energies Article
Predictive Control of Power Electronics Converters in Renewable Energy Systems Jiefeng Hu * and Ka Wai Eric Cheng Department of Electrical Engineering, The Hong Kong Polytechnic University, Hong Kong, China;
[email protected] * Correspondence:
[email protected]; Tel.: +852-2766-6140 Academic Editor: Chunhua Liu Received: 13 February 2017; Accepted: 7 April 2017; Published: 10 April 2017
Abstract: Predictive control has attracted much attention and has been widely used in power electronics and electric drives. However, further developments for applications in the field of renewable energy systems are still under investigation. In this paper, the principles of predictive control are studied with a focus on model predictive control (MPC) and vector-sequence-based predictive control (VPC). Based on these techniques, two control strategies for flexible power supply are developed. They are implemented in the most promising renewable energy systems, namely solar photovoltaic (PV) systems and wind generators, respectively. The experimental results based on a laboratory prototype show that the active and reactive powers supplied by the PV and wind generator can be controlled flexibly with excellent steady-state and transient performance. As the penetration level of the renewable energy sources in electricity network continues to rise, predictive control tends to be an attractive and powerful technique for power electronics converters in renewable energy systems. Keywords: predictive control; power converters; renewable energy; distributed generation
1. Introduction In electric drives and AC/DC or DC/AC power conversion, a variety of power electronics converters have been utilized, and the corresponding control strategies have been an ongoing research subject over the last few decades. Recently, due to the sharp increase in the exploitation of renewable energy sources such as wind, solar photovoltaic (PV), and wave energy, more and more power electronics converters have been used to integrate the energy sources into the AC and/or DC common buses in a distributed generation (DG) system [1,2]. As the penetration and capacities of DG units increase, the power converters are required to operate more efficiently and effectively to maintain high power quality and dynamic stability. To fulfill these requirements, advanced control techniques have been intensively investigated in the last years. Classic linear controllers, together with pulse width modulation (PWM) schemes and nonlinear controllers based on hysteresis comparators, have been the most widely studied and developed control strategies for power converters [3,4]. Later on more complex control techniques have been proposed as the computing power of microprocessors has increased dramatically. These include sliding mode control [5,6], fuzzy logic [7], genetic algorithms [8], and neural networks [9,10]. In the last few years, predictive control appears as an attractive alternative for power converters and has attracted much attention [11–14]. For example, predictive algorithms are used to control the current for a four-leg indirect matrix converter [12], the electromagnetic torque for machines [13], and the power for grid-connected two-level inverters [14]. The main characteristic of predictive control is the use of the system model for the prediction of the controlled variables. Next, predefined optimized criterion selects the appropriate control set. In fact, several kinds of control methods have Energies 2017, 10, 515; doi:10.3390/en10040515
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the name of predictive control [15]. The most important types are model predictive 2 of 14 control (MPC), vector-sequence-based predictive control (VPC), etc. Although predictive control has been widely used in power electronics and electric drives, been developed underare thestill name of predictive control [15]. The most important types are energy model further developments under investigation for applications in the field of renewable predictive control (MPC), vector-sequence-based predictive control (VPC), etc. systems, where DG sources are integrated to the local low voltage network through power Although predictive control of has widely used in power electric drives, converters. Taking the advantage thebeen excellent performance of theelectronics predictive and control, this type of further developments are still under investigation for applications in the field of renewable energy control approach is pointed to be a promising method in distributed generation and renewable systems, where DG aretechnique integratedistoemployed the local low network through power converters. energy systems. In sources [16], MPC in avoltage grid connected PV system. However, it is Taking the advantage of the excellent performance of the predictive control, this type of control only implemented in the boost converter for maximum power point tracking (MPPT). Whereas, the approach is pointed begrid-connected a promising method in distributed and energy systems. main converter, i.e.,tothe DC/AC inverter, is generation not studied. In renewable [17,18], predictive control In [16], MPC technique is employed in a grid connected PV system. However, it is only implemented