2.1 Topology of PET
PET can be divided into AC/AC type and AC/DC/AC type according to whether the intermediate conversion module has DC link. The latter has become the research focus because of its good controllability and high flexibility. AC/DC/AC type PET includes two basic structural forms: cascaded H-bridge type and Modular Multilevel Converter(MMC) type [5, 13]. Cascaded H-bridge PET has advantages of higher power density, and there is no bridge arm circulating current when three-phase star connection is connected, for which its research and application have received extensive attention. This paper will focus on the engineering practice and the LVRT strategy of cascaded H-bridge PET.
The basic structure of the cascaded H-bridge four-port PET is shown in Fig. 1. The ports are AC 10 kV, DC ±750 V, AC 380 V and DC ±375 V respectively.
The AC-DC module in Fig. 1 implements the power conversion between AC10kV and DC ± 750 V, which is a key component and bear the main function of the PET. The AC-DC module shown in Fig. 2(a) consists of two identical star cascaded units shown in Fig. 2(b). Two AC-DC converters of the same structure can realize DC bipolar output by symmetrical connection. Because the positive and negative poles of the bipolar AC-DC converter have the same topological structure, in this paper, the single-pole structure converter shown in Fig. 2(b) is studied, and the control strategy of the other pole is identical.
One of the main problems that need to be solved in the practical application of cascaded H-bridge PET is how to achieve the equalization of the three-phase DC voltage when asymmetric voltage sags occur in the power grid to ensure the safe operation of the converter. References [11, 12] proposes the use of zero sequence or negative sequence voltage injection strategies to achieve DC voltage equalization control, but it will lead to control complexity, and the time-delay effect of the control strategy will affect the equalization effect. In view of the above problems, this paper realizes the self-balancing of DC voltage between bridge arms through the optimization design of DC link topology, which is shown in Fig. 2(b) and Fig. 3. In Fig. 2(b), the sub-module of the cascaded bridge arm adopts a typical cascaded H-bridge structure on the AC side, and on the DC side all the three-phase sub-modules are uniformly connected in parallel to form a DC port; In Fig. 3, the sub-module of AC-DC module uses a resonant bidirectional DC-DC converter, and the double-sided H-bridge is connected through a high-frequency transformer with a resonant capacitor to achieve voltage level conversion and electrical isolation. The H-bridge on both sides modulate the DC voltage into a high-frequency square wave, and the power exchange is realized through the resonance link. When the operating frequency is near the resonant frequency, the DC-DC ratio of the converter is equal to the high-frequency transformer ratio, and the performance of the converter is stable, and the load capacity of the converter is strong [14, 15].
As shown in Fig. 2(b) and Fig. 3, the DC side adopts a unified parallel port, combined with the superior performance DC-DC converter, can realize the self-balancing of the sub-module voltage; the AC side adopts the series structure, which can ensure the input current of the sub-module is consistent, so the PET can realize the sub-module voltage and current self-balancing to achieve balanced distribution of power between sub-modules. The relationship between the AC side current, the DC side voltage and the submodule voltage and current can be obtained as shown in (1).
$$ \left\{\begin{array}{l}{u}_{dc_1k1}={u}_{dc_1k2}=\cdots ={u}_{dc_1 kN}={U}_{dc}/{n}_T\\ {}{i}_{ink1}={i}_{ink2}=\cdots ={i}_{ink N}={i}_k\end{array}\right. $$
(1)
Where k = a, b, or c is the phase of AC side, \( {u}_{dc_1} \) is DC-DC converter primary side voltage, Udc is DC port voltage, nT is the high frequency transformer ratio, ik is ac side current and iin is input current of submodule.
Therefore, adopting the above topology structure, when an asymmetric voltage sag occurs on the AC side, the DC side parallel modules can realize current self-balancing, thereby realizing the AC side series modules voltage self-balancing. Thus, there is no need to add the DC voltage balance control link, for which the device operating performance can be improved and the control system can be simplified.
2.2 LVRT strategy of PET
2.2.1 Control objectives of LVRT
AC-DC module of PET generally uses a dual closed-loop control strategy during normal operation, as shown in Fig. 4. According to the working conditions and control objectives of PET, the outer loop can be controlled by constant DC voltage or constant power respectively, the adjustment time of which is generally 40~100 ms. The current inner loop adopts the d-axis voltage-oriented feedforward decoupling control strategy to quickly track the d-axis and q-axis current instruction values generated by the outer loop controller to improve the control performance, and the tracking time is 2~5 ms.
