CN114355050A - Online identification method for dq impedance of MMC type direct-current ice melting device - Google Patents
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Abstract
The invention discloses a dq impedance online identification method of an MMC type direct current ice melting device, which comprises the steps of connecting the MMC type direct current ice melting device into a power grid through a multi-frequency voltage disturbance source, setting frequency, phase and amplitude parameters of the disturbance source, and collecting voltage and current data of a grid-connected point of the direct current ice melting device after the disturbance source is connected; establishing a double-input double-output dq impedance identification model, giving an initial order and parameters of the model, and performing impedance identification by adopting a recursive least square algorithm; calculating the error between the model output voltage and the actual acquisition voltage under the current order and the parameters, if the error is greater than a given threshold value, updating the order of the model, repeating the step 2 to form iteration, and outputting an impedance identification result until the error is less than the given threshold value; the requirements of the actual engineering site on rapid and accurate impedance identification can be met; the stability analysis of the MMC type direct-current ice melting device accessed to the power grid is effectively carried out, and basic data support can be provided for practical engineering scenes such as relay protection device setting value calculation, device working condition evaluation and the like.
Description
Technical Field
The invention belongs to the field of impedance identification of direct-current ice melting devices, and particularly relates to an online identification method for dq impedance of an MMC type direct-current ice melting device.
Background
In order to prevent the influence of extreme cold weather on electric equipment such as a power transmission line and the like, the MMC type direct-current ice melting device is increasingly widely applied to a modern power system. The device is based on a power electronic topology, interaction between multi-scale control dynamics and a power grid can be generated, and harmonic instability problems such as harmonic resonance and the like are caused. The modeling and stability analysis method based on dq impedance is mature, but the methods of the invention all require that the internal information such as the structure, parameters and control mode of the ice melting device is known. A large number of MMC type direct current ice melting devices with confidential internal information already operated exist in an actual engineering field, and no effective method exists for how such devices acquire dq impedance on line.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the dq impedance identification is carried out by means of a recursive least square algorithm through the current response of a multi-frequency voltage disturbance source excitation device aiming at the MMC type direct-current ice melting device with unknown internal information such as structure, parameters, control mode and the like, the identification calculation time is short, and the identification result precision is high.
The technical scheme of the invention is as follows:
a method for identifying dq impedance of an MMC type direct current ice melting device on line comprises the following steps:
step 2, establishing a double-input double-output dq impedance identification model, giving an initial order and parameters of the model, and performing impedance identification by adopting a recursive least square algorithm;
and 3, calculating the error between the model output voltage and the actual acquisition voltage under the current order and the parameters, updating the order of the model if the error is greater than a given threshold value, repeating the step 2 to form iteration until the error is less than the given threshold value, and outputting an impedance identification result.
The multi-frequency voltage disturbance source is defined by the following formula:
in the formula (f)k、
And AkThe frequency, the phase and the amplitude of the kth frequency component of the multi-frequency voltage disturbance source are shown, and K is the number of sine waves contained in the multi-frequency voltage disturbance source.
The frequency range of the multi-frequency voltage disturbance source is determined by the frequency range of attention of dq impedance of the MMC type direct-current ice melting device, and the frequency interval adopts 50 Hz.
Step 2, establishing double input and double outputThe dq impedance identification model gives the initial order and the parameters of the model, and the method for identifying the impedance by adopting the recursive least square algorithm comprises the following steps: converting the voltage and current data under a three-phase coordinate system into a dq0 coordinate system by abc-dq0 coordinate transformation based on the acquired voltage and current data, and converting the voltage and current data into d-axis and q-axis currents Id、IqAs model input, d-axis and q-axis voltages Ud、UqAnd for model output, carrying out dq impedance identification by adopting a recursive least square algorithm.
The identification model adopts an internal and external double-layer circulation algorithm structure, wherein the external circulation is used for selecting the optimal order of dq impedance, the initial order of the impedance is 1, the order change takes the error obtained by solving in the step 3 as an index, when the error threshold is not met, the orders are gradually increased, and the step length is increased to 1; the internal circulation is used for solving each parameter of dq impedance expression, and the initial value of the impedance parameter is selected to be 10-4Or is 104The parameter change is based on the parameters obtained by the previous test data and the new test data to carry out recursive update; and when the inner loop finishes the recursive calculation of the last test data point, ending the loop.
