CN117792063A - Hybrid modular multilevel converter AC/DC side precharge starting control strategy - Google Patents
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Abstract
The invention relates to the technical field of converter starting control, and discloses a mixed modularized multi-level converter alternating current/direct current side pre-charging starting control strategy. In order to realize lower switching loss, DS is controlled at lower frequency to realize combination and switching of the pre-charge state, and sub-modules in SC are switched alternately based on a sub-module boost control algorithm so as to adjust and maintain the pre-charge starting voltage value of each sub-module and the voltage balance between the sub-modules. The invention considers the active network power supply starting and the passive network power supply starting, realizes a safe and stable pre-charging control strategy of the HMC in the double-end and multi-end systems, and has good balance effect of the capacitance voltage of the sub-module in the pre-charging process.
Description
Technical Field
The invention relates to the technical field of converter starting control, in particular to a mixed modularized multi-level converter alternating current/direct current side pre-charging starting control strategy.
Background
At present, the traditional modularized multi-level converter (Modular Multilevel Converter, MMC) is widely applied to high-voltage direct-current transmission engineering due to the advantages of good harmonic characteristics, easy expansion and the like, and simultaneously, domestic and foreign scholars develop a great deal of researches on modeling, control, protection and the like of the MMC, and related theories and technologies gradually tend to be mature. In recent years, in order to further solve the problems of the conventional MMC, many scholars continuously improve and reform in terms of their topologies, and a hybrid modular multilevel topology concept is proposed, which includes a hybrid between different types of sub-modules, a hybrid between a power switch and a sub-module, and the like. The hybrid modular multilevel converter (Hybrid Multilevel Converter, HMC) has the characteristics of traditional MMC modularization, low harmonic wave and the like in a topological form of a submodule set (Submodule Collection, SC) combined Direction Switch (DS) formed by cascading full-bridge submodules, the quantity of the submodules is saved by about 59%, the capacitance value of the submodules is reduced by about 51%, the size and the weight of the converter are greatly reduced, the direct current fault ride-through capability is achieved, and the hybrid modular multilevel converter has stronger advantages in practical application with higher space requirements such as an offshore wind power station.
In practical engineering, the starting control is a basic condition for realizing the normal operation of the converter, and is generally required to be carried out with lower electric impact in a shorter time in the starting process, so that the equipment safety and the personal safety are ensured. At present, a plurality of scholars develop extensive researches on the starting control of the traditional MMC, and the scholars propose a control strategy for realizing the stable starting of the MMC through a three-phase alternating current power grid and a public direct current bus, and meanwhile, the balance problem of a submodule in the charging process is ensured; further, a plurality of students put forward a double-end precharge control strategy in the aspect of double-station cooperative start control, so that the unlocking conditions and the precedence relationship of the two stations are analyzed, and the problem of 'black start' of a power supply end of a passive system is solved; in the starting control of the multi-terminal system, a learner proposes to judge and select the charging mode of each terminal converter under the condition of the system short-circuit ratio, and a reliable unlocking scheme of the multi-terminal system comprising an active station and a passive station is provided. Since HMC was proposed, many students have studied on modulation, capacitance-voltage balance, sub-module redundancy design, etc., but all the above studies have been established under the condition that HMC is normally started and operated in an ideal state, and there are few intensive analyses of the HMC starting process and its voltage balance control. Meanwhile, due to topological deformation, the existing starting control strategy of the traditional MMC is relatively weak in applicability to the HMC, and in general, a feasible scheme for starting control of the HMC is lacking.
Disclosure of Invention
Aiming at the problems, the invention aims to provide a mixed modularized multi-level converter alternating current/direct current side pre-charge starting control strategy, which considers active network power supply starting and passive network power supply starting, realizes a safe and stable pre-charge control strategy of HMC in a double-end and multi-end system, and realizes a good balance effect of sub-module capacitor voltage in the pre-charge process. The technical proposal is as follows:
the alternating current side pre-charging starting control strategy of the hybrid modular multilevel converter comprises an upper group of direction switches and a lower group of direction switches in each phase of the topology structure of the hybrid modular multilevel converter, and a power supply is connected with the upper group of direction switches and the lower group of direction switches by the upper group of direction switches and the lower group of direction switchesNSC formed by cascading the full-bridge submodules; each group of direction switches comprisesN DS A plurality of series connected IGBTs/diodes; the alternating current side is provided with an alternating current side precharge current limiting resistorR lim Current limiting resistorR lim Two ends are connected with bypass switches in parallelK lim ；
The control strategy comprises the following steps:
step A1: open bypass switchK lim Connected into the current-limiting resistorR lim And an alternating-current side power supply for controlling the HMC to enter a three-phase full-bridge uncontrolled charging state;
step A2: detection of 3 in three-phase SCNThe capacitor voltage of each sub-module and the capacitor voltage of the direct current side reach steady state values, three groups of upper directional switches are conducted, the capacitors of the direct current side are cut off, and each phase of SC is alternately inputT AC The submodule is used for switching the HMC to the three-phase SC alternating charging state;
step A3: detection of 3 in three-phase SCNThe capacitor voltages of all the sub-modules reach rated values, all the sub-modules of the three-phase SC are cut off, the unlocking direct-current side capacitor is put into a charging loop, and the HMC is switched back to the three-phase full-bridge uncontrolled charging state;
step A4: detecting that the capacitor voltage at the direct current side reaches a steady-state value, and closing a bypass switchK lim Short-circuit alternating-current side precharge current-limiting resistorR lim The alternating-current side precharge is completed.
