NL2026118B1 - Method and system of general decentralized control for cascaded inverters - Google Patents
Method and system of general decentralized control for cascaded inverters Download PDFInfo
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- NL2026118B1 NL2026118B1 NL2026118A NL2026118A NL2026118B1 NL 2026118 B1 NL2026118 B1 NL 2026118B1 NL 2026118 A NL2026118 A NL 2026118A NL 2026118 A NL2026118 A NL 2026118A NL 2026118 B1 NL2026118 B1 NL 2026118B1
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
- H02J3/381—Dispersed generators
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
- H02M7/00—Conversion of ac power input into dc power output; Conversion of dc power input into ac power output
- H02M7/42—Conversion of dc power input into ac power output without possibility of reversal
- H02M7/44—Conversion of dc power input into ac power output without possibility of reversal by static converters
- H02M7/48—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
- H02M7/483—Converters with outputs that each can have more than two voltages levels
- H02M7/49—Combination of the output voltage waveforms of a plurality of converters
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/18—Arrangements for adjusting, eliminating or compensating reactive power in networks
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/18—Arrangements for adjusting, eliminating or compensating reactive power in networks
- H02J3/1821—Arrangements for adjusting, eliminating or compensating reactive power in networks using shunt compensators
- H02J3/1835—Arrangements for adjusting, eliminating or compensating reactive power in networks using shunt compensators with stepless control
- H02J3/1842—Arrangements for adjusting, eliminating or compensating reactive power in networks using shunt compensators with stepless control wherein at least one reactive element is actively controlled by a bridge converter, e.g. active filters
- H02J3/1857—Arrangements for adjusting, eliminating or compensating reactive power in networks using shunt compensators with stepless control wherein at least one reactive element is actively controlled by a bridge converter, e.g. active filters wherein such bridge converter is a multilevel converter
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/18—Arrangements for adjusting, eliminating or compensating reactive power in networks
- H02J3/1892—Arrangements for adjusting, eliminating or compensating reactive power in networks the arrangements being an integral part of the load, e.g. a motor, or of its control circuit
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
- H02J3/388—Islanding, i.e. disconnection of local power supply from the network
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
- H02M7/00—Conversion of ac power input into dc power output; Conversion of dc power input into ac power output
- H02M7/42—Conversion of dc power input into ac power output without possibility of reversal
- H02M7/44—Conversion of dc power input into ac power output without possibility of reversal by static converters
- H02M7/48—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
- H02M7/53—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal
- H02M7/537—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only, e.g. single switched pulse inverters
- H02M7/5387—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only, e.g. single switched pulse inverters in a bridge configuration
- H02M7/53871—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only, e.g. single switched pulse inverters in a bridge configuration with automatic control of output voltage or current
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J2300/00—Systems for supplying or distributing electric power characterised by decentralized, dispersed, or local generation
- H02J2300/40—Systems for supplying or distributing electric power characterised by decentralized, dispersed, or local generation wherein a plurality of decentralised, dispersed or local energy generation technologies are operated simultaneously
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
- H02M1/00—Details of apparatus for conversion
- H02M1/0003—Details of control, feedback or regulation circuits
- H02M1/0012—Control circuits using digital or numerical techniques
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
- H02M1/00—Details of apparatus for conversion
- H02M1/0067—Converter structures employing plural converter units, other than for parallel operation of the units on a single load
- H02M1/0074—Plural converter units whose inputs are connected in series
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
- Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
- Y02E40/20—Active power filtering [APF]
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
- Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
- Y02E40/30—Reactive power compensation
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- Engineering & Computer Science (AREA)
- Power Engineering (AREA)
- Inverter Devices (AREA)
Abstract
The present invention provides a method of general decentralized control for cascaded inverters and a system 5 thereof. The method includes steps of: detecting an instant current signal and an instant voltage signal from each cascaded inverter module; calculating active power and reactive power output from each module based on the instant voltage signal and the instant current signal in a grid— 10 connected. mode or an islanded mode; calculating' a current power factor angle based on the active power and the reactive power; obtaining, an angle frequency of each cascaded inverter module with a power factor angle droop control; obtaining a sinusoidal voltage reference; and obtaining a PWM signal for 15 controlling each module, based on the instant voltage signal, the instant current signal and the sinusoidal voltage reference with a dual control of voltage outer—loop and current inner—loop. 20 (Fig. 3)
Description
Method and system of general decentralized control for cascaded inverters Technical Field The present invention relates to the technical field of power electronics, in particular to a method and a system of general decentralized control for cascaded inverters. Technical Background Parallel and series (cascade) operations are two important ways to form a large-scale power system. Generally speaking, the parallel operation has been more widely used due to its ease of use and high reliability. For example, many micro- grids are formed by a large number of inverters in parallel.
