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Introduction • 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) Field Excitation 1 Q © Alexis Kwasinski, 2012 Introduction • Synchronous generators • Open circuit voltage: e NS d dt ERMS 4.44 K d K p fN S E N S 1 NR IR l A E Magneto-motive force (mmf) IR 2 © Alexis Kwasinski, 2012 Synchronous generators control • 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. 3 © Alexis Kwasinski, 2012 Synchronous generators control • Relationship between reactive power and field excitation http://baldevchaudhary.blogspot.co m/2009/11/what-are-v-andinverted-v-curves.html • 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 Field Excitation 4 © Alexis Kwasinski, 2012 Q Voltage and frequency control • The simplified equivalent circuit for a generator and its output equation is: Q, pE LOAD • Assumption: during short circuits or load changes E is constant • V is the output (terminal) voltage pe E.V E.V sin X X Electric power provided to the load XQ E V E 5 © Alexis Kwasinski, 2012 Voltage and frequency control • It can be found that d (t ) syn dt • Generator’s angular frequency • (Micro) Grid’s angular frequency • 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. 6 © 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 f f0 kP ( P P0 ) V V0 kQ (Q Q0 ) V f f0 V0 P0 7 P © Alexis Kwasinski, 2012 Q0 Q 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). V V0 kQ (Q Q0 ) f f0 kP ( P P0 ) V f f0 V0 P0 8 P © Alexis Kwasinski, 2012 Q0 Q 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 V f P 9 © Alexis Kwasinski, 2012 Q 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. V f f gen VG fG P 10 © Alexis Kwasinski, 2012 Q 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. Higher commanded frequencies f Higher power output Operating frequency No load droop line P1 11 P2 © Alexis Kwasinski, 2012 P 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. 12 © Alexis Kwasinski, 2012 DC microgrids (droop control) • Consider a microturbine in a microgrid controlled by droop control. • Primary control: vref vref , NL I T RD vref , NL vn VR / 2 VR I T ,max RD • Secondary control (voltage deviation compensation) vref K p (vMG ,ref vMG ) K i (vMG ,ref vMG )dt Depends on microgrid bus voltage vref ( vref vref , NL ) I T RD V [V] Source Interface NOTE: Based on Guerrero et al “Hierarchical Control of Droop-Controlled AC and DC Microgrids—A General Approach Toward Standardization” vref,NL 400 390 380 370 360 δvref Converter rating IμT IμT,max 0 13 vn © Alexis Kwasinski, 2012 ΔVR DC microgrids (droop control) • Tertiary control (associated with a grid tie): vref K p ( I g ,ref I g ) Ki ( I g ,ref I g )dt Depends on current to or from the grid vref ( vref vref , NL ) I T RD • 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. Grid interface converter V [V] -Ig,max 14 vref,NL Converter rating δvref Converter rating 400 390 380 370 360 NOTE: Based on Guerrero et al “Hierarchical Control of Droop-Controlled AC and DC Microgrids—A General Approach Toward Standardization” 0 © Alexis Kwasinski, 2012 Ig,max Ig Secondary control Tertiary control 15 © Alexis Kwasinski, 2012 DC microgrids (droop control) GRID MICROTURBINE MICROTURBINE GIC IμT DC bus (360 to 400 V) V [V] Droop slope (virtual dc output resistance) 0 16 Microturbine V [V] 0 © Alexis Kwasinski, 2012 LOAD Microturbine V [V] Current Limit “Power” demand Converter rating 400 390 380 370 360 Grid interface converter IL Voltage range “to allow for power sharing and voltage regulation using droop control” Converter rating Set by the utility company IμT Current Limit Ig I μT 0 I μT DC microgrids (droop control) MICROTURBINE MICROTURBINE IuT,1 uT DC