Optimal Energy Efficiency Tracking in the Energy-Stored Quasi-Z-Source Inverter

Abstract

In this paper, the interaction between the energy storage (ES) power distribution and system efficiency enhancement is researched based on the energy stored quasi-Z-source inverter. The corresponding current counteraction, stress reduction, power loss profile, and efficiency enhancement around the embedded energy storage units are studied in details. Firstly, the current counteraction effect on the device current is presented with the embedded ES source. The corresponding reduction in the device current stress is revealed. Then, the detailed device power loss expressions with current redistribution in the impedance network are explored mathematically. A quasi-inverted-trapezoidal power loss profile is found with the embedded source power distribution. To further increase the overall system efficiency, an optimal energy efficiency tracking strategy is proposed for the ES-qZSI (energy-stored quasi-Z-source inverter) based on the power distribution control. Both the simulation and the experiment verified that the power loss is reduced by over 40% through the proposed efficiency enhancement method. The device current and loss analysis for the embedding of energy storage can also be extended to the operating range optimization in other ES systems.

1. Introduction

The energy storage system (ESS) has been attractive in various ancillary services for renewable energy generation and other applications [1,2]. To supply energy for longer durations and improve the benefits provided by multi-energy storage systems, the optimal overall efficiency should be achieved considering each subordinate energy storage. Different from the power generation applications with maximum power point tracking (MPPT) requirement, like PV and wind turbines, an ideal energy storage system usually aims to achieve maximum energy efficiency tracking (MEET) [3,4]. A MEET scheme for the micro-grid was studied [5] through the optimal power distribution. The optimization criterion is based the system achieving high efficiency with a battery at a low state of charge (SOC). Improving efficiency through power distribution regulation was proposed [6]. These power distribution methods were also applied for applications such as electric vehicles and elevators [7,8,9]. MEET has proved to be effective for power conversion system (PCS) applications in AC or DC micro-grids. However, owing to the fluctuation in output power and SOC, the MEET for ESSs does not currently have the capability to handle a wide operation range.

The energy-stored quasi-Z-source inverter (ES-qZSI) is characterized by single-stage power conversion and high efficiency. Its operation principle with multiple energy storages, including both battery and ultra-capacitor, has been demonstrated [10,11]. The topology was researched widely for applications such as photovoltaic power generation and electric vehicles [12,13,14]. Methods like soft-switching and modulation strategy, aiming at device current stress reduction, were applied for efficiency improvement [15,16,17]. An optimal power distribution to improve efficiency has been given in [18,19], but the principle and operation range are still obscure due to the lack of interaction studies on the impedance network, the switching device stress, and the energy storage units.

In this paper, the principle for the current counteraction and stress reduction around the energy-storage units embedding in the ES-qZSI is studied in detail. The device power loss with the current redistribution in the impedance network is explored mathematically. A quasi-inverted-trapezoidal power loss profile is found with power distribution between the input source and the embedded source. Finally, a wide range optimal energy efficiency tracking technology in the ES-qZSI is proposed. The effectiveness of the theatrical analysis and proposed method are validated by both a simulation and experiment. The power loss of the ES-qZSI can be reduced by more than 40% compared with the conventional qZSI.

2. Principle of Current Counteraction in ES-qZSI

The circuit of the ES-qZSI is demonstrated in Figure 1. The input of the ES-qZSI, denoted as source 1, is connected with a DC source, such as PV, which is similar to the conventional qZSI topology. Compared with the conventional qZSI topology, an energy storage unit, such as a battery, is embedded parallel with the capacitor C₂ in the ES-qZSI and is denoted as source 2.

The system can be separated into two parts by the DC-bus based on the system operation, as shown as the AC and DC sides in Figure 1. In the shoot-through (ST) state, the switch S₇ in the DC side turns off and at least one phase leg in the AC side is short-circuited. In the non-shoot-through (NST) states, S₇ turns on and S₁–S₆ operate like the conventional voltage source inverter (VSI) [18].