is adopted to optimize the operational cost of microgrids with renewable energy sources and energy in the boost maximum poweraims pointfor tracking (MPPT). Whereas, mainhorizons converter, storage. The converter proposed for predictive controller system-level control usingthe control of i.e., the grid-connected DC/AC inverter, is not studied. In [17,18], predictive control is adopted several minutes or even hours, but it fails to consider the discrete-time models and behaviors of to optimize the operational cost of microgrids with renewable energy sources and energy storage. power converters that act as power electronic interface between the renewable energy sources and The proposed predictive controller aims for system-level control using control horizons of several the grid. minutes evenfills hours, but it failsgap to consider the discrete-time models and behaviors of power Thisor paper this important in the literature. Its contribution is to extend and explore the converters that act as power electronic interface between the renewable energy sources and the grid. feasibility of predictive control and to advance this one step further by developing appropriate This paper fills important gapsystems. in the literature. Its contribution is to extend and explore control strategies for this renewable energy Power converters will be modelled in the predictive the feasibility of predictive control and to advance thisbeone step further by developing controllers and the grid-connected operation will focused. Specifically, a MPCappropriate scheme is control strategies for renewable energy systems. Power converters will be modelled infor thedoubly-fed predictive developed for grid-connected solar PV systems, while a VPC approach is developed controllers and the grid-connected operation will be focused. Specifically, a MPC scheme is developed induction generator (DFIG) wind systems. The importance of this paper can be summarized in for grid-connected solar PV while aofVPC is developed induction ensuring more reliability forsystems, the operation gridapproach integration, exploitingfor thedoubly-fed capability of flexible generator (DFIG) wind systems. The importance of this paper can be summarized in ensuring power regulation of grid-connected distributed generations, and providing better steady-statemore and reliability for the operation of grid integration, exploiting the capability of flexible power regulation of dynamic response. grid-connected generations, and providing steady-state andofdynamic response. The rest ofdistributed this paper is organized as follows. Thebetter operating principles predictive control for The rest of this paper is organized as follows. The operating principles of predictive control power converters are reviewed in Section 2, where the most popular types, namely MPC and VPC for power converters are reviewed in Section 2, where the most popular types, namely MPC and are investigated. In Section 3, a MPC scheme is developed for grid-connected solar PV systems, while VPC are investigated. In Section 3, a MPC scheme is developed for grid-connected solar PV systems, a VPC approach is developed for DFIG based wind energy systems. In Section 4, experimental results while a VPC approach is developed for DFIG of based energycontrol systems. In Sectionfollowed 4, experimental are provided to validate the effectiveness the wind predictive strategies, by the results are provided to validate the effectiveness of the predictive control strategies, followed by the conclusion drawn in Section 5. conclusion drawn in Section 5. 2. Predictive Control Theory 2. Predictive Control Theory Predictive control refers to a very wide class of controllers that have been widely used in power Predictive control refers to a very wide class of controllers that have been widely used in power converters. Figure 1 shows the architecture of a typical predictive controller. The system model can converters. Figure 1 shows the architecture of a typical predictive controller. The system model can be expressed as a discrete-time state-space model, the output of which is determined by the input, be expressed as a discrete-time state-space model, the output of which is determined by the input, the current state of the model, and the discrete interval. In this way, the future behavior of the system the current state of the model, and the discrete interval. In this way, the future behavior of the system can be predicted over a time frame. By applying the optimal actuation that is obtained according to can be predicted over a time frame. By applying the optimal actuation that is obtained according a predefined optimization criterion, the control problem can be defined as the determination of an to a predefined optimization criterion, the control problem can be defined as the determination of appropriate control action that will force a generic system variable as close as possible to a desired an appropriate control action that will force a generic system variable as close as possible to a desired reference value. In this paper, two typical predictive control methods are studied and applied, reference value. In this paper, two typical predictive control methods are studied and applied, namely MPC and VPC. namely MPC and VPC.