The error index between the model output voltage and the actual acquisition voltage is calculated by the following formula:
in the formula: n is the total number of measured values; u. ofmRepresenting the voltage instantaneous value obtained by the m sampling point identification model; u. ofm0Representing the voltage instantaneous actually acquired at the m-th sampling point.
Calculating epsilon after one iterationREGiven a threshold value εRE0Relative error percentage εREWhen the error rate is larger than the given threshold value, the dq impedance order is increased, the step 2 is returned to for iterative identification until the relative error percentage epsilonREAnd outputting an impedance identification result when the impedance identification result is less than a given threshold value.
The method for determining the initial phase of each frequency voltage waveform of the multi-frequency voltage disturbance source comprises the following steps: defining a crest factor CF for selecting each frequencyThe initial phase of the rate voltage waveform,
in the formula, TmaxIs the least common multiple of the frequency component period of all frequency voltage sine waves of the multi-frequency voltage disturbance source u (T), and T is takenmax＝1s；
The larger the peak coefficient CF is, the larger the peak value of the multi-frequency voltage disturbance source signal is, therefore, in order to reduce CF, the following formula is adopted to optimize the sine wave phase of each frequency voltage,
amplitude u of disturbance voltage sourcepeakThe calculation formula of (2) is as follows:
upeak＝max[u(t)]＜10％U
and U is the rated voltage amplitude of the MMC type direct-current ice melting device to be tested.
The invention has the beneficial effects that:
the invention provides a dq impedance online identification method for an MMC type direct current ice melting device, which takes the MMC type direct current ice melting device with unknown internal information such as structure, parameters, control mode and the like as an object and aims at accurately acquiring the dq impedance of the device, thereby providing a rapid and accurate online identification method. The invention integrates the advantages of the recursive least square identification algorithm, realizes the on-line identification of dq impedance of the MMC type direct-current ice melting device, improves the impedance identification precision, shortens the calculation time, and can meet the requirement of the actual engineering site on the rapid and accurate impedance identification. Based on the identification result of dq impedance, the stability analysis of the MMC type direct-current ice melting device accessed to the power grid can be effectively carried out, and basic data support can be provided for practical engineering scenes such as relay protection device setting value calculation, device working condition evaluation and the like.
Drawings
FIG. 1 is a topological diagram of an MMC type direct current ice melting device in an embodiment of the present invention;
FIG. 2 is a comparison graph of waveforms before and after phase optimization of a multi-frequency disturbance voltage source according to an embodiment of the present invention;
FIG. 3 is a flowchart of a recursive least squares algorithm used in an embodiment of the present invention;
FIG. 4 is a schematic diagram of an identification method according to an embodiment of the present invention;
FIGS. 5(a), (b), (c), and (d) are graphs showing the identification results of ZDd, ZDq, Zqd, and Zqq according to the embodiment of the present invention;
Detailed Description
The method comprises the following specific steps:
a method for identifying dq impedance of an MMC type direct current ice melting device on line comprises the following steps:
s1, the MMC type direct current ice melting device is connected to a power grid through a multi-frequency voltage disturbance source, the frequency, phase and amplitude parameters of the disturbance source are reasonably set, and voltage and current data of a grid-connected point of the direct current ice melting device after disturbance access are collected;
s2, establishing a double-input double-output dq impedance identification model, giving an initial order and parameters of the model, and performing impedance identification by adopting a recursive least square algorithm;
and S3, calculating the error between the model output voltage and the actual acquisition voltage under the current order and the parameters, updating the order of the model if the error is greater than a given threshold value, repeating S2 to form iteration until the error is less than the given threshold value, and outputting an impedance identification result.
Further, step S1, the MMC dc ice melting device accesses the power grid through the multi-frequency voltage disturbance source, reasonably sets the frequency, phase and amplitude parameters of the disturbance source, collects the voltage and current data of the grid-connected point of the dc ice melting device after disturbance access, and specifically includes:
the MMC type direct current ice melting device is connected into a power grid through a multi-frequency voltage disturbance source, and the multi-frequency voltage disturbance source is defined by the following formula:
in the formula (f)k、
And AkIs the frequency, phase and amplitude of the kth frequency component of the multi-frequency voltage disturbance source. K is the number of sinusoids contained by the multi-frequency voltage perturbation source. The reasonable multi-frequency voltage disturbance source not only ensures the accurate acquisition of voltage and current data, but also avoids the influence of acquisition noise on the measurement data.
