1. 1 © Alexis Kwasinski, 2012 Introduction Field Excitation Q Synchronous generators Input: Mechanical power applied to the rotor shaft Field excitation to create a magnetic field constant in magnitude and that rotates with the rotor. Output: P and Q (electric signal with a given frequency for v and i)

2. 2 © Alexis Kwasinski, 2012 Introduction Synchronous generators Open circuit voltage: Magneto-motive force (mmf)

3. 3 © Alexis Kwasinski, 2012 Effect of varying field excitation in synchronous generators: When loaded there are two sources of excitation: ac current in armature (stator) dc current in field winding (rotor) If the field current is enough to generate the necessary mmf, then no magnetizing current is necessary in the armature and the generator operates at unity power factor (Q = 0). If the field current is not enough to generate the necessary mmf, then the armature needs to provide the additional mmf through a magnetizing current. Hence, it operates at an inductive power factor and it is said to be underexcited. If the field current is more than enough to generate the necessary mmf, then the armature needs to provide an opposing mmf through a magnetizing current of opposing phase. Hence, it operates at a capacitive power factor and it is said to be overexcited. Synchronous generators control

4. 4 © Alexis Kwasinski, 2012 Synchronous generators control Field Excitation Q Relationship between reactive power and field excitation The frequency depends on the rotor’s speed. So frequency is controlled through the mechanical power. Pmec is increased to increase f Pmec is decreased to decrease f http://baldevchaudhary.blogspot.co m/2009/11/what-are-v-and- inverted-v-curves.html

5. 5 © Alexis Kwasinski, 2012 Voltage and frequency control The simplified equivalent circuit for a generator and its output equation is: LOAD Assumption: during short circuits or load changes E is constant V is the output (terminal) voltage Electric power provided to the load

6. 6 © Alexis Kwasinski, 2012 Voltage and frequency control It can be found that Ideally, the electrical power equals the mechanical input power. The generator’s frequency depends dynamically on δ which, in turn, depends on the electrical power (=input mechanical power). So by changing the mechanical power, we can dynamically change the frequency. Likewise, the reactive power controls the output voltage of the generator. When the reactive power increases the output voltage decreases. Generator’s angular frequency (Micro) Grid’s angular frequency

7. 7 © Alexis Kwasinski, 2012 Voltage and frequency control Droop control It is an autonomous approach for controlling frequency and voltage amplitude of the generator and, eventually, the microgrid. It takes advantage that real power controls frequency and that reactive power controls voltage

8. 8 © Alexis Kwasinski, 2012 Voltage and frequency control Droop control Then a simple (e.g. PI) controller can be implemented. It considers a reference voltage and a reference frequency: If the output voltage is different, the field excitation is changed (and, thus, changes Q and then V). If the frequency is different, the prime mover torque is changed (and thus, changes P and then f).

9. 9 © Alexis Kwasinski, 2012 Voltage and frequency control Operation of a generator connected to a large grid A large grid is seen as an infinite power bus. That is, it is like a generator in which changes in real power do not cause changes in frequency changes in reactive power do not originate changes in voltage its droop control curves are horizontal lines

10. 10 © Alexis Kwasinski, 2012 Voltage and frequency control Operator of a generator connected to a large grid When connected to the grid, the voltage amplitude and frequency is set by the grid. In order to synchronize the oncoming generator, its frequency needs to be slightly higher than that of the grid, but all other variables need to be the same.

11. 11 © Alexis Kwasinski, 2012 Voltage and frequency control Operator of a generator connected to a large grid After the generator is paralleled to the grid then its output frequency and voltage will remain fixed and equal to the grid’s frequency and voltage, respectively. Output power is controlled by attempting a change in frequency by controlling the prime mover’s torque. By “commanding” a decrease in frequency, the output power will increase. A similar approach is followed with reactive power control, by controlling field excitation in an attempt to change output voltage. Operating frequency Higher commanded frequencies No load droop line Higher power output

12. 12 © Alexis Kwasinski, 2012 A brief summary In ac systems, large machine inertia helps to maintain stability. Since frequency needs to be regulated at a precise value, imbalances between electric and mechanical power may make the frequency to change. In order to avoid this issue, mechanical power applied to the generator rotor must follow load changes. If the mechanical power cannot follow the load alone (e.g. due to machine’s inertia), energy storage must be used to compensate for the difference. This is a situation often found in microgrids. Reactive power is used to regulate voltage. Droop control is an effective autonomous controller.