However, series operation is also indispensable to form a high-voltage apparatus or network. For instance, cascaded inverters are used for high-voltage motor divers, STATCOM, and energy storage systems.
In the past, most control systems for cascaded inverters adopt a centralized control scheme. However, the centralized control scheme depends on a real-time communication network and powerful centralized controllers, which often result in reduced reliability due to communication failures, and higher capital costs. Moreover, implementation of the centralized control scheme will become more difficult when there are a large number of inverter modules that are arranged remotely from each other.
Summary of the Invention In order to solve the above-mentioned problems, the present invention provides a method of general decentralized control for «cascaded inverters. The method includes steps of: detecting an instant current signal and an instant voltage signal from an output end of each cascaded inverter module; calculating active power and reactive power output from each cascaded inverter module based on the instant voltage signal and the instant current signal in a grid-connected mode or an islanded mode; calculating a current power factor angle based
— 2 _ on the active power and the reactive power; obtaining, based on nominal angle frequency, nominal voltage amplitude, nominal power factor angle and the current power factor angle, an angle frequency of each cascaded inverter module with a power factor angle droop control; obtaining, based on the angle frequency and the nominal voltage amplitude, a sinusoidal voltage reference; and obtaining a PWM signal for controlling each cascaded inverter module, based on the instant voltage signal, the instant current signal and the sinusoidal voltage reference with a dual control of voltage outer-loop and current inner-loop.
According to the method of the present invention, in the islanded mode, the active power and the reactive power of an ith cascaded inverter module are expressed as follows: V JL 7 f = DV, COS (5 -6, + Oo ) |Z; a] it | i Voo, , Ó, = f > V, sim (5 7 0, + Gro ) |Z | ja } } wherein: Vi and ¢&i represent an instant voltage and a phase angle of the ith cascaded inverter module, respectively; and Z'ìload and 8@'ioad are an impedance and an impedance angle of a generalized load including transmission line and load, respectively.
According to the method of the present invention, in the grid-connected mode, the active power and the reactive power of the ith cascaded inverter module are expressed as follows: | A A P= V.cos(ó 6, +8. |V cosld -ó +6, i | Zin | £ J ( i j line ) zg ( i Zz line ) V n oo . 0 = 7 | SV, sin (5, = +0,,.)-V, sind, -Ô, +0 ne) line j=l wherein Zinin represents a transmission line impedance, and Vs and òÒg represent a voltage amplitude and a phase angle of the grid, respectively.
According to the method of the present invention, in the
— 3 — step of calculating a current power factor angle based on the active power and the reactive power, the power factor angle in the islanded mode is as follows: 3 sin(5, 8; +s) pan zaan ' > cos(3, -Ó;+ Oa) ja while the power factor angle in the grid-connected mode is as follows: a 0 2: Sin, -ô, + 6e ) Va 5in (8, = 5, + Be) pan an ! 2) cos(ô, “Ó, + 6jne) Vr cos(ó, Ó. +6) i= wherein: Vi and di represent the voltage and the phase angle of the ith cascaded inverter module, respectively; Z7icad and 67 load are an impedance and an impedance angle of a generalized load including transmission line and load, respectively; Zine One represents the transmission line impedance; and Vs and òs represent the voltage amplitude and the phase angle of the grid, respectively.
According to the method of the present invention, in the step of obtaining, based on nominal angle frequency, nominal voltage amplitude, nominal power factor angle and the current power factor angle, an angle frequency reference of each cascaded inverter module with a power factor angle droop control, the power factor angle droop control is expressed as follows: 0=0" -n(g -p') ‚=P wherein wi is an angle frequency of the ith cascaded inverter module; ©", V and gt are the nominal angle frequency, the voltage amplitude and the power factor angle, respectively; m is a positive coefficient; and g: is the power factor angle of the ith cascaded inverter module.
