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Direct Active and Reactive Power Regulation of Grid-Connected DC/AC Converters Using Sliding Mode Control Approach Jiabing Hu, Member, IEEE, Lei Shang, Student Member, IEEE, Yikang He, Senior Member, IEEE, and Z. Q. Zhu, Fellow, IEEE
Abstract—This paper proposes a new direct active and reactive power control (DPC) for the three-phase grid connected dc/ac converters. The proposed DPC strategy employs a nonlinear sliding mode control (SMC) scheme to directly calculate the required converter’s control voltage so as to eliminate the instantaneous errors of active and reactive powers without involving any rotating coordinate transformations. Meanwhile, there are no extra current control loops involved, which simplifies the system design and enhances the transient performance. Constant converter switching frequency is achieved by using space vector modulation, which eases the design of the ac harmonic filter. Simulation and experimental results are provided and compared with those of the classic voltage-oriented vector control (VC) and conventional lookup table (LUT) DPC strategies. The proposed SMC-DPC is capable of providing enhanced transient performance similar to that of the LUT-DPC, and keeps the steady-state harmonic spectra at the same level as those of the VC scheme. The robustness of the proposed DPC to line inductance variations is also inspected during active and reactive power changes. Index Terms—DC/AC converters, direct power control (DPC), sliding mode control (SMC).
S Ig Lg , Rg Pg , Qg Ug, V g ω1
NOMENCLATURE Sliding surface. Converter current vector. Line inductance and resistance. Output active, reactive powers. Grid, converter voltage vectors. Angular frequency of grid voltage.
Superscripts ∧ Conjugate complex.
Manuscript received March 14, 2010; revised June 2, 2010; accepted June 28, 2010. Date of current version December 27, 2010. This work was supported in part by the Natural Science Foundation of China (Project No. 50907057). Recommended for publication by Associate Editor V. Staudt. J. Hu was with the College of Electrical Engineering, Zhejiang University, Hangzhou 310027, China. He is now with the Sheffield Siemens Wind Power Research Centre and the Department of Electronic and Electrical Engineering, The University of Sheffield, Sheffield S1 3JD, U.K. (e-mail:
[email protected]). L. Shang and Y. He are with the College of Electrical Engineering, Zhejiang University, Hangzhou 310027, China (e-mail:
[email protected];
[email protected]). Z. Q. Zhu is with the Department of Electronic and Electrical Engineering, The University of Sheffield, Sheffield S1 3JD, U.K. (e-mail:
[email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPEL.2010.2057518
∗ T
Reference value. Transposition. I. INTRODUCTION
ECAUSE of the rapid development of smart grid, power conditioning, and transmission equipments [1]–[3], including flexible ac transmission systems (FACTS), HVDC systems, and active power filter, and the extended penetrations of distributed and renewable power generation systems [4]–[6], such as wind, photovoltaic, fuel cell, there has been a tremendous increase on the application of grid-connected voltagesourced dc/ac converters. The converters feature several advantages [7], including sinusoidal line current with controllable power factor, high-quality dc voltage with a small filter capacitor, and the capability of independent control of active and reactive powers with bidirectional power flow. Classic control of grid-connected dc/ac converters is usually based on gridvoltage [8], [9] or virtual-flux [10] oriented vector control (VC) scheme. The scheme decomposes the ac current into active and reactive power components in the synchronously rotating reference frame. Decoupled control of instantaneous active and reactive powers is then achieved by regulating the decomposed converter currents using proportional integral (PI) controllers. One main drawback for this control method is that the performance highly relies on the completeness of current decoupling, the accurate tuning of PI parameters, and the connected grid voltage conditions. Based on the principles of direct torque control (DTC) [11], [12] strategy for ac machines, an alternative control approach, namely, direct power control (DPC) was developed for the control of grid-connected voltage-sourced converters [13]–[15]. Similar to the traditional DTC, lookup