Due to the embedded energy storage unit, V_bus is clamped by the voltages of sources 1 and 2. Then S₇ and the ST state are adopted to distribute the power between the two sources. Based on the power conservation, the source current distribution in the ES-qZSI is derived as Equation (1) [18], where D represents the ST duty ratio, I_source1 represents the current from source 1, and I_source2 represents the current from source 2. The current allocation of the two sources is achieved through the regulation of the ST duty ratio.

$$I_{\mathrm{bus}}=\left(1-2D\right)I_{\mathrm{source}1}+D{I}_{\mathrm{source}2}$$

(1)

Compared with the conventional qZSI, the current from source 2 has an impact on the internal current distribution of the impedance network on the DC side. For the traditional qZSI, the inductor current I_L2 is clamped by the inductor current I_L1 due to the zero average currents through C₁ and C₂, as shown in Equation (2), where V_bus is the DC-link voltage, P_o is the output power, and B is the ratio between V_bus and the voltage of source 1.

$$I_{\mathrm{L}2}=I_{\mathrm{L}1}=\frac{B{P}_{\mathrm{o}}}{V_{\mathrm{bus}}},B=\frac{V_{\mathrm{bus}}}{V_{\mathrm{source}1}}$$

(2)

For the ES-qZSI, the injected current from the embedded source 2 flows through the inductor L₂ and counteracts I_L1, as shown in Figure 1. Therefore, I_L2 is reduced. The current counteraction effect is demonstrated in Equations (3)–(5) based on the power conservation and the ampere-second balance, where P_source2 is the power of source 2 and K is the distribution ratio between P_source2 and P_o.

$$I_{\mathrm{L}1}=\frac{\left(1-K\right)B{P}_{\mathrm{o}}}{V_{\mathrm{bus}}}$$

(3)

$$I_{\mathrm{L}2}=I_{\mathrm{L}1}-I_{\mathrm{source}2}=\left(B-\frac{KB\left(B+1\right)}{B-1}\right)\frac{P_{\mathrm{o}}}{V_{\mathrm{bus}}}$$

(4)

$$K=\frac{P_{\mathrm{source}2}}{P_{\mathrm{o}}}$$

(5)

According to Equations (3)–(5), the inductor currents in ES-qZSI can be redistributed with K, which is the ratio of the power from source 2 to the output power. The inductor currents of qZSI in Equation (2) is a special case where I_source2 = 0 or K = 0. The embedded energy storage unit can help reduce both I_L1 and I_L2 by sharing part of the output power.

3. Stress Reduction and Power Loss Profile in ES-qZSI

3.1. Device Stress Analysis for ES-qZSI

The inductor current redistribution due to current counteraction can ease the switching device current stress in ES-qZSI. The current stress reduction is demonstrated with the current commutation in different states in Figure 2.

During the ST state, as demonstrated in Equation (6) and Figure 2(a2), the ST current I_ST equals the sum of I_L1 and I_L2, where the output power P_o can be expressed as Equation (7). M represents the modulation index, I_ph represents the amplitude of the phase current, and φ represents the power factor angle.

$$I_{\mathrm{ST}}=I_{\mathrm{L}1}+I_{\mathrm{L}2}=2\left(B-\frac{B^{2}K}{B-1}\right)\frac{P_{\mathrm{o}}}{V_{\mathrm{bus}}}$$

(6)

$$P_{\mathrm{o}}=\frac{\sqrt{3}}{2}M{V}_{\mathrm{bus}}{I}_{\mathrm{ph}}\cos \phi$$

(7)

For the AC-side switch devices, as the three-phase ST method [15] is adopted, the ST current is shared equally by the three bridges, and the device stress in any bridge is derived as:

$$I_{\mathrm{Sn}\text{-}\mathrm{ST}}=\frac{1}{3}{I}_{\mathrm{ST}}+\frac{1}{2}{I}_{\mathrm{ph}}$$

(8)

During the NST states, S₁–S₆ conduct the phase currents, so the device current stress is the same as the conventional VSI [20]:

$$I_{\mathrm{Sn}\text{-}\mathrm{NST}}=I_{\mathrm{ph}}$$

(9)

According to Figure 2(a1), the current expression of S₇ in the DC side during the NST state is:

$$I_{\mathrm{S}7}=I_{\mathrm{L}1}+I_{\mathrm{L}2}-I_{\mathrm{dc}\_\mathrm{link}}=I_{\mathrm{ST}}-I_{\mathrm{dc}\_\mathrm{link}}$$

(10)

I_{dc_link} is the DC-link current and its expression is 0, ±I_A, ±I_B, and ±I_C based on the states of S₁–S₆ [21]. Combining Equations (6), (8), and (10), the ST current and the current stress in S₁–S₇ can be alleviated through the power provided by the energy storage unit. This indicates that the device loss can be reduced and the energy transfer efficiency can be improved through power distribution in the ES-qZSI.

3.2. Power Loss Profile Derivation for ES-qZSI

In this section, the switching and conduction loss of the AC and DC sides are presented with the power distribution in ES-qZSI. The device current expressions in Section 3.1 are adopted for the power loss modeling. The inductors losses are also included. Due to the low internal resistance, the power loss of the energy storage unit is far less than in the power electronic devices. Therefore, the power loss of the energy storage unit can be neglected. The derivation is demonstrated in Appendix A and the result is shown in

Table 1. Power loss of the ES-qZSI.