Further, the steady state value of the capacitance voltage of each sub-module in the three-phase full-bridge uncontrolled charging state is approximately calculated as:
（1）；
（2）；
（3）；
（4）；
（5）；
when the charging loop enters steady state:
（6）；
（7）；
wherein,C sc the total capacitance value of each phase SC;C sm a single submodule capacitance value for each phase SC;Nthe number of SC sub-modules for each phase;U cdc the voltage value of the capacitor at the direct current side;U cdc （t) Is thattA capacitor voltage value at the DC side at the moment;C dc the capacitance value is the direct current side capacitance value;i uncontrolled （t) Is thattThe current in the loop is controlled in a moment three-phase full-bridge uncontrolled charging state;U csc a time domain representation of the total capacitance voltage value for single phase SC;U csc （t) Is thattTime domain representation of the time-of-day single-phase SC total capacitance voltage value;U lm is the alternating side line voltage peak;indicated at 0 to->Integration over a range of moments; />Indicated at 0 to->Integration within a range, +.>Representing the charging time of the capacitor in a charged state;U csm a single submodule capacitor voltage value for each phase SC;Mis a modulation degree;U dc the voltage value is rectified for the direct current side when the converter works normally;U csmN rated voltage value for each phase SC single submodule; in the three-phase full-bridge uncontrolled charging state,U cdc (0) AndU csc (0) The initial values of the DC side capacitance and the total capacitance voltage of each phase SC are respectively,U cdc (0)=U csc (0)=0；
the simultaneous formulas (1) to (7) obtain the capacitance voltage value of each phase SC single submodule when the three-phase full-bridge uncontrolled charging state of the HMC enters a steady stateU csm And a DC side capacitor voltage valueU cdc Is a value of (1):
（8）；
（9）；
wherein,K c is a coefficient of the capacitance ratio,＜0.5，/>。
further, in the step A2, the three-phase SC alternate charging steady-state equation is:
（10）；
（11）；
（12）；
（13）；
wherein,Q AC excision of the number of submodules for each phase of SC;T AC putting in the number of submodules for each phase of SC;ceilto round the function upwards, sub-module overcharging caused by calculation errors is avoided.
Further, in the step A3, the voltage at the steady state of the dc side capacitor in the charged state is:
（14）；
（15）；
wherein,U cdcN rated for direct current side capacitance; when each submodule of the three-phase SC is cut off, the steady voltage value of the capacitor voltage at the direct current side is 0.95-1.1 under the three-phase full bridge uncontrolled charging stateU cdcN 。
The DC side pre-charging starting control strategy of the hybrid modular multilevel converter comprises an upper group of direction switches and a lower group of direction switches in each phase of the topology structure of the hybrid modular multilevel converter, and a power supply circuit is connected with the upper group of direction switches and the lower group of direction switches in the topology structure of the hybrid modular multilevel converterNSC formed by cascading the full-bridge submodules; each group of direction switches comprisesN DS A plurality of series connected IGBTs/diodes; the upper direction switch group is connected with a DC side current limiting resistorR lim-DC And a charging loop current limiting resistorR lim-Loop Current limiting resistorR lim-DC AndR lim-Loop two ends are respectively connected with a bypass switch in parallelK lim-DC AndK lim-Loop ；
the control strategy comprises the following steps:
step B1: open bypass switchK lim-DC AndK lim-Loop connected into the current-limiting resistorR lim-DC AndR lim-Loop closing an isolation disconnecting link on a direct current bus and a direct current side capacitorC dc Charging;
step B2: detecting that the capacitor voltage at the direct current side reaches the rated value, and closing the bypass switchK lim-DC Cut off the DC side current limiting resistorR lim-DC Current limiting resistor for keeping charging loopR lim-Loop Put into a charging loop;
step B3: turning on a group of upward direction switch groupsSp i And two other sets of lower direction switch setsSn j AndSn k ，i=a,b,c；j=a，b,c；k=a,b,c；i≠j≠kthe method comprises the steps of carrying out a first treatment on the surface of the Controlling the HMC to enter a three-phase SC duplicate uncontrolled charging state;
step B4: detection of 3 in three-phase SCNThe capacitor voltage of each submodule reaches a steady-state value, the input quantity of the parallel two-phase SC submodules of the branch is kept, and the SC of the main circuit phase is alternately inputN i The sub-module is used for switching the HMC to the three-phase SC duplicate alternating charging state;
step B5: detection in the main road phase SCNThe capacitance voltage of each sub-module reaches rated value, and the upper direction switch group is turned offSp i And turn on the upper direction switch groupSp j And down direction switch groupSn k SC rotation input per phaseT DC The submodule is used for switching the HMC to a charging state of two-phase serial wheels;
step B6: detection of 2 in two-phase SCNThe capacitance voltage of each sub-module reaches rated value, and the bypass switch is closedK lim-Loop Short circuit charging loop current limiting resistorR lim-Loop The direct-current side precharge is completed.
Further, in the step B3, when the three-phase SC is in parallel connection and the uncontrolled charging state is stable, the capacitance voltage values of each sub-module of the three-phase SC are calculated as follows:
（16）；
（17）；
（18）；
（19）；
（20）；
（21）；
wherein,C sci the capacitance value of the main road phase SC in the three-phase SC duplicate uncontrolled charging state is obtained;C scj andC sck two-phase SC capacitance values of two branches under the three-phase SC duplicate uncontrolled charging state are respectively obtained,j，k≠i；C sm a single submodule capacitance value for each phase SC;C parallel equivalent capacitance value for parallel connection of the branches;U csmN rated voltage value for each phase SC single submodule;U dc is a direct-current side voltage value;U csmx is thati，j，kThe capacitance voltage value of a single sub-module of the three-phase SC,x =i，j，k；U cscx is thati，j，kThe voltage value of the three-phase SC capacitor,x =i，j，k；U csci （t）、U cscj （t) AndU csck （t) Is thattTime of dayi，j，kThree-phase SC capacitor voltage value;i series （t) Is thattDry circuit current value under three-phase SC duplicate uncontrolled charging state at moment;indicated at 0 to->Integration over a range of moments; />Representing the charging time of the capacitor in a charged state;U parallel （t) Is thattTime branch parallel connectionThe voltage value of the equivalent capacitor;
in the three-phase SC duplex uncontrolled charging state,U parallel (0) AndU csci (0) The initial voltage values of the branch parallel equivalent capacitor and the main circuit phase SC capacitor are respectively,U parallel (0)=U csci (0)=0。
further, in the step B3, the three-phase SC duplicate uncontrolled charging steady equation is:
（22）；
（23）；
（24）；
in step B4, the three-phase SC duplicate alternating charge state equation is:
（25）；
（26）；
（27）；
（28）；
（29）；
（30）；
wherein,U parallel the voltage value of the equivalent capacitor is connected in parallel to the branch circuit;N x the number of sub-modules is put into each period of each phase SC;U csci is thatiPhase SC capacitance voltage value;U csmi、 U csmj andU csmk respectively isi，j，kThree-phase SC single submodule capacitor voltage value;U dc the voltage value is rectified for the direct current side when the converter works normally;C eq-sci is thatiThe phase SC inputs an equivalent capacitance value in the charging loop every cycle;C sm a single submodule capacitance value for each phase SC;N i the number of inputs is changed for the trunk SC;U csmx is thati，j，kThe capacitance voltage value of a single sub-module of the three-phase SC,x =i，j，k；C eq-parallel is thatj、kThe equivalent capacitance value input into the charging loop every cycle when the two phases SC are connected in parallel;N parallel the same number of submodules is input for avoiding unbalance between parallel two-phase SCs when the charge state is changed for three-phase SC duplex connection;U csm-parallel is thatj、kThe capacitance voltage value of each sub-module when the two phases SC are connected in parallel;U ceqx put into each period for each phase SCN x Equivalent submodule pile SC constructed by submodules eqx Is used for the voltage value of the equivalent capacitor,x=i,j,k；U ceqi （t）、U ceqj （t) AndU ceqk （t) Respectively representtTime of dayi，j，kThree-phase SC input per cycleN x Equivalent submodule pile SC constructed by submodules eqx Is a capacitance equivalent voltage value;U eq-parallel （t) Is thattTime of dayj、kWhen the two phases SC are connected in parallel, the total voltage value of the submodule is input in each period;i roll （t) Is thattDry three-phase SC rotation switching under time reconnection stateA road current;indicated at 0 to->Integration over a range of moments; />Representing the charging time of the capacitor in a charged state;U ceqi (0) AndU eq-parallel (0) The initial values of the capacitor voltages respectively put into the charging loop for each cycle of the main circuit and the parallel circuit SC are expressed as follows:
（31）；
（32）；
wherein,U csmi (0) Is thatiPhase SC single submodule capacitor voltage initial value;U csm-parallel (0) Is thatj、kEach sub-module capacitor voltage initial value when the two phases SC are connected in parallel;N i the number of inputs is changed for the trunk SC.