table (LUT) DPC, as the name indicates, selects the proper converter switching signals directly from an optimal switching table on the basis of the instantaneous errors of active and reactive powers, and the angular position of converter terminal voltage [13] or the virtual flux vector that is the integration of converter terminal voltage measured with voltage transducers [14] or estimated based on the dc-link and the converter switch states [15]. The main disadvantage of LUT-DPC is the introduced variable switching frequency, which generates an undesired broadband harmonic spectrum range and makes it pretty hard to design a line filter. In [16], the authors presented a DPC scheme for an active frontend rectifier using model-based predictive control. With future values of voltage and current predicted from a discrete model,
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the active and reactive powers are directly controlled by selecting optimal switching state that is obtained via minimizing a cost function of the desired behavior of the converter. The main advantages of this method are that there is no need of linear current controller, coordinate transformations, or modulators. Despite that the current is sinusoidal with low harmonic distortions; its spectrum is distributed over a range of frequencies, which is considered as a disadvantage of the control strategy, and improvement of this aspect is a challenge for the future research work [16]. Various efforts [17]–[20] have been made for both DTC and DPC strategies to achieve constant switching frequency. In [17], the output voltage vector was selected using the conventional DTC switching table but the duration time of each voltage vector was determined by the torque-ripple minimum strategy. Whereas in [18] the converter control voltage was directly calculated based on the torque and flux errors within each sampling period and the space vector modulation (SVM) technique was used afterward. Similarly, for the grid-connected converters, the required control voltage was obtained based on the instantaneous errors of active and reactive powers [19] or from the outputs of active and reactive power PI controllers [20]. Meanwhile, the SVM module was also employed, and the control strategy in [19] was implemented in the synchronously rotating reference frame and PI controllers were necessitated in [20] as well. DPC/DTC strategies based on the predictive control approach were introduced for grid-connected dc/ac converters [21] and doubly fed induction machines [22], [23], respectively. The methods require complicated online calculation and are quite sensitive to system parameters’ variations [24]. Sliding mode control (SMC), based on the variable structure control strategy, is an effective and high-frequency switching control for nonlinear systems with uncertainties [25], [26]. The design principles of SMC and its applications to electrical drive systems were initially proposed in [25]. It features simple implementation, disturbance rejection, strong robustness, and fast responses, but the controlled state may exhibit undesired chattering. Thus, an SMC-based DTC drive for induction machine was proposed in [27] with stator flux oriented and regulated. It is named linear and variable structure control (LVSC) due to employing a switching component and a linear one. Owing to the robustness with respect to external disturbance and unmodeled dynamics of wind turbines and generators, a few second-order SMC approaches have been introduced for renewable energy applications in terms of aerodynamic control [28], [29] and power converters control [30]–[32]. For the rotor side converter of doubly fed induction generator (DFIG) driven by marine current turbine [30] and wind turbine [31], respectively, second-order SMC schemes were proposed to regulate the dand q-axis rotor currents or d-axis rotor current and electromagnetic torque with stator-flux oriented in the synchronous reference frame. Apparently, similar to VC [8]–[10] and predictive DPC [19] schemes, these converter’s control strategies [30], [31] based on SMC approach, also require synchronous coordinate transformation associated with the angular information of stator flux. Besides, identical to classic VC scheme, additional outer control loop for active/reactive powers is required to generate
(1)
Fig. 1. Equivalent circuit of the grid-connected dc/ac converter in the stationary frame.