bus (360 to 400 V) Voltage range “to allow for power sharing and voltage regulation using droop control” VDC bus [V] 400 390 380 370 360 DC bus voltage IuT,1 IμT,2 0 17 IμT,2 μT © Alexis Kwasinski, 2012 IL LOAD IμT,1+IμT,2 = IL 0 DC microgrids (droop control) MICROTURBINE MICROTURBINE IuT,1 uT DC bus (360 to 400 V) Voltage range “to allow for power sharing and voltage regulation using droop control” VDC bus [V] 400 390 380 370 360 IL LOAD IμT,1+IμT,2 = IL 0 When the load increases, current is shared between the two microturbines with the one with the highest capacity providing more current to the load IμT,2 0 IuT,1 18 IμT,2 μT © Alexis Kwasinski, 2012 DC microgrids (droop control) MICROTURBINE MICROTURBINE IuT,1 uT DC bus (360 to 400 V) IμT,2 μT Voltage range “to allow for power sharing and voltage regulation using droop control” VDC bus [V] LOAD IμT,1+IμT,2 = IL 0 400 390 380 370 360 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 0 19 IL IuT,1 IμT,2 © Alexis Kwasinski, 2012 DC microgrids (droop control) GRID MICROTURBINE MICROTURBINE GIC IuT,1 uT Ig DC bus (360 to 400 V) IμT,2 μT Voltage range “to allow for power sharing and voltage regulation using droop control” VDC bus [V] LOAD Ig+IμT,1+IμT,2 = IL 0 400 390 380 370 360 When the load increases even further the grid needs to provide the extra current in order to prevent voltage collapse 0 20 IL IuT,1 IμT,2 © Alexis Kwasinski, 2012 Ig DC microgrids (droop control) GRID MICROTURBINE MICROTURBINE GIC IuT,1 uT Ig DC bus (360 to 400 V) IμT,2 μT Voltage range “to allow for power sharing and voltage regulation using droop control” VDC bus [V] LOAD Ig+IμT,1+IμT,2 = IL 0 400 390 380 370 360 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) Ig 0 21 IL IuT,1 IμT,2 © Alexis Kwasinski, 2012 DC microgrids (droop control) GRID MICROTURBINE MICROTURBINE GIC IuT,1 uT Ig IμT,2 μT Voltage range “to allow for power sharing and voltage regulation using droop control” DC bus (360 to 400 V) VDC bus [V] LOAD Ig+IμT,1+IμT,2 = IL 0 400 390 380 370 360 When the load is light, extra power being generated by the microturbines can be injected back to the grid (see slide # 18) IuT,1 Ig 22 IL 0 IμT,2 © Alexis Kwasinski, 2012 DC microgrids (droop control) GRID MICROTURBINE MICROTURBINE GIC DC bus (380 V) Microturbine V [V] V [V] IL LOAD Microturbine V [V] Current Limit Converter rating 0 23 Primary control is combined with a secondary control to compensate voltage deviations Grid interface converter Converter rating Now, vref,NL can be adjusted with a δvref 400 390 380 370 360 IuT Current Limit IuT Ig 0 I μT 0 I μT Now, vref,NL can be adjusted with a δvref © Alexis Kwasinski, 2012 DC microgrids (droop control) MICROTURBINE MICROTURBINE IuT DC bus (380 V) IuT Primary control is combined with a secondary control to compensate voltage deviations VDC bus [V] 400 390 380 370 360 LOAD IμT,1+IμT,2 = IL Nominal Adjusted with δvref IuT,1 IμT,2 0 24 IL © Alexis Kwasinski, 2012 0 DC microgrids (droop control) MICROTURBINE MICROTURBINE IuT DC bus (380 V) IuT Primary control is combined with a secondary control to compensate voltage deviations VDC bus [V] LOAD IμT,1+IμT,2 = IL 0 400 390 380 370 360 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 IμT,2 0 IuT,1 25 IL © Alexis Kwasinski, 2012 DC microgrids (droop control) MICROTURBINE MICROTURBINE IuT DC bus (380 V) Primary control is combined with a secondary control to compensate voltage deviations VDC bus [V] 400 390 380 370 360 0 26 IuT Notice same δvref for both microturnines IuT,1 IμT,2 © Alexis Kwasinski, 2012 IL LOAD IμT,1+IμT,2 = IL 0 DC microgrids (droop control) GRID MICROTURBINE MICROTURBINE GIC IuT Ig DC bus (380 V) IuT Primary control is combined with