Further, in the step B4, the three-phase SC duplex alternating charging steady-state equation is:
（33）；
（34）；
in the formula (i),U csmi is thatiPhase SC single submodule capacitance voltage value;
in order to reduce the switching times and energy loss of the IGBT, the parallel two-phase SC of the branch circuit is kept not to act in the state, and only the trunk circuit phase submodule is switched alternately, so that the trunk circuit phase is switchedWhen the capacitor voltage of each sub-module of SC is charged to the rated value, the number of SC alternate inputs of the main road is reversely solvedN i The method is characterized by comprising the following steps:
（35）；
order theWherein->As a discrimination variable, when->When not less than 0N i With real solutions whenWhen less than 0N i No solution, at this point->Constant > 0 holds true, thus regardingN i The equations of (2) are solved as:
（36）；
（37）；
in the formula (i),N i1 andN i2 to be aboutN i Two solutions of the equation of (2);Nis the number of the full-bridge sub-modules,ceilis an upward rounding function; in order to avoid the problems of overcurrent of a charging loop and overcharge of a sub-module capacitor, the number of main circuit SC rotation inputs is taken:N i =ceil(N i1 )=ceil(0.674N)。
further, in the step B5, the two-phase serial wheel charging steady-state equation is:
（38）；
（39）；
（40）；
（41）；
wherein,Q DC excision of the number of submodules for each phase of SC;T DC putting in the number of submodules for each phase of SC;ceilfor the function of rounding upwards, the sub-module overcharge caused by calculation errors is avoided;U csm a single submodule capacitor voltage value for each phase SC.
Compared with the prior art, the invention has the beneficial effects that: the invention provides a starting precharge control strategy of a hybrid modular multilevel converter. To achieve lower switching loss, the DS is controlled at a lower frequency (50 Hz) to achieve the combination and switching of the precharge state, and the sub-modules in the SC are switched alternately based on a sub-module boost control algorithm to adjust and maintain the precharge starting voltage value of each sub-module and the voltage balance between the sub-modules. The invention considers the active network power supply starting and the passive network power supply starting, realizes a safe and stable pre-charging control strategy of the HMC in the double-end and multi-end systems, and has good balance effect of the capacitance voltage of the sub-module in the pre-charging process.
Drawings
Fig. 1 is a topological structure diagram of a hybrid modular multilevel converter.
Fig. 2 is a three-phase full-bridge uncontrolled state of charge equivalent circuit.
Fig. 3 is a three-phase SC-alternate state of charge equivalent circuit.
Fig. 4 is a dc side capacitor charging equivalent circuit.
Fig. 5 is an ac-side precharge control flow chart.
Fig. 6 is a dc side precharge equivalent loop.
Fig. 7 is a three-phase SC multiple uncontrolled state of charge equivalent charging loop.
Fig. 8 is a three-phase SC multiple alternate state charge equivalent circuit.
Fig. 9 is a series rotation state charge equivalent circuit.
Fig. 10 is a flowchart of the direct-current-side precharge control.
Detailed Description
The invention will now be described in further detail with reference to the drawings and to specific examples.
The topology structure of the hybrid modular multilevel converter of the invention is shown in figure 1, and each phase of the topology structure comprises an upper DS group and a lower DS group and a plurality of DS groupsNSub-module set SC formed by cascading all-bridge sub-modules (Full Bridge Submodule FBSM) x （x=a,b,c) Two parts, wherein each set of DS consists ofN DS The IGBTs/diodes are connected in series and are subjected to a part of voltage during normal operation.L sx （x=a,b,c) AndL dc the filter inductor is respectively an alternating current side three-phase filter inductor and a direct current side filter inductor;i sa、 i sb andi sc respectively the alternating current sidesa,b,cThree-phase current;C sm andC dc the full-bridge submodule capacitor and the direct-current side filter capacitor are respectively arranged;S px andS nx （x=a,b,c) Two groups of DS are respectively an upper group and a lower group;U s is the effective value of the alternating-current side phase voltage;U dc is a direct-current side voltage value;R lim the current limiting resistor is pre-charged on the alternating current side and is generally arranged on the network side of the connecting transformer, and can be replaced by a closing resistor in the circuit breaker on the alternating current side;R lim-DC andR lim-Loop the current limiting resistors are respectively precharged on the direct current side,K lim 、K lim-DC 、K lim-Loop and the bypass switches are respectively connected with the current limiting resistors in parallel. FBSM (Full Bridge Submodule) is a full-bridge sub-module.