The frequency range of the multi-frequency voltage disturbance source is determined by the frequency range of interest of dq impedance of the MMC type direct-current ice melting device, and the frequency interval generally adopts 50Hz so as to ensure the accuracy of identifying the integer harmonic impedance of the fundamental wave.
The voltage waveforms of multiple frequencies are mutually superposed to generate a larger waveform peak value, so that the running state of the MMC type direct-current ice melting device is easily changed, and the accuracy of dq impedance identification is influenced. The key to influence the multi-frequency voltage disturbance source is the phase of each frequency voltage signal, therefore, the crest factor is defined to reasonably select the initial phase of each frequency voltage waveform.
The multi-frequency disturbance voltage source needs to have a large enough amplitude to ensure that the MMC type direct-current ice melting device generates a strong enough current response, however, the too large amplitude can cause the device to have the phenomena of modulation saturation, change of working conditions and the like, and therefore, the amplitude u of the disturbance voltage source is definedpeakTo limit the total energy of the perturbation signal.
And setting a multi-frequency voltage disturbance source according to the above criteria, and acquiring voltage and current data of a grid-connected point of the MMC type direct-current ice melting device after the system stably operates.
Further, on the basis of step S1, a dual-input dual-output dq impedance identification model is established, an initial order and parameters of the model are given, and impedance identification is performed by using a recursive least square algorithm, which specifically includes:
based on the voltage and current data acquired by S1, converting the voltage and current data in a three-phase coordinate system into a dq0 coordinate system through abc-dq0 coordinate transformation, and converting the d-axis current I and the q-axis current I into the d-axis current I and the q-axis current Id、IqAs model input, d-axis and q-axis voltages Ud、UqAnd for model output, carrying out dq impedance identification by adopting a recursive least square algorithm.
The identification model provided by the invention adopts an internal and external double-layer circulation algorithm structure. Wherein, outsideThe partial loop is used for selecting the optimal order of dq impedance, the initial order of the impedance is 1, the order change takes the error obtained by solving in S3 as an index, when the error threshold is not met, the order is gradually increased, and the step length is increased to 1. The internal circulation is used for solving each parameter of dq impedance expression, and the initial value of the impedance parameter is selected to be sufficiently small (generally 10)-4) Or sufficiently large (typically 10)4) The parameter change is based on the parameters obtained from the previous test data and the new test data to carry out recursive update. When the inner loop completes the recursive computation of the last test data point, the loop ends and the process proceeds to step S3.
When a new group of voltage and current data is obtained, namely on the basis of the previous group of dq impedance identification results, the estimation result is corrected and updated, so that the method provided by the invention realizes online identification of the dq impedance of the MMC type direct current ice melting device, and the whole impedance model is dynamic.
Further, in step S3, on the basis of step S2, an error between the model output voltage and the actual acquisition voltage at the current order and parameter is calculated, and if the error is greater than a given threshold, the model order is updated, and S2 is repeated to form an iteration until the error is smaller than the given threshold, and an impedance identification result is output, which specifically includes:
defining an error index between the output voltage of the identification model and the actual acquisition voltage, and calculating by the following formula:
in the formula: n is the total number of measured values; u. ofmRepresenting the voltage instantaneous value obtained by the m sampling point identification model; u. ofm0Representing the voltage instantaneous actually acquired at the m-th sampling point.
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention
The invention aims to provide an MMC type direct current ice melting device dq impedance online identification method, which aims at MMC type direct current ice melting devices with unknown internal information such as structure, parameters, control modes and the like, carries out dq impedance identification based on a recursive least square algorithm, and has short identification calculation time and high identification result precision.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
FIG. 1 is a topology of an MMC type DC ice melting device, in which usa、usbAnd uscRepresenting the three-phase voltage of an alternating current network; r, L denotes the grid equivalent resistance, reactance; u. ofha、uhbAnd uhcRepresenting a three-phase voltage of a multi-frequency voltage disturbance source; r0、L0Representing the grid-connected equivalent resistance and reactance of the full-bridge submodule; i.e. iapAnd ianRepresenting the current of an upper bridge arm and a lower bridge arm; i isdc、UdcRepresents direct current, voltage; t1, T2, T3, and T4 are transistors.