the reference values of d- and q-axis rotor currents as well. As a consequence, by employing LVSC method in [27], a slidingmode DPC (SM-DPC) solution for wind-turbine DFIGs was presented in [32] to regulate the stator active and reactive powers directly. However, the rotor voltage reference was obtained in the synchronous reference frame and then transformed into the rotor reference frame to generate switching states with SVM. This process still requires synchronous coordinate transformation and angular information of stator flux. Moreover, for threephase rectifiers, a discrete-time SM DPC scheme implemented in a virtual-flux-oriented synchronous reference frame was proposed in [33]. Despite featuring better dynamic response, lower sensitivity to grid voltage unbalances and distortions than the classic grid-voltage-oriented VC scheme, this SM-DPC necessitates the angular information of virtual flux and synchronous coordinate transformations as well. The main contribution of this paper is to combine the DPC strategy, SM approach, and SVM modulation technique, so as to directly regulate the instantaneous active and reactive powers of grid-connected dc/ac converters without any current control loops and synchronous coordinate transformations involved. The required converter control voltage can be simply obtained in the stationary reference frame, and SVM technique is then employed to achieve constant switching frequency. As a result, enhanced transient performance similar to the conventional LUT-DPC is obtained and steady-state current harmonic spectra are kept at the same level as the classic VC strategy due to the use of SVM module. The rest part of this paper is organized as follows. Section II gives the instantaneous active and reactive power flows of a gridconnected voltage-sourced dc/ac converter. With conventional LUT-DPC briefly described, the SMC-based DPC strategy is proposed, designed, and analyzed in Section III. Sections IV and V present the simulation and experimental results, respectively, on a 3-kVA prototype dc/ac converter system to demonstrate the performance of the proposed SMC-DPC strategy. Finally, the conclusions are drawn in Section VI. II. MODELING OF GRID-CONNECTED DC/AC CONVERTERS Considering the supply network and the output from a threephase voltage-sourced dc/ac converter as ideal voltage sources, Fig. 1 shows the simplified equivalent circuit of the gridconnected dc/ac converter in the stationary reference frame. According to Fig. 1, the relationship between the supply, converter voltages, and line currents in the stationary reference frame is given as U g α β = I g α β Rg + Lg
dI g α β + V gαβ . dt
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In the stationary reference frame and for a balanced three-phase system, the instantaneous active and reactive power outputs, seen from the network side, can be defined as [34]–[36] 3 Pg + jQg = − U g α β × Iˆ g α β 2
(2)
and 3 Pg = − (ug α ig α + ug β ig β ) 2 (3) 3 Qg = − (ug β ig α − ug α ig β ) . 2 Differentiating (3) results in the instantaneous active and reactive power variations as 3 dig α dug α dig β dug β dPg =− + ig α + ug β + ig β ug α dt 2 dt dt dt dt dQg 3 dig α dug β dig β dug α =− + ig α − ug α − ig β ug β dt 2 dt dt dt dt (4) As represented in (4), to generate active and reactive power variation, the network voltage variations are required. With a nondistorted network considered, namely, ug α = Ug sin (ω1 t) ug β = −Ug cos (ω1 t)
(5)
the instantaneous grid voltage variation can be obtained as dug α = ω1 Ug cos (ω1 t) = −ω1 ug β dt (6) dug β = ω1 Ug sin (ω1 t) = ω1 ug α . dt Based on (1), the instantaneous current variations can be expressed with respective α, β components as 1 dig α = (ug α − ig α Rg − vg α ) dt Lg dig β 1 = (ug β − ig β Rg − vg β ) . dt Lg
(7)
Substituting (6) and (7) into (4) yields dPg 3 2 ug α + u2g β − (ug α vg α + ug β vg β ) =− dt 2Lg Rg − Pg − ω1 Qg Lg 3 dQg Rg =− [− (ug β vg α − ug α vg β )] − Qg + ω1 Pg dt 2Lg Lg
(8) which is the key expression for designing the proposed direct power control scheme in this paper. III. PROPOSED DIRECT POWER CONTROL USING SMC APPROACH
A. Conventional Lookup Table DPC According to the principle of conventional DPC [13]–[15] for a three-phase grid-connected dc/ac converter, an appropriate voltage vector is selected at each sampling instant by certain
Fig. 2. Schematic diagram of the conventional LUT-DPC for a grid-connected dc/ac converter.