The present invention further proposed a system of general decentralized control for cascaded inverters, including: a
— 4 — detection unit, for detecting an instant current signal and an instant voltage signal from an output end of each cascaded inverter module; a power calculation unit, for calculating active power and reactive power output from each cascaded inverter module based on the instant voltage signal and the instant current signal in a grid-connected mode or an islanded mode; a power factor angle calculation unit, for calculating a current power factor angle based on the active power and the reactive power; a power factor angle droop control unit, for obtaining, based on nominal angle frequency, nominal voltage amplitude, nominal power factor angle and the current power factor angle, an angle frequency of each cascaded inverter module with a power factor angle droop control; and a dual inner-loop control unit, for obtaining, based on the angle frequency and the nominal voltage amplitude, a sinusoidal voltage reference, and obtaining a PWM signal for controlling each cascaded inverter module, based on the instant voltage signal, the instant current signal and the sinusoidal voltage reference with a dual control of voltage outer-loop and current inner-loop.
According to the system of the present invention, in the islanded mode, the active power and the reactive power of an ith cascaded inverter module are expressed as follows: B= eos( 5, +L) toad | JA Vo : , 0 = Ta sin (3, -0, +6) load | it wherein: Vi and òÒ: represent an instant voltage and a phase angle of the i*™ cascaded inverter module, respectively; and 77 10aa and 8@'’load are an impedance and an impedance angle of a generalized load including transmission line and load, respectively.
According to the system of the present invention, in the grid-connected mode, the active power and the reactive power of the ith cascaded inverter module are expressed as follows: P= Lis V, cos(5, 5, +6, )~V, cos (8, =5, 4.)
— 5 — Vola, , Q = 7 $ V‚ sin (5 ~0,+8,, ) “Va sin (4, ~0, +0, ) wherein Zine Om represents a transmission line impedance, and Vg and òg represent a voltage amplitude and a phase angle of the grid, respectively.
According to the system of the present invention, in the power factor angle calculation unit, the power factor angle in the islanded mode is as follows: 0 sin (3-8; +604 ) ¢, = atan an ' > cos(8, 8; +a) a while the power factor angle in the grid-connected mode is as follows: n 5 2, sin(8, -ô, +60 )-Vysin(5, — 8, +6) P= A = AA ! >, cos($, -ó, + One) Ve cos(8; 8, + Ope ) ja wherein: Vi and ò: represent the voltage and the phase angle of the ith cascaded inverter module, respectively; Z’icad and @/’10ag are an impedance and an impedance angle of a generalized load including transmission line and load, respectively; Zin Oe represents the transmission line impedance; and Vg and òsg represent the voltage amplitude and phase angle of the grid, respectively.
According to the system of the present invention, in the power factor angle droop control unit, the power factor angle droop control is expressed as follows: =n" - m( = 7) v= wherein wi is an angle frequency of the ith cascaded inverter module; oo", V° and ¢° are the nominal angle frequency, the voltage amplitude and the power factor angle, respectively; m is a positive coefficient; and ¢@: is the power factor angle of the ith cascaded inverter module.
- 6 — Compared with the existing control strategies, the present invention provides the following advantages. The present invention is suitable for both of the grid-connected mode and the islanded mode. In addition, seamless transition between different modes can be achieved. Moreover, stable conditions in the grid-connected mode are irrelevant to the transmission line impedance. The present invention is suitable for all types of loads in the islanded mode, and also suitable for four-quadrant operation. Tests show that the present invention can achieve small signal stability. Moreover, the feasibility of the proposed scheme has been verified through simulations.
Other features and advantages of the present invention will be illustrated in the following description, and partly be obvious therefrom or understood through implementing the present invention. The objects and advantages of the present invention can be implemented and obtained through structures particularly specified in the description, claims and drawings.
