energies Article
A Modified One-Cycle-Control Method for Modular Multilevel Converters Xu Tian *, Yue Ma, Jintao Yu, Cong Wang and Hong Cheng School of Mechanical Electronic and Information Engineering, China University of Mining & Technology (Beijing), Beijing 100083, China;
[email protected] (Y.M.);
[email protected] (J.Y.);
[email protected] (C.W.);
[email protected] (H.C.) * Correspondence:
[email protected]; Tel.: +86-010-6233-1021 Received: 29 November 2018; Accepted: 27 December 2018; Published: 3 January 2019
Abstract: In this paper, a new One-Cycle-Control (OCC) method is designed for a modular multilevel converter (MMC) based on the principle of the equivalent resistance constant. The proposed controller has a simple structure and a small amount of calculation by cancelling the current inner loop proportional integral (PI) controller and the inverse transform in the traditional direct-quadrature (DQ) control. Compared to the traditional OCC controller, the new one separates the control method from the modulation strategy, making it possible to use not only carrier-based pulse-width modulation (PWM), but also nearest level modulation PWM to generate drive signals. Besides, the independent control of the active and the reactive power is implemented by injecting a reference current with the same phase of the supply voltage or a reference current which lags the supply voltage by π/2 into the controller, so the converter can operate in four quadrants and it can work in either a grid-connect or off-grid environment. The feasibility and the performance of the proposed OCC method have been validated by both the simulation under the MATLAB/SIMULINK (R2012a) environment and experimental results. Keywords: modular multilevel converter; One-Cycle-Control; four-quadrant operation; carrier-based PWM; nearest level modulation PWM
1. Introduction Modular multilevel converters (MMCs) have attracted wide attention from both industry and academia due to their advantages of full modularity, better scalability, high redundancy, and low switch voltage stress [1,2]. Consisting of a series connection of submodules (SMs), MMCs are suitable for large-voltage, high-power applications like high-voltage direct current (HVDC) transmission [3], medium-voltage high-power motor drives [4], and photovoltaic generation [5]. There are a great number of control methods which have been used in MMCs successfully since the circuit topology was proposed. Based on linear system theory, the proportional integral (PI) controller has been widely used in power electronic devices [6]. Since the PI controller cannot track the sinusoidal signal without phase error, the abc-to-dq-frame transformation is used to let the controlled variables change from alternating current (AC) to direct current (DC), and the controller output also needs coordinate transformation under this controller structure. To avoid the complicated calculations, the proportional resonant (PR) controller has also been used [7]. By replacing the integral with resonance, the PR controller can provide an infinite gain at the resonant frequency, which makes the PR controller able to track a sinusoidal signal without steady-state error. However, since the gain of the controller is rapidly reduced when the frequency is no longer equal to the resonant frequency, the resonant frequency of the PR controller must be accurately calculated. Except for the traditional control strategy, there are some new types of controllers that have been used in MMCs. Sliding Energies 2019, 12, 157; doi:10.3390/en12010157
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mode control (SMC) divides the state space by referencing controlled variables, and in each subspace the controlled variables are forced to slide along the boundaries by the different control structure. This control method can get good dynamic response when applied to MMCs [8]. Finite control set model predictive control (FCS-MPC) analyzes all possible operating states based on the circuit model and chooses the best one based on the cost function. The advantage of the FCS-MPC is that it can control multiple targets [9] and the disadvantage of it is the accuracy of the model plays an important role in the control effect. Repetitive control takes the previous behavior of the periodic controlled variables into consideration, obtaining a better steady-state response [10], but in order to optimize the dynamic response, it often needs to be used together with other control strategies. One-Cycle-Control (OCC) was proposed by Keyue M. Smedley in 1991 [11]. The basic principle is to let the average controlled variable value over a switch cycle be equal to the reference. Traditional OCC lets the controlled current run in the same phase with the input voltage, therefore, it has been widely used in power factor correction (PFC) [12] and active power filters (APF) [13]. However, the traditional OCC cannot control the reactive component so that the converter can only implement the unit power factor with no ability to output leading or lagging reactive power. This problem was discussed in References [14,15]; they let the APF compensate for only the harmonic components of load currents by injecting the reactive currents. Based on the same principle, OCC working on the grid-connected inversion mode was discussed in References [16,17]. The OCC-based MMC controller has been discussed in Reference [18], but it can only work in the unity power factor rectification mode and the control method must be used in conjunction with the carrier disposition PWM, which reduces the flexibility of the system. In this paper, a modified OCC for an MMC is proposed. As shown in Table 1, an OCC controller has less complexity and calculation demand than PI and PR controllers. Compared to other nonlinear control methods such as FCS-MPC, OCC does not rely on an accurate mathematical model and it can realize the constant switch frequency naturally. Compared with the existing OCC-based MMC controller, the modified OCC proposed in this paper can enable the bi-directional power flow, and the power factor can also be controlled, which expands the application scope of the control method. In addition, the modified OCC realizes the decoupling of the control strategy and the modulation strategy. It can work with several modulation strategies and is compatible with existing SM voltage balancing strategies. Table 1. Comparison between several control strategies for a modular multilevel converter (MMC). PI: proportional integral; PR: proportional resonant; FCS-MPC: finite control set model predictive control; OCC: One-Cycle-Control. Control Strategies
Phase Locked Loop (PLL)
Controller Structure
Calculation
Robustness
Modulation Strategy
Steady-State Error
PI PR FCS-MPC OCC [18] Modified OCC
Yes Yes Yes No Yes
Common Common Complex Simple Simple
Middle Small Large Small Small
Strong Less Less Strong Strong
Unlimited Unlimited Unlimited Limited Unlimited
No No No Yes No
The rest of this paper is organized as follows: the mathematical model of MMCs is briefly introduced in Section 2. The proposed OCC has been described in Section 3. In Section 4, the method that makes the OCC-controlled MMC operate in four-quadrants is described in detail. Section 5 covers the simulation and experimental results to validate the correctness and effectiveness of the proposed modified OCC, and finally, Section 6 summarizes the main points of the paper. 2. Mathematical Model of the MMC The topology of the single-phase MMC is shown in Figure 1, in which iAC , uAC are the AC side current and voltage, ip and iq are the upper arm current and the lower arm current, respectively.
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The phase leg consists of two arms, Energies 2019, 12, x FOR PEER REVIEW
which can be called upper arm and lower arm, respectively. 3 of 18 Both the two arms need an inductance L0 to suppress the circulating current. The arm is composed of the arms need an inductance to suppress the circulating The arm by is composed SMstwo in series, and the upper arm voltage up and the lower arm un current. can be controlled bypassing of or SMs in series, and the upper arm voltage and the lower arm can be controlled by bypassing inserting the SMs. Assuming the DC side output voltage of the MMC is UDC , based on Kirchhoff’s or inserting the SMs. Assuming the DC output voltage of the MMC is , based on current law (KCL), the current dynamics canside be given as follows: Kirchhoff’s current law (KCL), the current dynamics can be given as follows: dip UDC di − up − ip R0 − L0 d = uAC − iAC RC − LCd AC (1) 2 dt dt (1) 2 d d UDC didn di d un − + in R0 + L0 = uAC − iAC RC − LC AC (2) (2) . . 2 2 dtd ddt
Figure 1. Circuit topology of the single‐phase MMC. SM: submodule. Figure 1. Circuit topology of the single-phase MMC. SM: submodule.