switching rule to restrict the instantaneous active and reactive power variations within their required hysteresis bands, respectively, as illustrated in Fig. 2. The active and reactive power controllers can be two- or three-level hysteresis comparators, which, based on the active and reactive power errors, generate discrete signals as the inputs to the switching table. With the error signs from the hysteresis controllers and by referring to the sector where the grid voltage vector [13] or virtual flux vector [14], [15] is located, the converter’s switching signals are directly generated according to certain switching rule from a predefined lookup table. Therefore, the original DPC algorithm is accomplished in the stationary reference frame without any pulse width modulation module involved, which is possible to achieve the maximum dynamic performance available. Moreover, it requires no internal current control loop and coordinate transformations, with the coupling effects between transformed variables avoided. However, it has been highlighted that the conventional LUTDPC for the grid-connected dc/ac converters is a hysteresis bang–bang control by applying single full voltage vector within each sampling period and, hence, results in high chattering in the instantaneous active and reactive powers. Even worse, its main disadvantage is the nonfixed switching frequency, which is usually not bounded and depends mainly on the sampling time, the lookup table structure, the load parameters and the operational state of the system. As a result, the LUT-DPC strategy generates a dispersed harmonic spectrum, making it quite difficult to design a line filter for grid-connected converters, which, sometimes, could lead to possible grid resonance and worsen the operation stability of power system. Hence, LUT-DPC is hardly suitable for grid-connected operation of dc/ac converters. A new DPC using SMC approach and SVM scheme is proposed and designed for grid-connected dc/ac converters in the following section. In this way, high transient dynamics and constant switching frequency are both expected to be obtained. B. Proposed DPC Based on SMC The SMC strategy with variable control structure is based on the design of discontinuous control signal that drives the system operation states toward special manifolds in the state space [25], [26]. These manifolds are chosen in such a way that the control system will have the desired behavior as the states
HU et al.: DIRECT ACTIVE AND REACTIVE POWER REGULATION OF GRID-CONNECTED DC/AC CONVERTERS USING SMC APPROACH
converge to them. In this paper, based on the conventional LUTDPC concept, an SMC scheme for regulating the instantaneous active and reactive powers of grid-connected dc/ac converters is exploited. 1) Sliding Surface: The control objectives for dc/ac converters are to track or slide along the predefined active and reactive power trajectories. For this purpose, the sliding surface is set as S Q ]T .
S = [ SP
(9)
In order to maintain the enhanced transient response and minimize the steady-state error, the switching surfaces can be in the integral forms [37], [38], alternatively they can also be designed via back-stepping and nonlinear damping techniques [39] t SP = eP (t) + KP eP (τ )dτ − eP (0) 0 (10) t SQ = eQ (t) + KQ eQ (τ )dτ − eQ (0) 0
where eP (t) = Pg∗ − Pg and eQ (t) = Q∗g − Qg are the respective errors between the references and the actual values of instantaneous active and reactive powers. KP and KQ are the positive control gains. The manifolds SP = 0 and SQ = 0 represent the precise tracking of converter’s active and reactive powers. When the system states reach the sliding manifold and slide along the surface, we have SP = SQ =
dSQ dSP = = 0. dt dt
(11)
According to (10) and (11), the derivatives of SP and SQ are equal to zero, which gives deP (t) = −KP eP (t) dt deQ (t) = −KQ eQ (t) . dt
(12)
The aforementioned equations ensure the power errors converge to zero, where KP and KQ are positive constants and chosen for meeting the required system transients. Since (10) equals null at the beginning, the active and reactive power systems will converge asymptotically to the origin with the time constants of 1/KP and 1/KQ , respectively. Then, the design task is aimed at accomplishing SM in the manifolds SP = 0 and SQ = 0 with discontinuous converter voltage space vectors. 2) SMC Law: In the SMC design, as the name indicates, the task is to force the system state trajectory to the interaction of the switching surfaces aforementioned. In this paper, an SMC scheme is suggested to generate the converter output voltage reference as the input to SVM module. The motion projections of the system (3) and (8) on S subspace are derived by differentiating S in (10), i.e., deP (t) d dSP = + KP eP (t) = − Pg + KP Pg∗ − Pg dt dt dt deQ (t) dSQ d = + KQ eQ (t) = − Qg + KQ Q∗g − Qg . dt dt dt (13)
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Substituting (8) into (13) leads to dS = F + DV g dt
(14a)
where F = [ FP
FQ ]T
V g = [ vg α
vg β ]T
FP =
Rg 3 2 ug α + u2g β + Pg + ω1 Qg + KP Pg∗ − Pg 2Lg Lg
FQ =
Rg Qg − ω1 Pg + KQ Q∗g − Qg Lg
and 3 D=− 2Lg
ug α
ug β
ug β
−ug α
(14b)
.