Current State Future Control Actions
Future outputs
References
System Model Future Errors Optimization Criterion
Figure 1. 1. Basic Basic principle principle of of predictive predictive control. control. Figure
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2.1. 2.1. Model Model Predictive Predictive Control Control (MPC) (MPC) In MPC, aasystem systemmodel model is used to predict the behavior the variables over a time certain time In MPC, is used to predict the behavior of theofvariables over a certain horizon, horizon, and a cost function as the is criterion used the to select theswitching optimal switching [11]. The and a cost function as the criterion used toisselect optimal states [11].states The principle principle of this control scheme is illustrated in Figure 2a. All the possible system transitions yp)(tcan k+1) of this control scheme is illustrated in Figure 2a. All the possible system transitions yp (tk+1 can be predicted using the measured value y(t k ) at the control actions according to a prediction model be predicted using the measured value y(tk ) at the control actions according to a prediction model {y(tkk),), N}. prediction model model is is directly directlyderived derivedfrom fromthe thediscrete-time discrete-timemodel modelofofthe thesystem, system,and and {y(t N}. This This prediction it itis is various depending on the control objectives. Take N = 1 as an example, the system behavior at various depending on the control objectives. Take N = 1 as an example, the system behavior at k + 1 kinstant + 1 instant can be predicted the measured k) and n possible voltage vectors, resulting can be predicted withwith the measured valuevalue y(tk ) y(t and n possible voltage vectors, resulting in n in n possible values p1,,y.p2 , asdepicted depictedininFigure Figure2b. 2b. possible values yp1 , yyp2 . ,. …, , ypny,pnas Next, Next, aa cost cost function function will will be be formulated formulated to to evaluate evaluate the the effectiveness effectiveness of of all all the the possible possible voltage voltage vectors on the system performance. The voltage vector that minimizes the cost function vectors on the system performance. The voltage vector that minimizes the cost function will will be be chosen chosen for the next sampling period. For example, if y p3 is closest to y*, the voltage vector producing yp3 will for the next sampling period. For example, if yp3 is closest to y*, the voltage vector producing yp3 will be be selected selected to to control control the the converter converter between between kk and and kk ++ 11 instants. instants.
(a)
y yp1(tk+1)
y(tk)
yp2(tk+1) *
y
yp3(tk+1)
···
Ts
ypn(tk+1) tk+1
tk
t
(b) Figure Figure 2. 2.Illustration Illustrationof ofMPC MPCoperation, operation,(a) (a)block blockdiagram diagramof of MPC; MPC; (b) (b) vectors vectors evaluation evaluation and and selection. selection.
The advantage of MPC is that it allows the easy inclusion of system constraints, thus different The advantage of MPC is that it allows the easy inclusion of system constraints, thus different control objectives can be flexibly taken in account in different applications. Another remarkable merit control objectives can be flexibly taken in account in different applications. Another remarkable merit of MPC is the inclusion of nonlinearities, such as harmonic spectrum control and switching frequency of MPC is the inclusion of nonlinearities, such as harmonic spectrum control and switching frequency reduction. The key is to choose the appropriate weighting factors to get a satisfactory tradeoff reduction. The key is to choose the appropriate weighting factors to get a satisfactory tradeoff between between the control objectives. the control objectives. Notice that all the work mentioned above use a short horizon (usually equal to 1), which is called Notice that all the work mentioned above use a short horizon (usually equal to 1), which is called “Finite State Predictive Control”. There is another research area that considers longer control “Finite State Predictive Control”. There is another research area that considers longer control horizons horizons (N > 1) such as power management of a hydrogen-based microgrid in [19], and PV plants (N > 1) such as power management of a hydrogen-based microgrid in [19], and PV plants with energy with energy storage in [20]. For the sake of simplicity, N = 1 is adopted in this paper. storage in [20]. For the sake of simplicity, N = 1 is adopted in this paper. 