By summing Equations (1) and (2), the AC side current dynamics can be obtained as By summing Equations (1) and (2), the AC side current dynamics can be obtained as un − up R0 L0 diAC (3) + iAC + RC + LC + 2 = u. (3) AC . 2 2 22 2 dt Based on the above formula, the AC side equivalent model of the MMC is shown in Figure 2, in Based, on the abovethe formula, the AC side equivalent model ofcapacitance, the MMC isrespectively, shown in Figure which means equivalent inductance and equivalent and 2, in which L , R means the equivalent inductance and equivalent capacitance, respectively, and ej eq eq means the AC side output voltage of the MMC. They can be defined as: means the AC side output voltage of the MMC. They can be defined as:
(4) 2L0 Leq = Lc + (4) 2 (5) R20 Req = Rc + (5) 2 . (6) un 2− up e = . (6) j From Figure 2 it can be seen that the AC side model of MMC is no different from other voltage 2 source converters. Thus, the traditional control strategy can be used for the MMC to determine From Figure 2 it can be seen that the AC side model of MMC is no different from other voltage. Normally, the DC side voltage of the MMC is required to be stable at a fixed value, so the voltages source converters. Thus, the traditional control strategy can be used for the MMC to determine ej . of and the DC can also be determined by inserting or bypassing SMs. Normally, side voltage of the MMC is required to be stable at a fixed value, so the voltages of up and un can also be determined by inserting or bypassing SMs.
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Figure 2. Alternating current (AC) side equivalent model of the MMC. Figure 2. Alternating current (AC) side equivalent model of the MMC.
3. OCC for Multiple Modulation Strategies 3. OCC for Multiple Modulation Strategies The conventional OCC has been widely used in the field of unit power factor rectification [19]. The conventional OCC has been widely used in the field of unit power factor rectification [19]. The the input current directly compared withwith the carrier wavewave to generate the drive The original original OCC OCC uses uses the input current directly compared the carrier to generate the signal, and since there is no reference voltage generation during this process, the controller can only drive signal, and since there is no reference voltage generation during this process, the controller use the carrier phase-shift PWM modulation strategy and this limits the design of the SM voltage can only use the carrier phase‐shift PWM modulation strategy and this limits the design of the SM balancing strategy. voltage balancing strategy. In this paper, the OCC is analyzed based on the equivalent resistance constant so that the AC side In this paper, the OCC is analyzed based on the equivalent resistance constant so that the AC output voltage of the converter can be calculated most of the modulation strategies can be side output voltage of the converter can be and calculated and existing most of the existing modulation used directly. strategies can be used directly. The OCC is is to to let let thethe average controlled variable valuevalue over over a switch cycle The basic basic principle principle ofof the the OCC average controlled variable a switch be equal the reference. For the For equivalent circuit shown Figurein 2, Figure 2, in order toin make it to operate cycle be to equal to the reference. the equivalent circuit inshown order make in it the unity power factor state, as Figure 3 shows, the MMC can be equivalent to a resistive load R after e operate in the unity power factor state, as Figure 3 shows, the MMC can be equivalent to a resistive ignoring the equivalent parasitic resistance Req and the equivalent inductance Leq . load after ignoring the equivalent parasitic resistance and the equivalent inductance .
Figure 3. Equivalent circuit in unit power factor rectification mode. Figure 3. Equivalent circuit in unit power factor rectification mode.
In in a cycle T be In order order to to let let the the behavior behavior of of the the MMC MMC in a switch switch cycle be equivalent equivalent to to an an emulated emulated resistance the control equation of the conventional OCC can be expressed as follows: resistance Re ,, the control equation of the conventional OCC can be expressed as follows: Z 11 T ej d dt = Re. . T 0 iAC
(7) (7)
Due to the high switching frequency of the MMC, the change of the current in a switch Due to the high switching frequency of the MMC, the change of the current iAC in a switch cycle cycle can be ignored, so the control law of the conventional OCC can be expressed as: can be ignored, so the control law of the conventional OCC can be expressed as: . (8) ej = Re iAC . (8) and can be determined based on Once the is determined, the arm voltages, Equation (6). The inserted SM numbers of the upper and lower arms are also determined. However, Once the ej is determined, the arm voltages, up and un can be determined based on Equation (6). which SM should be inserted has not been determined. In addition to making the AC side current The inserted SM numbers of the upper and lower arms are also determined. However, which SM change be as inserted expected, another major control target is to keep the SM the capacitor voltages balance. should has not been determined. In addition to making AC side currentin change as That can be implemented by several modulation strategies [20–23], which balances the SM capacitor expected, another major control target is to keep the SM capacitor voltages in balance. That can be voltage by controlling the insertion and bypass time of each SM. implemented by several modulation strategies [20–23], which balances the SM capacitor voltage by One of the the most commonly controlling insertion and bypassused timemodulation of each SM. strategies is nearest level modulation (NLM) [20,21]. As Figure 4 shows, the basic principle of NLM is to One of the most commonly used modulation strategies is determine the number of inserted SMs nearest level modulation (NLM) [20,21]. according to the required bridge arm voltage and the SM voltage to minimize the error between the As Figure 4 shows, the basic principle of NLM is to determine the number of inserted SMs according actual bridge arm voltage and the voltage. algorithm sorts the SMs the to the required bridge arm voltage andreference the SM voltage to The minimize the error between thebased actual on bridge voltage of the SM and insert the SMs from large to small, or from small to large, according to the arm voltage and the reference voltage. The algorithm sorts the SMs based on the voltage of the SM direction of current to balance the SM capacitor voltages.
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and insert the SMs from large to small, or from small to large, according to the direction of current to Energies 2019, 12, x FOR PEER REVIEW 5 of 18 balance the SM capacitor voltages. Energies 2019, 12, x FOR PEER REVIEW 5 of 18
Figure 4. Principle of the nearest level modulation (NLM) strategy. Figure 4. Principle of the nearest level modulation (NLM) strategy. Figure 4. Principle of the nearest level modulation (NLM) strategy.
Another popular modulation strategy for the MMC is carrier phase‐shift PWM (CPS‐PWM) [22]. Another popular modulation strategy for the MMC is carrier phase-shift PWM (CPS-PWM) [22]. Another popular modulation strategy for the MMC is carrier phase‐shift PWM (CPS‐PWM) [22]. The basic basic principle principle of of CPS-PWM CPS‐PWM is is shown shown in in Figure Figure 5. 5. The generated by by The The switching switching signals signals are are generated The basic principle of CPS‐PWM is shown in Figure 5. The switching signals are generated by comparing the reference voltage with several carrier waves. For an N+1 level converter, N carrier comparing the reference voltage with several carrier waves. For an N+1 level converter, N carrier comparing the reference voltage with several carrier waves. For an N+1 level converter, N carrier waves waves are are needed needed and and each each one one has has aa phase phase shift shift of of 2π The outputs outputs are are the the control control signals signals for for the the N .. The waves are needed and each one has a phase shift of . The outputs are the control signals for the upper arm SMs, and the control signals for the lower arm SMs can be generated by inverting the upper arm SMs, and the control signals for the lower arm SMs can be generated by inverting the upper upper arm SMs, and the control signals for the lower arm SMs can be generated by inverting the upper upper ones. ones. ones.