13. 13 © Alexis Kwasinski, 2012 DC microgrids (droop control) NOTE: Based on Guerrero et al “Hierarchical Control of Droop-Controlled AC and DC Microgrids—A General Approach Toward Standardization” Consider a microturbine in a microgrid controlled by droop control. Primary control: Secondary control (voltage deviation compensation) Depends on microgrid bus voltage

14. 14 © Alexis Kwasinski, 2012 DC microgrids (droop control) NOTE: Based on Guerrero et al “Hierarchical Control of Droop-Controlled AC and DC Microgrids—A General Approach Toward Standardization” Tertiary control (associated with a grid tie): Could be the input for a grid interface converter or the input for the distributed generation sources interface. The latter applies when there is a direct connection to a stiff grid because the stiff grid fixes the microgrid voltage. When there is a grid outage, the tertiary control is replaced by the secondary control. When the grid is present the secondary control is replaced by the tertiary control. Depends on current to or from the grid

15. 15 © Alexis Kwasinski, 2012 Tertiary control Secondary control

16. 16 © Alexis Kwasinski, 2012 ILIL LOAD IgIg GRID GIC IμTIμT IμTIμT Set by the utility company Droop slope (virtual dc output resistance) DC microgrids (droop control) Voltage range “to allow for power sharing and voltage regulation using droop control”

17. 17 © Alexis Kwasinski, 2012 DC microgrids (droop control) ILIL LOAD I uT IμTIμT ILIL LOAD I uT,1 I μT,2 0 I μT,1 +I μT,2 = I L I uT,1 I μT,2 DC bus voltage Voltage range “to allow for power sharing and voltage regulation using droop control”

18. 18 © Alexis Kwasinski, 2012 DC microgrids (droop control) ILIL LOAD I uT IμTIμT ILIL LOAD I uT,1 I μT,2 0 I μT,1 +I μT,2 = I L I uT,1 I μT,2 When the load increases, current is shared between the two microturbines with the one with the highest capacity providing more current to the load Voltage range “to allow for power sharing and voltage regulation using droop control”

19. 19 © Alexis Kwasinski, 2012 DC microgrids (droop control) ILIL LOAD I uT IμTIμT ILIL LOAD I uT,1 I μT,2 0 I μT,1 +I μT,2 = I L I uT,1 I μT,2 As the load increases, the voltage drops so current output from the microturbines can increase. Still, the microturbine with the highest capacity providing more current to the load Voltage range “to allow for power sharing and voltage regulation using droop control”

20. 20 © Alexis Kwasinski, 2012 IgIg GRID GIC DC microgrids (droop control) ILIL LOAD IgIg GRID GIC I uT IμTIμT IgIg GRID GIC ILIL LOAD IgIg GRID GIC I uT,1 I μT,2 0 IgIg I g +I μT,1 +I μT,2 = I L I uT,1 I μT,2 When the load increases even further the grid needs to provide the extra current in order to prevent voltage collapse Voltage range “to allow for power sharing and voltage regulation using droop control”

21. 21 © Alexis Kwasinski, 2012 IgIg GRID GIC DC microgrids (droop control) ILIL LOAD IgIg GRID GIC I uT IμTIμT IgIg GRID GIC ILIL LOAD IgIg GRID GIC I uT,1 I μT,2 0 IgIg I g +I μT,1 +I μT,2 = I L I uT,1 I μT,2 Current from the grid can be used to reduce the current from the microturbines and increase the dc bus voltage (see the voltage in the case with the same load in slide #19) Voltage range “to allow for power sharing and voltage regulation using droop control”