Item		Expression	Coefficient
Switching loss	DC side	$P_{\mathrm{sw}\text{-}\mathrm{S}7}=2{\alpha }_1{f}_{\mathrm{s}}{V}_{\mathrm{bus}}\left|I_{\mathrm{ST}}\right|$	${\alpha }_1=\{\begin{array}{ll}{E}_{\mathrm{IGBT}}& I_{\mathrm{ST}}<0\\ E_{\mathrm{Diode}}& I_{\mathrm{ST}}\ge 0\end{array}$ ${\alpha }_2=\{\begin{array}{ll}{E}_{\mathrm{Diode}}& I_{\mathrm{ST}}<0\\ E_{\mathrm{IGBT}}& I_{\mathrm{ST}}\ge 0\end{array}$ ${\alpha }_3=\{\begin{array}{ll}{E}_{\mathrm{IGBT}}+E_{\mathrm{Diode}}\hfill & \left|I_{\mathrm{ST}}\right|/I_{\mathrm{ph}}\le 1.5\hfill \\ 0\hfill & \left|I_{\mathrm{ST}}\right|/I_{\mathrm{ph}}>1.5\hfill \end{array}$ ${\alpha }_4=\{\begin{array}{ll}2V_{\mathrm{CE}0}\hfill & \left|I_{\mathrm{ST}}\right|/I_{\mathrm{ph}}\le 1.5\hfill \\ 0\hfill & \left|I_{\mathrm{ST}}\right|/I_{\mathrm{ph}}>1.5\hfill \end{array}$ ${\alpha }_5=\{\begin{array}{ll}{r}_{\mathrm{on}}{I}_{\mathrm{ph}}\hfill & I_{\mathrm{ST}}\ge I_{\mathrm{ph}}or{I}_{\mathrm{ST}}\le 0\hfill \\ r_{\mathrm{on}}{I}_{\mathrm{ph}}+V_{\mathrm{CE}0}\hfill & 0<I_{\mathrm{ST}}<I_{\mathrm{ph}}\hfill \end{array}$ ${\alpha }_6=\{\begin{array}{ll}-\frac{\sqrt{3}}{2}M{V}_{\mathrm{CE}0}{I}_{\mathrm{ph}}\cos \phi & I_{\mathrm{ST}}\ge I_{\mathrm{ph}}\\ \frac{\sqrt{3}}{2}M{V}_{\mathrm{CE}0}{I}_{\mathrm{ph}}\cos \phi & I_{\mathrm{ST}}<I_{\mathrm{ph}}\end{array}$
	AC side	$\begin{array}{ll}{P}_{\mathrm{sw}\text{-}\mathrm{ac}}& =2{\alpha }_2{f}_s{V}_{\mathrm{bus}}\left|I_{\mathrm{ST}}\right|+\frac{6}{\pi }\left(E_{\mathrm{IGBT}}+E_{\mathrm{Diode}}\right)f_s{V}_{\mathrm{bus}}{I}_{\mathrm{ph}}\\ & +\frac{1}{\pi }{\alpha }_3{f}_{\mathrm{s}}{V}_{\mathrm{bus}}\left[\sqrt{9I_{\mathrm{ph}}^2-4I_{\mathrm{ST}}^2}-2\left|I_{\mathrm{ST}}\right|\arccos \frac{2\left|I_{\mathrm{ST}}\right|}{3I_{\mathrm{ph}}}\right]\end{array}$
Conduction loss	DC side	$\begin{array}{ll}{P}_{\mathrm{con}\text{-}\mathrm{S}7}& =\left(1-D\right)r_{\mathrm{on}}{I}_{\mathrm{ST}}^2+\left(1-D\right)V_{\mathrm{CE}0}{I}_{\mathrm{ST}}-\sqrt{3}{\alpha }_{5}M{I}_{\mathrm{ST}}\cos \phi \\ & +\frac{M}{2\pi }{r}_{\mathrm{on}}{I}_{\mathrm{ph}}^2\left(3+2\cos 2\phi \right)+{\alpha }_6\end{array}$
	AC side	$\begin{array}{ll}{P}_{\mathrm{con}\text{-}\mathrm{ac}}& =\frac{6\left(1-D\right)}{\pi }{V}_{\mathrm{CE}0}{I}_{\mathrm{ph}}+\frac{6-3D}{4}{r}_{\mathrm{on}}{I}_{\mathrm{ph}}^2\\ & +2D{V}_{\mathrm{CE}0}\left|I_{\mathrm{ST}}\right|+\frac{2}{3}D{r}_{\mathrm{on}}{I}_{\mathrm{ST}}^2\\ & +\frac{2}{\pi }{\alpha }_{4}D\left(\sqrt{9I_{\mathrm{ph}}^2-4I_{\mathrm{ST}}^2}-2\left|I_{\mathrm{ST}}\right|\arccos \frac{2\left|I_{\mathrm{ST}}\right|}{3I_{\mathrm{ph}}}\right)\end{array}$
Inductor loss		$P_{\mathrm{L}}=r_{\mathrm{L}}{\left(\frac{P_{\mathrm{o}}+V_{\mathrm{source}2}{I}_{\mathrm{ST}}}{V_{\mathrm{bus}}}\right)}^2+r_{\mathrm{L}}{\left(\frac{-P_{\mathrm{o}}+V_{\mathrm{source}2}{I}_{\mathrm{ST}}+V_{\mathrm{source}1}{I}_{\mathrm{ST}}}{V_{\mathrm{bus}}}\right)}^2$