Figure 5. Principle of carrier phase-shift (CPS)-PWM. (a) Reference voltage and carrier waves; Figure 5. Principle of carrier phase‐shift (CPS)‐PWM. (a) Reference voltage and carrier waves; (b) Figure 5. Principle of carrier phase‐shift (CPS)‐PWM. (a) Reference voltage and carrier waves; (b) (b) output voltage. output voltage. output voltage.
Both the modulation strategies have their own advantages and disadvantages [23]. Compared Both the modulation strategies have their own advantages and disadvantages [23]. Compared to NLM,Both the modulation strategies have their own advantages and disadvantages [23]. Compared CPS-PWM can generate more accurate voltage, and because the switching devices under to NLM, CPS‐PWM can generate more accurate voltage, and because the switching devices under theto NLM, CPS‐PWM can generate more accurate voltage, and because the switching devices under CPS-PWM strategy have nearly the same turn-on time, the loss of the electronic components are the CPS‐PWM strategy have nearly the same turn‐on time, the loss of the electronic components are the CPS‐PWM strategy have nearly the same turn‐on time, the loss of the electronic components are basically identical. However, because the traditional CPS-PWM cannot balance the SM capacitor basically identical. However, because the traditional CPS‐PWM cannot balance the SM capacitor basically identical. However, because the traditional cannot the SM capacitor voltages, additional controllers are often required for eachCPS‐PWM SM to balance thebalance SM capacitor voltages voltages, additional controllers are often required for each SM to balance the SM capacitor voltages voltages, additional controllers are often required for each SM to balance the SM capacitor voltages in actual applications. The additional controllers increase the calculations and this will put higher in actual applications. The additional controllers increase the calculations and this will put higher in actual applications. The additional controllers increase the calculations and this will put higher requirements for the performance of the microprocessor. Therefore, CPS‐PWM is suitable for requirements for the performance of the microprocessor. Therefore, CPS‐PWM is suitable for medium‐ and low‐voltage applications needing fewer SMs such as a variable‐frequency drive, medium‐ and low‐voltage applications needing fewer SMs such as a variable‐frequency drive, while for the high‐voltage applications such as HVDC, NLM is more suitable because in these while for the high‐voltage applications such as HVDC, NLM is more suitable because in these occasions the system often requires a large number of SMs. For the OCC described in this paper, occasions the system often requires a large number of SMs. For the OCC described in this paper,
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of the microprocessor. Therefore, CPS-PWM is suitable for medium6 of 18 and low-voltage applications needing fewer SMs such as a variable-frequency drive, while for the high-voltage applications such as NLM is more suitable , because in these occasions the system Energies 2019, 12, x FOR PEER REVIEW HVDC, 6 of the 18 since the controller calculates the AC side output voltage compared to traditional OCC, often requires a large number of SMs. For the OCC described in this paper, since the controller modulation strategy is no longer limited, and both NLM and CPS‐PWM can be used. since the controller calculates the AC output tovoltage , compared to traditional OCC,isthe calculates the AC side output voltage ej ,side compared traditional OCC, the modulation strategy no The basic form of the proposed OCC controller is shown in Figure 6. An outer DC‐side voltage modulation strategy is no longer limited, and both NLM and CPS‐PWM can be used. longer limited, and both NLM CPS-PWM can used. to maintain the DC bus voltage control loop implemented by and a PI controller is be designed ∗ The basic form of the proposed OCC controller is shown in Figure 6. An outer DC‐side voltage The basic form of the proposed OCC controller is shown in Figure 6. An outer DC-side voltage tracking the reference value . In order to make the controlled variable positively related to the control loop implemented implemented byby a controller PI controller is designed to maintain bus uvoltage control loop a PI is designed to maintain the DCthe busDC voltage DC tracking controller output, the PI controller output is set as the admittance of equivalent resistance and it ∗ ∗ . In order tracking the reference value . In order to make the controlled variable positively related to the the reference value u to make the controlled variable positively related to the controller determines the input active power. Then, dividing the AC side input current by the admittance, DC controller output, the PI controller output is set as the admittance of equivalent resistance and it output, the PI controller output is set as and the admittance of equivalent resistance Re and it determines which is equivalent to multiplying , the AC side output voltage of the MMC can be determines the input active power. Then, dividing the AC side input current by the admittance, the input active power. Then, dividing the AC side input current iAC by the admittance, which is derived. Finally, the switching signals are generated by the modulation strategy. which is equivalent to multiplying and equivalent to multiplying Re and iAC , the AC side, the AC side output voltage of the MMC output voltage of the MMC ej can be derived. can be Finally, the switching signals are generated by the modulation strategy. derived. Finally, the switching signals are generated by the modulation strategy.
Figure 6. OCC algorithm for the unit power factor rectifier.
Figure 6. OCC algorithmthe for the unithas power rectifier. Figure 6. OCC algorithm for the unit power factor rectifier. Compared to other control strategies, OCC a factor simpler control structure and less
calculation. This method can be implemented without a PLL or even an AC side voltage sensor. Compared to control strategies, the OCC has a simpler control structure and less calculation. Compared to other other control strategies, the OCC has a simpler control structure and less However, this control strategy can only implement the unity power factor rectifier and the power This method can be implemented without a PLL or even an AC side voltage sensor. However, calculation. This be implemented without a PLL an AC side voltage sensor. factor cannot be method set. In can addition, because the influence of or the even inductance is neglected in the this control strategy can only implement the unity power factor rectifier and the power factor cannot However, this control strategy can only implement the unity power factor rectifier and the power theoretical analysis, there is an error in the power factor, so it is only suitable for some limited be set. cannot In addition, because the influence of the the inductanceof is the neglected in the is theoretical analysis, factor be set. In addition, because inductance neglected the applications, such as the active front‐end (AFE) influence rectifier, which allows for a certain power in factor there is an error in the power factor, so it is only suitable for some limited applications, such as the theoretical analysis, there is an error in the power factor, so it is only suitable for some limited error. active front-end (AFE) rectifier, which allows for a certain power factor error. applications, such as the active front‐end (AFE) rectifier, which allows for a certain power factor error. 4. Four‐Quadrant Operation for OCC Controlled MMC 4. Four-Quadrant Operation for OCC Controlled MMC 4. Four‐Quadrant Operation for OCC Controlled MMC 4.1. Reactive Power Control 4.1. Reactive Power Control For with the the reactive reactive power power output, output, it be equivalent equivalent using method For the the rectifier rectifier with it can can also also be using the the method 4.1. Reactive Power Control described in the previous section. Similar to Figure 3, the MMC rectifier with reactive power output described in the previous section. Similar to Figure 3, the MMC rectifier with reactive power output For the rectifier the in reactive it or can be equivalent the method can be equivalent to a resistor in parallel with a capacitor or an inductor, which is determined by can be equivalent to awith resistor parallelpower with aoutput, capacitor analso inductor, which is using determined by the described in the previous section. Similar to Figure 3, the MMC rectifier with reactive power output the power factor angle. Figure 7 shows the equivalent circuit of a rectifier with a lagging power power factor angle. Figure 7 shows the equivalent circuit of a rectifier with a lagging power factor, can be equivalent to a resistor in parallel with a capacitor or an inductor, which is determined by factor, where is the equivalent resistance is the equivalent inductance. and , where R resistance and Le and is the equivalent inductance. iAC,d and i,AC,q are the e is the equivalent the power factor through angle. Figure 7 shows the equivalent circuit of a respectively, rectifier with a be lagging power are the currents flowing through the resistance and the inductor, which can also be currents flowing the resistance and the inductor, respectively, which can also considered as factor, where is the equivalent resistance and i of is respectively. the equivalent , and i The , considered the active or reactive component input current , respectively. the active or as reactive component of the input current Theinductance. relationship between AC , the AC,d , are the currents flowing through the resistance and the inductor, respectively, which can also be relationship between can be written as iAC,q , and iAC can be written , , as , , and considered as the active or reactive component the , respectively. The iAC = iAC,d +of iAC,q . input current (9) . (9) , , relationship between , , , , and can be written as
,
,
.