2.2. 2.2. Vector-Sequence-Based Vector-Sequence-Based Predictive Predictive Control Control (VPC) (VPC) This inin such a This predictive predictive control controlstrategy strategyselects selectsan anoptimal optimalset setofofconcatenated concatenatedvoltage voltagevectors vectors such way that a way thatthe thecontrolled controlledvariables variablesconverge convergetoward towardthe thereference referencevalues valuesalong along aa fixed fixed predefined predefined switching period [21]. Figure 3a depicts the basic principle of this method. In order to correct the error switching period [21]. Figure 3a depicts the basic principle of this method. In order to correct the between the reference and the measured value, i.e., to enable the controlled variables to track the error between the reference and the measured value, i.e., to enable the controlled variables to track reference, an appropriate vector sequence is is selected. After that, the reference, an appropriate vector sequence selected. After that,the theoptimized optimizedduration durationof of each each voltage vector applied within the control period is calculated according to some specified criteria. voltage vector applied within the control period is calculated according to some specified criteria. The illustrated in in Figure 3b,3b, it could be forcing y equal to y*toaty* the The criteria criteriacould couldbe bedifferent. different.AsAs illustrated Figure it could be forcing y equal atend the of the period, or making the mean value of y equal to y* over the entire period, or making the root-mean-square (RMS) value of y over one period to be minimal. The key of this predictive control
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4 ofthe 14 or making the mean value of y equal to y* over the entire period, or making root-mean-square (RMS) value of y over one period to be minimal. The key of this predictive control method is to to calculate calculate the theoptimized optimizeddurations durations(t(t i) of vectors using the measured y(k), the reference method is i ) of vectors using the measured y(k), the reference y*, y*, and the derivatives σ 1 , σ 2 , and σ 7 . These derivatives indicatethe the effects effects of of vector vector sequences sequences on and the derivatives σ1 , σ2 , and σ7 . These derivatives indicate on the the controlled controlled variables. variables. Energies 10, 515 end of 2017, the period,
(a)
(b) Figure Figure 3. 3. Illustration Illustration of of VPC VPC operation, operation, (a) (a) block block diagram diagram of of VPC; VPC; (b) (b)vectors vectorsevaluation evaluation and and selection. selection.
This method presents several advantages including the elimination of PWM modulators, This method presents several advantages including the elimination of PWM modulators, excellent reference tracking ability, and constant switching frequency. It has been utilized in many excellent reference tracking ability, and constant switching frequency. It has been utilized in many systems, e.g., power control of rectifiers/inverters [22], torque and power control of electrical systems, e.g., power control of rectifiers/inverters [22], torque and power control of electrical machines [23]. machines [23]. 3. Application of Predictive Control in Renewable Energy Systems 3. Application of Predictive Control in Renewable Energy Systems In this Section, the predictive control approaches will be implemented in practical renewable In this Section, the predictive control approaches will be implemented in practical renewable energy systems. Because wind and solar PV are the two most promising and fastest growing energy systems. Because wind and solar PV are the two most promising and fastest growing renewable renewable energy resources in the world [24,25], they will be used here as application examples to energy resources in the world [24,25], they will be used here as application examples to demonstrate demonstrate the effectiveness of the predictive control strategies. The conventional three-phase twothe effectiveness of the predictive control strategies. The conventional three-phase two-level IGBT level IGBT power converters are adopted. power converters are adopted. 3.1. 