22. 22 © Alexis Kwasinski, 2012 IgIg GRID GIC DC microgrids (droop control) ILIL LOAD IgIg GRID GIC I uT IμTIμT IgIg GRID GIC ILIL LOAD IgIg GRID GIC I uT,1 I μT,2 0 IgIg I g +I μT,1 +I μT,2 = I L I uT,1 I μT,2 When the load is light, extra power being generated by the microturbines can be injected back to the grid (see slide # 18) Voltage range “to allow for power sharing and voltage regulation using droop control”

23. 23 © Alexis Kwasinski, 2012 ILIL LOAD IgIg GRID GIC I uT Primary control is combined with a secondary control to compensate voltage deviations Now, v ref,NL can be adjusted with a δv ref ILIL LOAD IgIg GRID GIC I uT Primary control is combined with a secondary control to compensate voltage deviations DC microgrids (droop control)

24. 24 © Alexis Kwasinski, 2012 DC microgrids (droop control) 0 I μT,1 +I μT,2 = I L I uT,1 I μT,2 ILIL LOAD I uT Primary control is combined with a secondary control to compensate voltage deviations ILIL LOAD I uT Primary control is combined with a secondary control to compensate voltage deviations Nominal Adjusted with δv ref

25. 25 © Alexis Kwasinski, 2012 DC microgrids (droop control) 0 I μT,1 +I μT,2 = I L I uT,1 I μT,2 ILIL LOAD I uT Primary control is combined with a secondary control to compensate voltage deviations ILIL LOAD I uT Primary control is combined with a secondary control to compensate voltage deviations Notice that the currents are the same than in the case with no secondary control (slide #18) but now the voltage is kept at 380 V

26. 26 © Alexis Kwasinski, 2012 DC microgrids (droop control) 0 I μT,1 +I μT,2 = I L I uT,1 I μT,2 Notice same δv ref for both microturnines ILIL LOAD I uT Primary control is combined with a secondary control to compensate voltage deviations ILIL LOAD I uT Primary control is combined with a secondary control to compensate voltage deviations

27. 27 © Alexis Kwasinski, 2012 DC microgrids (droop control) 0 I uT,1 I μT,2 Notice lower δv ref than previous slide ILIL LOAD IgIg GRID GIC I uT Primary control is combined with a secondary control to compensate voltage deviations ILIL LOAD IgIg GRID GIC I uT Primary control is combined with a secondary control to compensate voltage deviations IgIg I g +I μT,1 +I μT,2 = I L Now, δv ref is changed in order to control the current from or to the grid

28. 28 © Alexis Kwasinski, 2012 DC microgrids (droop control) 0 IgIg I g +I μT,1 +I μT,2 = I L I uT,1 I μT,2 ILIL LOAD IgIg GRID GIC I uT Primary control is combined with a secondary control to compensate voltage deviations ILIL LOAD IgIg GRID GIC I uT Primary control is combined with a secondary control to compensate voltage deviations Secondary control can be used to optimize efficiency but when optimizing efficiency the controller may not do a proportional load sharing because the load sharing condition of a given source may not be its optimal operating point

29. 29 © Alexis Kwasinski, 2012 0 IgIg I g +I μT,1 +I μT,2 = I L I uT,1 I μT,2 ILIL LOAD IgIg GRID GIC I uT Primary control is combined with a secondary control to compensate voltage deviations ILIL LOAD IgIg GRID GIC I uT Primary control is combined with a secondary control to compensate voltage deviations DC microgrids (droop control)

30. 30 © Alexis Kwasinski, 2012 IwIw IsIs IbIb ILIL LOAD IgIg GRID GIC DC microgrids (droop control) NOTE: Slide prepared by Prof. Dushan Boroyevich from VT Paper: Boroyevich et al “Future Electronic Power Distribution Systems – A contemplative view –” Voltage range “to allow for power sharing and voltage regulation using the droop control” Set by the utility company Droop slope (virtual dc output resistance)