In the SMC, a Lyapunov approach is usually used for deriving conditions on the control law that will drive the state orbit to the equilibrium manifold. The quadratic Lyapunov function is selected as W = 0.5 S T S ≥ 0.
(15)
The time derivative of W on the state trajectories of (14) is then given by dW 1 dS T dS T dS = +S = S T (F + DV g ). S = ST dt 2 dt dt dt (16) The switch control law must be properly chosen so that the time derivative of W is definitely negative with S = 0. Therefore, the following control law is selected
0 FP KP 1 sgn(SP ) V g = −D −1 (17) + 0 KQ 1 sgn(SQ ) FQ where KP 1 and KQ 1 are the positive control gains, sgn(SP ) and sgn(SQ ) are the respective switch functions for active and reactive powers. 3) Proof of the Stability: For the stability against sliding surfaces, it is sufficient to have dW/dt < 0. By setting appropriate switch functions, stability can be achieved provided the following condition is satisfied, viz., if SP sgn(SP ) > 0 and SQ sgn(SQ ) > 0, then
0 KP 1 sgn(SP ) dW T dS T =S = −S . (18) dt dt 0 KQ 1 sgn(SQ ) The time derivative of Lyapunov function dW /dt is then definitely negative so that the control system becomes asymptotically stable. 4) Proof of the Robustness: In the practical operation, the sliding surface S will be affected by the parameter variations, AD sample errors and measurement noises, etc. Thus, (14a) should be rearranged as dS = F + DV g + H dt where H = [ HP
HQ ]T represents system disturbances.
(19)
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TABLE I PARAMETERS OF THE TESTED DC/AC CONVERTER SYSTEM
Fig. 3. Schematic diagram of the proposed SMC-based DPC for a gridconnected dc/ac converter.
In this way, (18) can be rewritten as
HP KP 1 dW T dS T =S =S − dt dt 0 HQ
TABLE II CONTROL PARAMETERS OF SMC REGULATOR
0 KQ 1
. sgn(SQ ) sgn(SP )
(20) It is worth noting that if the positive control gains fulfill the following condition, viz.,KP 1 > |HP | and KQ 1 > |HQ |, the time derivative of Lyapunov function dW /dt is still definitely negative. Therefore, the SMC obviously features strong robustness. 5) Remedy of Power Chattering Problem: The SMC scheme developed earlier guarantees the fast tracking of instantaneous active and reactive powers of grid-connected dc/ac converters. However, fast switching may generate unexpected chattering, which may excite unmodeled high-frequency system transients and even result in unforeseen instability. To eliminate this problem, the discontinuous part of the controller is smoothed out by introducing a boundary layer around the sliding surface. As a result, a continuous function around the sliding surface neighborhood is obtained as ⎧ 1, if Sj > λj ⎪ ⎨ Sj (21) sgn(Sj ) = λ , if |Sj | ≤ λj ⎪ ⎩ j −1, if Sj < −λj where λj > 0 is the width of the boundary layer and j represents P and Q, respectively. According to (17) and (21), the converter output voltage reference is obtained in the stationary reference frame and, then, can be directly transferred to the SVM module [40] for generating the required switching voltage vectors and their respective duration times. 6) System Implementation: Fig. 3 shows the schematic diagram of the proposed DPC strategy using SMC approach. The outer loop in the figure actually should have contained a dc-link voltage PI controller, which produces active power reference for the active power controller, but is not included here. As shown, the developed SMC-DPC strategy is capable of directly generating converter voltage reference in the stationary reference frame according to the instantaneous active and reactive power errors. Since the maximum output voltage from a dc/ac converter is limited by its dc-link voltage, the large variations of active and/or reactive power references during transient con-