3.1. MPC MPC for for PV PV Systems Systems Solar being widely exploited all around the world. PV Solar energy energy isisaarenewable renewablepower powersource source being widely exploited all around the world. technology involves converting solar energy directly into electrical power by means of solar cells, PV technology involves converting solar energy directly into electrical power by means of solar which are usually manufactured andand combined intointo modules. For cells, which are usually manufactured combined modules. ForPV PVsystem, system, several several useful useful topologies have been studied and applied [26]. Figure 4 shows a typical configuration of PV system topologies have been studied and applied [26]. Figure 4 shows a typical configuration of PV system where where several several strings strings are are interfaced interfaced with with their their own own DC-DC DC-DC converter converter for for voltage voltage boosting boosting and and then then connected connected to to aa common common DC DC bus. bus. After After that, that, aa common common DC-AC DC-AC inverter inverter is is used used for for grid grid interfacing. interfacing. Usually the MPPT MPPTisisimplemented implemented DC-DC converter, the synchronization grid synchronization and Usually the onon thethe DC-DC converter, whilewhile the grid and power power regulation are achieved by the grid-side inverter. regulation are achieved by the grid-side inverter. Since the MPPT techniques are mature and well developed, in this paper we concentrate on the control of the grid-side common inverter of the PV system (see Figure 4). Although many control schemes have been developed for grid-connected inverters, MPC is seldom mentioned in this application. Actually grid-connected PV systems should be controlled to regulate active and reactive powers flexibly for voltage support and power quality improvement [27]. In this sense, flexible power
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Since the MPPT techniques are mature and well developed, in this paper we concentrate on the control of the grid-side common inverter of the PV system (see Figure 4). Although many control schemes have been developed for grid-connected inverters, MPC is seldom mentioned in this application. Actually grid-connected PV systems should be controlled to regulate active and Energies 2017, 10, 515 5 of 14 Energies 2017, 10, 515 flexibly for voltage support and power quality improvement [27]. In this sense, 5 of 14 reactive powers flexible power regulation a DG unit becomes more and moreHere, significant. Here, a MPC regulation capability for acapability DG unit for becomes more and more significant. a MPC strategy of regulation capability for a inverters DG unit becomes more and more significant. Here, a MPC strategy of strategy of grid-connected for PV system is developed and implemented. For two-level grid-connected inverters for PV system is developed and implemented. For two-level inverters, there grid-connected inverters for PV system is developed and implemented. For two-level inverters, there inverters, there arevoltage eight possible vectors generated the inverter (six active vectors and two are eight possible vectorsvoltage generated by the inverterby (six active vectors and two null vectors), are eight possible voltage vectors generated bysix thesectors, inverter (six active vectors5.and two null vectors), null vectors), and the α-β plane is divided into as shown in Figure and the α-β plane is divided into six sectors, as shown in Figure 5. and the α-β plane is divided into six sectors, as shown in Figure 5.
PV PV Panel Panel
PV PV Panel Panel
PV PV Panel Panel
String String Converter Converter
+ +
+ +
PV PV Panel Panel
PV PV Panel Panel
String String Converter Converter
+ +
+ +
..
Common Common Inverter Inverter
..
+ +
~ ~
L L
R R
Utility Utility
~~
PV PV Panel Panel
Figure 4. A typical configuration of PV system. Figure Figure 4. 4. A A typical typical configuration configuration of of PV PV system. system.
Figure 5. Possible voltage vectors generated by the inverter and sector division. Figure 5. 5. Possible Possible voltage voltage vectors vectors generated generated by by the the inverter inverter and and sector sector division. division. Figure