31. 31 © Alexis Kwasinski, 2012 DC microgrids (droop control) In the presence of constant-power loads, regulators in source converters cannot use PI controllers. From a static perspective, regulators designed for constant-power loads will make the source converter output characteristic to look like MPP trackers. Battery interfaces have different characteristic depending on the state of charge of the batteries. For example, at the float voltage, the battery may take no current (if the state of charge is 100 %) or may take some current if the state of charge is less than 100 %. Droop controllers without secondary controls cannot be used if batteries are directly connected to the microgrid main bus.

32. 32 © Alexis Kwasinski, 2012 IwIw IsIs 0 I w +I s = I L 0= I L IwIw IsIs IgIg I w +I s +I g = I L IgIg IwIw IsIs I w +I s +I g +I b = I L IwIw IsIs IgIg IbIb ILIL IsIs IwIw IbIb LOAD IgIg GRID GIC I w +I s +I g = I L IwIw IsIs IbIb I w +I s +I b = I L NOTE: Slide prepared by Prof. Dushan Boroyevich from VT Paper: Boroyevich et al “Future Electronic Power Distribution Systems – A contemplative view –” DC microgrids (droop control)

33. 33 © Alexis Kwasinski, 2012 ILIL LOAD IgIg DC GRID I uT With a stiff grid there is no limit to I g I g is regulated by adjusting δv ref ILIL LOAD I uT DC microgrids (droop control) Voltage is kept fixed by the stiff grid so no voltage regulation is necessary (but it is not possible to have batteries directly connected to the main bus)

34. 34 © Alexis Kwasinski, 2012

35. 35 © Alexis Kwasinski, 2012 DC microgrids (droop control) IgIg I uT,1 I μT,2 ILIL LOAD I uT ILIL LOAD IgIg DC GRID I uT 0 I g +I μT,1 +I μT,2 = I L Voltage is kept fixed by the stiff grid so no voltage regulation is necessary (but it is not possible to have batteries directly connected to the main bus)

36. 36 © Alexis Kwasinski, 2012 0 IgIg I g +I μT,1 +I μT,2 = I L I uT,1 I μT,2 ILIL LOAD IgIg I uT ILIL LOAD IgIg DC GRID I uT DC microgrids (droop control) Voltage is kept fixed by the stiff grid so no voltage regulation is necessary (but it is not possible to have batteries directly connected to the main bus)

37. 37 © Alexis Kwasinski, 2012 AC microgrids revisited (droop control) Sources with a dc output or an ac output with a frequency different from that of the microgrid main bus need to use an inverter to be integrated into an ac microgrid. When implementing droop control, the P-ω and Q-E droop regulators are used to emulate the inertia of an ac machine. Issues when implementing conventional droop control in ac systems with inverters: –Droop current-sharing methods are affected by harmonic content created by non-linear loads. These issues can be solved by distorting the voltage signal intentionally which leads to further issues. –Frequency is dependent on load levels in the same way that voltage levels depend on load levels. Also, frequency goals for two inverters with different capacity may be different. Frequency deviations dependant on load levels may lead to loss of synchronization when attempting to connect the microgrid directly to a main grid. Hence, it is only applicable to islanded operation and makes transition into grid connected operation complicated. –In islanded mode there is both frequency and voltage deviations leading to tradeoffs inherent to droop control in islanded mode. Secondary controls have been proposed in order to solve these issues without the need for communication links.

38. 38 © Alexis Kwasinski, 2012 NOTE: Figure from Guerrero et al “Hierarchical Control of Droop-Controlled AC and DC Microgrids—A General Approach Toward Standardization” Now tertiary control depends on real and reactive power flow from or to the grid Now secondary control depends on microgrid bus voltage and frequency - G P (s) and G Q (s) represent PI or P controllers. - ω*, E*, P* and Q* are reference signals, so when P=P*, ω=ω* and when Q=Q*, E=E*