In the case of AC power grid failure causing AC bus voltage drop, PET operating in constant voltage mode can transfer voltage control function to other equipment, thus the DC voltage can be maintained during the low voltage ride through operation, then blocking voltage and reactive power outer loop. When the DC bus voltage is controlled by other equipment such as energy storage systems, PET can work in constant power control mode and can directly block the outer power loop. Thus, the current inner loop is directly used for control during the LVRT operation to improve the overall response speed by blocking the outer loop of the controller.
When the AC grid is short-circuited and the voltage sags, the PET should realize LVRT without off-grid to improve the stability of the grid operation and the reliability of the power supply. At present, there are few researches on PET LVRT control strategies, and this paper attempts to make up for this deficiency. PET is interconnected with the AC grid via an inverter, which is similar to photovoltaic power and direct drive wind turbine. Therefore, their LVRT control targets also have similarities for the purposes of ensuring the safe operation of the inverter and maintaining the stability of grid. In the design of the LVRT strategy of this paper, the relatively mature LVRT methods of renewable energies are used for reference. The main difference between PET LVRT control and renewable energies is that the power transmission direction of the later is one-way, while PET acts as a substation device with active power, for which the power bidirectional transmission characteristics need to be considered and special treatment is required in the given algorithm of the active current instruction value in PET LVRT strategy. Moreover, as an interconnected equipment for AC-DC hybrid distribution network, PET needs to meet the requirements of power supply reliability and power quality maintenance. In this paper, for the purposes of maintaining stable operation of the power grid, assisting grid voltage recovery and ensuring the safety of PET itself, the basic control objectives of PET LVRT are proposed as follows:
-
1)
When an asymmetric short circuit fault occurs in the power grid, the negative sequence current is eliminated by the negative sequence current suppression measures to ensure the symmetry of the current injected into the grid;
-
2)
According to the degree of positive sequence voltage sag on the AC side, the reactive current injection is automatically adjusted to help the grid voltage recovery;
-
3)
According to the active power condition before the voltage sag and the degree of positive sequence voltage sag on the AC side, the active transmission level and direction are maintained as far as possible under the premise of ensuring that the PET current does not exceed the limit, for which the disturbance to the AC/DC grid is reduced.
The block diagram of the LVRT strategy is shown in Fig. 5, In which α is the positive sequence voltage sag degree, which is the ratio of the positive sequence voltage amplitude during voltage sag to the normal operation voltage amplitude, that is:
$$ \alpha ={u}_{sd+}^{+}/{u}_{sd0} $$
(2)
When PET detects α < 0.9, it is switched to LVRT control mode automatically. In the case of AC power grid failure causing AC bus voltage drop, it is considered that the energy storage equipment is connected to the DC grid, for which the DC voltage can be maintained during the low voltage ride through operation. The current inner loop is directly used for control to improve the overall response speed by blocking the outer loop of the controller.
2.2.2 Implementation of LVRT
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A.
Inner loop design
The PET pre-stage AC-DC converter realizes the power conversion between AC and bipolar DC. The transformation modules of the two star cascaded structures are identical, so the mathematical model and control strategy are also identical. Therefore, this section only discusses the transformation module between the AC side and the unipolar DC.
The mathematical model of the AC side of the AC-DC module of PET shown in Fig. 2 is
$$ \left\{\begin{array}{c}{L}_{arm}\frac{di_a}{dt}+{R}_{eq}{i}_a={u}_{sa}-{u}_a\\ {}{L}_{arm}\frac{di_b}{dt}+{R}_{eq}{i}_b={u}_{sb}-{u}_b\\ {}{L}_{arm}\frac{di_c}{dt}+{R}_{eq}{i}_c={u}_{sc}-{u}_c\end{array}\right. $$
(3)
In (3), Larm is the bridge arm filter inductor, Req is the series equivalent resistance of the IGBT turn-on resistors of cascaded H-bridge sub-module and filter inductor additional resistor, usa, usb and usc are the point of common connection (PCC) voltage, isa, isb and isc are the grid-connected current, ua, ub and uc are multi-level voltages obtained by superimposing the output of sub-module on the AC side of the AC-DC module.
The overall mathematical model of the AC-DC module in the three-phase stationary coordinate system shown in (3) is not conducive to the control system design, and it can be transformed into a two-phase rotating coordinate system, that is
$$ \left\{\begin{array}{c}{L}_{arm}\frac{di_d}{dt}+{R}_{eq}{i}_d={u}_{sd}-{u}_d+\omega {L}_{arm}{i}_q\\ {}{L}_{arm}\frac{di_q}{dt}+{R}_{eq}{i}_q={u}_{sq}-{u}_q\hbox{-} \omega {L}_{arm}{i}_d\end{array}\right. $$
(4)
During voltage asymmetric sags, the system voltage and current will contain positive and negative sequence components. Performing positive and negative sequence decomposition on mathematical model shown in (4) in a double dq coordinate system, and the AC side mathematical model of the AC-DC module of PET in the forward and the reverse rotation coordinate system can be obtained as (5) and (6).