Brief Description of the Drawings Drawings, which constitute a part of the description, are used to provide a further understanding of the present invention, and explain the present invention together with embodiments thereof. The drawings are not intended to restrict the present invention in any manner. In the drawings: Fig. 1 schematically shows a structural block diagram of a cascaded inverter system according to one embodiment of the present invention; Fig. 2 schematically shows a principle diagram of a power factor angle droop control according to one embodiment of the present invention; Fig. 3 schematically shows a general flow chart of a control method according to one embodiment of the present invention;
- 7 = Fig. 4a schematically shows a curve graph of changes of frequency of the cascaded inverter system over time in two modes according to one embodiment of the present invention; Figs. 4b and 4c respectively show curve graphs of changes of active power and reactive power of the cascaded inverter system over time in two modes according to one embodiment of the present invention; Figs. ba to 5c respectively show curve graphs of changes of frequency, active power and reactive power of the cascaded inverter system over time under three types of loads according to one embodiment of the present invention; Figs. 6a to 6c respectively show curve graphs of changes of frequency, active power and reactive power of the cascaded inverter system over time in four-quadrant operation according to one embodiment of the present invention; Figs. 7a to 7c respectively show curve graphs of changes of frequency, active power and reactive power of the cascaded inverter system over time with respect to various impedances of transmission line according to one embodiment of the present invention; and Figs. 8a and 8b respectively show curve graphs of changes of frequency and power factor angle of the cascaded inverter system over time in four-quadrant operation according to one embodiment of the present invention.
Detailed Description of the Invention In order to enable the objectives, technical solutions and advantages of the present invention self-evident, the present invention will be described in further detail with reference to preferred embodiments in combination with the accompanying drawings.
Recently, decentralized control strategies of cascaded inverters have received wide attention because they could
- 8 - overcome the drawbacks of the centralized control methods as mentioned above. For the cascaded inverters in an islanded mode, a power factor droop control is firstly presented, which is suited for only resistance inductance (RL) loads. To broaden the scope of applications of the above method, an f- P/Q method is proposed, which is suitable for both RL and resistance capacitance (RC) loads. However, it is still unfeasible {for pure resistance load. Meanwhile, it further surfers from the problem of multiple equilibrium points, which may bring about some undesired operating states.
Further, one prior art proposes an improved decentralized control with unique equilibrium point. Contrast to the islanded mode, the situation in the grid-connected mode is totally different. Another prior art proposes a {fully decentralized control, which is the first attempt to control the cascaded inverters in the decentralized manner. However, they are only suitable for some specific transmission lines. Another prior art presents a distributed power control for grid-tied photovoltaic generation. However, PCC voltage information must be available for each module, which increases the difficulty in implementation of the method. Current decentralized control schemes are suitable for the islanded mode or the grid-connected mode, so that a decentralized control suited for both of them is desirable in practice.
To address the concerns above, the present invention proposes a general decentralized control of cascaded inverters for operations in both of the grid-connected and islanded modes. Compared to the existing methods, the proposed power factor angle droop control has the following features.
First, it is a unified control scheme. Specifically, the proposed scheme is a unified control scheme for both modes, and thus seamless transition therebetween can be realized. Second, it is suitable for all types of loads. The current methods are only suitable for either RL loads or RC loads, while the proposed scheme is suitable for all types of loads. Third, it has unique equilibrium point. The current methods
— 9 — each suffer from the problem of multiple equilibrium points, while the proposed one holds a unique equilibrium point. Fourth, it is able to achieve four-quadrant operation. The current methods could only work partially for four guadrant operation, while the proposed one can realize the four- quadrant operation completely. As shown in Fig. 1, the structure of a cascaded inverter system consisting of n DG units is provided. Different from conventional cascaded inverter systems, the DG units may be distributed in broader areas where real-time communication is unavailable. The cascaded inverter system could be operated in the grid-connected mode or the islanded mode by switching a static transfer switch (8TS).