According to the topological structure characteristic of HMC and its normal operation mechanism, in order to maintain the energy exchange balance in HMC period, the modulation degree of the normal operation of the topology is constrained as follows，/>. Meanwhile, along with the increase of the modulation degree, the voltage born by each phase SC in normal operation is changed from small to large, and the maximum bearing voltage value isU csc-max =0.82U dc . In order to ensure that the HMC is normally started within the constraint range of the whole modulation degree, the steady-state voltage value of the SC precharge of each phase should not be lower than the maximum bearing voltage value, so that in ideal cases, the capacitor voltage rating of each phase SC submodule is set to beU csmN =/>。
In actual engineering, if the current of a charging loop is suddenly changed due to improper starting control of an inverter, serious overvoltage and overcurrent are formed, so that great impact is caused on equipment and a power grid, and stable operation and personal safety of the power grid are not facilitated. Therefore, the invention provides a pre-charging control strategy based on state combination for HMC, and pre-charging starting control is respectively carried out through an alternating current side and a direct current side according to working conditions such as active network power supply starting and passive network power supply starting, so that the three-phase SC sub-module capacitor and the direct current side capacitor of the HMC are stably charged to rated voltage, the electric impact on a power grid system and the converter itself when a converter station is started is relieved, meanwhile, the voltage equalizing problem of the sub-module capacitor is considered, the phenomenon of unbalanced capacitor voltage in the pre-charging process of the sub-module is avoided, and the following two starting control methods are respectively introduced as follows:
1. active network power-on precharge control strategy
For HMC with an active network in an alternating current system, the HMC can be precharged and supplied with energy through an alternating current side network, and the capacitance voltage of the submodule and the capacitance voltage of the direct current side are gradually increased to rated values by switching the charging state. In actual engineering, the IGBT in the HMC circuit generally adopts a self-energy-taking mode to provide a driving voltage for the IGBT, and the driving voltage is generally 600 to 800v, so that the HMC is in a three-phase full-bridge uncontrolled charging state at the initial stage of the pre-charging on the ac side.
Step 1: first of all, a bypass switch connected in parallel with a current limiting resistor is openedK lim Charging circuit with current limiting resistorR lim And (3) accessing an alternating-current side power supply, and enabling the HMC to enter a three-phase full-bridge uncontrolled charging state.
In the three-phase full-bridge uncontrolled charging state, the IGBTs in the submodule and the direction switch are both turned off, the submodule is in a locking state, and the charging loop of the HMC is connected in series by each phase SC on the alternating current sideNThe sub-module capacitor and the three-phase full-bridge uncontrollable rectification no-load circuit with the capacitor at the direct current side are formed, and the precharge equivalent circuit is shown in figure 2. Wherein,U sx （x=a,b,c) Is the effective value of three-phase voltage at the alternating current side;is an ac side common connection point.
In the three-phase full-bridge uncontrolled charging loop, the DC side outputs voltageU cdc The ripple voltage is output six times in one cycle, each time the ripple voltage is the current maximum line voltage. According to the conduction principle of the IGBT anti-parallel diode, the alternating-current side three-phase SC is alternately input into the charging loop in the three-phase full-bridge uncontrolled charging state, so that each SC charging time is 2/3 of the power frequency period, the direct-current side capacitor is always input into the charging loop, the three-phase SC voltage and the submodule capacitor voltage are the same in the steady state, and the sum of the two-phase SC voltage and the direct-current side capacitor voltage input into the charging loop reaches the maximum value of the line voltageU lm 。
Considering that the capacitors of the three-phase SC submodules are identical ideal elements, neglecting the influence of the filter inductance, the steady-state value of the capacitor voltage of each submodule in the three-phase full-bridge uncontrolled charging state can be approximately calculated as:
（1）；
（2）；
（3）；
（4）；
（5）；
when the charging loop enters steady state:
（6）；
（7）；
wherein,C sc the total capacitance value of each phase SC;C sm a single submodule capacitance value for each phase SC;Nthe number of SC sub-modules for each phase;U cdc the voltage value of the capacitor at the direct current side;U cdc (t) Is thattA capacitor voltage value at the DC side at the moment;C dc the capacitance value is the direct current side capacitance value;i uncontrolled (t) Is thattThe current in the loop is controlled in a moment three-phase full-bridge uncontrolled charging state;U csc a time domain representation of the total capacitance voltage value for single phase SC;U csc (t) Is thattTime domain representation of the time-of-day single-phase SC total capacitance voltage value;U lm is the alternating side line voltage peak;indicated at 0 to->Integration within the time range, +.>Indicated at 0 to->Integration within the time range, +.>Representing the charging time of the capacitor in a charged state;U csm a single submodule capacitor voltage value for each phase SC;Mis a modulation degree;U dc the voltage value is rectified for the direct current side when the converter works normally;U csmN rated voltage value for each phase SC single submodule; in the three-phase full-bridge uncontrolled charging state,U cdc (0) AndU csc (0) The initial values of the DC side capacitance and the total capacitance voltage of each phase SC are respectively,U cdc (0)=U csc (0)=0。
the simultaneous formulas (1) to (7) can be obtained:
（8）；
（9）；
wherein,K c is a coefficient of the capacitance ratio,＜0.5，/>。
so that the number of the parts to be processed,U csm =＜0.55/>＜U csmN if the inverter is unlocked at this time, a large electrical shock is still caused, so that further control is required to makeU csm And (5) lifting to a rated voltage value.
Step 2: after the three-phase full-bridge uncontrolled charging state is stable, the HMC is switched to other charging states, and the charging steady-state voltage is further improved.
When detecting that the HMC enters a steady state in a three-phase full-bridge uncontrolled charging state, namelyU csm =And is also provided with。
At this time, all IGBTs in the converter have reached the driving condition, and the HMC can be switched to other charging states by further control. In order to reduce the mutual influence between the direct-current side capacitor and the submodule capacitor, the invention provides that the three-phase SC and the direct-current side capacitor are respectively subjected to independent boost control by combining different charging states so as to achieve the starting condition of the HMC, and the specific strategy is as follows:
step 2.1: and switching the HMC to a three-phase SC alternating charging state, and further improving the capacitance voltage of each phase of submodule to a rated value based on a boost control algorithm.
First turn onS pa 、S pb 、S pc The three upper directional switches cut off the direct-current side capacitor, and only put the three phases SC into the charging circuit, and the equivalent charging circuit is shown in figure 3.
Because of three-phase symmetry, each period in the charging loop is alternately input with two phases SC to bear line voltage togetherU lm At steady state, the following conditions are satisfied:
（10）；
as can be seen from the above, the two-phase SC in the charging loop is reduced in line voltageU lm Number of sub-modules of (a)NThe steady-state value of the capacitor voltage of the input submodule can be further improved. Meanwhile, considering the capacitance and voltage balance of each sub-module of the SC, the voltage value in the two-phase SC input into the charging loop is larger based on the sequencing algorithm in each periodQ AC The sub-modules are cut out of the charging circuit so that in each phase SCT AC The capacitor voltage of each sub-module is put into the charging loop and supports the peak value of the line voltage at two ends of the charging loop in steady stateU lm The method is specifically as follows:
（11）；
（12）；
in this state, the capacitance voltage values of each submodule of the three-phase SC at steady state are:
（13）；
wherein,Q AC excision of the number of submodules for each phase of SC;T AC putting in the number of submodules for each phase of SC;ceil（x) To round the function upwards, sub-module overcharging caused by calculation errors is avoided.