(9)
Figure 7. Equivalent circuit for reactive power output. Figure 7. Equivalent circuit for reactive power output.
Figure 7. Equivalent circuit for reactive power output. In addition, the output voltage of the MMC can be written as , , . In addition, the output voltage of the MMC can be written as ,
,
.
(10) (10)
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In addition, the output voltage of the MMC can be written as The reactive component of the input current , can be expressed as Equation (11). It shows Energies 2019, 12, x FOR PEER REVIEW 7 of 18 by . Thus, a sine wave in phase with that the ej = Re iAC,d = Re iAC − iAC,q . , can be obtained by a PLL or by (10) , lags
by a quarter of a cycle. The amplitude of the delaying the , determines the value of The reactive component of the input current , can be expressed as Equation (11). It shows The reactive component of the input current iAC,q can be expressed as Equation (11). It shows that reactive power. by . Thus, a sine wave in phase with , can be obtained by a PLL or by that the , lags the iAC,q lags uAC by π2 . Thus, a sine wave in phase with iAC,q can be obtained by a PLL or by delaying by a quarter of a cycle. The amplitude of the determines the value of delaying the (11) the uAC by a quarter of a cycle. The amplitude of, the iAC,q determines the, value of reactive power. reactive power. uACpower controller is shown in Figure 8. The The block diagram of the OCC with ia reactive (11) AC,q , = jωL (11) e active power controller is the same as the controller described in Section 3. The control of reactive power is implemented by injecting a reactive current . The phase of the virtual current , into The block block diagram diagram the OCC with a reactive power controller is shown in Figure The The ofof the OCC with a reactive power controller is shown in Figure 8. The 8. active is obtained by delaying the AC voltage by a quarter of a cycle and the amplitude can obtained active power controller is the same as the controller described in Section 3. The control of reactive power controller is the same as the controller described in Section 3. The control of reactive power is by a PI controller, which is used to maintain the reactive power tracking the reference voltage power is implemented by injecting a reactive current into implemented by injecting a reactive current iAC,q into iAC . , The phase. The phase of the virtual current of the virtual current is obtained ∗ . Positive amplitude means output current lags system voltage while negative amplitude means is obtained by delaying the AC voltage by a quarter of a cycle and the amplitude can obtained by delaying the AC voltage uAC by a quarter of a cycle and the amplitude can obtained by a PI output current leads system voltage. by a PI controller, which used to the maintain power the tracking reference voltage controller, which is used tois maintain reactivethe reactive power Q tracking referencethe voltage Q∗ . Positive ∗ . Positive amplitude means output current lags system voltage while negative amplitude means amplitude means output current lags system voltage while negative amplitude means output current output current leads system voltage. leads system voltage.
Figure 8. OCC algorithm with reactive power controller.
Compared to the traditional control strategies based on coordinate transformation, although Figure 8. OCC algorithm with reactive power controller. Figure 8. OCC algorithm with reactive power controller. the proposed controller still needs a PLL and DQ transform, the inverse transformation is no longer needed. In addition, since the DQ transform or the PLL is only used in the outer power loop and the Compared control strategies based on on coordinate transformation, although the Compared to to the the traditional traditional control strategies based coordinate transformation, although outer loop has a lower frequency than the inner current loop, the proposed one has less calculation proposed controller still needs a PLL and DQ transform, the inverse transformation is no longer needed. the proposed controller still needs a PLL and DQ transform, the inverse transformation is no longer and because it requires less hardware, it also has used cost in advantages. However, it also has some In addition, since the DQ transform or the PLL is only the outer power loop and the outer loop needed. In addition, since the DQ transform or the PLL is only used in the outer power loop and the limitations; because the controller can only output the positive active power, the MMC can only has a lower frequency than the inner current loop, the proposed one has less calculation and because outer loop has a lower frequency than the inner current loop, the proposed one has less calculation work in the rectifier mode, therefore it is still not suitable for applications requiring four‐quadrant it requires lessit hardware, alsohardware, has cost advantages. it also has some limitations; because and because requires it less it also has However, cost advantages. However, it also has some operations such as HVDC. the controller can only output the positive active power, the MMC can only work in the rectifier mode, limitations; because the controller can only output the positive active power, the MMC can only therefore it is still not suitable for applications requiring four-quadrant operations such as HVDC. work in the rectifier mode, therefore it is still not suitable for applications requiring four‐quadrant 4.2. Inversion operations such as HVDC. 4.2. Inversion When is negative, the system will have a pole at the right half of the s‐plane and it will When Re is negative, system pole at the right the s-planeto and it will a 4.2. Inversion cause a stability problem the [17]. Thus, will have must a be positive and half it is of impossible make the cause circuit stability problem [17]. Thus, R must be positive and it is impossible to make the circuit work in the work When in the inverter mode by as a a negative value directly. for the it OCC e setting the is negative, the system will have pole at the right half of Therefore, the s‐plane and will inverter mode by setting the Re as amode, negative value directly. Therefore, for the OCC control algorithm control algorithm in the inverter the injection method described in the previous section is cause a stability problem [17]. Thus, must be positive and it is impossible to make the circuit in the inverter mode, the injection method described in the previous section is still used. still used. work in the inverter mode by setting the as a negative value directly. Therefore, for the OCC The equivalent circuit forfor the inverter modemode underunder both the grid-connected and off-grid The algorithm equivalent inverter both the grid‐connected and condition off‐grid control in circuit the inverter the mode, the injection method described in the previous section is is shown in Figure 9. The output current iAC is the sum of is the sum of iS and the fictitious current if . If if is negative. condition is shown in Figure 9. The output current and the fictitious current still used. and work under the inverter mode. |, the converter will work under the inverter mode. | | | will If |iThe is negative and f | > |is |, the converter equivalent circuit for the inverter mode under both the grid‐connected and off‐grid condition is shown in Figure 9. The output current is the sum of and the fictitious current . If is negative and | | | |, the converter will work under the inverter mode.
Figure 9. Equivalent circuit for inverter mode. Figure 9. Equivalent circuit for inverter mode.
Similar to Equation (10), the output voltage of the MMC can be written as Figure 9. Equivalent circuit for inverter mode.