According to the equivalent circuit in Figure 4, the system mathematical model can be expressed as: According to the equivalent circuit in Figure 4, the system mathematical model can be expressed as: According to the equivalent circuit in Figure 4, dIthe system mathematical model can be Vi Vg IR L dI (1) expressed as: Vi Vg IR L dt (1) dI Vi = Vg + IR + Ldt (1) where Vi and Vg are the inverter output voltage vector anddt grid voltage vector, respectively; I the line where Vi and Vg are the inverter output voltage vector and grid voltage vector, respectively; I the line currentVvector; thethe filter inductance; the filter resistance. instantaneous active andIreactive where inverter outputRvoltage vector and gridThe voltage vector, respectively; the line i and V gL are current vector; L the filter inductance; R the filter resistance. The instantaneous active and reactive powers between the PV andRthe can be The expressed as: current exchanged vector; L the filter inductance; theutility filter grid resistance. instantaneous active and reactive powers exchanged between the PV and the utility grid can be expressed as: powers exchanged between the PV and3 the utility grid 3 can be expressed as: P 3 Re{Vg I **} 3 Vg I Vg I (2) P 3 2 Re{Vg I } 23 Vg I Vg I (2) 2 {Vg I∗ } = 2 Vgα Iα + Vgβ Iβ P = Re (2) 23 32 * Q 3 Im{Vg I *} 3 Vg I Vg I (3) Q 3 2 Im{ Vg ∗I } 23Vg I Vg I (3) 2 2 Q = Im Vg I = Vgβ Iα − Vgα Iβ (3) 2 imaginary components 2 where α and β represent the real and of the space vector expressed in the where α and β represent the real and imaginary components of the space vector expressed in the stationary frame. According to Equations (2) and (3), the active and reactive power derivatives can stationary frame. According to Equations (2) and (3), the active and reactive power derivatives can be calculated as: be calculated as: dI dI dVg dP 3 dVg (4) dP 3 dVg I Vg dI dVg I Vg dI dt 2 dt I Vg dt dt I Vg dt (4) dt 2 dt dt dt dt
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where α and β represent the real and imaginary components of the space vector expressed in the stationary frame. According to Equations (2) and (3), the active and reactive power derivatives can be calculated Energies 2017, as: 10, 515 6 of 14 dVgβ dIβ 3 dVgα dIα dP = Iα + Vgα + I + Vgβ (4) dt 2 dt dt dt β dt dI dI dVg dQ 3 dVg I Vg dV I Vg dI (5) dQdt 32 dVdtgβ dI gα β α dt = Iα + Vgβ − dt Iβ − Vgαdt (5) dt 2 dt dt dt dt Considering sinusoidal and balanced line voltage, one can obtain: Considering sinusoidal and balanced line voltage, one can obtain: dVg (6) dVgα g Vg dt = −ω g · Vgβ (6) dt dVg dVgβ g Vg (7) dt = ω g · Vgα (7) dt Thus, Thus, the the inverter inverter output output active active and and reactive reactive power power derivatives derivatives can can be be obtained obtained by by substituting substituting Equations Equations (1), (1), (6) (6) and and (7) (7) into into Equations Equations (4) (4) and and (5) (5) as: as:
2 dP R 3 * dPdt LRP g Q 2L Re3VgVi Vg ∗ 2 = − P − ωg Q + Re Vg Vi − Vg dt L 2L
dQ R 3 g P Q R Im V3gVi* dQ dt = ω PL − 2Q L + Im Vg Vi∗ g
dt L 2L Therefore, the predicted power at the end of the sampling period Ts can be expressed as: Therefore, the predicted power at the end of the sampling period Ts can be expressed as: P
k +1
2 3 R Pk 1 TRs P g Q 3 Re VgVi* Vg P k ∗ L ω g Q + 2L Re Vg V − Vg 2 = Ts − P − + Pk i
L
k 1
2L
(8) (8) (9) (9)
(10) (10)
R 3 Ts g P Q Im VgVi* Qk R L 2L3 ∗
Q (11) Im Vg Vi + Qk Qk+1 = Ts ω g P − Q + (11) L 2L Now the predictive model has been obtained mathematically with Equations (10) and (11). Now the predictive hasofbeen obtained MPC mathematically Equations (10) and (11). Figure 6 depicts the blockmodel diagram the proposed strategy forwith grid-connected PV systems. Figurethe 6 depicts block diagram the is proposed MPC foreach grid-connected PVon systems. After power isthe predicted, the nextofstep to evaluate thestrategy effects of voltage vector active After the power is predicted, the next step is to evaluate the effects of each voltage vector on active and reactive powers and then select the one producing the least power ripple according to a specific and function. reactive powers andcost then select the one producing the considering least power ripple according to apriority specific cost Here, the function is defined as follows the same weighting cost function. Here, the cost function is defined as follows considering the same weighting priority for for P and Q: P and Q: J ( P * P k 1 )22 (Q * Q k 1 ) 2 2 (12) J = ( P ∗ − P k +1 ) + ( Q ∗ − Q k +1 ) (12)
Once the optimal optimalvoltage voltagevector vector is determined, it will be applied during thesampling next sampling Once the is determined, it will be applied during the next period period to control the inverter. to control the inverter. Vdc=300 V
P* Vi(k)
Vg(k) I (k)
Q*
Cost Function (12) Predictive Model P(k+1) (10), (11) Q(k+1)
Figure Figure 6. 6. Block Blockdiagram diagramof of MPC MPC strategy strategy of of PV PV systems. systems.