In the structure of Fig. 1, power transmission characteristic of the system is as follows. In the islanded mode, the active power Pi and the reactive power Oi output from an ith DG unit are derived through the following equation: B+ JO, =1e" [Se fide =! (1) wherein Vi and &: represent the voltage and the phase angle of the ith DG unit, respectively; and Z7icad and 671cad are respectively the impedance and impedance angle of the generalized load, which includes the transmission line and the load. Through decomposing equation (1) into real and imaginary parts, the power transmission characteristic in the islanded mode is given by P= i y 1 cos(8, = 3, +6, ) [Zina] (2) Q = 7 > I” sin (3 0, +0, ) fad JE (3) In the grid-connected mode, Pi and Qi: are expressed as P+j0 =Tet | Vie Fel | / Ze" | ” (4)
— 1 0 — wherein Z ine Ore represents the transmission line impedance, and Vg and òÒg represent the voltage amplitude and the phase angle of the grid, respectively. The power transmission characteristic in the grid-connected mode is as follows: P= lg cos(8 -5, +0; ) 1, cos(8 —&, +6, ) | ie jl ( 5 ) 0 = J [£ [i sin (5 = a, + Orne ) = Fe sin (3 = 8, + Ore ) VA j=l ’ Ù { 6 ) Fig. 2 shows a control principle diagram for power factor angle droop control strategy according to one embodiment of the present invention.
As shown in Fig. 2, the power factor angle of the current output power of an individual inverter module is obtained based on values of the active power and the reactive power. Then, the power factor angle droop control strategy is used to control the angle frequency of the power output from the individual inverter module at a next moment, on the basis of the nominal angle frequency, the nominal voltage amplitude, the nominal power factor angle and the power factor angle of the current output power, with the power factor angle droop control strategy.
The proposed power factor angle droop control strategy of cascaded inverters can be expressed as oz’ MG rg © (2-9) (7) hel (8) wherein w: is the angle frequency; oo, V and ¢° are the nominal angle frequency, the voltage amplitude and the power factor angle, respectively; m is a positive coefficient; and pi is the power factor angle.
As seen from the above, the proposed scheme according to equations (7) and (8) only needs local information of each module, and thus it is a decentralized approach.
Finally, as shown in Fig. 2, a PWM signal for controlling
— 11 — power output from each cascaded inverter module is obtained based on the angle frequency and the nominal voltage amplitude via a dual inner-loop control. Fig. 3 shows a general flow chart of the method according to one embodiment of the present invention.
In step S301, an instant voltage signal and an instant current signal from the output end of each cascaded inverter module are detected.
Then, in step S302, the active power and the reactive power output from each cascaded inverter module in the grid- connected mode or the islanded mode are calculated based on the instant voltage signal and the instant current signal. In step S303, a current power factor angle is calculated based on the active power and the reactive power as obtained. In step S304, an angle frequency of each cascaded inverter module is obtained based on nominal angle frequency, nominal voltage amplitude, nominal power factor angle and the current power factor angle, with the power factor angle droop control. In step S305, a sinusoidal voltage reference is formed based on the angle frequency as obtained and the nominal voltage amplitude. Finally, in step S306, a PWM signal for controlling each cascaded inverter module is obtained, based on the instant voltage signal, the instant current signal and the sinusoidal voltage reference, with a dual control of voltage outer-loop and current inner-loop.
In the {following steady-state analysis on the system according to the present invention is provided. In the steady- state, from equation (7), it can be obtained Pi = @F (2) wherein 1, j € {1, 2, .., n}.
In the islanded mode, according to equations (2), (3), (8) and (9), it is easy to obtain the following equation: [e+ 100, (10)
— 12 — In the grid-connected mode, similar conclusions about the active power and the reactive power can be drawn as above.
Small signal stability analysis on the system according to the present invention is further provided.
To prove the stability of the proposed method in the islanded and grid- connected modes, the small signal analysis near the equilibrium point is carried out.
Assuming &s is the synchronous phase-angle of cascaded inverters in the steady state, and denoting % 707% ,, equation (7) can be rewritten, in view of %=%, as follows: 5=a" —m{p, -¢") (11) Through linearizing equation (11) around the equilibrium point, it can be obtained AS, = mA, ( 1 2 ) In the islanded mode, equations (2) and (3) are combined to obtain 3 sin( ö = 8, + Ona) @ = atan = an ‘ D cos(á = 8, +904} ist (13) Then, through linearizing equation (13), it can be obtained Ap, “15a —A8,) oe (14) Combining equation (12) with equation (14), it can be obtained AS, (ag, —A8,} n j=l ’ ( 1 5 ) Through rewriting equation (15) as a matrix form, it can be obtained X =AX (16)
— 1 3 — ni _ 5 … , 7 A oe L ' . . wherein X =[Aò as] n , and ZL is a Laplacian matrix expressed as al 1 es 1 1 n-t e ~1 L= : : : -1 1 onl (17) The eigen values of A are expressed as A(4} = 0.4 (A)= = 4, (A) = =m (18) Clearly, the system is stable in the islanded mode.