Step 2.2: and switching the HMC back to the three-phase full-bridge uncontrolled charging state, and further improving the direct-current side capacitor voltage to the rated value by utilizing the characteristic of an uncontrolled rectifying circuit.
And (3) conducting the two upper pipes of all the submodules in the three-phase SC, cutting off the two lower pipes, cutting off all the submodules, and throwing the unlocking direct-current side capacitor into a charging loop, wherein the equivalent charging loop is shown in fig. 4.
The voltage at the steady state of the DC side capacitor in this charge state is:
（14）；
（15）；
wherein,U cdcN is rated as DC side capacitance, and has modulation degree due to normal operation of HMCTherefore, when each submodule of the three-phase SC is cut off, the steady voltage value of the capacitor voltage at the direct current side is 0.95-1.1 under the state of uncontrolled charging of the three-phase full bridgeU cdcN 。
Step 3: after the capacitors of each submodule of the three-phase SC and the capacitor at the direct current side reach steady-state rated values in different charging states, a bypass switch connected in parallel with the current-limiting resistor is closedK lim Short-circuit alternating-current side precharge current-limiting resistorR lim Unlocking HMC and putting into normal operation.
In summary, when the active network supplies power, the ac side can supply power to the HMC, and the state combination-based ac side precharge control strategy provided by the present invention can smoothly and effectively implement the HMC start, and the specific process is shown in fig. 5.
2. Passive network power supply starting precharge control strategy
In the double-end flexible direct current transmission project, if a power failure accident occurs at the receiving end, the power grid of the receiving end can be equivalent to a passive network, and when the sending end establishes direct current voltage through the alternating current side, the power grid can be equivalent to a direct current voltage source to start the power supply for the receiving end. In the same way, in the multi-terminal flexible direct current transmission project, if the converter is connected with a passive island or one end of the converter is cut off due to power failure, black start can be performed through the established direct current bus voltage, and the equivalent circuit is shown in fig. 6. Wherein,U dc and the equivalent voltage of the direct current bus established for the transmitting end.
During the direct-current side precharge process, 6 groups of direction switchesS pj 、S nj （j=a，b，c) Since the IGBTs connected in series with each group of direction switches are connected in parallel to the dc side, the dc side precharge initial stage can be brought into a controllable charge state unlike the ac side precharge control. Therefore, the invention provides a state combination-based precharge control strategy for direct current side precharge, which is specifically introduced as follows:
step 1: first of all, a bypass switch connected in parallel with a current limiting resistor is openedK lim-DC AndK lim-Loop input DC side current limiting resistorR lim-DC And a charging loop current limiting resistorR lim-Loop Closing an isolation disconnecting link on a direct current bus and a direct current side capacitorC dc Charging is performed.
Step 2: capacitor at DC sideC dc After the voltage is stabilized, i.eU cdc =U dc The first stage of charging is finished, and the bypass switch is closedK lim-DC Cut off the DC side current limiting resistorR lim-DC Maintaining current limiting resistanceR lim-Loop And the device is put into a charging loop, and the direct current bus cooperates with the direct current side capacitor to precharge and supply power to the HMC.
Step 3: turning on a group of upward direction switchesS Pi （i=a,b,c) And two sets of down direction switchesS nj 、S nk （j=a，b,c;k=a,b,c;i≠j≠k) Since the capacitors of the sub-modules of the three-phase SC are not charged and the IGBT does not have driving conditions, HMC is represented by a three-phase SC in a parallel uncontrolled state of charge, and the equivalent circuit thereof is shown in fig. 7.
When the three-phase SC is in parallel connection and the uncontrolled charging state is stable, the capacitance voltage value of each submodule of the three-phase SC is calculated as follows:
（16）；
（17）；
（18）；
（19）；
（20）；
（21）；
when the charging loop enters a steady state, the following conditions are satisfied:
（22）；
in the above-mentioned description of the invention,C sci the capacitance value of the main road phase SC in the three-phase SC duplicate uncontrolled charging state is obtained;C scj ，C sck （j,k≠i) Two-phase SC capacitance values of two branches in a three-phase SC duplicate uncontrolled charging state are respectively obtained;C parallel equivalent capacitance value for parallel connection of the branches;U csmx is thati，j，kThe capacitance voltage value of a single sub-module of the three-phase SC,x =i，j，k；U cscx is thati，j，kThe voltage value of the three-phase SC capacitor,x =i，j，k；U csci （t）、U cscj （t) AndU csck （t) Is thattTime of dayi，j，kThree-phase SC capacitor voltage value;i series （t) Is thattDry circuit current value under three-phase SC duplicate uncontrolled charging state at moment;indicated at 0 to->Integration within the time range, +.>Representing the charging time of the capacitor in a charged state;U parallel （t) Is thattThe voltage value of the equivalent capacitor is connected in parallel with the branch circuit at the moment; in the three-phase SC duplex uncontrolled charging state,U parallel (0) AndU csci (0) The initial voltage values of the branch parallel equivalent capacitor and the main circuit phase SC capacitor are respectively,U parallel (0)=U csci (0)=0。
the simultaneous equations above can be obtained:
（23）；/>
（24）；
at this time, the liquid crystal display device,U csmi ≈0.81U csmN ，U csmj ＝U csmk ≈0.41U csmN if the inverter is unlocked at this time, a large electrical shock is still caused, so that further control is required to makeU csmx （x=i,j,k) And (5) lifting to a rated voltage value.
Step 4: when the HMC is stable in the three-phase SC duplicate uncontrolled charging state, each sub-module IGBT of the three-phase SC has driving conditions, the invention provides that the main circuit and the branch circuit phases SC are respectively subjected to independent boosting control by combining different charging states so as to achieve the starting conditions of the HMC, and the specific strategy is as follows:
step 4.1: and switching the HMC to the three-phase SC duplicate alternating charging state, and further improving the capacitance voltage of each submodule of the main road phase SC to the rated value based on a boost control algorithm.