Similar to Equation (10), the output voltage of the MMC can be written as
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Similar to Equation (10), the output voltage of the MMC can be written as . (12) (12) ej = Re is = Re (iAC − if ). As for the grid‐connected condition, the is a sine wave with the same frequency and phase as the input voltage u , so it can be easily derived by sampling the . Denote the amplitude of As for the grid-connected condition, the if is a sine wave with the same frequency and phase as the and as , , respectively. If , the converter will work under the rectifier the input voltage uAC , so it can be easily derived by sampling the uAC . Denote the amplitude of mode the if and when the , the converter will work under the inverter mode. For the off‐grid condition, and is as If , Is , respectively. If If > − IS , the converter will work under the rectifier mode and when the determines the frequency of the output voltage. Ithe frequency of the work under the inverter mode. For the off-grid condition, the frequency of f < − IS , the converter will the if The block diagram of the overall control strategy for the four‐quadrant OCC‐controlled MMC determines the frequency of the output voltage. is shown in Figure 10. active power and the power have been controlled by the The block diagram Both of thethe overall control strategy forreactive the four-quadrant OCC-controlled MMC is injecting strategy. The emulated resistance can be given as any positive value, but in order to shown in Figure 10. Both the active power and the reactive power have been controlled by the injecting control the conveniently, the Re can can be be given given the maximum input voltage divided strategy. The emulated resistance asas any positive value, but in order to controlby thethe if converter’s maximum allowable current , the amplitude of can be limited as 0, 2maximum and conveniently, the Re can be given as the maximum input voltage divided by the converter’s the phase current is always to the of phase Thus, the the amplitude belongs to allowable Imaxopposite , the amplitude if canof bethe limited. as phase is of always opposite [0, 2Iwhen max ] and , the system works under the rectifier mode and when it belongs to [ ,2 ], the system to0,the phase of the uAC . Thus, when the amplitude of if belongs to [0, Imax ], the system works under works under the inverter mode. the rectifier mode and when it belongs to [Imax , 2Imax ], the system works under the inverter mode.
Figure 10. The block diagram of the overall control strategy. Figure 10. The block diagram of the overall control strategy.
This can implement four-quadrant operation for the MMCMMC with This control control module module can implement four‐quadrant operation for OCC-controlled the OCC‐controlled less computation, but compared to other control modules introduced in this paper, its structure is with less computation, but compared to other control modules introduced in this paper, its slightly complicated. This chapter introduces three different OCC control modules and they meet the structure is slightly complicated. This chapter introduces three different OCC control modules and requirements for the MMC in most applications, so the most suitable control modules can be selected they meet the requirements for the MMC in most applications, so the most suitable control modules to balance the features and costs. can be selected to balance the features and costs. 5. Simulation and Experimental Results 5. Simulation and Experimental Results In In order order to to verify verify the the correctness correctness of of the the proposed proposed control control scheme, scheme, some some simulations simulations and and experiments To ensure experiments based based on on single-phase single‐phase MMC MMC have have been been carried carried out. out. To ensure the the accuracy accuracy of of the the simulations and the experiments, both of them use the same parameters which have been listed in simulations and the experiments, both of them use the same parameters which have been listed in Table 2. Table 2. Table 2. Parameters used in the simulations and experiments. Table 2. Parameters used in the simulations and experiments. Symbol
Description
Symbol uAC f u
Value
Description Value AC system voltage 110 V(rms) AC system voltage 110 V(rms) Power frequency 50 Hz Power frequency 50 Hz DC-side voltage 330 V DC‐side voltage 330 V Number of SMs in each arm 4 SM capacitance µF Number of SMs in each arm 780 4 Arm inductance 14.7 mH 780 μF SM capacitance Control frequency 10 kHz Arm inductance 14.7 mH Equivalent control frequency 40 kHz Control frequency 10 kHz Equivalent control frequency 40 kHz
DC
N CSM N L0 fc fe
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5.1. Simulation Results 5.1. Simulation Results 5.1. Simulation Results In order to verity both the steady-state performance and dynamic characteristics of the proposed In order to verity both the steady‐state performance and dynamic characteristics of the order to several verity both the steady‐state dynamic characteristics of the controlIn strategies, simulations have beenperformance carried out and based on the MATLAB/ SIMULINK proposed control strategies, several simulations have been carried out based on the MATLAB/ proposed control strategies, several simulations have been carried out based on the MATLAB/ platform and all the three control modules mentioned in this paper have been tested. SIMULINK platform and all the three control modules mentioned in this paper have been tested. SIMULINK platform and all the three control modules mentioned in this paper have been tested. 5.1.1. Basic OCC Controller 5.1.1. Basic OCC Controller 5.1.1. Basic OCC Controller Figure 11 shows the steady-state performance of the basic unit power factor OCC controller which Figure 11 shows the steady‐state performance of the basic unit power factor OCC controller Figure 11 shows the steady‐state of when the basic unit power OCC controller is shown showsperformance the situation IAC = 6A and Ifactor = 12 A, respectively. AC6 A which in is Figure shown 6. in Figure Figure 11a,b 6. Figure 11a,b shows the situation when and 12 A, which is shown in Figure 6. Figure 11a,b shows the situation when 6 A and 12 A, Both of them have sinusoidal current waveforms with few ripples, but as described in Section 4.1, respectively. Both of them have sinusoidal current waveforms with few ripples, but as described in therespectively. Both of them have sinusoidal current waveforms with few ripples, but as described in phases of the voltage and current are not exactly the same. The current always lags behind the Section 4.1, the phases of the voltage and current are not exactly the same. The current always lags Section 4.1, the phases of the voltage and current are not exactly the same. The current always lags voltage and the situation becomes more severe as the current increases. behind the voltage and the situation becomes more severe as the current increases. behind the voltage and the situation becomes more severe as the current increases.
(a) (a)
(b) (b)
Figure 11. The steady‐state performance of the unit power factor OCC controller: (a) 6 A; (b) Figure 11. The steady-state performance of the unit power factor OCC controller: (a) IAC = 6 A; Figure 11. The steady‐state performance of the unit power factor OCC controller: (a) 6 A; (b) 12 A. (b) IAC = 12 A. 12 A.
The dynamic characteristics of this control strategy is shown in Figure 12. When t 0.4 0.4 s, the The dynamic characteristics of this control strategy is shown in Figure 12. When t = s, the DC The dynamic characteristics of this control strategy is shown in Figure 12. When t 0.4 s, the ∗ ∗ increased DC voltage reference increased from 330 to 390 V. Then, because of the effect of the PI voltage reference uDC from 330 to 390 V. Then, because of the effect of the PI controller, DC voltage reference ∗ increased from 330 to 390 V. Then, because of the effect of the PI controller, the current increases rapidly and the DC voltage gradually rises. By the same time, the the current increases rapidly and the DC voltage gradually rises. By the same time, the current begins controller, the current increases rapidly and the DC voltage gradually rises. By the same time, the current begins to decrease gradually and after a short adjustment, when t 0.5 s, the entire system to current begins to decrease gradually and after a short adjustment, when decrease gradually and after a short adjustment, when t = 0.5 s, the entire system regains a new t 0.5 s, the entire system regains a new steady state, and compared to the original state, the new one has a ripple larger due DC side steady state, andsteady compared thecompared original state, the new one hasthe a larger DChas sidea to the regains a new state, toand to the original state, new one larger DC side ripple due to the increased DC side power. increased DC side power. ripple due to the increased DC side power.
Figure 12. The situation when the direct current (DC) voltage reference changed. Figure 12. The situation when the direct current (DC) voltage reference changed. Figure 12. The situation when the direct current (DC) voltage reference changed.
