Power compensation for vector-based current control of a modular multilevel converter (MMC) based STATCOM

A. U. Lawan 1, S. Babani 2, A. Abdulkarim3, G. S. Shehu4, Y. Jibril M, 5 I. S. Madugu6 1 Department of Electrical & Electronic Engineering, University of Nottingham, Malaysia. 2 Department of Electrical Engineering, Bayero Univeristy Kano, 10 Gwarzo Road, Nigeria 3,4,5 Department of Electrical Engineering, Ahmadu Bello Univeristy Zaria, Nigeria. 6 Department of Electrical Engineering, Kano University of Science and Technology, Nigeria


INTRODUCTION
Power quality can be affected by many types of disturbances which can affect or precisely reduce grid power performance [1]. Depending on the issues arising such as distortions, voltage transients, sags, flickers, swells, unbalances among voltages, and interruptions. Custom power devices (CPDs) technology has been used to mitigate power problems and improve power quality (PQ) [1][2][3]. Some of these devices such as the univer¬sal power quality conditioner (UPQC), static compensator (STATCOM), and dynamic voltage restorer (DVR) can be implemented in voltage source multilevel converters (VSMCs) topologies [4][5][6]. Shunt devices such as STATCOM which is applied in distribution grids called distribution static compensator (DSTATCOM) exists, it's mainly for reactive power compensation, flicker mitigation, voltage regulation, harmonic filtering, and load voltage balancing. There are series connection devices [7], typical one is dynamic voltage restorer (DVR) commonly used for stabilization of voltage for critical end users. DVR normally comes with an energy facility for storage and short voltage-dip control or short loss of a generation plant from the power network source [7]. Also, there are combined shunt and series connection devices such as univer¬sal power quality conditioner (UPQC) [8,9] that can be employed. Electric drives such as driving pumps, high-power consuming blowers,etc. need a high level of electric power conversion for their operation. As the power level reaches many megawatts, their oper¬ations at electrical medium voltage (MV) up to 8 kilovolt (kV) has become advantageous option. However, other issues that are of less importance for low-power drives become issues in medium-voltage operations [10,11]. For instance, at high power and

VECTOR CONTROL FOR MODULAR MULTILEVEL CONVERTER (MMC) INVERTER
In the vector control scheme depicted in Figure 1, the VSC based MMC system in the three phase voltages and currents are transformed into a direct-quadrature (d-q) rotating frame. From Figure 1 and Figure  2 which presents the vector control scheme, applying Kirchhoff's voltage principles, and based on the Laplace transform, the relationship between the grid AC voltage fdq V and the MMC system voltage cdq V of Figure 1 can be written as follows [39][40][41]: Where: T R is the effective resistance between the MMC system and the grid T L is the effective inductance between the MMC system and the grid. If a constant power grid system is assumed, then the resultant system could be linear and autonomous. Hence the system is assumed to be an independent variable that is independent of time.This assumption is valid since very small deviations of frequency are expected in a healthy and normal operation of a grid power system. These small variations can only happened as grid is expected to have a constant voltage. From Figure 2 (a), a transfer function for the MMC based VIS q-axis voltage can be written as follows: Where fq I is the output AC current at the point of coupling (PCC) in the q-axis and cq V is the MMC system output voltage in the q-axis. From (2), the poles of the grid connected MMC system will be roots of the system characteristics equation (denominator of (2):   where f is the AC network frequency assumed 50Hz, these poles of the non -feedback system will be complex in nature, hence the system will be oscillatory. In other words, the grid -connected MMC system will have a bad dynamic performance and poorly damped. To solve this control problem of the non-feedback MMC system, the grid-connected MMC current at the PCC (i.e. fd I and fq I ) has to be fed back to the dq-controllers so as to close the current loops. This control improvement is shown in Figure 2 (b). The feedback control loops will improve the system response by shifting the poles of the system open loop transfer function of Figure 2 (a) towards the real axis, thereby pushing the system to have a critically damped response [32]. Assuming the dq-controller to be a simple gain controller (P-controller with ( ) P C s K  ), then block diagram of Figure 2 (b) can be in a transfer function form with outer feedback loops given by: Assuming the inner current controller gain is much more higher than the value of the effective resistance between the MMC system and the grid (i.e. P T K R  ), then the equivalent representation of the grid connected MMC system in block diagram will be as shown in figure 3 therefore it is possible to derive a q-axis current transfer function given by (4) and (5). Where * fq I is the grid -connected MMC system q-axis reference current for the inner current control scheme.The same principles applies to their corresponding daxis current.   The system obtained from the (5) is a first order system, hence employing a P-controller will improve the system response and helps in the steady state by eliminating the cross coupled interaction between the d-axis and q-axis of the system. The controller will also reduce the effect of the variations in the AC output voltage at the PCC [13]. During the steady state condition (i.e.