From the capacitor voltage of each phase SCU cscx （x=i,j,k) Capacitance voltage with sub-module thereofU csmx （x=i,j,k) As can be seen from the relationship of (a) in the charging circuit in this state, if the number of submodules charged into each phase SC is reducedNThe steady-state value of the capacitor voltage of the input submodule can be further improved, the three-phase SC and the capacitor voltage balance of each submodule are considered, and the capacitor voltage of the input submodule is balanced at the SC based on a sequencing algorithm i ，SC j ，SC k The input quantity of the three-phase inner wheel replacement in each period isN i ,N j ,N k To avoid energy unbalance between the parallel two phases SC at this stage, the submodule with the lowest capacitance voltage is used to makeN j =N k =N parallel And (2) andN i ,N j ,N k ≤N，N i +N j +N k <3N。
during the rapid rotation of the sub-modules of each phase SC, each sub-module of each phase SC is charged, but each phase SC only exists in the same periodN x （x=i,j,k) The sub-modules remain in the charging loop, so each phase SC can be equivalentlyN/N x The same branch circuits are connected in parallel, each branch circuit is connected in seriesN x Equivalent circuits of sub-modules, each defined byN x The branch circuit formed by serially connecting the sub-modules is an equivalent sub-module stack SC eqx （x=i,j,k) As shown in fig. 8.
When the three-phase SC cascade rotation charging state is stable, the capacitance voltage value of each phase SC submodule is calculated as follows:
（25）；
（26）；
（27）；
（28）；
（29）；
（30）；
when the charging loop enters a steady state, the following conditions are satisfied:
（31）；
wherein,U csmi is thatiPhase SC single submodule capacitance voltage value;C eq-sci is thatiThe phase SC inputs an equivalent capacitance value in the charging loop every cycle;N i the number of inputs is changed for the trunk SC;C eq-parallel is thatj、kThe equivalent capacitance value input into the charging loop every cycle when the two phases SC are connected in parallel;N parallel the same number of submodules is input for avoiding unbalance between parallel two-phase SCs when the charge state is changed for three-phase SC duplex connection;U csm-parallel is thatj、kThe capacitance voltage value of each sub-module when the two phases SC are connected in parallel;U ceqx put into each period for each phase SCN x Equivalent submodule pile SC constructed by submodules eqx Is used for the voltage value of the equivalent capacitor,x= i,j,k；U ceqi （t）、U ceqj （t) AndU ceqk （t) Respectively representtTime of dayi，j，kThree-phase SC input per cycleN x Constructed of sub-modulesEquivalent submodule stack SC eqx Is a capacitance equivalent voltage value;U eq-parallel （t) Is thattTime of dayj、kWhen the two phases SC are connected in parallel, the total voltage value of the submodule is input in each period;i roll （t) Is thattMain circuit current when three-phase SC switches in turn under the state of time reconnection;indicated at 0 to->Integration within the time range, +.>Representing the charging time of the capacitor in a charged state;U ceqi (0) AndU eq-parallel (0) The initial values of the capacitor voltages respectively put into the charging loop for each cycle of the main circuit and the parallel circuit SC are expressed as follows:
（32）；
（33）；
the simultaneous equations above can be obtained:
（34）；
（35）；
wherein,U csmi is thatiPhase SC single submodule capacitance voltage value;U csmi (0) AndU csm-parallel for the steady-state voltage value of the three-phase SC parallel uncontrolled charging state,U csmi (0)=，U csm-parallel (0)=/>. As can be seen from the above, whenN i AndN parallel when determining%N i ，N parallel ≤NAnd is an integer),U csmi there is a corresponding unique solution.
In order to reduce the switching times and energy loss of the IGBT, two parallel-connected branch circuits are kept not to act in the state, and only the trunk circuit phase submodules are alternately switched, so that when the capacitor voltage of each submodule of the trunk circuit phase SC is charged to the rated value, the number of trunk circuit SC alternately switched can be reversely solvedN i The method is characterized by comprising the following steps:
N parallel =N（36）；
（37）；
=0（38）；
the simultaneous equations above can be relatedN i Is a unitary quadratic equation of (a):
（39）；
the distinguishing method comprises the following steps:=0.77/>> 0, thus concerningN i The equations of (2) are solved as:
（40）；
（41）；
in the formula (i),N i1 andN i2 to be aboutN i Two solutions of the equation of (2);Nis the number of the full-bridge sub-modules,ceilis an upward rounding function; in order to avoid the problems of overcurrent of a charging loop and overcharge of a sub-module capacitor, the number of main circuit SC rotation inputs is taken:N i =ceil(N i1 )=ceil(0.674N)。
in summary, in the state of charge of the multiple rotation, the parallel-branch two-phase SCNThe submodules are fully put into charge, and the main road SC phase is alternately put into charge with lower voltage based on a sequencing algorithmN i A sub-module, whereinN i =ceil(0.674N), it can be known from the formula (37) that the dry phase SC voltage value can be raised toU csmi =Left and right, at this time, the parallel connection two-phase SC voltage value is increased toU csm-parallel= />＜U csmN It is therefore necessary to continue switching the state of charge to boost the parallel two-phase SC voltage to nominal.
Step 4.2: after the three-phase SC multi-connection alternating charging state is stable, switching to the two-phase SC serial alternating charging state further improves the capacitance voltage of each sub-module of the two-phase SC of the parallel branch to the rated value.
First turn offiPhase direction switch setS ui Excision of SC i On, turn onjPhase direction switch setS uj Andkphase-down direction switch groupS uk So that SC j And SC (SC) k A series charging loop is formed with the dc side voltage as shown in fig. 9.
In this charging state, the voltage values in the two phases SC fed into the charging circuit are respectively increased in each cycle based on the ranking algorithmQ DC The sub-modules are cut out of the charging circuit so that in each phase SCT DC The capacitor voltage of each sub-module is put into the charging loop and bears the direct current voltage at two ends of the charging loop in steady stateU dc The method is specifically as follows:
（42）；
（43）；
（44）；
in this state, the capacitance voltage values of each submodule of the two-phase SC at steady state are:
（45）；
wherein,Q DC excision of the number of submodules for each phase of SC;T DC putting in the number of submodules for each phase of SC;ceil（x) To round the function upwards, sub-module overcharging caused by calculation errors is avoided.
Step 5: when each submodule of the three-phase SC reaches a steady-state rated value in different charging states, a bypass switch connected in parallel with the current-limiting resistor is closedK lim-Loop Short circuit charging loop current limiting resistorR lim-Loop Unlocking HMC and putting into normal operation.