As shown in fig. 1, the dq impedance online identification method for the MMC direct-current ice melting device provided by the present invention is based on the topology structure shown in fig. 1, and the method includes the following steps:
s1, the MMC type direct current ice melting device is connected to a power grid through a multi-frequency voltage disturbance source, the frequency, phase and amplitude parameters of the disturbance source are reasonably set, and voltage and current data of a grid-connected point of the direct current ice melting device after disturbance access are collected; the method specifically comprises the following steps:
the MMC type direct current ice melting device is connected into a power grid through a multi-frequency voltage disturbance source, and the multi-frequency voltage disturbance source is defined by the formula (1):
in the formula (f)k、
And AkIs the frequency, phase and amplitude of the kth frequency component of the multi-frequency voltage disturbance source. K is the number of sinusoids contained by the multi-frequency voltage perturbation source. The reasonable multi-frequency voltage disturbance source ensures the accurate acquisition of voltage and current dataAnd the influence of collected noise on the measurement data is also avoided.
The frequency range of the multi-frequency voltage disturbance source is determined by the frequency range of interest of dq impedance of the MMC type direct-current ice melting device, and the frequency interval generally adopts 50Hz so as to ensure the accuracy of identifying the integer harmonic impedance of the fundamental wave.
The voltage waveforms of multiple frequencies are mutually superposed to generate a larger waveform peak value, so that the running state of the MMC type direct-current ice melting device is easily changed, and the accuracy of dq impedance identification is influenced. The key to influence the multi-frequency voltage disturbance source is the phase of each frequency voltage signal, and therefore, the crest factor CF is defined to reasonably select the initial phase of each frequency voltage waveform, as shown in equation (2).
In the formula, TmaxIs the least common multiple of the frequency component period of all frequency voltage sine waves of the multi-frequency voltage disturbance source u (T), and in the invention, T is takenmax＝1s。
As can be seen from equation (2): the larger the peak coefficient CF is, the larger the peak value of the multi-frequency voltage disturbance source signal is, so in order to reduce CF, the present invention optimizes the phase of the sine wave of each frequency voltage by using equation (3), and the waveform pair before and after optimization is as shown in fig. 2. In fig. 2, the waveforms are formed by superimposing 30 voltage sine waves with amplitude of 1V, the phases of the frequency waveforms of the black solid line are set to 0, and the phases of the frequency waveforms of the red dotted line are optimized according to equation (3).
In the formula, it generally makes
The other variables have the same meanings as in formula (1).
As can be seen from fig. 2: the waveform amplitude peak of the unoptimized multi-frequency voltage disturbance source is 26V, the waveform amplitude peak after the phase optimization of the formula (3) is 14V, and is reduced by 46 percent compared with the waveform amplitude peak before the unoptimization.
The multi-frequency disturbance voltage source needs to have a large enough amplitude to ensure that the MMC type direct-current ice melting device generates a strong enough current response, however, the too large amplitude can cause the device to have the phenomena of modulation saturation, change of working conditions and the like, and therefore, the amplitude u of the disturbance voltage source is definedpeakSo as to limit the total energy of the disturbance signal, as shown in equation (4).
upeak＝max[u(t)]＜10％U (4)
In the formula: rated voltage amplitude value of U-measured MMC type direct-current ice melting device
And setting a multi-frequency voltage disturbance source according to the above criteria, and acquiring voltage and current data of a grid-connected point of the MMC type direct-current ice melting device after the system stably operates.
S2, establishing a double-input double-output dq impedance identification model, giving an initial order and parameters of the model, and performing impedance identification by adopting a recursive least square algorithm; the method specifically comprises the following steps:
and converting the voltage and current data under the three-phase coordinate system into a dq0 coordinate system through abc-dq0 coordinate transformation based on the voltage and current data acquired in S1. With d-axis and q-axis currents Id、IqAs model input, d-axis and q-axis voltages Ud、UqFor model output, the dq impedance model to be identified is expressed by a differential equation shown in equation (5)
In the formula ud(k)、id(k) Is the k-th observed value u of the d-axis voltage and current of the deviced(k-1)、id(k-1) is the k-1 th observed value of the voltage and the current of the d axis of the device, and so on, and the q axis is the same; dud,m、eud,j、fud,jD-axis voltage coefficients are respectively, d-axis voltage corresponds to d-axis and q-axis current coefficients, and q-axis is the same, wherein m is the mth data point, and j is the jth data point; epsilonud(k)、εuqFor identifying modelsErrors between d-axis and q-axis voltages and actual voltages are obtained; n is1、n2The optimal order of d-axis voltage and q-axis current is obtained.