Where fq V is the AC voltage at the PCC in the q-axis and * fd I is the AC current at the PCC in the d-axis.
Also from (6), the same principle applies to its corresponding d-axis quantities, where their gains can be found by just subtitling the q-axis quantities with the d-axis ones. Analyzing (6) The STATCOM device is a shunt device hence connected in parallel a with the grid in the power system via a series impedance Zf which contains a coupling inductor and an assumed negligible series resistance at the PCC [6]. The shunt grid connection is employed using the MMC topology is shown in Figure 1 to derive the proposed control schemes. The basic function of the shunt VAR compensation is to give a power factor enhancement or a voltage support by reducing the voltage drop across the uncertain cumulative buffer and coupling impedances Zt. Hence increases the transmissible power along the grid in a power system. The amount of the required power that will produce the required STATCOM current c i that flows through the coupling impedance f Z is dependent on the difference in voltage between the STATCOM AC output voltage c V and the voltage at the PCC f V . If the STATCOM is less in voltage than grid PCC f V .
The STATCOM absorbs reactive power from the AC power system. Otherwise it injects reactive power. From Figure 1, the cq i represents the reactive current of the STATCOM while cd i is the active current used in charging and discharging the two DC-link capacitors.
Based on the equation (9) using the diagram representations of Figure 1 the transfer function equations of the STATCOM in d,q-representation is given by: Where f L and f R are the A.C coupling inductance and resistance respectively while r L and r R are MMC inverter buffer inductance and resistance. The cumulative MMC inverter to grid connection inductance and resistance is then defined [22] by (11) when the source impedance is neglected.
) between the MMC output and the grid.Integrating (10) between the present sample (k) and the next sample (k+1) the average estimated d,qvariables can be as follows: Where the relationship between rates of change of the MMC Inverter output dq currents, the effective inductance in which the current changes and d-q variables respectively is defined in (14) and (15).
, 1 q k k Q  from the period of (k) to (k+1) can be got using PI controllers [26] as: These d,q-variables can be used to obtain their corresponding d,q-voltage components at the MMC inverter during the same sample period ((k) to (k+1)) as follows:  ( , ) i d q T are respectively given by: For a linear transition between the two sampling periods of (i.e.   1 k to k  . (21) and (22) (21) and (22) into (16) and (17) respectively and using (23) to be represented in a separate d,q form as: Due to the action of the PI variables represented in the (24) and (25). The grid d,q voltages and the MMC based STATCOM output d,q voltages are assumed to be the : , 1 (17) and (18) gives the d,q voltage components at the MMC STATCOM inverter, which serve as the d,q voltage references employed using the PI controllers. These voltage references are defined by: (30) and (31) (26) and (27) respectively represent the settled dq variables (i.e. d Q and q Q ) given in (34) and (35), obtained as outputs of the d,q-PI controllers of a voltage control dynamic model based on the decoupled inner current control of the STATCOM grid connected system [26], shown in Figure 4.  [12]. Applying the Kirchhoff's theory, the AC voltage in the arm as an output can be derived as follows: i is the circulating current and dc V is the cumulative dc -link voltage across the arms. r L is the buffer arm inductance of each arm. r R is the series resistance associated with each buffer inductance that is usually assumed negligible [27]. f L and f R are the AC coupling inductance and its corresponding series resistance respectively. If the MMC is connected to grid, then there will be a source impedance s R and s L (i.e. the AC source inductance and its corresponding AC source series resistance respectively). The mathematical relationship between the MMC output current of each phase, the arm upper and lower currents, the circulating current and output voltage could be as: Many attempts to enhance grid voltage or power factor were considered using external reactive currents such as in [6], [31]. These external compensating reactive currents were made from the q-axis components only and introduced as a means of compensating the line load reactive current references. But the d-axis component compensation generation was not considered. Given by (34) and (35) and figure 1, based on the d,q-frame nature of d,q-inner current vector control there will always be the d-axis and q-axis in its implementation. Also considering the facts that the PI controllers are implemented in d,q independent form to control the active and reactive power independently for getting a decoupled dynamic response [22], this work introduced another components (i.e. d-axis active vector compensation components) to compensate for the d-axis segment of the d,q-variable (i.e. d Q and q Q ), plus the q-axis reactive vector compensation components) to compensate for the q-axis segment of the d,q-variable. The variables (i.e. d Q and q Q ) were obtained and applied for the corresponding d,q-PI controllers of the d,q-inner current controllers.This external compensation is important considering the facts that all VSI inverters have either a dc link capacitor(s) or source of dc-link voltages that need an active power control which are mostly carried out by either from set of a reference active power or by the use of a reference voltage to control the dc link voltage as a means of controlling the active power. In other word, the variation of the MMC based STATCOM active power within its cells is also tackled using the d-axis components compensation in this work, considering the widened causes and forms of STATCOM variations. On the other hand, given by (40) and (14) and Figure 8. It can be seen that the extraction of the q-axis current components ) was derived to basically to produce an opposite d,q-power commands to the d,q-PI controller's output variables ( d Q and q Q ) in response to the STATCOM active and reactive currents variation during the steady state operation. Assuming that in the STATCOM non-ideal operation, the output current has not only the reactive current components fq I but also has a very small active current components [5] in it its operations fd I that has some variations.
