I. INTRODUCTION

With the ever-increasing application of semiconductor devices in power systems, power quality tends to deteriorate because of power factor decline, voltage instability, and increased harmonics. In addition, the reliability of power grids gradually decreases because of the connection of distributed power supplies, such as wind or solar generation systems. Reactive power compensation technology, which is applied to correct the power factor or stabilize grid voltage, has been widely used to promote power quality [1]. Generally, a static var compensator (SVC) is usually installed near a load in a power system for PFC. The main types of SVC include thyristor switched capacitors (TSCs) [2], thyristor controlled reactors (TCRs), static synchronous compensators (STATCOMs) [3], and parallel-connected magnetic energy recovery switches (MERS) [4].

Unlike TSCs, TCR ssupply continuous inductive reactive power but not fixed capacitive reactive power. As high current harmonics are inserted into the grid, TCRs have been replaced with other SVCs. STATCOMs, which can supply continuous inductive reactive power and capacitive reactive power and produce low harmonics, have attracted significant attention in the area of power quality improvement [5]. However, this continuous reactive power controller always suffers from high frequency losses [6] and control method [7]. Some cascaded H-bridge STATCOMs exhibit a complex circuit structure and require additional current filters [8]. An emerging SVC called the MERS, which is used to supply continuous capacitive reactive power, was proposed about a decade ago. Its advantages include simple circuit structure, line frequency control, low losses, and small capacitors [9] and [10].

MERS, which is used as a series compensator in [11] and [12], is connected to the power grid in parallel [13] as a shunt compensator, as shown in Fig. 1(a). Control methods based on a current phase are no longer suitable for shunt MERS because of the uncertainty of the grid current. After one switch is turned off in advance, the minimum voltage of a dc capacitor (VC-min) is regulated [13]. This method can broaden the reactive power compensation range of MERS, but the distortion of the current waveform quickly increases. In addition, the large delay angle applied exceeds the high peak voltage of the dc capacitor (VC-peak) and total harmonic distortion (THD) generated.

Fig. 1.Circuit configuration of MERS.

To improve the performance of a parallel-connected MERS, we first rebuild a mathematic model on the basis of the phase of the grid voltage.

Then, a new method adopting a cooperative control between parameters α and VC-min is proposed. The optimal control function and evaluation model are developed to optimize the effect of system control. A computer simulation and experiments are conducted, and the results support the conclusions. The proposed SVC and STATCOMs are also compared to expound the feasibility and advantages of the former.

II. PARALLEL-CONNECTED MAGNETIC ENERGY RECOVERY SWITCH

This section introduces the theoretical analysis, including the circuit configuration and operating principle. According to the voltage and current waveforms of MERS, its mathematical model is rebuilt on the basis of the phase source voltage. Then, some disadvantages of the existing control are pointed out in detail.

A. Circuit Configuration

As described in the reference [12], a single MERS consists of four switches and a dc capacitor. Three MERSs are used in a three-phase system. Between the grid and the MERS, a small inductor needs to be connected when the SVC is installed. The parallel-connected MERS is shown in Fig. 1(a). Fig. 1(b) shows four types of MERS. Only the full-bridge MERS is considered in this study.

B. Operating Principle and Mathematical Model

The four switches of the full-bridge MERS are divided into two groups, namely T1–T3 and T2–T4. Every group is usually opened at the same time but is closed asynchronously. The states of different switches, which are determined by control parameters VC-min and α, can lead to different running modes. When VC-min and α are equal to zero, the mode is referred to as a balanced mode. The output reactive power (Qout) of this mode is defined as Q0. Increasing VC-min or α separately results in Qout being lower or higher than Q0, respectively. Using the control method proposed in [13] and taking the source voltage for reference, we obtain the current and voltage waveforms of the MERS, which are shown in Fig. 2. The two control styles [13] are presented in Figs. 2(a) and (b). The former one is under a dc off-set mode, and the latter one is under a discontinuous mode. In sum, VC-min control means changing the closing time, whereas α control means regulating the opening time.

Fig. 2.Current and voltage waveforms using the existing control method.

The circuit of the shunt MERS can be simplified, as shown in Figs. 3(a) and (b), when the dc capacitor is bypassed or connected in series. RLine is the equivalent resistance of the line, and ωt is the variable phase angle. us is the ac source voltage. Taking a single cycle for transient state analysis, we establish voltage balance equations on the basis of Kirchhoff's voltage law as follows:

(1) ωt∈[-α, α] or[π-α, π+α]

(2) ωt∈[α, π-α] or[π+α, 2π-α]

Where Um denotes the amplitude of us and ω is the angular speed (ω = 2πf, f is the grid frequency). Sgn (x) is a signum function that outputs +1 if x≥0, else −1.