And (3) performing z transformation on the differential equation in the formula (5) to obtain a dq impedance transfer function matrix of the MMC direct-current ice melting device, wherein the dq impedance transfer function matrix is as follows:
in the formula:
as can be seen from equation (6): the dq impedance identification of the MMC type direct current ice melting device mainly aims to determine coefficients (impedance parameters to be identified) d, e and f of voltage and current in the formula (6) based on actually measured voltage and current disturbance data, and finally obtains a dq impedance value in the formula (6).
The invention adopts a recursive least square algorithm to solve and identify dq impedance coefficients, and the basic calculation formula is as follows:
in the formula: thetaud、θuqIs a d-axis and q-axis voltage parameter vector, namely:
hud、huqto identify the test matrix, h is satisfiedud(k)＝[UdIdIq]T；huq(k)＝[UqIdIq]T(ii) a Wherein:
the identification model provided by the invention adopts an internal and external double-layer circulation algorithm structure. The external circulation is used for selecting the optimal order of dq impedance, the initial order of the impedance is 1, the order change takes the error obtained by solving in S3 as an index, when the error threshold is not met, the order is gradually increased, and the increasing step length is 1. The internal circulation is used for solving each parameter of dq impedance expression, and the initial value of the impedance parameter is selected to be sufficiently small (generally 10)-4) Or sufficiently large (typically 10)4) The parameter change is based on the parameters obtained from the previous test data and the new test data to carry out recursive update. When the inner loop completes the recursive computation of the last test data point, the loop ends and the process proceeds to step S3. The algorithm flow chart is shown in fig. 3.
S3, calculating the error between the model output voltage and the actual acquisition voltage under the current order and the parameters, if the error is greater than a given threshold value, updating the order of the model, repeating S2 to form iteration until the error is less than the given threshold value, and outputting an impedance identification result; the method specifically comprises the following steps:
defining an error index between the output voltage of the identification model and the actual acquisition voltage, and calculating by using an equation (2):
in the formula: n is the total number of measured values; u. ofmRepresenting the voltage instantaneous value obtained by the m sampling point identification model; u. ofm0Represents the m-th sampling pointThe voltage transient actually collected.
Calculating epsilon after one iterationREGiven a threshold value εRE0Relative error percentage εREWhen the error rate is larger than the given threshold value, the dq impedance order is increased, the step 2 is returned to for iterative identification until the relative error percentage epsilonREAnd outputting an impedance identification result when the impedance identification result is less than a given threshold value. The recognition principle is illustrated in fig. 4, and the final recognition result is illustrated in fig. 5.
The invention provides a dq impedance online identification method for an MMC type direct current ice melting device, which takes the MMC type direct current ice melting device with unknown internal information such as structure, parameters, control mode and the like as an object and aims at accurately acquiring the dq impedance of the device, thereby providing a rapid and accurate online identification method. The invention integrates the advantages of the recursive least square identification algorithm, realizes the on-line identification of dq impedance of the MMC type direct-current ice melting device, improves the impedance identification precision, shortens the calculation time, and can meet the requirement of the actual engineering site on the rapid and accurate impedance identification. Based on the identification result of dq impedance, the stability analysis of the MMC type direct-current ice melting device accessed to the power grid can be effectively carried out, and basic data support can be provided for practical engineering scenes such as relay protection device setting value calculation, device working condition evaluation and the like.