In summary, the power supply of the HMC can be performed by the established dc bus voltage during the passive network power supply, and the state combination-based dc side precharge control strategy provided by the present invention can smoothly and effectively implement the HMC start, and the specific process is shown in fig. 10.
Claims (9)
1. The alternating current side pre-charging starting control strategy of the hybrid modular multilevel converter comprises an upper group of direction switches and a lower group of direction switches in each phase of the topology structure of the hybrid modular multilevel converter, and a power supply is connected with the upper group of direction switches and the lower group of direction switches by the upper group of direction switches and the lower group of direction switchesNSC formed by cascading the full-bridge submodules; each group of direction switches comprisesN DS A plurality of series connected IGBTs/diodes; the alternating current side is provided with an alternating current side precharge current limiting resistorR lim Current limiting resistorR lim Two ends are connected with bypass switches in parallelK lim ；
The control strategy is characterized by comprising the following steps:
step A1: open bypass switchK lim Connected into the current-limiting resistorR lim And an alternating-current side power supply for controlling the HMC to enter a three-phase full-bridge uncontrolled charging state;
step A2: detection of 3 in three-phase SCNThe capacitor voltage of each sub-module and the capacitor voltage of the direct current side reach steady state values, three groups of upper directional switches are conducted, the capacitors of the direct current side are cut off, and each phase of SC is alternately inputT AC The submodule is used for switching the HMC to the three-phase SC alternating charging state;
step A3: detection of 3 in three-phase SCNThe capacitor voltages of all the sub-modules reach rated values, all the sub-modules of the three-phase SC are cut off, the unlocking direct-current side capacitor is put into a charging loop, and the HMC is switched back to the three-phase full-bridge uncontrolled charging state;
step A4: detecting that the capacitor voltage at the direct current side reaches a steady-state value, and closing a bypass switchK lim Short-circuit alternating-current side precharge current-limiting resistorR lim The alternating-current side precharge is completed.
2. The hybrid modular multilevel converter ac side precharge starting control strategy of claim 1, wherein the steady state value of each sub-module capacitor voltage in the three-phase full-bridge uncontrolled charge state is approximately calculated as:
（1）；
（2）；
（3）；
（4）；
（5）；
when the charging loop enters steady state:
（6）；
（7）；
wherein,C sc the total capacitance value of each phase SC;C sm a single submodule capacitance value for each phase SC;Nthe number of SC sub-modules for each phase;U cdc the voltage value of the capacitor at the direct current side;U cdc （t) Is thattA capacitor voltage value at the DC side at the moment;C dc the capacitance value is the direct current side capacitance value;i uncontrolled （t) Is thattThe current in the loop is controlled in a moment three-phase full-bridge uncontrolled charging state;U csc a time domain representation of the total capacitance voltage value for single phase SC;U csc （t) Is thattTime domain representation of the time-of-day single-phase SC total capacitance voltage value;U lm is the alternating side line voltage peak;indicated at 0 to->Integration over a range of moments; />Indicated at 0 to->Integration within a range, +.>Representing the charging time of the capacitor in a charged state;U csm a single submodule capacitor voltage value for each phase SC;Mis a modulation degree;U dc the voltage value is rectified for the direct current side when the converter works normally;U csmN rated voltage value for each phase SC single submodule; in the three-phase full-bridge uncontrolled charging state,U cdc (0) AndU csc (0) The initial values of the DC side capacitance and the total capacitance voltage of each phase SC are respectively,U cdc (0)=U csc (0)=0；
the simultaneous formulas (1) to (7) obtain the capacitance voltage value of each phase SC single submodule when the three-phase full-bridge uncontrolled charging state of the HMC enters a steady stateU csm And a DC side capacitor voltage valueU cdc Is a value of (1):
（8）；
（9）；
wherein,K c is a coefficient of the capacitance ratio,＜0.5，/>。
3. the hybrid modular multilevel converter ac side precharge start control strategy of claim 2, wherein in step A2, the three-phase SC alternate charge steady state equation is:
（10）；
（11）；
（12）；
（13）；
wherein,Q AC excision of the number of submodules for each phase of SC;T AC putting in the number of submodules for each phase of SC;ceilto round the function upwards, sub-module overcharging caused by calculation errors is avoided.
4. A hybrid modular multilevel converter ac side precharge start-up control strategy according to claim 3, wherein in step A3, the voltage at steady state of the dc side capacitor in the charged state is:
（14）；
（15）；
wherein,U cdcN rated for direct current side capacitance; when each submodule of the three-phase SC is cut off, the steady voltage value of the capacitor voltage at the direct current side is 0.95-1.1 under the three-phase full bridge uncontrolled charging stateU cdcN 。
5. The DC side pre-charging starting control strategy of the hybrid modular multilevel converter comprises an upper group of direction switches and a lower group of direction switches in each phase of the topology structure of the hybrid modular multilevel converter, and a power supply circuit is connected with the upper group of direction switches and the lower group of direction switches in the topology structure of the hybrid modular multilevel converterNSC formed by cascading the full-bridge submodules; each group of direction switches comprisesN DS A plurality of series connected IGBTs/diodes; the upper direction switch group is connected with a DC side current limiting resistorR lim-DC And a charging loop current limiting resistorR lim-Loop Current limiting resistorR lim-DC AndR lim-Loop two ends are respectively connected with a bypass switch in parallelK lim-DC AndK lim-Loop ；
the control strategy is characterized by comprising the following steps:
step B1: open bypass switchK lim-DC AndK lim-Loop connected into the current-limiting resistorR lim-DC AndR lim-Loop closing an isolation disconnecting link on a direct current bus and a direct current side capacitorC dc Charging;
step B2: detecting that the capacitor voltage at the direct current side reaches the rated value, and closing the bypass switchK lim-DC Cut off the DC side current limiting resistorR lim-DC Current limiting resistor for keeping charging loopR lim-Loop Put into a charging loop;
step B3: turning on a group of upward direction switch groupsSp i And two other sets of lower direction switch setsSn j AndSn k ，i=a,b,c；j=a，b,c；k=a,b,c；i≠j≠kthe method comprises the steps of carrying out a first treatment on the surface of the Controlling the HMC to enter a three-phase SC duplicate uncontrolled charging state;
step B4: detection of 3 in three-phase SCNThe capacitor voltage of each submodule reaches a steady-state value, the input quantity of the parallel two-phase SC submodules of the branch is kept, and the SC of the main circuit phase is alternately inputN i The sub-module is used for switching the HMC to the three-phase SC duplicate alternating charging state;
step B5: detection in the main road phase SCNThe capacitance voltage of each sub-module reaches rated value, and the upper direction switch group is turned offSp i And turn on the upper direction switch groupSp j And down direction switch groupSn k SC rotation input per phaseT DC The submodule is used for switching the HMC to a charging state of two-phase serial wheels;
step B6: detection of 2 in two-phase SCNThe capacitance voltage of each sub-module reaches rated value, and the bypass switch is closedK lim-Loop Short circuit charging loop current limiting resistorR lim-Loop The direct-current side precharge is completed.