3.2. 3.2. VPC VPCfor forWind WindPower PowerGeneration Generation The The DFIG DFIG and and permanent permanent magnet magnet synchronous synchronous generator generator (PMSG) (PMSG) have have dominated dominated the the global global wind generator market. In this paper, the DFIG based wind system is studied. The DFIG has wind generator market. In this paper, the DFIG based wind system is studied. The DFIG has several several advantages advantages including including maximum maximum power power capture capture over over aa wider wider speed speed range range and and decoupled decoupled active active and and reactive power control. It also allows the use of a partially rated converter which reduces the system cost [28]. Figure 7 shows the scheme of a DFIG based wind power generation system. The stator is directly connected to the grid, while a partial-scale power converter controls the rotor frequency and thus the rotor speed. Usually, the controller of the rotor side converter regulates the electromagnetic torque and supplies part of the reactive power to maintain the magnetization of the machine, while
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reactive power control. It also allows the use of a partially rated converter which reduces the system cost [28]. Figure 7 shows the scheme of a DFIG based wind power generation system. The stator is directly connected to the grid, while a partial-scale power converter controls the rotor frequency and Energies 2017, 10, 515 7 of 14 thus the rotor speed. Usually, the controller of the rotor side converter regulates the electromagnetic torque and supplies part of the reactive power to maintain the magnetization of the machine, while the the controller controller of of the thegrid gridside sideconverter converterregulates regulatesthe thepower powerfactor factorand andmaintains maintainsthe theDC DClink linkvoltage. voltage. In side converter converter is is focused. focused. In this this paper, paper, the the control control of of rotor rotor side
Figure Figure7. 7.DFIG DFIGbased basedwind windsystem systemstructure structureand and the the block block diagram diagram of of the the proposed proposed VPC VPC scheme. scheme.
Here, the VPC will be adopted to control the rotor-side converter. As illustrated in Section 2, the Here, the VPC will be adopted to control the rotor-side converter. As illustrated in Section 2, objective of the VPC is to evaluate the effects of the possible vectors on the control variables, and then the objective of the VPC is to evaluate the effects of the possible vectors on the control variables, arrange an optimal set of concatenated voltage vectors, in such a way that the controlled objective and then arrange an optimal set of concatenated voltage vectors, in such a way that the controlled converges toward the reference. Therefore, it is necessary to find out the effects of vectors on the wind objective converges toward the reference. Therefore, it is necessary to find out the effects of vectors on power generator system. The mathematical equations for a DFIG are now well known but for the wind power generator system. The mathematical equations for a DFIG are now well known but completeness they can be expressed in the rotor frame using complex vectors as: for completeness they can be expressed in the rotor frame using complex vectors as: Voltage equations: Voltage equations: ddψ ss VV jωrr ψ (13) +j Rss Iss + (13) s s= R s s dt dt
Flux equations: Flux equations:
dψr Vr = Rr Ir +d r Vr Rr I r dt dt
(14) (14)
ψs = Ls Is + Lm Ir
(15)
LsmIIs s+LmLIr Ir r ψr s = L
(15) (16)
r Lm I s Lr I r
Power equations:
P=
Power equations:
3 ω g λLm Im{ψr∗ ψs } 2
(16) (17)
3 ∗ * { ψ ψs }] ω g λ[3Lr |ψs |2 − Lm Re (18) (17) 2 P g Lm Im{ r s } r 2 The derivatives of the stator output active and reactive powers can be expressed as: 3 2 Q g [ Lr s Lm Re{ r* s }] (18) 3 2 dP = ω g λLm [Im{Vi∗ ψs } + ωs Re{ψs ψr∗ }] (19) dt 2 The derivatives of the stator output active and reactive powers can be expressed as: dQ 3 dP = − 3 ω g λLm [Re{V* i∗ ψs } − ωs Im{ψ*r∗ ψs }] (20) 2 g Lm [Im{Vi s } s Re{ s r }] dt (19) dt 2 According to Equations (19) and (20), the power derivatives against rotor flux position in steady dQ can be 3 state for a DFIG wind generator as * graphically* depicted in Figure 8a. Now let us obtained, g Lm [Re{Vi s } s Im{ r s }] (20) dt 2 Q=
According to Equations (19) and (20), the power derivatives against rotor flux position in steady state for a DFIG wind generator can be obtained, as graphically depicted in Figure 8a. Now let us perform an analysis of the power derivatives. For instance, assuming that the rotor flux is located at the sector S3 while the active and reactive powers are both greater than the referenced values:
