21 Primary Control Revisited once more 36 º 32 º 28 º 24 º 23.5 º 20 º 16 º 12 º 8 º 68 º 72 º 76 º 80 º 84 º 88 º 92 º 96 º Gandhinagar Diu Daman & Diu Dadra & Nagar Haveli Mumbai Panaji Silvasaa Pondicherry (Mahe) Kavarati Jaipur Bangalore Thiruvananthapuram Srinagar Chandigarh Bhopal Shimla Dehradun New Delhi Hyderabad Lucknow Raipur Chennai Pondicherry (Puducherry) Pondicherry (Karaikal) Patna Ranchi Pondicherry (Yanam) Gangtok Bhubaneshwar National Capital State Capital Union Territory Capital Mi Km Kolkata Guwahati Shillong Agartala Aizwal Itanagar Kohima Imphal Port Blair Governors in the Grid Need for Secondary Control Synchronization sometimes fails: en.wikipedia.org/wiki/2012_india_blackouts 50.2 Frequency July 30, 2012 Blackout 50 Mumbai Kanpur Gujarat Lakshadweep Islands Rajasthan States and Union Territories Jammu & Kashmir Map of India Haryana Goa Karnataka Himachal Pradesh Punjab Tamil Nadu Uttaranchal Uttar Pradesh Madhya Pradesh Maharashtra Kerala Andhra Pradesh Chhattisgarh Orissa Bihar Sikkim JharkhandWest Bengal Meghalaya Tripura Arunachal Pradesh Assam Andaman & Nicobar Islands Nagaland Manipur Mizoram Need for responsive regulation. How is this possible, given the state of art of distributed control? 8 / 8