However, the stability does not depend on load parameters, which 1s a very important characteristic of the present invention.
In the grid-connected mode, equation (5) is combined with equation (6) to obtain:
Vr, sin(ò, = 8, +0, ) Vg sin{, = 8, + Be} P= ann NF cos( = 3, +8, ) Ty cos(d, = 5, + Oe} = (19) Linearization of equation (19) around the equilibrium point results in Ap=aAò, +b 3 Ad, 2 0 J=lizy { 2 0 ) wherein: xx 2 2 a. ~ ~ (=n )(1") +17 + (1-20), cos(ë, —ò,) n? (7) +17 —2n VT, cos(ò, ~ dy) (21) 1 Fr cos(8, =, ) nl” y nH (17) 1 = 20877 cos(ò, ~ 5, (22) Substituting equation (20) into equation (12) yields X =BX (23) wherein
— 1 4 — h == ' b a …. b B=-m : : : b b ee a (24) The eigen values of B are given by &(B)=-mr (Vn cos = 6,)). 4p (B) = 4,(B)=-m (25) I nV cos(ò -5,)20 Clearly, if 2” cos(c %)z ‚ the system will be stable in the grid-connected mode, and that the stability conditions are irrelevant to the transmission line impedance and load. In another aspect, to verify the effectiveness of the power factor angle droop control, simulations are performed on Matlab/Simulink platform for the technical solution of the present invention. The related parameters of the tested system comprised of four DG units are listed in Table I.
TABLE IT Parameters Values Parameters Values Ve(V) 315 Zine (CQ) j0.314 ff (Hz) 50/[49, 51] VV) 315/4 m 0.5 0" 0.2 Case 1: Unified control In this case, test is carried out when the grid-connected mode is switched to the islanded mode. The frequencies of inverters are shown in Fig. 4a, which illustrates that the proposed scheme can realize seamless transition between said two modes. The active and reactive power allocations are shown in Figs. 4b and 4c, respectively. Therefore, the proposed scheme is a unified control approach for cascaded inverters to work in the grid-connected mode and the islanded mode. Case 2: Suitable for all types of loads In this case, the operation in the islanded mode is tested under pure resistance load, resistance-inductance load and resistance-capacitance load, respectively. During interval
- 15 = [0s, 6s], the system load is a pure resistance load; during interval [6s, 12s], the load is changed into a resistance- inductance load; and after that, the load is further changed into a resistance-capacitance load.
Figs. 5a to 5c show the waveforms of frequency, active power and reactive power of all modules from top to bottom, respectively.
As shown in the figures, the frequencies of all the modules converge quickly after start-up, and then they are always synchronous no matter how the loads change.
However, the frequency changes with the load power factor.
The frequency under the resistance- capacitance load is higher than that under the resistance- inductance load, which is in consistency with what equation (7) implies.
Meanwhile, the performance in the active and reactive power allocation is excellent.
As shown in the figures, the proposed scheme is suitable for all types of loads.
Case 3: Unique equilibrium point In this case, the cascaded inverters operate in the islanded mode.
The initial phase angle of inverter #1 is set in I, II, III, IV quadrants in intervals [0s, 5s], [5s, 10s], [10s, 15s] and [15s, 20s], respectively, and the initial phase angles of other inverters are all set as zero.
The waveforms of frequency, active power and reactive power are illustrated in Figs. 6a, 6b and 6c, respectively.
As shown in the figures, the proposed power factor angle droop control scheme always has a unique equilibrium point, and is irrelevant to the initial states.
Case 4: Suitable for all types of transmission line impedance In this case, operation is carried out in the grid- connected mode when the capacitive, inductive and resistive transmission lines are fed in intervals [0s, 5s], [5s, 10s], [10s, 15s] and [15s, 20s], respectively.
The simulation results of frequency, active power and reactive power are depicted in Figs. 7a, Jb and 7c, respectively.
It can be understood from the simulation results that the proposed scheme is suitable for all types of transmission line impedance.