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For the reactive‐power‐controlled OCC controller, which is shown in Figure 8, the steady‐state 5.1.2. Reactive‐Power‐Controlled OCC Controller 5.1.2. Reactive-Power-Controlled OCC Controller performances are shown in Figure 13. Figure 13a,b shows the input current and voltage waveforms For the reactive‐power‐controlled OCC controller, which is shown in Figure 8, the steady‐state , controller, , respectively, all of in them have same active when the factor angles φ are OCC For thepower reactive-power-controlled whichand is shown Figure 8, the the steady-state performances are shown in Figure 13. Figure 13a,b shows the input current and voltage waveforms performances shown in Figure 13a,b shows the input and voltage in waveforms current. From are Figure 13a,b it can 13. be Figure seen that the controller has current good performance both the , respectively, and all of them have the same active when the power factor angles φ πare π, when the power factor angles ϕreactive − 4 , respectively, and all ofFigure them have the same active current. capacitive and the inductive output situations. 13c shows the current and S are , power current. From Figure 13a,b it can 4be seen that the controller has good performance in both the From Figure 13a,b can be seen that thesituation, controllerand has good performance both the Figure capacitive the voltage under the itunit power factor comparing Figure in13c with 11b and shows capacitive and the inductive reactive power output situations. Figure 13c shows the current and inductive power 13camplitude shows the current and voltage underlikely the unit that both reactive of them have output almost situations. the same Figure current but Figure 13c is more to voltage under the unit power factor situation, and comparing Figure 13c with Figure 11b shows implement unit power factor. Figure 13d the equivalent side output voltage of the power factorthe situation, and comparing Figure 13cshows with Figure 11b showsAC that both of them have almost that both of them have almost the same current amplitude but Figure 13c is more likely to MMC calculated by Equation (6); 13c the five‐level output can be clearly seen Figure from 13d the the same current amplitude but Figure is more likelyvoltage to implement the unit power factor. implement the unit power factor. Figure 13d shows the equivalent AC side output voltage of the shows the equivalent AC side output voltage of the MMC e calculated by Equation (6); the five-level figure and at the same time the voltage fluctuation caused by the charge and the discharge of the j output can be clearly seen from the MMC calculated by Equation (6); the five‐level voltage voltage output can be clearly seen from the figure and at the same time the voltage fluctuation caused SM capacitors can also be seen from the figure. figure and at the same time the voltage fluctuation caused by the charge and the discharge of the by SM capacitors can also be seen from the figure. the charge and the discharge of the SM capacitors can also be seen from the figure.
(a) (a)
(c) (c)
(b) (b)
(d) (d)
Figure 13. The steady‐state performance of the reactive‐power‐controlled OCC controller: (a) Figure 13. The steady‐state performance of the reactive‐power‐controlled OCC controller: (a) Figure 13. The steady-state performance of the reactive-power-controlled OCC controller: (a)φϕφS = ; π4 ; ; (b) (b) φSφ= 0; 0; (d) the equivalent AC side output voltage of the MMC. ; (c) 0; (d) the equivalent AC side output voltage of the MMC. (b) ϕφS φ = − π4 ; (c) ; (c) ϕ (d) the equivalent AC side output voltage of the MMC.
The dynamic characteristic is shown in Figure 14. When t = 0.4tts, let the let reactive power reference The dynamic characteristic is shown shown in Figure 14. 0.4 s, power The dynamic characteristic is in 14. When When 0.4 s, let the the reactive reactive power become the opposite of the original value. The current changes quickly after the reference changes and reference become the opposite of the original value. The current changes quickly after the reference reference become the opposite of the original value. The current changes quickly after the reference is basically stable after half a grid voltage cycle. changes and is basically stable after half a grid voltage cycle. changes and is basically stable after half a grid voltage cycle.
Figure 14. The dynamic state performance of the reactive‐power‐controlled OCC controller. Figure 14. The dynamic state performance of the reactive-power-controlled OCC controller. Figure 14. The dynamic state performance of the reactive‐power‐controlled OCC controller.
The steady‐state performance of the four‐quadrant OCC controller which has been described in section 4.2 is shown in Figure 15. In these cases, the DC side is connected to a 400 V DC power supply. Figure 10a,b shows the situation in the inversion mode under the grid‐connect or off‐grid situation, respectively. For the off‐grid MMC, the AC power is replaced by a 10 Ω resistor and the Energies 2019, 12, 157 11 of 17 reactive power controller is no longer need. Since the AC power supply no longer needs to output active power to maintain the DC side voltage, it is possible to only output the reactive power to the AC side. Figure 10c,d shows the case when the current lags or leads the AC source voltage , 5.1.3. Four-Quadrant OCC Controller respectively. The steady-state performance of the four-quadrant OCC controller which has been described in The dynamic characteristic of the four‐quadrant OCC controller is shown in Figure 16. When ∗ cases, the DC side is connected to a 400 V DC power supply. Section 4.2 is shown in Figure 15. In these t 0.4 s, the active power reference changes from positive to negative, which means the system Figure 15a,b shows the situation into the inversion modeThe under the grid-connect or off-grid situation, switches from rectification mode inversion mode. current changes quickly after the mode respectively. For the off-grid MMC, the AC power is replaced by a 10 Ω resistor and the reactive changes and is basically stable after half a grid voltage cycle. power controller is no longer need. Since the AC power supply no longer needs to output active To further verify the performance of the proposed controller, the AC currents under different power to maintain the DC side voltage, it is possible to only output the reactive power to the AC side. operating conditions have been analyzed in the frequency domain. The total harmonic distortions Figure 15c,d shows the case when the current lags or leads the AC source voltage π2 , respectively. (THDs) in the inversion and rectification conditions are 0.54% and 0.45%, respectively, and during The dynamic characteristic of the four-quadrant controller shownare in Figure 16. When the capacitive and inductive reactive power output OCC conditions, the isTHDs 0.4% and 0.43% ∗ tseparately. = 0.4 s, theThe active power reference P changes from to negative, the system spectrum analysis results under the positive four conditions are which shown means in Figure 17. As switches from rectification mode to inversion mode. The current changes quickly after the mode shown in the figure, although there are slight differences in the THDs, the AC currents have almost changes and is basically stable after half a grid voltage cycle. no harmonic contents under all the operating conditions.
(a)
(b)
(c)
(d)
Figure 15. The steady‐state performance of the four‐quadrant OCC controller: (a) Grid‐connect inversion; Figure 15. The steady-state performance of the four-quadrant OCC controller: (a) Grid-connect (b) off‐grid inversion; (c) capacitive reactive power output; (d) inductive reactive power output. inversion; (b) off-grid inversion; (c) capacitive reactive power output; (d) inductive reactive Energies 2019, 12, x FOR PEER REVIEW 12 of 18 power output.
Figure 16. The dynamic state performance of the four-quadrant OCC controller. Figure 16. The dynamic state performance of the four‐quadrant OCC controller.
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To further verify the performance of the proposed controller, the AC currents under different operating conditions have been analyzed in the frequency domain. The total harmonic distortions (THDs) in the inversion and rectification conditions are 0.54% and 0.45%, respectively, and during the capacitive and inductive reactive power output conditions, the THDs are 0.4% and 0.43% separately. The spectrum analysis results under the four conditions are shown in Figure 17. As shown in the Figure 16.are Theslight dynamic state performance of thethe four-quadrant OCC controller. figure, although there differences in the THDs, AC currents have almost no harmonic contents under all the 16. operating conditions. Figure The dynamic state performance of the four-quadrant OCC controller.