Fig. 3.Simplified circuit when MERS runs in different modes.

As Fig. 3 shows, the curves of VMERS and iMERS can be separately expressed with odd and even functions, respectively.

Where bn and Imk denote the amplitudes of each voltage and current harmonic component, respectively.

In addition, the MERS voltage can be formulated with a piecewise function in the cycle from -α to 2π-α. In sum, uMERS can be described by UC, which is mentioned in equation (2). Then, the amplitude of the fundamental MERS voltage (b1) is obtained by ignoring the high-order harmonics through the fast Fourier translation, as expressed in equation (5).

Where Im1 is the amplitude of the fundamental MERS current. B* is a high-order component.

By substituting equations (3) and (4) into equation (2), we can obtain the relationship between b1 and Im1 while ignoring the high-order harmonics, as shown in equation (6).

For the dc off-set mode, α is set to zero, similar to VC-min, which is fixed to zero under the discontinuous mode. With equations (5) and (6), Im1 can be solved. According to Ohm’s law, the equivalent capacitances of the dc off-set and discontinuous modes are described in equation (7).

where D= XL/(π•XCdc) and X1* and X2* are high-order components that are generally ignored.

Then, XP-C MERS is deduced with equation (8).

where P-C MERS denotes the parallel-connected MERS.

The model of Qout as a novel compensator can be finally formulated as follows:

C. Shortcomings to be Addressed

Theoretically, XP-C MERS can be regulated from 0 to infinity using equation (8). However, power quality severely declines that the range of control parameters VC-min or α becomes limited, as revealed in Fig. 2. Hence, Qout must be controlled within a limited range. For instance, the output reactive power of MERS is not lower than 0.9Q0 and not higher than 1.4Q0 in reference [4]. As shown in Fig. 2, increasing α causes VC-peak to increase, and large VC-min and α correspond to a high current THD.

However, the curves presented on top of Fig. 2(a) show that increasing VC-min can cause VC-peak to decline. Thus, regulating this parameter could possibly decrease the peak voltage of the capacitor successfully. The triple harmonic is a major part of the MERS current, except for the fundamental harmonic under the discontinuous mode.

As α increases, the sinusoid current may be acquired if the triple harmonic is filtered [13]. This characteristic is specially fit for triangle-connected triple shunt MERSs in three-phase systems. The control effects of VC-min and α on regulating Qout and power quality arelisted in Table I. To promote the capability of the parallel-connected MERS in terms of CRP control, a considerably wide range of parameters VC-min and α should be applied when meeting the power quality requirements in the power grid. Therefore, a new control method is proposed in the present work by changing VC-min and α concurrently.

TABLE ICONTROL EFFECT OF PARAMETERS VC-MIN AND A

III. PERFORMANCE IMPROVEMENT USING COOPERATIVE CONTROL PARAMETERS

To restrain current harmonics and VC-peak, we first develop a type of cooperative control between parameters α and VC-min. By establishing an optimal control function and an evaluation model, the system control strategy realizes perfect continuous reactive power tracking and reaches the best working points consistently.

A. Cooperative Control between Parameters α and VC-min

Using the same method as that deduced in equation (7), we build a new capacitance model when neither VC-min nor α is fixed to zero. The formulation is shown in equation (10). Then, equation (10) is substituted into equation (9), and a function of Qout based on variable VC-min and α is obtained in equation (11).

Where X* is a high-order component.

where X* is extremely small and thus negligible.

Unlike that in the existing control method, the same Qout is determined not with only one working point but with a series of working points, as shown in equation (11). These points comprise a line, which is called the equivalent reactive power line (ERPL). By taking the variable VC-min for the vertical axis and the variable α for the horizontal axis, we plot several ERPLs in a plane of rectangular coordinates, as shown in Fig. 4.

Fig. 4.ERPLs with the proposed control method.

The simulation model is set up in PSIM as follows. Some points, which are marked as squares in Fig. 4, are measured to verify the existence of an ERPL via simulation. A waveform comparison between point-(250, 0V) and point-(280, 58V) is shown in Fig. 4. These two points generate the same Qout, but point-(250, 0V) suffers from larger VC-peak and harmonics in comparison with point-(280, 58 V).