$$ \left\{\begin{array}{c}{L}_{arm}\frac{di_{d+}^{+}}{dt}+{R}_{eq}{i}_{d+}^{+}={u}_{sd+}^{+}-{u}_{d+}^{+}+\omega {L}_{arm}{i}_{q+}^{+}\\ {}{L}_{arm}\frac{di_{q+}^{+}}{dt}+{R}_{eq}{i}_{q+}^{+}={u}_{sq+}^{+}-{u}_{q+}^{+}-\omega {L}_{arm}{i}_{d+}^{+}\end{array}\right. $$
(5)
$$ \left\{\begin{array}{c}{L}_{arm}\frac{di_{d-}^{-}}{dt}+{R}_{eq}{i}_{d-}^{-}={u}_{sd-}^{-}-{u}_{d-}^{-}-\omega {L}_{arm}{i}_{q-}^{-}\\ {}{L}_{arm}\frac{di_{q-}^{-}}{dt}+{R}_{eq}{i}_{q-}^{-}={u}_{sq-}^{-}-{u}_{q-}^{-}+\omega {L}_{arm}{i}_{d-}^{-}\end{array}\right. $$
(6)
The ‘+’ in the lower corner of each variable in the equation represents the forward rotation coordinate system, and the ‘-’ represents the reverse rotation coordinate system. The ‘+’ in the upper corner indicates the positive sequence component, and the ‘-’ indicates the negative sequence component.
The PI controller is used for current regulation and current feedforward decoupling. According to the mathematical models shown in (5) and (6), the positive and negative sequence dq axis voltage instruction values can be obtained as (7) and (8), the corresponding LVRT block diagram is shown in Fig. 6.
$$ \left\{\begin{array}{l}{u}_{d+}^{+\ast }=-\left[{k}_p\left({i}_{d+}^{+\ast }-{i}_{d+}^{+}\right)+{k}_i\int \left({i}_{d+}^{+\ast }-{i}_{d+}^{+}\right) dt\right]\\ {}\kern2.5em +{u}_{sd+}^{+}+\omega {L}_{arm}{i}_{q+}^{+}\\ {}{u}_{q+}^{+\ast }=-\left[{k}_p\left({i}_{q+}^{+\ast }-{i}_{q+}^{+}\right)+{k}_i\int \left({i}_{q+}^{+\ast }-{i}_{q+}^{+}\right) dt\right]\\ {}\kern2.5em +{u}_{sq+}^{+}-\omega {L}_{arm}{i}_{d+}^{+}\end{array}\right. $$
(7)
$$ \left\{\begin{array}{l}{u}_{d-}^{-\ast }=-\left[{k}_p\left({i}_{d-}^{-\ast }-{i}_{d-}^{-}\right)+{k}_i\int \left({i}_{d-}^{-\ast }-{i}_{d-}^{-}\right) dt\right]\\ {}\kern2.5em +{u}_{sd-}^{-}-\omega {L}_{arm}{i}_{q-}^{-}\\ {}{u}_{q-}^{-\ast }=-\left[{k}_p\left({i}_{q-}^{-\ast }-{i}_{q-}^{-}\right)+{k}_i\int \left({i}_{q-}^{-\ast }-{i}_{q-}^{-}\right) dt\right]\\ {}\kern2.5em +{u}_{sq-}^{-}+\omega {L}_{arm}{i}_{d-}^{-}\end{array}\right. $$
(8)
The unified control block diagram model after decoupling the current inner loop is shown in Fig. 7, in which x* and x represent the current instruction values and actual values in Fig. 6(a) and Fig. 6(b) respectively. The design principle of the current inner loop PI controller in Fig. 7 is the same with that of the steady-state control strategy because the control block diagram is consistent. The current inner loop can be guaranteed to have good tracking performance by optimizing the regulator parameters. The current inner loop controller parameters are set in the light of the typical I-type system, for which the current inner loop can be equivalent to the first-order inertia unit [16], and its time constant is 2~5 ms.
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B.
Negative sequence current elimination
During the asymmetric voltage sag of the grid voltage, Negative sequence current is eliminated in order to ensure the symmetry of the three-phase current injected into the grid to reduce the impact on the grid, as shown in (9). The negative sequence current dq-axis component instruction value in the reverse rotation coordinate system shown in Fig. 6(b) is given as zero, and the negative sequence current dq-axis component will quickly follow the instruction value shown in (9) to achieve the function of negative sequence current elimination.
$$ \left\{\begin{array}{l}{i}_{d-}^{-\ast }=0\\ {}{i}_{q-}^{-\ast }=0\end{array}\right. $$
(9)
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C.