. Due to the combination of the ST current and the phase current in the devices S₁–S₇, as in Equations (8) and (10), the zero-crossing point of device current and the commutation duration of the diode change. Its effect on the device power losses is represented by the coefficients α₁–α₆ in Table 1.

According to Table 1, the variation in the system power losses with respect to I_ST is demonstrated in Figure 3. It can be seen that the system power losses can be divided into three types based on their variation profiles.

(1) As shown in Equations (8) and (9), the coefficient of I_ST is smaller compared with that of I_ph. Therefore, the AC side device switching loss P_sw-ac and conduction loss P_con-ac are mainly dominated by I_ph and are relatively insensitive to I_ST, as shown in Figure 3.

(2) The coefficient of I_S7 in Equation (10) increases. Therefore, the DC-side device switching loss P_sw-S7 and conduction loss P_con-S7 are more sensitive to I_ST. It can be seen from Table 1 that P_sw-S7 varies as a V-type curve. Its minimum value appears at the operation point O₁ where I_ST reaches zero. For P_con-S7, the variation curve also presents as a V-type curve, as shown in Figure 3. According to Equation (10), I_ST is fully counteracted by I_ph at the operation point O₂ where I_ST equals I_ph, and thus the minimum value of P_con-S7 appears.

(3) As shown in Table 1, P_L is a quadratic function of I_ST. Thus, the profile P_L varies like a parabolic curve. Its minimal point is located between O₁ and O₂, so the variation in P_L within this operation range is flat.

The total system loss P_loss can be obtained by combining P_con-S7, P_sw-S7, P_L, P_con-ac, and P_sw-ac. As the profiles of P_con-S7 and P_sw-S7 are V-type curves with different minimal points, their combination forms a quasi-inverted-trapezoidal profile with a flat valley. The parabolic profile of P_L also contributes to shaping a quasi-inverted-trapezoidal profile, whereas P_con-ac and P_sw-ac have a minimal effect on the total power loss profile. Thus, P_loss appears as a quasi-inverted-trapezoidal profile with respect to I_ST, as shown in Figure 3. The flat valley of P_loss, which represents the optimal efficiency operation range, is located between the minimal points of P_con-S7 and P_sw-S7 (O₁–O₂).

According to Equations (6) and (7), the conventional qZSI operates at O₃ where K is zero and I_ST equals $\sqrt{3}$BMI_ph (B means the ratio of V_bus to V_source1, M means the modulation index and I_ph means the amplitude of the phase current). For high boost ratio applications, like BM ≥ 1, O₃ is located outside the optimal efficiency operation range (O₁–O₂), as shown in Figure 3. Thus the efficiency gets enhanced in the ES-qZSI compared with the conventional qZSI.

4. Optimal Energy Efficiency Tracking and Practical Implementation

An optimal energy efficiency tracking method is presented in this section to guide the ES-qZSI working at the optimal operation range O₁–O₂. From Equations (6) and (7), the expression of K is derived as:

$$K=-\frac{B-1}{\sqrt{3}{B}^2}\cdot \frac{I_{\mathrm{ST}}}{M{I}_{\mathrm{ph}}\cos \phi }+\frac{B-1}{B}$$

(11)

Then, the corresponding power distribution ratios at O₁ (I_ST = I_ph) and O₂ (I_ST = 0) can be obtained as:

$$K_{\mathrm{O}1}=\frac{B-1}{B},K_{\mathrm{O}2}=\frac{B-1}{B}-\frac{B-1}{\sqrt{3}{B}^{2}M\cos \phi }$$

(12)

According to Equation (12), the optimal efficiency tracking can be implemented based on the regulation of K. The control scheme is embedded in the vector control for the ES-qZSI, as shown in Figure 4a. The practical implementation for optimal efficiency tracking is divided into three steps and demonstrated by the flowchart in Figure 4b.