B. Optimal Control Function and Evaluation Model

Not all points are allowed on an ERPL. Some points with low current harmonics and VC-peak, similar to the second point shown in Fig. 5, are the optimal ones sought in this work.

Fig.5.Waveform comparison when MERS supplies the same Qout.

VC-max is defined as the maximum voltage to be endured by the capacitor and IGBTs. THDmax, with a triple harmonic filtered in the MERS current, is defined as the maximum harmonic share to be accepted by the power grid. In the case of Qout, VC-min can be expressed with a function, with α serving as the independent variable. Then, the optimal control function is established, as shown in equation (12). In ensuring the exact value of VC-min and α, the initial VC-min is always zero when Qout is greater than Q0. Conversely, the initial α is equal to zero when Qout

To evaluate the performance of a chosen point, we develop a test function, which is shown in equation (13). A large F indicates that the currently working point performs satisfactorily. On the contrary, a low F indicates that a better working point should be selected.

Where λTHD and λVc-peak are defined as follows:

C. Improved Performance with the Proposed Method

In PSIM, a simulation model is first set up. Its main system parameters are marked in Fig. 6, which also shows the logical process of control signal production. Using this model, we derive a curve surface on the basis of the simulation results shown in Fig. 7. This figure describes the output reactive power of MERS. Every Qout corresponds to a plane that is parallel to the coordinate plane. A line intersecting a Qout plane and the curve surface is an ERPL. Therefore, the range of working points is broadened and demonstrated.

Fig. 6.Simulation model of single-phase shunt MERS.

Fig. 7.Curve surface for describing the output reactive power.

As shown in Fig. 7, parameters VC-min and α show the same control effect as that presented in Table 1. When THDmax and VC-max are supplied, such as THDmax =6% and VC-max =1,000V, the improved power quality of MERS is revealed (Fig. 8). In Fig. 8, the dotted line denotes the current THD or VC-peak before the improvement with the control method. The THD of the MERS current shown in Fig. 8(a) does not include a triple harmonic. The left picture indicates that a large Qmax and a small Qmin are allowed after the improvement with the control method. Both types of output reactive power do not equate to current THD that exceeds the limited range. The rightmost picture supports a large Qout while satisfying the highest peak voltage limit. Finally, the practical operating range of the novel CRPC is approximately expanded from 0.7Q0 to 3.0Q0. However, the output range after using the existing control method is only 0.9Q0–1.4Q0. The performance of the developed method is clearly better than that of the existing method.

Fig. 8.Improved performance with the proposed control method.

D. Control Strategy for Unit Power Factor Correction

To calculate the present power factor, we first track the phase difference between the grid voltage ψGV and current ψGI. Then, it is determined with equation (15). A PI controller is used to convert the error of the power factor to the changed reactive power ΔQout.

where ΔψGVI is ψGV−ψGI.

To search for optimal control parameters, we adopt VC and THDi, as well as ΔQout, on the basis of equations (11) to (14). Furthermore, the output of an actual reactive power is derived from ΔQout and Qout supplied by the previous cycle.

Finally, control signals are produced for the 12 switches in a three-phase MERS. Fig. 9 presents the process of power factor correction as analyzed above.

Fig. 9.Control strategy for three-phase parallel-connected MERS.

IV. SIMULATIONS AND EXPERIMENTS

A three-phase power system, which consists of an experimental MERS as well as variable loads and an ac source, is set up. The proposed control method is verified by simulations and experiments. The proposed system is compared with STATCOMs in terms of factors such as loss and soft switching. The results are then analyzed to explain the feasibility and advantages of the proposed system.

A. Experimental System

Fig. 10 shows the structure of the experimental system. The simulation model is set up in the same way as that in PSIM. It mainly includes MERS, TSC, and a variable load. TSCs are employed to support MERS in generating a large amount of reactive power. The circuit characteristics are listed in Table II.

Fig. 10.Circuit structure for power factor correction system.

TABLE IISYSTEM SPECIFICATION FOR SIMULATION OR EXPERIMENTAL MODEL

An existing digital controller called Expert III is applied. This controller can run a self-designed program with a DSP C6713 integrated as its core chip. In addition, a special software called PE-View 9 is installed in a computer for managing the controller. The testing equipment includes TPS 2024 (200MHz), Fluke 43B Power Quality Analyzer, etc. We design a control program to realize the control strategy proposed in Fig. 9. Fig. 11 shows the working process.

Fig. 11.Control program adopted in Expert III.