ditions could lead to large power errors within one sampling period. Accordingly, the required converter’s voltage V g , calculated from (17), might exceed the voltage capability of the converter. Hence, V g must be limited properly to improve the transient response of the converter. Besides, it is worth pointing out that the proposed control strategy does not require any rotating coordinate transformations as well as the angular information of grid voltage. IV. SIMULATION RESULTS In order to verify the performance of the proposed DPC strategy based on the SMC approach, comparative simulation studies, involving classic voltage-oriented VC [9], conventional LUT-DPC [13], and SMC-DPC schemes, were carried out by using MATLAB/Simulink. Discrete models were used with a simulation step time of 1 μs. The electric parameters of the tested system are listed in Table I. A dc voltage source of 250 V was connected to the dc-link, making it possible to apply various output active and reactive power steps. In the simulations, a sampling frequency of 10 kHz was used for the classic VC and the proposed SMC-DPC, which corresponds to 2.5-kHz switching frequency due to that an asymmetric SVM technique was used. While for the LUT-DPC, the sampling frequency was at 40 kHz and its active/reactive power hysteresis band was 0.02 p.u. The PI parameters of the VC’s current controller were 5 and 0.005 s, respectively, while for the proposed SMC-DPC approach, the control parameters are listed in Table II. Dead time of 2 μs was employed for all of the three different control strategies. Fig. 4(A)–(C) compares the system response during various active and reactive power steps for the conventional LUT-DPC, proposed SMC-DPC, and classic VC, respectively. As shown in
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Fig. 4. Simulation results using the three different control strategies during various active and reactive power steps. (a) Active power output (W). (b) Reactive power output (Var). (c) Three-phase ac currents (A). (A) conventional LUT-DPC. (B) proposed SMC-DPC. (C) classic VC.
Fig. 4, the active power is stepped from 0 to 2 kW (export of active power from the converter to grid) at 0.03 s and then backed to 0 at 0.07 s, while the reactive power is stepped from −1 kVar (inductive) to 1 kVar (capacitive) at 0.03 s and backed to −1 kVar at 0.07 s. The transient responses of both active and reactive powers for the two DPC strategies are within a few milliseconds, whereas the dynamic response of the VC is largely dependent on the PI parameters of current controller. It is clearly seen that the LUT-DPC causes larger power ripples and seriously distorted ac current. To further compare the performance of the three control methods, Fig. 5 gives the current harmonic spectra with Pg = 2 kW and Qg = 1 kVar for each control strategy. Again,
conventional LUT-DPC results in more serious current harmonic distortions than those in the SMC-DPC and classic VC. Besides, the LUT-DPC generates broadband harmonic spectra, whereas SMC-DPC produces similar deterministic harmonics as the VC with dominant harmonics around the switching frequency of 2.5 kHz and multiples thereof. Thus, it can be concluded that the proposed SMC-based DPC is capable of providing enhanced transient performance similar to the LUT-DPC and, meanwhile, keeping the steady-state harmonic spectra at the same level as those of the classic VC. In order to confirm the effectiveness of the remedy for power chattering problems, Fig. 6 shows the active and reactive power
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Fig. 6.
Active and reactive power errors and their associated switch functions.
Fig. 7.
Configuration of the tested rig.
Fig. 5. Measured current harmonic spectra by simulation: P g = 2 kW, Q g = 1 kVar. (a) Conventional LUT-DPC, sampling frequency = 40 kHz, THD = 9.65%. (b) Proposed SMC–DPC: switching frequency = 2.5 kHz, THD = 5.89%. (c) Classic VC: switching frequency = 2.5 kHz, THD = 5.78%.