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perform an analysis of the power derivatives. For instance, assuming that the rotor flux is located at the sector S3 while the active and reactive powers are both greater than the referenced values: V 4 produces negative active power derivative (or “slope”) and negative reactive power slope; V 5 produces negative Energies 2017, 10, 515 8 of 14 active power slope and positive reactive power slope; while the null vectors (V 0 and V 7 ) generates very small slopes. this analysis, if the vector –V 5vector –V 0 is sequence applied, the active (V0 and V7)power generates veryBased smallon power slopes. Based on thissequence analysis, Vif4the V4–V 5–V0 and reactive power can be well controlled, which is well illustrated in Figure 8b. In this way, the first is applied, the active and reactive power can be well controlled, which is well illustrated in Figure 8b. two active are used to correct while the presence the the nullpresence vector isof very In this way,vectors the first two active vectorsthe arepower used toerrors, correct the power errors, of while the useful at steady stateuseful becauseatitsteady produces relatively power variation, in the reduction null vector is very state becausesmall it produces relativelyresulting small power variation, of power ripples. resulting in the reduction of power ripples. 7
d P / dt
2
x 10
V5
V6
V1
V2
V3
V5
V6
V1
V2
V4
1 V0,7 0 -1
7
d Q / dt
2
x 10
V4
1
V3
V0,7
0 -1 S1
S2
S3
(a)
S4
S5
S6
(b)
Figure 8. 8. Effects Effects of of voltage voltage vectors vectors on on DFIG DFIG stator stator output output powers, powers, (a) (a) active active and and reactive reactive power power Figure derivatives against rotor flux position; (b) power waveforms of three-vector-based strategy. derivatives against rotor flux position; (b) power waveforms of three-vector-based strategy.
The vector selection scheme of VPC is summarized in Table 1. The vector sequence selection is The vector selection scheme of VPC is summarized in Table 1. The vector sequence selection is related to the sign of the active power error ∆P because reactive power will be also controlled related to the sign of the active power error ∆P because reactive power will be also controlled regardless regardless of ∆Q sign, due to the fact that the first two active vectors produce opposite reactive power of ∆Q sign, due to the fact that the first two active vectors produce opposite reactive power slopes, slopes, as illustrated in Figure 8a. Notice that the null vector should be chosen between V0 and V7 as illustrated in Figure 8a. Notice that the null vector should be chosen between V 0 and V 7 according according to the principle of switching frequency reduction. After the three vectors are selected, the to the principle of switching frequency reduction. After the three vectors are selected, the next step is next step is to calculate the vector durations of t1 and t2, according to a specified criteria, as illustrated to calculate the vector durations of t1 and t2 , according to a specified criteria, as illustrated in Section 2. in Section 2. Here, t1 and t2 are computed by making the values of P and Q equal to their references Here, t1 and t2 are computed by making the values of P and Q equal to their references at the end of at the end of each sampling period. The overall control strategy of VPC is illustrated in Figure 7. First, each sampling period. The overall control strategy of VPC is illustrated in Figure 7. First, the wind the wind generator status such as grid voltage, stator current, and rotor speed are measured. Based generator status such as grid voltage, stator current, and rotor speed are measured. Based on these, on these, the actual active and reactive powers will be calculated. Next, voltage vector sequences will the actual active and reactive powers will be calculated. Next, voltage vector sequences will be chosen be chosen from Table 1 according to the actual values of powers and the rotor flux position. Once the from Table 1 according to the actual values of powers and the rotor flux position. Once the vector vector sequences are determined, the optimum duration of each voltage vector will be computed sequences are determined, the optimum duration of each voltage vector will be computed with the with the purpose of forcing the actual powers to track the references. Finally, the gate driving signals purpose of forcing the actual powers to track the references. Finally, the gate driving signals will be will be produced in PWM modulator. produced in PWM modulator. Table 1. Vector selection strategy. Table 1. Vector selection strategy. ∆P (P*–P) Vector Sequence (k is the Sector Number) >0 (P*–P) k−1is –Vthe k-2–V 0,7 ∆P Vector SequenceV(k Sector Number) 0 V k −1 –V k −2 –V 0,7