- 16 - To verify the capability of four quadrant operation of the proposed method, grid-connected operation with the power factor angle reference being set as m/4, 3n/4, -3n/4, and -n/4 in intervals [0s, 5s], [5s, 10s], [10s, 15s], and [15s, 20s], respectively, is tested. The waveform of power factor angle is presented in Fig. 8a, in which the actual one can track its reference. The waveform of the frequency is shown in Fig. 8b, which always converges to 50Hz. Therefore, the proposed scheme can realize the four-quadrant operation.
The present invention provides a general decentralized control strategy of cascaded inverters, i.e., power factor angle droop control. Compared with current control strategies, it has the following advantages. 1) The present invention is suitable for both of the grid-connected mode and the islanded mode. 2) Seamless transition between different modes can be achieved. 3) Stable conditions in the grid-connected mode are irrelevant to the transmission line impedance. 4) The present invention is suitable for all types of loads in the islanded mode. 5) The present invention is suitable for four-quadrant operation. Tests show that the present invention can achieve small signal stability. Moreover, the feasibility of the proposed scheme has been verified through simulations.
It should be understood that embodiments of the present invention are not limited to the specific structures, process steps or materials disclosed herein, but should extend to the equivalent substitutes for these features that the ordinary ones skilled in the related art can understand. It still should be conceived that terms herein are merely used for description of the specific embodiments, not the limitation thereof.
“One embodiment” or “embodiments” mentioned in the description means the specific features, structures, and characteristics illustrated in combination with embodiments are included at least one embodiment of the present invention. Therefore, the phrases “one embodiment” or “embodiments” recited throughout the whole description do not necessarily
- 17 — mean the same embodiment.
The above description of specific embodiments of the present invention has been described with reference to the accompanying drawings, but is not intended to limit the scope of the invention. Other different forms of modifications or variations may be made by those skilled in the art in light of the above description. There is no need and no way to exhaust all of the implementation modes. On the basis of the technical solutions of the present invention, various modifications or variations that can be made by those skilled in the art without any creative effort are still within the scope of the present invention.
Aspects of the invention are itemized in the following section.
1. A method of general decentralized control for cascaded inverters, including steps of: detecting an instant current signal and an instant voltage signal from an output end of each cascaded inverter module; calculating active power and reactive power output from each cascaded inverter module based on the instant voltage signal and the instant current signal in a grid-connected mode or an islanded mode; calculating a current power factor angle based on the active power and the reactive power; obtaining, based on nominal angle frequency, nominal voltage amplitude, nominal power factor angle and the current power factor angle, an angle frequency of each cascaded inverter module with a power factor angle droop control; obtaining, based on the angle {frequency and the nominal voltage amplitude, a sinusoidal voltage reference; and obtaining a PWM signal for controlling each cascaded inverter module, based on the instant voltage signal, the instant current signal and the sinusoidal voltage reference with a dual control of voltage outer-loop and current inner-loop.
2. The method according to claim 1, wherein in the islanded mode, the active power and the reactive power of an
— 1 38 _ ith cascaded inverter module are expressed as follows: P= Jy V, cos (5 TÔ +0. ) |Z oes j=l 0 = Ji 3 V sind, ~8,+0, , ) |Z} | ja ’ ’ wherein: Vi and &i represent an instant voltage and a phase angle of the ith cascaded inverter module, respectively; and Z'ì1o0ad and 6710ad are an impedance and an impedance angle of a generalized load including transmission line and load, respectively.
3. The method according to claim 2, wherein in the grid-connected mode, the active power and the reactive power of the ith cascaded inverter module are expressed as follows: P= Lis V‚ cos(5, 8, +6, )~V, cos(5,~3, +6, ) 0 = ls V,sin(8,~5, +6, ) =, sin(6, —5, +6, ) |Z me jl wherein Zin me represents a transmission line impedance, and Vy and òg represent a voltage amplitude and a phase angle of the grid, respectively.