This small active current variation was considered due to a very small real power exchange assuming a steady state operation of the STATCOM. Therefore, during the transients (i.e. Figure 5), the active current fd I flows in order to maintain the capacitors voltages during charging and discharging. Hence, a small internal active power loss is associated across the resistance T R . Also assuming the power loss due to the voltage drop L v across the cumulative inductance T L considering the STATCOM operation in quadrant I and quadrant II regions of Figure 5. In these two regions, the STATCOM injects positive reactive power to the grid and absorb a very negligible amount of active power for the dc voltage maintenance respectively. Then the STATCOM can attain a steady state, when compensated and it's the d-axis and q-axis current components fd I and fq I in (34)  with the available AC voltage at the grid PCC as shown in figure 1. From the Figure 1 it can be seen that the at the steady state condition, the grid AC voltage d V will also be in phase with STATCOM output AC   figure 4, can be seen that the cumulative inductance T L is not only employed for filtering purpose and coupling but is also inevitable for creating a very small phase shift δ that will enable the active power exchange during the capacitors transients. On the other hand, from the (9) Figure 6 depicts the regions below and above the active power axis, also shows the under excitation and over citation regions, where the converter injects and absorbs reactive power from and to grid. Therefore for a successful control of an MMC Inverter, the net reactive power q Q available for manipulation at the PCC filter bus should be greater than the q Q absorbed by the cumulative filter inductance. Based on (57), the cumulative filter inductance T L must be selected assuming the active and reactive power MMC inverter capability at a maximum active and reactive power values. Therefore, (58) can be rewritten as: For an ideal reactive power STATCOM applications in a steady state, the active power d Q in (58) can be considered negligible ( d Q =≃0), therefore (58) can be reduced to: However, due to the MMC inverter nonlinearity in its typical control operations , there is always, a small voltage difference between the STATCOM output voltage c V and the grid voltage f V ( which is assumed to be constant). In other word, the voltage difference l v is not exactly equal to zero even during the steady state operation.
. To enhance the control in pushing the load line current signals ( fd I and fq I ) in tracking their desired values * fd I and * fq I , the proposed d,q algorithm is employed to detects the voltage difference which are proportional to the externally provided proposed d,q-power algorithm variables as a feedforward terms to the decoupling inner current control scheme. These provided d,q power variables are added to the outputs of the d,q-PI controllers in a decoupled form compensating the variables to the STATCOM reactive and active power variations. Note: the active power variation is negligible compared to the reactive power) variations. From (53 and 54), the proposed d,q-power algorithms will die when the STATCOM resultant output voltage * c V has reached its steady state value of unity.
This compensated state would be reached as soon as the dq-power variables have pushed the STATCOM controlled system attained the maximum values available for control at the PCC bus. This coincides with the points in figure 5 where the maximum power is achieved (PF is unity based on the load reactive current) after overcoming the required minimum values for the power absorption in the interfacing reactors. Figure 7 shows the block diagram of the proposed compensating dq power variables for the MMC based STATCOM decoupled inner current control (MMC external control). Finally, the compensating d,q power variables ( dcom Q and qcom Q ) are then added to the d,q-PI controller terms ( d Q and q Q ) in (32 and 33) respectively to form the final d,q-voltage component references ( respectively of the decoupled current vector control for the modulation as follows: This transient action would help in tackling the natural poor dynamics of d, q-PI controllers that produced d,q-PI variables therefore, enhancing the overall control system response of the MMC based STATCOM. In other words, the integral controller of the inner current d, q-PI controllers accepts the efforts provided by the transient compensator. Once the MMC based STATCOM current is driven into state of a desired current, the steady state inner current controller would produce a PCC voltage command consistent with the MMC based STATCOM line current, Therefore depressing the contribution effort provided by the external transient state compensator. Sine well designed PI controller's exhibit the properties of improved rise time and also has the integral function to eliminate the steady state error. They have been chosen and employed in this paper for achieving fast and better control of the STACOM reactive and compensated for an improved transient responses.