6. The dc side precharge starting control strategy of the hybrid modular multilevel converter according to claim 5, wherein in the step B3, when the three-phase SC is stable in the parallel uncontrolled charging state, the capacitance voltage values of each sub-module of the three-phase SC are calculated as follows:
（16）；
（17）；
（18）；
（19）；
（20）；
（21）；
wherein,C sci the capacitance value of the main road phase SC in the three-phase SC duplicate uncontrolled charging state is obtained;C scj andC sck two-phase SC capacitance values of two branches under the three-phase SC duplicate uncontrolled charging state are respectively obtained,j，k≠i；C sm a single submodule capacitance value for each phase SC;C parallel equivalent capacitance value for parallel connection of the branches;U csmN rated voltage value for each phase SC single submodule;U dc the voltage value is rectified for the direct current side when the converter works normally;U csmx is thati，j，kThe capacitance voltage value of a single sub-module of the three-phase SC,x =i，j，k；U cscx is thati，j，kThe voltage value of the three-phase SC capacitor,x =i，j，k；U csci （t）、U cscj （t) AndU csck （t) Respectively representtTime of dayi，j，kThree-phase SC capacitor voltage value;i series （t) Is thattDry circuit current value under three-phase SC duplicate uncontrolled charging state at moment;indicated at 0 to->Integration over a range of moments; />Representing the charging time of the capacitor in a charged state;U parallel （t) Is thattThe voltage value of the equivalent capacitor is connected in parallel with the branch circuit at the moment;U parallel the voltage value of the equivalent capacitor is connected in parallel to the branch circuit;
in the three-phase SC duplex uncontrolled charging state,U parallel (0) AndU csci (0) The initial voltage values of the branch parallel equivalent capacitor and the main circuit phase SC capacitor are respectively,U parallel (0)=U csci (0)=0。
7. the hybrid modular multilevel converter dc-side precharge start control strategy of claim 5, wherein in step B3, the three-phase SC parallel uncontrolled charge steady state equation is:
（22）；
（23）；
（24）；
in step B4, the three-phase SC duplicate alternating charge state equation is:
（25）；
（26）；
（27）；
（28）；
（29）；
（30）；
wherein,U parallel the voltage value of the equivalent capacitor is connected in parallel to the branch circuit;N x the number of sub-modules is put into each period of each phase SC;U csci is thatiPhase SC capacitance voltage value;U csmi、 U csmj andU csmk respectively isi，j，kThree-phase SC single submodule capacitor voltage value;U dc the voltage value is rectified for the direct current side when the converter works normally;C eq-sci is thatiThe phase SC inputs an equivalent capacitance value in the charging loop every cycle;C sm a single submodule capacitance for each phase SC;N i the number of inputs is changed for the trunk SC;C eq-parallel is thatj、kThe equivalent capacitance value input into the charging loop every cycle when the two phases SC are connected in parallel;N parallel the same number of submodules is input for avoiding unbalance between parallel two-phase SCs when the charge state is changed for three-phase SC duplex connection;U csm-parallel is thatj、kThe capacitance voltage value of each sub-module when the two phases SC are connected in parallel;U ceqx put into each period for each phase SCN x Equivalent submodule pile SC constructed by submodules eqx Is used for the voltage value of the equivalent capacitor,x=i,j,k；U csmx is thati，j，kThe capacitance voltage value of a single sub-module of the three-phase SC,x =i，j，k；U ceqi （t）、U ceqj （t) AndU ceqk （t) Respectively representtTime of dayi，j，kThree-phase SC input per cycleN x Equivalent submodule pile SC constructed by submodules eqx Is a capacitance equivalent voltage value;U eq-parallel （t) Is thattTime of dayj、kWhen the two phases SC are connected in parallel, the total voltage value of the submodule is input in each period;i roll （t) Is thattMain circuit current when three-phase SC switches in turn under the state of time reconnection;indicated at 0 to->Integration over a range of moments; />Representing the charging time of the capacitor in a charged state;U ceqi (0) AndU eq-parallel (0) The initial values of the capacitor voltages respectively put into the charging loop for each cycle of the main circuit and the parallel circuit SC are expressed as follows:
（31）；
（32）；
wherein,U csmi (0) Is thatiPhase SC single submodule capacitor voltage initial value;U csm-parallel (0) Is thatj、kEach sub-module capacitor voltage initial value when the two phases SC are connected in parallel;N i the number of inputs is changed for the trunk SC.
8. The hybrid modular multilevel converter dc-side precharge start control strategy of claim 7, wherein in step B4, the three-phase SC multiple alternate charge steady state equation is:
（33）；
（34）；
in the formula (i),U csmi is thatiPhase SC single submodule capacitance voltage value;
in order to reduce the switching times and energy loss of the IGBT, two parallel-connected branches of the SCs are kept not to act in the state, and only the trunk-phase submodules are switched alternately, so that when the capacitor voltage of each submodule of the trunk-phase SC is charged to the rated value, the number of the trunk-phase SC switched alternately is solvedN i The method is characterized by comprising the following steps:
（35）；
order theWherein->As a discrimination variable, when->When not less than 0N i With real solution, when->When less than 0N i No solution, at this point->Constant > 0 holds true, thus regardingN i The equations of (2) are solved as:
（36）；
（37）；
in the formula (i),N i1 andN i2 to be aboutN i Two solutions of the equation of (2);Nis the number of the full-bridge sub-modules,ceilis an upward rounding function; in order to avoid the problems of overcurrent of a charging loop and overcharge of a sub-module capacitor, the number of main circuit SC rotation inputs is taken:N i =ceil(N i1 )=ceil(0.674N)。
9. the hybrid modular multilevel converter dc-side precharge start control strategy of claim 8, wherein in step B5, the two-phase series wheel charge steady state equation is:
（38）；
（39）；
（40）；
（41）；
wherein,Q DC excision of the number of submodules for each phase of SC;T DC putting in the number of submodules for each phase of SC;ceilas a function of rounding upThe sub-module overcharging caused by calculation errors is avoided;U csm a single submodule capacitor voltage value for each phase SC.
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