a secondary control to compensate voltage deviations VDC bus [V] 400 390 380 370 360 Notice lower δvref than previous slide Now, δvref is changed in order to control the current from or to the grid 0 27 IuT,1 IμT,2 © Alexis Kwasinski, 2012 Ig IL LOAD Ig+IμT,1+IμT,2 = IL 0 DC microgrids (droop control) GRID MICROTURBINE MICROTURBINE GIC IuT Ig DC bus (380 V) IuT Primary control is combined with a secondary control to compensate voltage deviations 0 400 390 380 370 360 28 LOAD Ig+IμT,1+IμT,2 = IL VDC bus [V] 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 IL Ig 0 IuT,1 IμT,2 © Alexis Kwasinski, 2012 DC microgrids (droop control) GRID MICROTURBINE MICROTURBINE GIC IuT Ig DC bus (380 V) Primary control is combined with a secondary control to compensate voltage deviations IL LOAD Ig+IμT,1+IμT,2 = IL VDC bus [V] 0 400 390 380 370 360 Ig 29 IuT 0 IuT,1IμT,2 © Alexis Kwasinski, 2012 DC microgrids (droop control) GRID WIND TURBINE SOLAR ARRAY ENERGY STORAGE Paper: Boroyevich et al “Future Electronic Power Distribution Systems – A contemplative view –” GIC Ig Is DC bus (360 – 400 V) V [V] IL Voltage range “to allow for power sharing and voltage regulation using the droop control” Droop slope (virtual dc output resistance) Solar converter Wind converter V [V] LOAD Battery storage converter V [V] V [V] Ig 0 © Alexis Kwasinski, 2012 Is 0 Iw Ibdsoc 0 Operating range Converter rating Actual MPPT Converter rating Ibcsoc 0 30 Ib Actual MPPT “Power” demand Converter rating 400 390 380 370 360 Grid interface converter Iw Converter rating Set by the utility company NOTE: Slide prepared by Prof. Dushan Boroyevich from VT Ib 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 Microturbine with Battery storage the microgrid main bus. Constant Power Load converter V [V] V [V] 0 31 IμT © Alexis Kwasinski, 2012 Ibdsoc 0 Operating range Constant Power Output Converter rating Ibcsoc Ib DC microgrids (droop control) GRID SOLAR ARRAY WIND TURBINE ENERGY STORAGE Paper: Boroyevich et al “Future Electronic Power Distribution Systems – A contemplative view –” GIC Ig DC bus Is Iw Ib IL 360 – 400 V VDC bus [V] Iw+IIws+IIgsw+I +Ig0= bs= IL 400 390 380 370 360 Ig Ib 32 NOTE: Slide prepared by Prof. Dushan Boroyevich from VT 0 Iw IIwIswIww IIbsIIss IIsg Ig © Alexis Kwasinski, 2012 LOAD 0 DC microgrids (droop control) MICROTURBINE IuT Ig DC bus (380 V) With a stiff grid there is no limit to Ig MICROTURBINE IuT 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) Grid interface converter Microturbine V [V] V [V] 0 0 33 LOAD Microturbine V [V] Current Limit 400 390 380 370 360 IL Current Limit DC GRID I μT 0 I μT Ig is regulated by adjusting δvref © Alexis Kwasinski, 2012 34 © Alexis Kwasinski, 2012 DC microgrids (droop control) DC GRID MICROTURBINE IuT Ig DC bus (380 V) MICROTURBINE 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) IL LOAD Ig+IμT,1+IμT,2 = IL VDC bus [V] 0 400 390 380 370 360 IuT,1 Ig 0 IμT,2 35 IuT © Alexis Kwasinski, 2012 DC microgrids (droop control) DC GRID MICROTURBINE IuT Ig DC bus (380 V) MICROTURBINE 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) IL LOAD Ig+IμT,1+IμT,2 = IL VDC bus [V] 0 400 390 380 370 360 Ig 36 IuT 0 IuT,1IμT,2 © 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. 37 © Alexis Kwasinski, 2012 Now secondary control depends on microgrid bus voltage and frequency * GP ( s )( P P*) E E * GQ ( s )(Q Q*) - GP(s) and GQ(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* Now tertiary control depends on real and reactive power flow from or to the grid NOTE: Figure from Guerrero et al “Hierarchical Control of Droop-Controlled AC and DC Microgrids—A General Approach Toward 38 Standardization” © Alexis Kwasinski, 2012