An MMC control strategy without bridge arm current sensors

Each bridge arm of a modular multilevel converter (MMC) is connected in series with multiple submodules. This structure increases the amount of current detection, making it necessary to have a number of current sensors in operation, which increases the system cost. For this reason, this paper proposes an MMC control strategy that does not require bridge arm current sensors. Firstly, the nearest level modulation (NLM) strategy requires the bridge arm current to be used to determine the submodule entry direction. In this case, this article proposes a method for determining the input direction of the submodule based on the capacitive voltage of the submodule, which calculates the input method of the submodule by analyzing the state quantities in the bridge arm voltage switching function, omitting the bridge arm current sensor and reducing the cost. Secondly, the traditional MMC circulation suppression method needs to detect the bridge arm current to calculate the circulation. However, this paper proposes an indirect circulation suppression method by suppressing the unbalanced voltage based on the analysis of the circulation generation mechanism. Finally, simulations and experiments validate the effectiveness of this method and lay the foundation for the next engineering application.


Introduction
As a new generation of DC transmission technology, flexible DC transmission technology is now widely used in distributed power access, grid interconnection, passive network power supply, and long-distance high-capacity transmission.The modular multilevel converter is an important part of the development of this technology [1] .The advantages of MMC include low switching frequency, low voltage change rate, and good wave quality, especially using the module grouping method.Multiple sub-series are easy to achieve modular design, which is conducive to significantly improving the system voltage level and capacity.This is why the converter has attracted so much attention from the community [2] [3] .At present, the focus and difficulty of research on MMC are mostly focused on stability analysis [4] , modulation strategies [5] , and circulating current suppression [6] [7] .
The key problem with MMC is that the structure of multiple submodules in series leads to the need for numbers of sensors in the control, increasing the amount of information to be collected [8] .In order to solve this problem, most of the existing solutions have been studied from the point of view of reducing the voltage and current sensors.For voltage sensors, Abushafa et al.'s study [9] is based on a Kalman filtering algorithm to estimate submodule voltages, allowing only one voltage sensor per set of bridge arms, but it is susceptible to circuit parameter shifts that can deteriorate system control performance.To address the degradation of converter performance due to the reduced number of voltage sensors, a capacitive voltage estimation method is proposed based on group measurement (GM), which significantly improves the voltage estimation accuracy [10] .Regarding the current sensor, it is mainly used to measure the bridge arm current, which is mainly used for the determination of submodule charging and discharging in Nearest level modulation (NLM) and the calculation of circulating current in circulating current suppression.Reddy and Shukla [6] improve the equalization process of the NLM modulation method.It effectively achieves bridge-arm current sensor-free control of the converter.Still, this method can only be achieved by adding hardware filters for circulating current suppression, which adds additional hardware costs.
This paper proposes a modulation method for current sensors without bridge arms based on the NLM modulation method from the perspective of current sensors, which effectively suppresses circulating current.Finally, the feasibility of this method was verified through experimental comparison.

NLM control strategy without bridge arm current
Nearest-level approximation modulation is a modulation strategy dedicated to multilevel converters, which is based on the basic principle that a certain number of submodules are put in place to approximate the modulating wave in each control cycle.For MMC systems, this is shown in Figure 1: In Figure 1, u uref and u lref are the modulating waves of the upper and lower bridge arms of the MMC, respectively; U c is the capacitance-voltage rating, round(x) is the rounding function; u cx is the submodule capacitance-voltage of the x-bridge arm; i x is the x-bridge arm bridge arm current; n is the number of submodules to be put into operation during the system.During modulation, the positive and negative values of i x are first determined by a voltage equalization algorithm.When i x ≥0, u cx is sorted from smallest to largest voltage, and n submodules with the smallest voltage are put in successively; when i x <0, u cx is sorted from largest to smallest voltage, and n submodules with the largest voltage are put in successively.The positive and negative values of i x are used to determine the status of the capacitor.
It is assumed that S k is the switching function of the kth submodule, C is the capacitance capacity of the corresponding submodule, u ck is the capacitance-voltage of that submodule, and i arm is the current flowing through the submodule bridge arm.The switching function of the submodule capacitor is shown in Equation (1): Considering the errors that occur during the production and use of the capacitance capacity, Equation ( 1) is transformed into Equation (2):   where x is the error in the capacitance value, x takes values between 0.05 and -0.05 and 1+x is mathematically positive.Then, Equation ( 2) can be converted to Equation (3): Extending the above equation to the whole bridge arm gives the bridge arm voltage equation for the MMC (4): It is known that the capacitance on the right side of the equation is greater than 0, (1+x) is greater than 0, and the submodule switching function S k is equal to 1 or 0. When the equation is non-zero, the bridge arm current i arm is the same as the positive and negative states on the left side of the above equation.The positive or negative value of this value can be used instead of the bridge arm current to determine the state of the submodule capacitors, as shown in Figure 2. Figure 3 shows the bridge arm capacitor charging and discharging state judgment, where Signum represents the function that takes the positive and negative signs, in which 1 represents the capacitor charging and -1 represents the capacitor discharging.This verifies the feasibility of using the proposed bridge armless current sensor modulation algorithm for capacitor charging and discharging state judgment.As shown in the figure, the results of the bridge-armless current sensor method proposed are consistent with those of the conventional method.