Step 1: Obtain the system operation parameters like V_source1, V_source2, I_ph, M, and φ. Then, calculate P_o according to Equation (7).

Step 2: Based on Equation (12), find the boundaries of the efficiency enhancement range K_O1 and K_O2. Select the K reference between K_O1 and K_O2.

Step 3: Calculate the reference value of I_source based on Equation (5). Then, the ST duty ratio D is adopted to regulate I_source based on Equation (1).

Figure 5 shows the theoretical loss with different output powers. It is obtained from the parameters in

Table 2. System parameters of the test platform.

Item	Value
Frequency of the grid fg	50 Hz
Switching frequency fs	10 kHz
Voltage of source 2 Vsource2	50 V
Voltage of source 1 Vsource1	100 V
Inductors L1, L2	4 mH
Capacitors C1, C2	820 μF
Inductor parasitic resistance rL	80 mΩ
Switching Device S1–S7	IKW40N120T2

. We found that the power losses related to S₇ and inductors are significantly reduced in the energy efficiency enhancement range. The system efficiency of ES-qZSI working within K_O1–K_O2 improved compared with the conventional qZSI (K = 0). The efficiency enhancement was found to be effective for different output powers.

5. Simulation and Experimental Verification

The effectiveness of the proposed analysis and optimal energy efficiency tracking was verified by a simulation and an experiment. The simulation was performed with the software platform PLECS based on the parameters from the datasheet of the switching device. The experimental platform is demonstrated in Figure 6 and the system parameters are listed in Table 2.

Figure 7 and Figure 8 show the device current waveforms in one switching period for the DC and AC sides. The output power was 400 W. Figure 7 shows the current waveform of S₇ on the DC side. In the conventional qZSI (K = 0), the current stress for S₇ in the active states is 9 A, which is much larger than the phase current (3.8 A). This results in S₇ suffering from large current stress. In Figure 7b, the operation point O₁ is reached when K is 0.5. Thus, I_ST decreases to zero and the current stress for S₇ in the active states is close to the phase current value (3.8 A). Thereby, the current stress alleviation based on Equation (10) was verified.

Figure 8 shows the current waveform of S₁ on the AC side during one switching period. The current during the ST state reduced from 5 to 2 A as K increased from 0 to 0.5. The results match the calculation based on Equation (8) and I_ST and I_ph in Figure 7.

The experimental power loss profile between O₁ and O₃ is demonstrated in Figure 9. A low valley appears within the operation range of O₁–O₂, verifying the analysis for profile of P_loss. From the experiment, the total power loss was reduced by up to 40% with the power distribution regulation in ES-qZSI compared with the conventional qZSI. More than 70% of reduction was provided by S₇ and the passive components.

Figure 10 shows the simulation verification for the optimal energy efficiency tracking method. Initially, the system works as the conventional qZSI with K = 0. A large current value in I_ST can be observed. After that, the optimal energy efficiency tracking is activated and the system enters the optimal operation range. I_source2 from the energy storage units helps to reduce I_ST. Then, the system efficiency is improved by more than 4% through the regulation of the power distribution.

The related experimental results are shown in Figure 11. With increasing I_source2, the system efficiency increased to over 93%. Meanwhile, the shoot-through current increased up to 8 A when K = 0, which caused large current stress on S₇. Through the power distribution, the ST current was reduced to nearly zero, which relieved the current stress on S₇.

Figure 12 demonstrates the experiment waveforms to validate the optimal energy efficiency tracking method with a load power variation. In Figure 12a, the optimal energy efficiency tracking is not used and I_source2 is kept unchanged. Thus, I_ST increased when the load power increased, and the efficiency decreased to below 92%. In Figure 12b, I_source2 is regulated according to the optimal energy efficiency tracking method. The system operated around O₁ when I_ST was kept at a low value during the output power variation. Then, the efficiency was maintained above 92% and the optimal energy efficiency tracking was verified.

6. Conclusions

This paper presented a detailed system power loss analysis for the ES-qZSI from the power distribution view. The current counteraction effect was studied to alleviate the device current stress. An efficiency enhancement scheme was then presented based on the quasi-inverted-trapezoidal loss profile and power distribution around the embedded energy storage units. The effectiveness of the proposed efficiency enhanced method was verified by a simulation and an experiment, resulting in a power loss decrease of over 40%. The analysis and proposed scheme may also be extended to other impedance-source-network-based energy storage systems.