4. The method according to claim 3, wherein in the step of calculating a current power factor angle based on the active power and the reactive power, the power factor angle in the islanded mode is as follows: 0 sin (6-6, +84) pam, = alan J > cos(á 8; +6 J=1 while the power factor angle in the grid-connected mode is as follows: a , DV, sin(8, 6, +6, )~V,sin(8,~5, +6 ) p, = atan an mmm ' 2 V; cos(ó, -Ó;+ One) —V, cos (5 —6, + Orie) jz wherein: Vi and òÒi represent the voltage and the phase angle of the ith cascaded inverter module, respectively; Z'io0ad and 67 i1caq are an impedance and an impedance angle of a generalized load including transmission line and load, respectively; Ziel
— 19 _ represents the transmission line impedance; and Vg and òg represent the voltage amplitude and the phase angle of the grid, respectively.
5. The method according to claim 4, wherein in the step of obtaining, based on nominal angle frequency, nominal voltage amplitude, nominal power factor angle and the current power factor angle, an angle frequency reference of each cascaded inverter module with a power factor angle droop control, the power factor angle droop control is expressed as follows: 0=0" -n(q -p') vr wherein wi is an angle frequency of the ith cascaded inverter module; ©", V and gt are the nominal angle frequency, the voltage amplitude and the power factor angle, respectively; m is a positive coefficient; and g: is the power factor angle of the ith cascaded inverter module.
6. A system of general decentralized control for cascaded inverters, including: a detection unit, for detecting an instant current signal and an instant voltage signal from an output end of each cascaded inverter module; a power calculation unit, for calculating active power and reactive power output from each cascaded inverter module based on the instant voltage signal and the instant current signal in a grid-connected mode or an islanded mode; a power factor angle calculation unit, for calculating a current power factor angle based on the active power and the reactive power; a power factor angle droop control unit, for obtaining, based on nominal angle frequency, nominal voltage amplitude, nominal power factor angle and the current power factor angle, an angle frequency of each cascaded inverter module with a power factor angle droop control; and a dual inner-loop control unit, for obtaining, based on the angle frequency and the nominal voltage amplitude, a sinusoidal voltage reference, and obtaining a PWM signal for controlling each cascaded inverter module, based on the
— 2 0 — instant voltage signal, the instant current signal and the sinusoidal voltage reference with a dual control of voltage outer-loop and current inner-loop.
7. The system according to claim 6, wherein in the islanded mode, the active power and the reactive power of an ith cascaded inverter module are expressed as follows: p= LL SY cos(6 6,40) |Zo j=1 0 = bi 3 V,sin(8,~8, +6) |Z ja ’ ’ wherein: Vi and ¢&i represent an instant voltage and a phase angle of the ith cascaded inverter module, respectively; and Z'ìload and 8@'ioad are an impedance and an impedance angle of a generalized load including transmission line and load, respectively.
8. The system according to claim 7, wherein in the grid-connected mode, the active power and the reactive power of the ith cascaded inverter module are expressed as follows: P= zi cos(8, ~8, +8, )~, cos(8, 6, +44.) |Z ne) j=l V 7 O= $ V‚sin(8 -8, +6, )~V,sin(8, 8, +6, ) (Ze A wherein Zine Ome represents a transmission line impedance, and Vg and òg represent a voltage amplitude and a phase angle of the grid, respectively.
9. The system according to claim 8, wherein in the power factor angle calculation unit, the power factor angle in the islanded mode is as follows: a 0 > sin(8, = 8, +6 ) gaan an ' > cos(, ~&, + Ora) Ja while the power factor angle in the grid-connected mode is as follows: n 5 2 sin(5, 8; +6, )—V,sin(8, = 5, +6) P= AI A DV, cos(ó, =, +6, )—V, cos(8, = 5, +6.) j=
— 21 _ wherein: Vi and òÒi represent the voltage and the phase angle of the ith cascaded inverter module, respectively; Z'io0ad and 67 i1caq are an impedance and an impedance angle of a generalized load including transmission line and load, respectively; Zine 2 pe represents the transmission line impedance; and Vy and òg represent the voltage amplitude and phase angle of the grid, respectively.
10. The system according to claim 9, wherein in the power factor angle droop control unit, the power factor angle droop control is expressed as follows: 0=0" -n(q -p') ver wherein wi: is an angle frequency of the ith cascaded inverter module; ©", V and gt are the nominal angle frequency, the voltage amplitude and the power factor angle, respectively; m is a positive coefficient; and ¢@: is the power factor angle of the ith cascaded inverter module.
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