Circulating current suppression strategy without bridge arm current
Circulating current is generated by the structural characteristics of the MMC.When the MMC is in operation, the voltage constantly charges and discharges causing fluctuations in the capacitor voltage, leading to voltage imbalance between the DC side and the submodules, forming a circulating current.u diffj is defined as the unbalanced voltage of phase j, thus the MMC's bridge arm voltage can be expressed as: According to the modulation function of the MMC, the voltages of the bridge arms can also be written as: where N represents the number of submodules, u cuj and u clj are the submodule capacitance voltages, F uj and F lj are the modulation functions of bridge arms, and u cuj and u clj can be expressed as: where A and B are, respectively: where m is the voltage modulation ratio, and the modulation function expression is Equation (9).
Combining Equations ( 5)-( 9), the unbalanced voltage is given by Equation ( 10): As shown in Equation ( 10), the unbalanced voltage of the MMC is the source of its circulating current generation, mainly the second harmonic component [7] .While the conventional circulating current suppression strategy requires calculations from bridge arm currents, this paper suppresses the current by suppressing the unbalanced voltage, which does not require the detection of the bridge arm currents, which principle is shown in Figure 4.In the diagram, the unbalanced voltage can be calculated using Equation (11): where u cuji and u clji represent the voltage of the ith submodule in the bridge arms of phase j, and n is the number of submodules put into operation.The unbalanced voltages calculated are Park transformed to obtain the dc component in the dq coordinate system, which is then adjusted by the PI regulator for the d-and q-axis error components after the difference with zero to achieve the purpose of static-free regulation of the loop.

Experimental results
Some experimental tests were carried out on the MMC cabinet to verify the effectiveness of the control strategy proposed in this paper.For safety reasons, the experimental tests were carried out at a lower voltage level.The experimental environment was that the MMC was connected to the laboratory 380 V supply via an isolation transformer with a DC side voltage of 700 V.The whole experimental platform is shown in Figure 5.
Experimental tests were conducted on the MMC under three different operating conditions to verify the control effect of the control strategy proposed in the paper.The experimental results are shown in Figures 6-8, where P is active power and Q is reactive power.(a) The method proposed in this paper (b) Traditional method Figure 8. Waveform of u sa , i a and the THD of the current (P=0 W Q=1000 var) Figure 6 shows the experimental results of the converter when the active power P flows, supposing P is 1000 W and Q is 0 Var.As can be seen from the figures, the method proposed in this paper still maintains good steady state results after omitting the current sensors from the bridge arm, with good current-voltage waveform sinusoidal and 1.1% current THD, which is better than the traditional method.
Figures 7-8 show the experimental results of MMC under capacitive and inductive operating conditions, assuming P of 0 W and Q of -1000 var and +1000 var, respectively.As can be seen from the figures, the converter can still maintain good control under these two operating conditions, and the current harmonic content is only 1.3% and 1.4%, meeting the 5% grid connection standard.In summary, as can be seen, the method introduced in this article can still maintain excellent performance after optimizing the merged structure.Good control effects can be controlled and maintained under constant conditions.

Conclusion
In response to the high cost of the MMC control scheme and the large number of required sensors. in this paper, we propose a control strategy that does not require a bridge-arm current sensor.To further overcome the shortcomings of the conventional method that cannot suppress the circulating currents in the absence of the bridge arm currents, a method for suppressing the unbalanced voltage circulating current was introduced and later verified experimentally, which led to the following conclusions.
(1) The NLM method without bridge arm current uses the differentiation of the sum of the submodule capacitance voltages to determine the submodule input direction, which has high accuracy.
(2) The circulating current is suppressed indirectly in this paper by suppressing the unbalance voltage, effectively reducing the bridge arm current distortion of the submodule voltage fluctuations.
(3) Optimized control strategy without bridge arm current sensor has excellent steady-state performance, fast power response, and low hardware cost.

Figure 2 .
Figure 2. Modulation schematic of NLM without arm current.
5th International Conference on Energy Systems and Electrical Power