H AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS Qing-Chang Zhong zhongqc@ieee.org Electrical Drives, Power and Control Group Dept. of Electrical Eng. & Electronics The University of Liverpool United Kingdom Q.-C. ZHONG: H AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS p. 1/33
Outline Introduction System structure Modelling and controller design Experimental results Overview of other projects Q.-C. ZHONG: H AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS p. 2/33
DC-AC converters in the context of distributed generation Local generator Diode Rectifier DC link DC-AC Converter Microgrid grid Gas turbines Wind-mills etc. Fuel cells Photo-voltaic etc. Q.-C. ZHONG: H AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS p. 3/33
Control problems involved V DC e a e b e c L s, R s i a i b i c v c v b v a L g, R g Circuit Breaker v ga v gb v gc - C Power quality control: to reduce THD Provision of a a non-drifting neutral point/line Power flow control: to regulate P/Q Phase-locked loop (PLL): to synchronise with the grid Q.-C. ZHONG: H AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS p. 4/33
Power quality improvement Power quality is an important problem for renewable energy and distributed generation. The maximum total harmonic distortion (THD) of output voltage allowed is 5% (12V 69kV ). The maximum THD allowed in current is below: Odd harmonics Maximum current THD < 11 th < 4% 11 th 15 th < 2% 17 th 21 th < 1.5% 23 rd 33 rd <.6% > 33 rd <.3% Q.-C. ZHONG: H AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS p. 5/33
H repetitive voltage-controlled VSIs Transformer DC power source Inverter bridge LC filter u gc i a i b i c u ga u gb PWM modulation u a u b u c abc I d I q dq θ PLL θ abc u dq I d I q U d U q Internal model M and stabilizing compensator C e - - - u ref abc dq PI controllers I d * I q * Voltage controller Power controller An inner voltage loop to track the reference voltage u ref An outer power loop to regulate active power P and reactive power Q. Q.-C. ZHONG: H AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS p. 6/33
Repetitive control Incorporating an internal model, a local positive feedback of a delay line e τ ds cascaded with a low-pass filter W(s), to track or reject periodic signals with a period τ. Normally, τ d τ. A stabilising controller is normally needed. P W ( s) e τ s d w u g u ref u plant stabilizing compensator e internal model M p C Q.-C. ZHONG: H AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS p. 7/33
Poles of the internal model 1 x 14.8.6.4 Im.2.2.4.6.8 * o true poles approximated poles Res k 1 τ d ln 1 18 16 14 12 1 8 6 4 2 Re τ d ω c (τd ω c ) 2 (2kπ) = 1 ln 2 2τ d ( 1 ( 2kπ ) ) 2, τ d ω c Im s k 2kπ tan 1 2kπ τ d ω c τ d 2kπ τ d ( 1 1 ). τ d ω c Q.-C. ZHONG: H AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS p. 8/33
Single-phase circuit V DC - u PWM Inverter bridge u f S u c o i 1 i c L g i 2 R f L f R g filter inductor C f grid interface inductor u c u g grid R d neutral Consists of the inverter bridge, an LC filter (L f and C f ), a grid interface inductor L g, and a circuit breaker S C u f u: the PWM block and the inverter bridge can be ignored when designing the controller. Q.-C. ZHONG: H AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS p. 9/33
Modelling States: x = [ i 1 i 2 u c ] T External inputs: w = [ u g u ref ] T and u. Output: e = u ref u, where u = u c R d (i 1 i 2 ) is the output voltage of the inverter. The plant P can then be described by the state equation and the output equation ẋ = Ax B 1 w B 2 u y = e = C 1 x D 1 w D 2 u Q.-C. ZHONG: H AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS p. 1/33