Figure 17. Harmonic comparison in different modes. Figure modes. Figure17. 17.Harmonic Harmoniccomparison comparisoninindifferent different modes.
5.2. Experiment Results 5.2. Experiment Results 5.2.To Experiment test the Results working condition of the controller in the real environment, a 200 W MMC To test the working condition of the controller inThe the real environment, a 200 W MMC prototype was the builtworking in the laboratory bridge was made up byprototype the To test condition environment. of the controller half in the realSM environment, a 200 W IGBT MMC was built in the laboratory environment. The half bridge SM was made up by the IGBT IKCM15F60GA IKCM15F60GA (600 V/15 A, Infineon). The digital control was implemented on a floating-point prototype was built in the laboratory environment. The half bridge SM was made up by the IGBT (600 V/15 A, Infineon). The digital control was implemented on a floating-point digital signal (FPGA) process digital signal process (DSP) TMS320F28335 and control a field-programmable gate IKCM15F60GA (600 V/15 A, Infineon). The digital was implemented on array a floating-point (DSP) TMS320F28335 and a field-programmable gate array (FPGA) Xilink-XC6SLX25. As Figure 18 Xilink-XC6SLX25. As Figure 18 shows, the DSP was to calculate the output voltage the digital signal process (DSP) TMS320F28335 andused a field-programmable gate arrayand (FPGA) shows, the DSP was used to calculate the output voltage and the FPGA generated the switching signals. FPGA generated theAs switching signals. The signal wastoimplemented the analog-to-digital Xilink-XC6SLX25. Figure 18 shows, the DSPsample was used calculate theby output voltage and the The signal (ADC) sample chip was implemented by the analog-to-digital converter (ADC) chip the AD7606. Other converter AD7606. Other parameters are shown in Table 1 and experiment FPGA generated the switching signals. The signal sample was implemented by the analog-to-digital parameters are shown in Table 1 and the experiment prototype is shown in Figure 19. prototype shown in Figure 19. converteris (ADC) chip AD7606. Other parameters are shown in Table 1 and the experiment prototype is shown in Figure 19.
Figure 18. 18. The The hardware architecture architecture and and functional introduction of the control system. DSP: digital Figure process. signal process. Figure 18. The hardware architecture andsignal functional introduction of the control system. DSP: digital signal process.
The current and voltage waveforms under the unit power factor situation controlled by the conventional power factor OCC controller and the reactive-power-controlled OCC controller are shown in Figure 20a,b, respectively, and both of them have sinusoidal current waveforms with fewer ripples. Compared with the simulation results, the current in the experiment is smaller due to the limitation of the hardware conditions, but the conclusion that the current waveform shown in Figure 20b is closer to the unit power factor relative to Figure 20a can be obtained by observing the zero-crossing point of the current waveform. Figure 21 shows the equivalent AC side output voltage of the MMC and the five-level voltage output can be clearly seen from that figure.
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Figure19. 19.Experiment Experimentprototype. prototype. Figure
The current current and and voltage voltage waveforms waveforms under under the the unit unit power power factor factor situation situation controlled controlled by by the the The conventional power factor OCC controller and the reactive-power-controlled OCC controller are conventional power factor OCC controller and the reactive-power-controlled OCC controller are shown in in Figure Figure 20a,b, 20a,b, respectively, respectively, and and both both of of them them have have sinusoidal sinusoidal current current waveforms waveforms with with shown fewer ripples. Compared with the simulation results, the current in the experiment is smaller due to fewer ripples. Compared with the simulation results, the current in the experiment is smaller due to the limitation of the hardware conditions, but the conclusion that the current waveform shown in the limitation of the hardware conditions, but the conclusion that the current waveform shown in Figure 20b 20b isis closer closer to to the the unit unit power power factor factor relative relative to to Figure Figure 20a 20a can can be be obtained obtained by by observing observing the the Figure zero-crossing point of the current waveform. Figure 21 shows the equivalent AC side output zero-crossing point of the current waveform. Figure 21 shows the equivalent AC side output voltageof ofthe theMMC MMCand andthe thefive-level five-level voltage outputcan can beclearly clearlyseen seenfrom fromthat thatfigure. figure. Figure 19. Experiment Experiment prototype. voltage voltage output be Figure 19. prototype. The current and voltage waveforms under the unit power factor situation controlled by the conventional power factor OCC controller and the reactive-power-controlled OCC controller are shown in Figure 20a,b, respectively, and both of them have sinusoidal current waveforms with fewer ripples. Compared with the simulation results, the current in the experiment is smaller due to the limitation of the hardware conditions, but the conclusion that the current waveform shown in Figure 20b is closer to the unit power factor relative to Figure 20a can be obtained by observing the zero-crossing point of the current waveform. Figure 21 shows the equivalent AC side output voltage of the MMC and the five-level voltage output can be clearly seen from that figure. (a) (a)
(b) (b)
20. The under the the unit unit power power factor factor situation situation controlled controlled by: Figure 20. 20. The current current and and voltage voltage waveforms waveformsunder controlledby: Figure powerfactor factorOCC OCCcontroller; controller;(b) (b)reactive-power-controlled reactive-power-controlledOCC OCCcontroller. controller. (a) traditional traditional unit unit power power factor OCC controller; (a) controller.
(a)
(b)
Figure 20. The current and voltage waveforms under the unit power factor situation controlled by: (a) traditional unit power factor OCC controller; (b) reactive-power-controlled OCC controller.
Figure21. 21.The Theequivalent equivalentAC ACside sideoutput outputvoltage voltageof of the the MMC. MMC. Figure
The dynamic characteristics of the conventional unit power factor OCC controller are shown ∗ . changed, because of the effect of the PI controller, in Figure 22. After DC voltage reference uDC the current increases rapidly and the DC voltage gradually rises. The variation of three SM capacitor voltages are also shown, where VSM1 and VSM2 are the upper arm SM voltages and VSM3 is a lower arm SM voltage. It can be seen that the voltages of the three SMs are basically the same throughout the entire process and the voltage oscillation increases as the current increases. Figure 21. The equivalent AC side output voltage of the MMC.
The dynamic characteristics of the conventional unit power factor OCC controller are shown in The dynamic characteristics of the conventional unit power factor OCC controller are shown in ∗∗ Figure 22. Figure 22. After After DC DC voltage voltage reference reference 𝑢DC changed, changed, because because of of the the effect effect of of the the PI PI controller, controller, the the current current increases increases rapidly rapidly and and the the DC DC voltage voltage gradually gradually rises. rises. The The variation variation of of three three SM SM capacitor capacitor voltages are also shown, where 𝑉SM1 and the upper arm SM voltages and 𝑉SM3 is a lower voltages are also shown, where and 𝑉SM2 are are the upper arm SM voltages and is a lower arm SM2019, voltage. arm SM voltage. It can be seen that the voltages of the three SMs are basically the same throughout Energies 12, 157 It can be seen that the voltages of the three SMs are basically the same throughout 14 of 17 the entire process and the voltage oscillation increases as the current increases. the entire process and the voltage oscillation increases as the current increases.