B. Verification by Simulations and Experiments

A simulation is first completed to verify the transient response when the load changes. The performance of some working points represented by the function F is also measured. The transient response and steady-state characteristic are demonstrated through experiments.

1) Simulation Verification: Fig. 12 shows the response of the power factor correction in the simulation when the load increases. The first change in load occurs at 5.6 s. The reactive power of the load increases from 7.0 kVar to 10 kVar. The grid power factor decreases obviously but reverts to a unit after about 0.05 s. In this recovery process, only TSC1 is switched on, and MERS is left unchanged. The second change in load occurs at 5.8 s. TSC2 is also applied, and the MERS current increases at the same time. The second recovery process takes about 0.04 s. The top part of Fig. 12 shows changes in grid power; the waveforms of the phase voltage and current are shown in the picture below the power grid.

Fig. 12.Response characteristics when Qout increases.

The verification of the decrease in load is also completed, as shown in Fig. 13. The load changes twice at 9.62 and 9.86 s. The reactive power of the load decreases from 18 kVar to 10.0 kVar at the first period of change and from 10 kVar to 5.0 kVar at the second period of change. TSC1 and TSC2 are cut off from the grid one by one. The shunt MERS works as a continuous reactive power compensator to precisely track the reactive power of the load.

Fig. 13.Response characteristics when Qout decreases.

Using the evaluation model proposed in equation (12), we test the distribution of the optimal working points through simulation (Fig. 14). The points of the same color have the same value of F. Fig. 14 shows the variation tendency of F, which aids in determining the best working point.

Fig. 14.Performance of working points measured by simulation.

(2) Experiment verification: With MERS and TSCs, a continuous and wide-ranging reactive power is supplied to maintain the balance of the grid power. The experimental results verify this feature in practical applications (Fig. 15). Before the load increases, the power grid reaches a balance, as shown in Fig. 15(a). The connected TSC1 and MER generate the same reactive power needed by the load. TSC2 is also switched in the grid a few moments after the load increases at 0.9 s. MERS starts to regulate the power factor at the same time. Point A is in a state when the balance of the grid is restored. TSC1 is cut off from the grid because the load decreases at 5.3 s. The system returns to normal quickly. Point B is in a state when the balance of the grid is restored. Fig. 15(b) shows the phase voltage and current waveforms of the grid at points A and B. Fig. 15(c) shows the MERS capacitor voltage and current of these two points. Finally, the power factor is corrected to a value higher than 0.95.

Fig. 15.Experimental results for power factor correction.

Using the novel continuous reactive power compensator, we also test its steady-state performance and present the result in Fig. 16.The improvement of the power factor with a continuously increasing load is concluded by comparing the cases with and without MERS. The power factors simulated in the computer are also measured and presented in Fig. 16 as a reference.

Fig. 16.Steady-state performance for power factor correction.

C. Comparison with STATCOMs

The feasibility of the proposed switch as a novel continuous reactive power compensator is verified. Compared with STATCOMs, the parallel-connected MERS offers more remarkable advantages.

1) Low Losses

Although a three-phase MERS comprises two more switches relative to STATCOMs, the numbers of switches of the two systems operating at any given time are the same. For a triangle-connected three-phase MERS, each phase voltage is higher than that for STATCOMs. Therefore, the phase current of a STATCOM is larger than that of the proposed compensator when they work in the same conditions and supply the same reactive power. Thus, a STATCOM experiences more conduction loss than the proposed device on each IGBT. Moreover, the high-frequency control for a STATCOM leads to considerable switching losses.

2) Small DC Capacitor

A dc capacitor is adopted for the shunt MERS and STATCOM. Even though three capacitors are installed in the three-phase system, the size of the dc capacitor of the system is several times smaller than that of a STATCOM. Furthermore, its equivalent capacitance is controllable and tends to increase with increasing α.

3) Easy to Control

The developed control method is based on the phase-delay control. The generation of driven signals under this method is simple because of the absence of complex calculations or coordinate transformations. In addition, every phase of the proposed MERS can be regulated separately.

V. CONCLUSIONS

A novel type of SVC called MERS is investigated. In the theoretical analysis, MERS is first introduced, along with its circuit configuration, operating principle, and mathematical model. To improve the effect of reactive power compensation, we propose a new control method for this device to restrain current harmonics and the peak voltages of capacitors. Then, this control method is tested through simulations and experiments. The new compensator is also compared with a STATCOM. The feasibility and advantages of the shunt MERS as an emerging reactive power controller are finally verified.