Claims (9)
1. A method for identifying dq impedance of an MMC type direct current ice melting device on line comprises the following steps:
step 1, connecting an MMC type direct-current ice melting device into a power grid through a multi-frequency voltage disturbance source, setting parameters of frequency, phase and amplitude of the disturbance source, and collecting voltage and current data of a grid-connected point of the direct-current ice melting device after the disturbance source is connected;
step 2, establishing a double-input double-output dq impedance identification model, giving an initial order and parameters of the model, and performing impedance identification by adopting a recursive least square algorithm;
and 3, calculating the error between the model output voltage and the actual acquisition voltage under the current order and the parameters, updating the order of the model if the error is greater than a given threshold value, repeating the step 2 to form iteration until the error is less than the given threshold value, and outputting an impedance identification result.
2. The method for identifying dq impedance of the MMC type direct current ice melting device according to claim 1, characterized in that: the multi-frequency voltage disturbance source is defined by the following formula:
in the formula (f)k、
And AkThe frequency, the phase and the amplitude of the kth frequency component of the multi-frequency voltage disturbance source are shown, and K is the number of sine waves contained in the multi-frequency voltage disturbance source.
3. The method for identifying dq impedance of MMC type direct current ice melting device according to claim 2, characterized in that: the frequency range of the multi-frequency voltage disturbance source is determined by the frequency range of attention of dq impedance of the MMC type direct-current ice melting device, and the frequency interval adopts 50 Hz.
4. The method for identifying dq impedance of MMC type direct current ice melting device according to claim 2, characterized in that: step 2, the method for establishing the double-input double-output dq impedance identification model, giving the initial order and the parameters of the model and adopting the recursive least square algorithm to identify the impedance comprises the following steps: converting the voltage and current data under a three-phase coordinate system into a dq0 coordinate system by abc-dq0 coordinate transformation based on the acquired voltage and current data, and converting the voltage and current data into d-axis and q-axis currents Id、IqAs model input, d-axis and q-axis voltages Ud、UqAnd for model output, carrying out dq impedance identification by adopting a recursive least square algorithm.
5. The method for identifying dq impedance of MMC type direct current ice melting device according to claim 4, characterized in that: the identification model adopts an algorithm structure of inner and outer double-layer circulation, wherein the outer circulation is used for selecting the optimal order of dq impedanceCounting, wherein the initial order of the impedance is 1, the order change takes the error obtained by solving in the step 3 as an index, when the error threshold is not met, the order is gradually increased, and the increasing step length is 1; the internal circulation is used for solving each parameter of dq impedance expression, and the initial value of the impedance parameter is selected to be 10-4Or is 104The parameter change is based on the parameters obtained by the previous test data and the new test data to carry out recursive update; and when the inner loop finishes the recursive calculation of the last test data point, ending the loop.
6. The method for identifying dq impedance of MMC type direct current ice melting device according to claim 4, characterized in that: the error index between the model output voltage and the actual acquisition voltage is calculated by the following formula:
in the formula: n is the total number of measured values; u. ofmRepresenting the voltage instantaneous value obtained by the m sampling point identification model; u. ofm0Representing the voltage instantaneous actually acquired at the m-th sampling point.
7. The method for identifying dq impedance of MMC type direct current ice melting device according to claim 6, characterized in that: calculating epsilon after one iterationREGiven a threshold value εRE0Relative error percentage εREWhen the error rate is larger than the given threshold value, the dq impedance order is increased, the step 2 is returned to for iterative identification until the relative error percentage epsilonREAnd outputting an impedance identification result when the impedance identification result is less than a given threshold value.
8. The method for identifying dq impedance of the MMC type direct current ice melting device according to claim 1, characterized in that: the method for determining the initial phase of each frequency voltage waveform of the multi-frequency voltage disturbance source comprises the following steps: the crest factor CF is defined to select the initial phase of the voltage waveform for each frequency,
in the formula, TmaxIs the least common multiple of the frequency component period of all frequency voltage sine waves of the multi-frequency voltage disturbance source u (T), and T is takenmax＝1s；
The larger the peak coefficient CF is, the larger the peak value of the multi-frequency voltage disturbance source signal is, therefore, in order to reduce CF, the following formula is adopted to optimize the sine wave phase of each frequency voltage,
9. the method for identifying dq impedance of the MMC type direct current ice melting device according to claim 1, characterized in that: amplitude u of disturbance voltage sourcepeakThe calculation formula of (2) is as follows:
upeak＝max[u(t)]＜10％U
and U is the rated voltage amplitude of the MMC type direct-current ice melting device to be tested.
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