A = B 1 = R fr d L f R d L g R d L f 1 L f R gr d L g 1 L g 1 C f 1 C f 1 L g, B 2 = 1 L f,, C 1 = [ R d R d 1 ], D 1 = [ 1 ], D 2 =. The transfer function from [ w u ] T to e is then [ ] A B1 B P = 2. C 1 D 1 D 2 Q.-C. ZHONG: H AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS p. 11/33
Formulation as an H problem ~ P b z~ w ~ v ξ a W µ w u d W d P e ~ y u C Break the loop involving the delay Add the computational delay block W d Q.-C. ZHONG: H AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS p. 12/33
W = [ Aw B w C w ] = [ ωc ω c 1 ] W d = [ Ad B d C d D d ] = [ 2 T 4 T 1 1 ] P = A B 2 C d B 1 B 2 D d A d B d B w C 1 B w D 2 C d A w B w ξ B w D 1 B w D 2 D d D w C 1 D w D 2 C d C w D w ξ D w D 1 D w D 2 D d µ C 1 D 2 C d ξ D 1 D 2 D d Q.-C. ZHONG: H AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS p. 13/33
System stability The original closed-loop system is exponentially stable if the designed closed-loop system is stable and its transfer function from a to b, denoted T ba, satisfies T ba < 1, where T ba = = 1 A B 2 C 1 D 2 W d C 1 A B 2 C d B 2 D d C c A d B d C c B c C 1 B c D 2 C d A c B c D 2 D d C c B c C w A w B w C 1 D 2 C d D 2 D d C c C w W. Q.-C. ZHONG: H AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS p. 14/33
Design example Parameters of the inverter Parameter Value Parameter Value L f 15µH R f.45ω L g 45µH R g.135ω C f 22µF R d 1Ω 42V DC voltage source The generated three-phase voltage is connected to the grid via a controlled circuit breaker and a step-up transformer. The sampling frequency is 5 khz and the PWM switching frequency is 2 khz. Q.-C. ZHONG: H AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS p. 15/33
Experimental setup Q.-C. ZHONG: H AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS p. 16/33
Measure 1 Local load PCB Measure 2 Transformer DC power source Inverter Output filter d a d b d c i u Circuit breaker u g dspace 114 Q.-C. ZHONG: H AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS p. 17/33
Controller design [ ] 255 255 W = for f = 5Hz and 1 [ ] 1 2 W d =. 1 1 ξ = 2.5 and µ =.8. Using the MATLAB hinfsyn algorithm, the H controller C which nearly minimises the H norm of the transfer matrix from w to z is obtained as C(s) = 735.2737(s 1e4)(s 2 9132s 4.58e8) (s 1.19e4)(s 255)(s 2 9515s 4.232e8). The resulting T ba is.8426. Q.-C. ZHONG: H AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS p. 18/33
Controller reduction C(s) = 735.2737(s 1e4)(s 2 9132s 4.58e8) (s 1.19e4)(s 255)(s 2 9515s 4.232e8). It can be reduced to C(s) = 735.27 s 255 = K pw(s) with K p = 735.27 255 without causing noticeable performance degradation, after cancelling the poles and zeros which are close to each other. This leads to T ba =.8222, which still maintains the stability of the system. Q.-C. ZHONG: H AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS p. 19/33
Resulting controller P e τ d s w u g u ref u plant e W (s) internal model M K p C P W ( s) e τ s d w u g u ref u plant stabilizing compensator e internal model M p C Q.-C. ZHONG: H AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS p. 2/33
Steady-state responses 2 4 Voltage [V] 1-1 #1:2 #1:1 Voltage error [V] 2-2 #1:1-2..1.2.3.4.5-4..1.2.3.4.5 Time [sec] Time [sec] (a) voltage u A and its reference u ref (b) voltage tracking error e 4 Current [A] 2-2 #1:2 #1:1-4..1.2.3.4.5 Time [sec] (c) output current i A and its reference The recorded current THD was 2.47%, while the output voltage THD was 1.74% and the grid voltage THD was 2.11%. Q.-C. ZHONG: H AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS p. 21/33
Transient responses 4 2 2 1 #1:2 Current [A] #1:2 #1:1 Voltage [V] #1:1-2 -1-4 3.6 3.65 3.7 3.75 3.8 3.85 3.9-2 3.6 3.65 3.7 3.75 3.8 3.85 3.9 Time [sec] Time [sec] (a) current output i A and its reference i ref (b) voltage output u A and its reference u ref 4 Voltage error [V] 2-2 #1:1-4 3.6 3.65 3.7 3.75 3.8 3.85 3.9 Time [sec] (c) voltage tracking error e Q.-C. ZHONG: H AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS p. 22/33
