Multi - objective optimization evaluation method based on coordination control algorithm for magnetic energy recovery switch

The Magnetic Energy Recovery Switch is a kind of novel reactive power compensation device which supplies continuous reactive power. In this paper, the conventional control method of the Magnetic Energy Recovery Switch is introduced, and then the coordination algorithm based on phase delay control and minimum capacitor voltage control is analyzed emphatically. The Magnetic Energy Recovery Switch working curve is obtained under the premise of reaching required reactive power in the grid. And then for the all operating points in the curve have been assessed to find the optimal operating point of Magnetic Energy Recovery Switch. Finally, a simulation is conducted to verify the effectiveness and rapid dynamic performance of the evaluation method.


Introduction
With the advent of new power electronic devices, especially in recent years, the rapid development of full-controlled devices such as gate turn-off thyristor (GTO) and insulated gate bipolar transistor (IGBT) etc., promoting the diversification of reactive power compensation technology development, and thus derived a series of new reactive power compensation devices such as static synchronous series compensator (SSSC), gate converter series capacitor (GCSC) and so on. The static synchronous compensator (STATCOM) based on voltage source converter (VSC) is the fastest developed paralleled reactive power compensation device in recent years [1][2][3][4][5]. Compared with reactive power compensator controlled by thyristor, STATCOM generally uses high-frequency switching control, with the characteristics of high compensation precision, fast response, and direct reactive power generation [6][7][8]. Also, due to the use of full-controlled semiconductor devices to make its high quality harmonic performance [9][10][11][12].
The Magnetic Energy Recovery Switch (MERS) is a compensator based on single-phase VSC, which is controlled by grid frequency [8][9][10]. Compared with other voltage compensators such as SSSC, it has the advantages of smaller fixed capacitor in VSC circuit. However, the shortcomings of the Magnetic Energy Recovery Switch are also obvious: When it is used, the current harmonic which is injected into the grid is relatively large, the DC side of the capacitor voltage is easy to steep rise, threatening the safety of the operating environment. To solve the problems and shortcomings up above, this paper proposed a multi-objective optimization evaluation method based on coordinated control algorithm of Magnetic Energy Recovery Switch. Through the cooperative control of the traditional phase delay and the minimum voltage of the capacitor, the equal power curve of the Magnetic Energy Recovery Switch is obtained under the premise that the reactive power compensation power of the grid is reached [13][14]. On the basis of this, all the operating point on the equal power curve are evaluated according to the objective function that acquired from evaluation model proposed in this paper, and finally the optimal operating point satisfying the reactive power compensation is obtained.

Circuit configuration and schematic of magnetic energy recovery switch
Magnetic Energy Recovery Switch(MERS) topology is shown in Figure1. Vertical pairs switches T1 ~ T4 (including its reverse-parallel diodes D1 ~D4) and DC capacitor Xdc, semiconductor switches are insulated gate bipolar transistor (referred to as IGBT), Tx and Dx (x = 1~4) complemental paralleled each other conventionally , The left and the right pairs of switches are connected in series to form two arms, the bridge arm and the DC side capacitor XC are connected in parallel, where point a and b are connected with the live line L and neutral line N of the single phase power grid respectively, also a current limiting inductor XL is connected in circuit to prevent current shaking.  The upper and lower switches of the same arm are controlled by complemental switching signals, which means that in addition to the dead time, switches of the same arm cannot be both ON and not more than two of the four IGBT can be ON at the same time. By controlling the two pairs of switches, different combination results could be obtained according to its switch state, as shown in Table 1. Figure.2.has showed the current loop under condition of double tube turning on. Figure. Figure.3. shows the MERS single bypass mode current path diagram, each kind of current outflow direction has two paths to choose from, at this time, capacitor does not inject any power to the AC bus,   Figure.4. The phase of the AC bus as a reference can be traced by the phase-locked loop technique, then adjusting the trigger hysteresis to control the output of the compensated reactive power. In Figure.4, π is the conduction pulse width, which is the delay trigger pulse angle. GT1, GT3 and GT2, GT4 are two pairs of complemental conduction IGBT turn-on switch signals.  Figure.6. shows the reactive power compensation characteristic of MERS. It can be seen that the output of reactive power, current total distortion rate (THD) and capacitance peak voltage soars with the increase of the  . Also, the peak voltage of the capacitor grows slowly at the beginning, and finally increases exponentially. The total distortion rate (excluding the triple harmonic) has a process of rapid increase and then a slight decrease. Therefore, if improving the reactive power output of the Magnetic Energy Recovery Switch is wanted, merely increasing in the trigger delay angle will cause the total distortion of the current (excluding the triple harmonic) and fixed capacitor peak voltage bounce, which will eventually affect the selection range of the operating point and results in the limited reactive power adjustment range.  Figure7. shows the circuit diagram of the minimum voltage control of capacitor (MVCC). In the Magnetic Energy Recovery Switch, the fixed capacitor in the circuit plays a role in storing energy. Some control methods have been taken to make sure that the capacitor discharge is not complete to zero but still saves a certain amount of electricity when operating, thus corresponds to increasing the equivalent capacitance of the capacitor, can expand the ranges of reactive power compensation adjustment. There are two primary ways to achieve the minimum voltage control of the capacitor: changing the early turn-off angle and controlling capacitor minimum voltage Vc-min directly. Generally, the control characteristics obtained by directly controlling the minimum voltage of the capacitor is better, because the capacitor voltage value can be detected directly, while changing the early turn-off angle may exist a secondary error. It can be seen from Figure 8 that the MVCC can achieve a better operating characteristic of voltage and current. As can be seen in Figure. 9, the output reactive power of the MERS decreases as Vc-min increases, but it is noteworthy that the capacitor voltage also has the same tendency to change. The total current distortion rate decreases at the beginning then increases rapidly as Vc-min increases. In summary, increasing the delay trigger angle  increases the output reactive power of MERS, but the fixed capacitor voltage and current total distortion rate increase as well; increasing Vc-min can reduce the capacitive reactive power output, achieving the goal of capacitor voltage peak adjustment, then the current harmonics would have a process of increasing rapidly at the beginning then decreasing gradually. In actual operation, the reactive power output range of the MERS is mainly affected by the current harmonics and the capacitor voltage. The current harmonics make the lower limit of the reactive power compensation boundary rises, and the capacitance withstand voltage causes the upper limit down, resulting in its adjustable range narrowing. To restrain current harmonics and peak voltage of capacitor concurrently a novel kind of Multi-Objective Optimization Evaluation Method Based on Magnetic Energy Recovery Switch Coordinated Control Algorithm is proposed. A considerably wide range of parameters Vc-min and  should be coordinated when meeting the power quality requirements in the grid. By establishing a coordination control and evaluation model, the proposed control algorithm realizes a better working performance compared to conventional control strategy. Meanwhile, the optimal operating point is attained.