errors and their associated continuous switch functions. Taking the shadow in Fig. 6 as an example, the active power error during the sampling period is within the width of the boundary layer, viz., −100 < SP < 100, thus the active power switch function sgn(SP ) equals to SP /λP . While so far as the reactive power is concerned, the error is beyond the width, which makes SQ < −200 and, as a result, the reactive power switch function sgn(SQ ) is set at −1. The switch functions during other sampling periods are similar, which is not explained thoroughly here due to space limitation. V. EXPERIMENTAL VALIDATION Experimental tests on a grid-connected dc/ac converter, identical to that used for simulation, were performed, and Fig. 7 schematically shows the tested rig. The dc/ac converter was controlled by a TI’s TMS320F2812 DSP. During experiments, a three-phase variac was used to decrease the three-phase source voltage from 380 to 133 V, and a dc supply rated at 3 kW (300 V/10 A) was connected to the converter’s dc-link to implement various active and reactive power step changes. The preexisting fifth and seventh harmonics in the lab’s three-phase
source voltage were detected being around 0.76% and 0.65%, respectively. The voltage unbalance ratio of the three-phase source was about 1% throughout the entire tests. A. Comparative Studies For the same conditions as those in the simulation results, as shown in Fig. 4, Fig. 8(a)–(c) compares the measured results of the three different control methods. As can be seen from the waveforms in Figs. 4 and 8, the experimental results are in well accordance with the simulated ones. Again, pretty good transient response during active and reactive power steps are achieved for both DPC strategies with little power or ac current overshoot. Whereas the response of the VC method is largely dependent on the current PI controller’s parameters and has obviously longer settling time. It can be measured from Fig. 8(a) and (b) that the response times of active and reactive power steps are around only 1 and 1.5 ms for the LUT-DPC and SMC-DPC, respectively. Comparing Fig. 8(a) with (b), it is also clearly
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Fig. 8. Experimental results using three different control strategies during various active and reactive power steps: (1) Active power output (1 kW/div). (2) Reactive power output (1 kVar/div). (3)–(5) Three-phase ac currents (10 A/div). (A) conventional LUT-DPC. (B) proposed SMC-DPC. (C) classic VC.
seen that the conventional LUT-DPC results in significant current harmonic distortions and reactive power ripples, while the proposed SMC-DPC has achieved much improved performance with well-smoothed active/reactive powers and ac currents. To further illustrate and validate such improvements, Fig. 9 shows the measured results with different active and reactive power combinations, viz., Pg = 2 kW and Qg = 1 kVar
(capacitive), and the associated ac current harmonic spectra for the three different methods. Once again, the improvements are evident by the proposed SMC-DPC method. Besides, as shown in Fig. 9a(6), b(6), and c(6), the measured ac current harmonic spectra and the total harmonic distortions (THDs) with the three different control strategies are all in good agreement with those obtained by simulations, as shown in Fig. 5. The slight increases
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Fig. 9. Experimental results and measured ac current harmonic spectra with P g = 2 kW and Q g = 1 kVar: (1) Active power (1 kW/div). (2) Reactive power (1 kVar/div). (3)–(5) Three-phase currents (10 A/div). (6) Measured ac current harmonic spectra. (A) Conventional LUT-DPC, sampling frequency = 40 kHz, THD = 10.39%. (B) Proposed SMC-DPC: switching frequency = 2.5 kHz, THD = 6.05%. (C) Classic VC: switching frequency = 2.5 kHz, THD = 5.87%.
in the measured THDs by experiments are reasonable due to the preexisting fifth and seventh harmonics as well as unbalance in the lab’s three-phase source voltage. B. Tracking Behavior In the applications of renewable power generation systems, i.e., wind and photovoltaic generations, maximum power point tracking is usually required. Thus, the required active power
references for the grid-connected dc/ac converters may also be variable. Under such circumstance, the adopted control strategy should guarantee that the actual values should possess the ability of tracking their references as closely as possible. Consequently, it is important to inspect SMC-DPC’s tracking capability with high-control bandwidth. Fig. 10(A) and (B) shows the measured results, where a sinusoidal varying reference with amplitude of 0.1 p.u. (0.2 kW) and respective two different
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Fig. 10. Tracking behavior of the proposed SMC DPC with reactive power being 0 Var and active power sinusoidally varying and step changes. (1) Reactive power (1 kVar/div). (2) Active power reference (1 kW/div). (3) Active power response (1 kW/div). (4) Instantaneous errors of active power (1 kW/div). (5)–(7) Three-phase currents (10 A/div). (A) With 100 Hz pulsations in the active power. (B) With 10 Hz pulsations in the active power.
frequencies of 100 and 10 Hz, is imposed to the average active power reference. The average active power demands were step changed from 0 to 2 kW and, backward, with reactive power being null. As can be seen, the proposed SMC-DPC strategy is capable of providing accurate tracking for active and reactive powers even with time-varying demanded references and, meanwhile, keeping excellent transient responses and good decoupling behavior for instantaneous active and reactive powers.