H repetitive current-controlled VSIs Proposed control algorithms to improve total harmonic distortion using H and repetitive control. Transformer DC power source Inverter bridge LC filter i a i b i c u ga u gb u gc PWM modulation u u ga u gb u gc Phase-lead low-pass filter u Internal model M and stabilizing compensator C u ga u gb u gc e - - - i ref PLL θ dq abc I d * I q * Current controller H repetitive current-controlled VSIs 3 Current [A] 2 1-1 -2 #1:1 #1:2 The recorded current THD was.99%, while the grid voltage THD was 2.21%. -3..1.2.3.4.5 Time [sec] Q.-C. ZHONG: H AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS p. 23/33
Synchronverters(Patent pending) Synchronverters are inverters that are operated according to the mathematical model of synchronous generators and thus are grid-friendly. Can work alone or in parallel without an external communication channel. Can work in grid-connected mode and island mode. In the grid-connected mode, they can easily take part in the regulation of real power and reactive power. P (W) and Q (Var) 2 P Q Time (Second) Q.-C. ZHONG: H AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS p. 24/33
AC Ward Leonard drive systems (Patent pending) Extended the concept of Ward Leonard drive systems to AC machines. Inverter Prime mover Constant speed Load Variable speed V DC Prime mover Variable speed SG SM/IM Load Variable speed Controllable field Fixed field Fixed field (a) Conventional (DC) Ward Leonard drive systems (b) AC Ward Leonard drive systems (c) Experimental results when reversing the motor: speed (left) and current (right) Q.-C. ZHONG: H AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS p. 25/33
Parallel Operation of Inverters E δ S = P jq 1 1 1 1 2 2 2 1 2 2 V S = P jq E δ R o1 Z R o2 3 3 P/ W 2 1 P 1 P 2 P/ W 2 1 P 1.5 1 1.5 2 P 2.5 1 1.5 2 15 15 Q/ Var 1 5 Q 1 Q/ Var 1 5 Q 1 Q 2.5 1 1.5 2 t/s (a) Joining of Inverter 2 Q 2.5 1 1.5 2 t/s (b) Change of loads Q.-C. ZHONG: H AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS p. 26/33
Inverter-dominated Power Systems Generator 1 Renewable Energy Source Generator 2 Renewable Energy Source Generator n Renewable Energy Source Energy Storage Energy Storage Energy Storage Inverter Inverter Inverter Circuit Breaker Circuit Breaker Circuit Breaker AC BUS Public Grid Q.-C. ZHONG: H AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS p. 27/33
A demonstration wind power system Patented by Nheolis, France, installed on the department s rooftop Control panel Q.-C. ZHONG: H AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS p. 28/33
Buck Converter Boost Converter Q.-C. ZHONG: H AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS p. 29/33
Regulation of induction generators for wind power Q P Q.-C. ZHONG: H AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS p. 3/33
Energy recovery from landing aircraft Aircraft Risen slope to fall when energy recovery is activated Coils Runway Magnets with alternative poles (N, S, N, ) Q.-C. ZHONG: H AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS p. 31/33
Voltage and current (zoomed) 6 Phase A voltage 4 2-2 -4-6.1.2.3.4.5 1 x 15 Phase A current.5 -.5-1.1.2.3.4.5 Time Q.-C. ZHONG: H AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS p. 32/33
Phase A voltage Phase A current 6 4 2-2 -4-6 5 1 15 2 25 3 2 1-1 -2 5 1 15 2 25 3 Time (a) Phase current and the generated voltage (phase) 8 6 d 4 2 v a p E 1 5-5 -1 2 x 17 1 1 x 17 5 5 1 15 2 25 3 Time (b) Distance, speed, deceleration, power and energy Q.-C. ZHONG: H AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS p. 33/33