Reactive power injection
The q-axis positive sequence current instruction value is shown in (10). In the case of a voltage sag of less than 10%, PET can operate stably according to the normal control strategy, at this time \( {i}_{q+}^{+\ast }=0 \) to achieve unit power factor operation. When the voltage sags by more than 10%, for every 10% sag, PET provides 15% reactive power compensation to the AC grid, supporting the PCC voltage of the grid to help restore the grid voltage. The maximum compensation capacity of PET is 1.2 times the rated current.
$$ {i}_{q+}^{+\ast }=\left\{\begin{array}{l}0\kern0.5em ,\alpha >0.9\\ {}1.5\left(0.9-\alpha \right)\kern0.5em ,0.1<\alpha <0.9\\ {}1.2\kern0.5em ,\alpha <0.1\end{array}\right. $$
(10)
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D.
Active power maintenance
The main practice of renewable energies to achieve LVRT is to perform dynamic reactive power support according to the degree of system voltage drop, but the instruction value of active current is not clearly defined. Based on the dynamic reactive power support, the LVRT strategy proposed in this paper gives a novel active current instruction value algorithm to maintain the transmission direction and level of active power of PET in normal and LVRT conditions as much as possible, thus reducing the disturbance to the AC-DC hybrid distribution network.
During the grid voltage sag, the active power absorbed by PET from the grid is shown in (11).
$$ p={u}_{sd+}^{+}{i}_{d+}^{+}+{u}_{sq+}^{+}{i}_{q+}^{+}+{u}_{sd-}^{-}{i}_{d-}^{-}+{u}_{sq-}^{-}{i}_{q-}^{-} $$
(11)
When the positive sequence d-axis voltage orientation is adopted, \( {u}_{sq+}^{+}=0 \). During LVRT operation, the negative sequence current can quickly track the instruction value of (9), that is, \( {i}_{d-}^{-}={i}_{q-}^{-}=0 \). The positive sequence d-axis current is also able to quickly track its instruction value. From the above analysis, the PET absorption power during the voltage sag can be obtained as shown in (12).
$$ p={u}_{sd+}^{+}{i}_{sd+}^{+\ast } $$
(12)
The power absorbed by PET from the grid before the grid voltage sags is
$$ {p}_0={u}_{sd0}{i}_{d0}^{\ast } $$
(13)
PET transmission loss is neglected. It can be seen from the combination of (2), (12) and (13) that during the voltage sag, in order to maintain the active transmission level, the amplitude algorithm of the active current instruction value must be (14), which will change according to the degree of voltage drop to maintain the level of active power before and after the fault.
$$ {i}_{d+}^{+\ast }={i}_{d0}^{\ast }/\alpha $$
(14)
Therefore, the d-axis positive sequence current instruction value represented by (15) can be obtained. The level of active power exchange before the voltage sag is maintained as far as possible based on the q-axis positive sequence current instruction value which has been given in (10), and the 1.2 times current-carrying restriction condition is considered. In (15), sign is a symbol function, for which the transmission direction of the active power before the voltage sag can be obtained, so that the LVRT strategy can adapt to the characteristics of the PET bidirectional power transmission. This is the adaptation and improvement of the renewable energy LVRT. \( \sqrt{1.2^2-{i}_{q+}^{+\ast 2}} \) is the maximum allowable active current instruction value after reactive compensation according to (10).
$$ {i}_{d+}^{+\ast }=\mathit{\operatorname{sign}}\left({i}_{d0}^{\ast}\right)\times \min \left\{\left|{i}_{d0}^{\ast}\right|/\alpha, \sqrt{1.2^2-{i}_{q+}^{+\ast 2}}\right\} $$
(15)
Substituting (10) into (15), the relationship between the positive sequence active current instruction value upper limit and the positive sequence active current instruction demand value for maintaining the active level before voltage sag and the voltage sag depth is shown in Fig. 8. The solid line in the figure is the maximum allowable active current after reactive power compensation, that is, the upper limit of active current. As the voltage sag depth deepens, the reactive power demand gradually increases, and the active power upper limit gradually decreases. The dotted clusters in the figure represent the amount of active output required to maintain the active level before and after the voltage sag. The dotted line from bottom to top respectively indicates that the PET is from no load to full load before the voltage sag, and the interval is 0.1p.u. It can be seen from Fig. 8 that the requirement of maintaining the active level before the voltage sag can be achieved according to the (14). Taking the active current instruction value of 0.6 before the voltage sag as an example, as shown in Fig. 8, the horizontal dotted line in the figure is the active current before the voltage sag. Under the condition that the voltage sag is not less than 55%, the control strategy can ensure the active before and after the voltage sag. The transmission level and direction remain constant.