C. Robustness to the Variations of Line Inductance Further tests for the impact of line inductance variations on both steady-state and transient performance with the SMC-DPC strategy were carried out. With the same conditions as for Fig. 4(B), Fig. 11 compares the tested results with inductance value used in the control system varied by ±25%, respectively. During tests, the reactive power is kept at 0 Var with active power step changes, while the active power is
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Fig. 11. System responses using SMC DPC strategy with line inductance errors. (1) Active power output (1 kW/div). (2) Active power output (1 kVar/div). (3)–(5) Three-phase ac currents (10 A/div). (A) With −25%L g error. (B) With −25%L g error.
fixed at 0 W with reactive power step changes. By comparing Fig. 11 with Fig. 4(B), where no inductance errors were applied, it can be concluded that such line inductance’s errors have nearly little influence on system transient and steady-state behavior. The responses are quite identical for the three different line inductance values. Consequently, the robustness of proposed SMC-DPC to line inductance variations is convincingly verified. VI. CONCLUSION This paper proposes a new direct power control for gridconnected dc/ac converters based on SMC approach. System responses with the proposed SMC-DPC method are validated via both simulations and experiments, and compared with those of conventional LUT-DPC and classic VC strategies. The pretty well features of the proposed SMC-DPC strategy are verified. 1) No rotating coordinate transformation and angular information of grid voltage or virtual flux are required. 2) Enhanced transient performance similar to the conventional LUT-DPC is obtained.
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HU et al.: DIRECT ACTIVE AND REACTIVE POWER REGULATION OF GRID-CONNECTED DC/AC CONVERTERS USING SMC APPROACH
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Jiabing Hu (S’05–M’10) received the B.Sc. and Ph.D. degrees from the College of Electrical Engineering, Zhejiang University, Hangzhou, China, in 2004 and 2009, respectively. He is currently a Research Associate at Sheffield Siemens Wind Power Research Centre and the Department of Electronic and Electrical Engineering, The University of Sheffield, Sheffield, U.K. From 2007 to 2008, he was a Visiting Scholar at the Department of Electronic and Electrical Engineering, University of Strathclyde, Glasgow, U.K. His current research interests include motor drives and the application of power electronics in renewable energy conversion, especially the control and operation of doubly fed induction generator and permanent magnet synchronous generator for wind power generation.
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Lei Shang (S’10) was born in Haicheng, China. He received the B.Sc. degree in 2008 from the College of Automation, Nanjing University of Posts and Telecommunications, Nanjing, China. He is currently working toward the Master’s degree in the College of Electrical Engineering, Zhejiang University, Hangzhou, China. His current research interests include digital control and application of power converters in renewable energy conversion, especially the control and operation of doubly fed induction generator for wind power generation using direct power control.
Yikang He (SM’90) was born in Changsha, China. He graduated from the Department of Electrical Engineering, Tsinghua University, Beijing, China, in 1964. Since graduation, he has been with the College of Electrical Engineering, Zhejiang University, Hangzhou, China, as a Teacher, where he is currently a Professor. His current research interests include electric machinery, motor control, power electronics and renewable energy conversion.
Z. Q. Zhu (M’90–SM’00–F’09) received the B.Eng. and M.Sc. degrees in electrical and electronic engineering from Zhejiang University, Hangzhou, China, in 1982 and 1984, respectively, and the Ph.D. degree in electronic and electrical engineering from The University of Sheffield, Sheffield, U.K., in 1991. From 1984 to 1988, he was a Lecturer in the Department of Electrical Engineering, Zhejiang. University. Since 1988, he has been with The University of Sheffield, where he was initially a Research Associate and was subsequently appointed to an established post as Senior Research Officer/Senior Research Scientist. Since 2000, he has been a Professor of electrical machines and control systems in the Department of Electronic and Electrical Engineering, The University of Sheffield, and is currently the Head of the Electrical Machines and Drives Research Group. His research interests include design and control of permanent-magnet brushless machines and drives, for applications ranging from automotive and aerospace to renewable energy.