RESULT AND DISCUSION
The STATCOM is built based on the MMC topology for a five level operations using a Simulink model and the grid emulator is developed using the parameters shown in Table 1. The control gains for the MMC internal control were also summarized in Table 2. The preliminary setup of the experimental system is underway, built based on the same 5-level phase shifted PWM and balancing technique.

SIMULATION RESULTS
The controllers have a time delay of 200milliseconds and, each MMC cell employed the ideal IGBTs that have no dead time. Since each MMC cell has a carrier frequency of 4 kHz. This means the total switching frequency of the MMC system is 16 kHz (4 kHz times 4). In order to authenticate the proposed control and its theoretical analysis validity, two operating conditions of STATCOM (i.e. capacitive and inductive mode) were considered in these simulations. The active and reactive loads shown in Figure 7 and Figure 8 respectively have better dynamic responses that reached stability at almost 8 cycles before the step change with better responses to the change of the load at 0.4s. Figure 8 depicts the load reactive power transition from capacitive to inductive to state of both the conventional and The proposed scheme has reached its steady value at about 0.01 seconds from the start of the simulation, but in the conventional scheme, the response has fluctuated before settling at time 0.2 seconds which equivalent to 10 cycles based on the 50Hz used, these responses have shown the superiority of the proposed scheme. Figure 9 shows the load power factor response during the transition from capacitive to inductive state of the MMC based STATCOM operations But the overshoot in the Figure 9 is dominated by the green colour, meaning the overshoot of the conventional is more than that of the proposed scheme at the transition state. The power factor was chosen to be 0.7 for the capacitive and inductive load (500VAR). Figure 11 shows the MMC based STATCOM AC output voltage fast Fourier transform (FFT) analysis for the voltage harmonics using the proposed decoupled inner current control. It can be seen that the proposed control based output voltage has FFT of 1.50 %( Figure 11). While its counterpart in the conventional has 2.07% ( Figure 12). Also, from the graphical results, both have shown that at fundamental frequency there is significant level of harmonics magnitude ( i.e. of about more than one (1) magnitude total harmonic distortion (THD)) and almost the same level at second harmonic both with reducing magnitudes, but in the proposed control scheme, there is better level of harmonics. tthough both have complied with IEEE standard (i.e. less than 5% THD). Figure 12 depicts the FFT analysis of the controlled capacitors voltage harmonics during the STATCOM and balancing control operations using the proposed decoupled inner current control of the MMC based STATCOM with grid. The total harmonics level in Figure 12 has to be 44.98% THD, the controlled capacitors voltage has shown an overshoot in the response of about 60vdc but settled at about 0.14 seconds which is shorter time. Figure 13 has shown the FFT analysis of the controlled capacitors voltage harmonics during the STATCOM and balancing control operations based on the conventional scheme with about 77.77% THD (1.7 times 44.98%) which has almost doubled that of the proposed scheme. Also the proposed response has settled at about 0.14 seconds which is faster than the conventional response with about 0.04 seconds (2-50 Hz cycles).From the figures (Figure 12 and 13), it can be seen that the forth order harmonic and above (firth, six, seven etc.), both the even and odd values are almost zero in both control schemes (i.e. conventional and proposed scheme But for the proposed method, is only the fundamental and second order harmonics are close

CONCLUSION
This paper has investigated simplicity of carrier-based PWM technique in the STATCOM applications, afterwards, an enhancement on the performance of vector control based MMC is exploited. This has been achieved without the use of additional equipment or use of low switching complicated technique such the SHE. The proposed transient action introduced has helped in tackling the setback of dynamics of PI controllers and the STATCOM non-idealities; thus, it has enhanced the overall control system response of the MMC based STATCOM system. Finally, simulation are presented. In other words, the integral controllers of the inner current PI controllers have accepted the efforts provided by the transient compensators. This development can be used to achieve the practical realization of STATCOM with reduced variations.