Figure thethe dynamic response when thethe DCDC voltage reference changed: (a) Figure 22. 22.Experiment Experimentresults resultsforfor dynamic response when voltage reference changed: Figure 22. Experiment results for the dynamic response when the DC voltage reference changed: (a) DC bus voltage; (b) SM voltages. (a) DC bus voltage; (b) SM voltages. DC bus voltage; (b) SM voltages.
For the OCC controller, thethe situations are shown in Figure 23, the23, power For reactive-power-controlled OCC controller, situations are in the For the reactive-power-controlled reactive‐power‐controlled OCC controller, the situations are shown shown in Figure Figure 23, the π π π π factor angles ϕS are 4φ and all of them have thehave samethe active current. dynamic power factor angles ,,− ,, respectively, and all of them have the same active current. The respectively, and all of them same active The current. The are are power factor angles φ,S − 4 , respectively, 4 4 responseresponse when thewhen reactive power reference becomesbecomes the opposite of the original value isvalue shown dynamic the reactive power reference the opposite of the original is dynamic response when the reactive power reference becomes the opposite of the original value is in Figure 24. As can be seen from the figure, the adjustment of the reactive power is completed in shown in Figure 24. As can be seen from the figure, the adjustment of the reactive power is shown in Figure 24. As can be seen from the figure, the adjustment of the reactive power is two cycles and although and the DC side voltage has some slighthas fluctuation duefluctuation to the influence of the completed the DC voltage due DC side side voltage has some some slight slight fluctuation due to to the the completed in in two two cycles cycles and although although the disturbance, the steady-state value of the DC voltage has not changed significantly, which means the influence of the disturbance, the steady-state value of the DC voltage has not changed significantly, influence of the disturbance, the steady‐state value of the DC voltage has not changed significantly, active means power the has active not been affected by the change of reactive power.of reactive power. which power has not been affected by the change which means the active power has not been affected by the change of reactive power.
(a) (a)
(b) (b)
Figure23. 23.Experiment Experimentresults resultsfor forthe thesteady-state steady-stateperformance performanceof ofthe thereactive-power-controlled reactive-power-controlled OCC OCC Figure Figure 23. Experiment results for the steady‐state performance of the reactive‐power‐controlled OCC 𝜋 𝜋 controller: (a) (a) φ ϕ = π4;; (b) ; (b)φ ϕSS==−− .π4. . controller: (b) φ controller: (a) φSS = 4
4
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Figure 24.Experiment Experiment results forthe the dynamic response when the reactive reactive power reference Figure 24. results for response when the power reference changed. Figure 24. Experiment results fordynamic the dynamic response when the reactive power reference changed.
The steady-state performance ofof thethe four-quadrant OCC controller is shown in Figure 25. During The steady-state performance four-quadrant OCC controller is shown in Figure 25. 25. The steady-state performance of the four-quadrant OCC controller is shown in Figure these tests, thetests, DC side is connected to a 400 VtoDC power supply. Figure 25a,b shows25a,b the situation in During these the DC side is connected a 400 V DC power supply. Figure shows the During these tests, the DC side is connected to a 400 V DC power supply. Figure 25a,b shows the the inversion mode under the grid-connect or off-grid situation, respectively. For the off-grid MMC, situation in the mode under the grid-connect or off-grid situation, respectively. For For the the situation in inversion the inversion mode under the grid-connect or off-grid situation, respectively. the AC MMC, power the is replaced byisa replaced 100 Ω resistor. Figure 25c,d shows the case when the current lags off-grid AC power by a 100 Ω resistor. Figure 25c,d shows the case when the off-grid MMC, the AC powerπis replacedπby a 100 Ω resistor. Figure 25c,d shows the case when the πThe dynamic or leadslags the or ACleads source , respectively. is shown in 26; current thevoltage AC voltage , respectively. Thecharacteristic dynamic characteristic is Figure shown in in current lags or leads the source AC 2source voltage , respectively. The dynamic characteristic is shown 2 2 the working state of the system finishes the change from rectification mode to inversion mode in two Figure 26; the statestate of the finishes the change fromfrom rectification mode to inversion Figure 26; working the working of system the system finishes the change rectification mode to inversion cycles,inwhich showswhich the superior dynamic characteristic of the controller. mode two cycles, shows the superior dynamic characteristic of the controller. mode in two cycles, which shows the superior dynamic characteristic of the controller.
(a) (a)
(b) (b)
(c) (c)
(d) (d)
Figure 25. results for performance of the four-quadrant OCC controller: (a) (a) Figure 25.Experiment Experiment results forthe thesteady-state steady-state performance of of the four-quadrant OCC controller: Figure 25. Experiment results for the steady-state performance the four-quadrant OCC controller: grid-connect inversion; (b) off-grid inversion; (c) capacitive reactive power output; (d) inductive (a) grid-connect inversion; (b) off-grid inversion; (c) capacitive reactive power output; (d) inductive grid-connect inversion; (b) off-grid inversion; (c) capacitive reactive power output; (d) inductive reactive power output. reactive power output. reactive power output.
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Figure Figure 26. 26. The performance performance when when changed changed from from rectification rectificationmode modeto toinversion inversionmode. mode.
6. Conclusions 6. Conclusions This paper proposes a modified OCC for MMCs. It uses the equivalent resistance constant This paper proposes a modified OCC for MMCs. It uses the equivalent resistance constant principle so that the modulation strategy can be separated from the control strategy. By adding the principle so that the modulation strategy can be separated from the control strategy. By adding the equivalent impedance into the controller, the proposed OCC-based MMC controller can control reactive equivalent impedance into the controller, the proposed OCC-based MMC controller can control power output and makes MMC operate in the inverter mode. Compared with the traditional OCC reactive power output and makes MMC operate in the inverter mode. Compared with the used in MMCs, the proposed one has the following advantages: (1) unlike the traditional controller traditional OCC used in MMCs, the proposed one has the following advantages: (1) unlike the which can only use CPS-PWM to generate the switch signals, the modified one can be combined with traditional controller which can only use CPS-PWM to generate the switch signals, the modified both NLM and CPS-PWM; (2) compared to the traditional one which can only operate at the unity one can be combined with both NLM and CPS-PWM; (2) compared to the traditional one which can power factor, the proposed one expands the range of applications for the OCC-based MMC controller. only operate at the unity power factor, the proposed one expands the range of applications for the Finally, the proposed controllers have been evaluated and validated by both simulation under the OCC-based MMC controller. Finally, the proposed controllers have been evaluated and validated MATLAB/SIMULINK platform and an experiment on a five-level single-phase MMC prototype. by both simulation under the MATLAB/SIMULINK platform and an experiment on a five-level single-phase MMC prototype. Author Contributions: X.T. and Y.M. conceived and designed the study; Y.M. and J.Y. performed the simulations and experiments; C.W. and H.C. reviewed the manuscript and provided valuable suggestions; Y.M. wrote the paper.Contributions: X.T. and Y.M. conceived and designed the study; Y.M. and J.Y. performed the Author simulations experiments; C.W. H.C. Key reviewed the manuscript and provided valuable suggestions; Funding: Thisand research was funded byand National R&D Program of China under grant number 2017YFB1200800 Y.M.National wrote the paper.Science Foundation of China grant number 51707194. and Natural Conflicts Interest: The authors declare by no conflict of interest. Funding:ofThis research was funded National Key R&D Program of China under grant number 2017YFB1200800 and National Natural Science Foundation of China grant number 51707194.
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