4.1.Principle of regulation
As shown in Figure. capacitor lower than the settled threshold Vc-min, T3 will turn off to bypass the fixed capacitor in advance. In this coordination algorithm, the control of Vc-min and  is independent respectively and does not interfere with each other. Therefore, these two variables could be controlled at the same time.
During the overall operation, Control of  increases reactive power output, while Vc-min suppresses harmonics and peak capacitor voltage. The purpose of coordinated control is to find the optimal operating point of the MERS in the process of reactive power compensation, broaden its reactive power compensation range, and reduce the total current distortion rate (THD) and the capacitor voltage in the circuit.

Multi-objective optimization evaluation method
Using the control model and run the test several times then plot the simulation data to the working surface shown in Figure.11. The output of MERS reactive power, peak capacitor voltage and the total current distortion rate with the trigger delay angle  and Vc-min changes could be observed vividly.

Multiple regression analysis
As shown in Figure 12.

( , )
,, The regression coefficients are used in the least-square-method to change A and fitting repeatedly to choose the maximum of Multiple Correlation Coefficient R. Relationship between arguments and dependent variables can be seen as closer with larger R, the largest R corresponds to the most suitable power A.

4.4.dynamic weighted round-robin
Due to the evaluation system involves two physical quantities: peak of capacitor voltage and total current distortion rate. Cannot unify order of magnitude and dimension of numerical values, it is obviously illogically to use constant weight method. Hence, this paper chooses dynamic weighted round-robin for object functions evaluation system.
For each evaluate index, construct three-grade evaluation criterion, the numerical values in the table are percentage of evaluation objects input upper limits. As shown in table 2.   80%,100% According to the reality of evaluation, the influences of indexes to the final fitted number satisfy a characteristic which increase slowly firstly, grow rapidly in the middle time then trend gently to the maximum. Considering that, partial normal distribution function is selected as dynamic weighted function, that is: conditions should satisfy the upper limits of the two indexes and function relationship fitted with evaluation function. The specific expressions are as follows: . 1 , ( , ) peak peak peak

Sample analysis
To verify the validity of above method, this paper uses the output reactive power 1000 Var as a sample to solve the optimal operating point of the Magnetic Energy Recovery Switch. The coefficients in equation (3)  Plugging all the operating points into the multivariate nonlinear regression functions in the second third and fourth rows, the 12 sets of peaks of capacitor voltage and total current distortion rate obtained can be sorted by fitness according to equation (5) and (6), Finally, the two-dimensional operating point corresponded to the minimum fitness is selected as the optimum. From the result of fitness order in table 5 and Figure.13 Figure 14. It is obviously that under optimum operating condition the voltage amplitude and triple or more harmonic rate of MERS are lower than non-optimal operating point which means the goal of proposed algorithm has attained. Figure 15 shows the dynamic response of the load switching. The first switching occurs at 1.12s, The grid power factor drops immediately and reverts to a unit after 0.06s.The second load change at 1.3s,and the recovery takes about 0.06s.The first part of Figure 15 shows changes in grid power, the waveforms of voltage and current are shown in the below. Adopting the evaluation algorithm proposed in this paper, The MERS works as a compensator to track the reactive power in the grid. The feasibility and rapid dynamic performance are finally verified.

Conclusions
Magnetic Energy Recovery Switch as a novel reactive power compensator is investigated., several works have been done as following. Firstly, the conventional phase delay control and minimum voltage control of capacitor for Magnetic Energy Recovery Switch are introduced, Secondly, the feasibility and superiority of the parameter coordination control are clarified. And the coordinated control of the Magnetic Energy Recovery Switch is analyzed in detail. Thirdly, the multi-objective optimization evaluation method based on the coordinated control algorithm of Magnetic Energy Recovery Switch is proposed. The method finds the optimal operating point of the MERS based on the target for retraining current harmonics and peak voltage of the capacitors. Finally, a simulation is set up to validate that the proposed method is effective and has the performance of fast dynamic response.