Research on Simpliﬁed Model of AC / DC Hybrid Microgrid for Fault Analysis

: The AC / DC hybrid microgrid, which takes into account the access requirements of AC and DC sources and loads, optimizes the structure of traditional distribution networks. The application of power electronic transformers as the core of its energy management, with electrical isolation and accurate control of the voltage, current and power ﬂow by the control system, enables the microgrid to achieve a more ﬂexible and stable transmission mode. Because the power electronic transformer combines the power electronic device and the high-frequency transformer, its frequent switching causes the electromagnetic transient simulation to take too long. Therefore, by simplifying control loops and converters, this paper proposes a simpliﬁed model for the microgrid system power ﬂow and the dynamic response under exposure to a fault. The mathematical model equivalent simpliﬁcation method is used in this paper. This method is concise and e ﬃ cient and does not rely on the performance of a computer or change the program algorithm of the software. The simpliﬁed model was built based on PSCAD (Power System Computer Aided Design) simulation software and was carried out under short circuit fault conditions to verify its validity. The comparison of the simulation’s time consumption and accuracy shows that model simpliﬁcation can signiﬁcantly improve the simulation speed, with an acceptable error rate, and its dynamic response maintains good consistency with that of the detailed electromagnetic transient model. Therefore, it can be applied to the transient electromagnetic simulation fault analysis of the AC / DC hybrid microgrid.


Introduction
As a system with various distributed generators, AC and DC loads, and self-adjusting and control capabilities [1,2], the microgrid applies power electronic transformers, which not only enables it to carry out the power transmission and electrical isolation of traditional transformers, but also realizes harmonic and reactive power compensation. The microgrid supports accurate and bidirectional power flow regulations [3][4][5] and has broad application prospects in this field. In [3][4][5], the topology and control strategy of the AC/DC hybrid microgrid is proposed to achieve the reliable and efficient operation of the AC/DC hybrid microgrid. In [6], Power Electronics Transformer (PET) topologies for three-phase AC distribution networks were discussed. By using space vectors, a mathematical model for MMC and a method for controlling the power flow were proposed. In [7], the typical control strategy for parallel operation was studied to realize the rational distribution of active and reactive power between power electronics transformers operating in parallel. In [8], a new type of power distribution transformer for the power distribution system was proposed, called the flexible Grid AC 1   The AC-DC hybrid microgrid including three-stage AC-DC-AC power electronic transformers with AC and DC interfaces improves the connection between the microgrid and the utility grid and various AC and DC sources and loads. The power electronic transformer consists of three parts: the input stage, isolation stage, and output stage. The input stage connected to the utility grid is a rectifying part, which rectifies the input alternating current at 50 Hz into direct current; the isolation stage consists of a pulse modulation, high frequency transformer, and pulse demodulation [9], which converts the DC inverter of the input stage output into a high frequency square wave and then couples it to the secondary side through a transformer and then rectifies to a direct current to supply power to the DC load; the output stage is the inverter part, which inverts the DC output of the isolation stage into a three-phase 50 Hz AC power supply for the load. Its structure and control system are shown in Figure 2.  Both the input and output stage control systems use dual loop control. The outer loop is the voltage and power loop, and the inner loop is the current loop. Current inner loop decoupling control is shown in Figure 3. The AC-DC hybrid microgrid including three-stage AC-DC-AC power electronic transformers with AC and DC interfaces improves the connection between the microgrid and the utility grid and various AC and DC sources and loads. The power electronic transformer consists of three parts: the input stage, isolation stage, and output stage. The input stage connected to the utility grid is a rectifying part, which rectifies the input alternating current at 50 Hz into direct current; the isolation stage consists of a pulse modulation, high frequency transformer, and pulse demodulation [9], which converts the DC inverter of the input stage output into a high frequency square wave and then couples it to the secondary side through a transformer and then rectifies to a direct current to supply power to the DC load; the output stage is the inverter part, which inverts the DC output of the isolation stage into a three-phase 50 Hz AC power supply for the load. Its structure and control system are shown in Figure 2.
Electronics 2020, 9,   The AC-DC hybrid microgrid including three-stage AC-DC-AC power electronic transformers with AC and DC interfaces improves the connection between the microgrid and the utility grid and various AC and DC sources and loads. The power electronic transformer consists of three parts: the input stage, isolation stage, and output stage. The input stage connected to the utility grid is a rectifying part, which rectifies the input alternating current at 50 Hz into direct current; the isolation stage consists of a pulse modulation, high frequency transformer, and pulse demodulation [9], which converts the DC inverter of the input stage output into a high frequency square wave and then couples it to the secondary side through a transformer and then rectifies to a direct current to supply power to the DC load; the output stage is the inverter part, which inverts the DC output of the isolation stage into a three-phase 50 Hz AC power supply for the load. Its structure and control system are shown in Figure 2.
High frequency square wave Duty：50% Both the input and output stage control systems use dual loop control. The outer loop is the voltage and power loop, and the inner loop is the current loop. Current inner loop decoupling control is shown in Figure 3. Both the input and output stage control systems use dual loop control. The outer loop is the voltage and power loop, and the inner loop is the current loop. Current inner loop decoupling control is shown in Figure 3.  Due to the symmetry of the two current inner loops, iq is taken as the object of discussion. The delay of the current inner loop signal sampling and the small inertia characteristics of the Pulse Width Modulation (PWM) control are considered. The structure of the decoupled iq current inner loop is shown in Figure 4. Ts is the sampling period of the current inner loop (which is also the PWM switching period), and KPWM is the equivalent gain of the bridge PWM. To simplify the analysis, the perturbation of uq is not considered, and the PI regulator transfer function is written as a pole-zero form, as shown in Equation (1).
The small time constants 0.5TS and TS are combined to produce a simplified current inner loop structure, as shown in Figure 5.  Due to the high switching frequency of power electronics, the switching period is very short. The transfer function is approximately equivalent to 1. Since the current inner loop responds faster than the outer loop, the response time scale is small. Therefore, the simplified model ignores the dynamic process of the current inner loop in the double loop control, where the input value of the inner loop is equal to the output value, and the converter is replaced with the controlled power sources. The simplified model structure and control system are shown in Figure 6. Due to the symmetry of the two current inner loops, i q is taken as the object of discussion. The delay of the current inner loop signal sampling and the small inertia characteristics of the Pulse Width Modulation (PWM) control are considered. The structure of the decoupled i q current inner loop is shown in Figure 4.
Electronics 2020, 9, x FOR PEER REVIEW 4 of 10 Due to the symmetry of the two current inner loops, iq is taken as the object of discussion. The delay of the current inner loop signal sampling and the small inertia characteristics of the Pulse Width Modulation (PWM) control are considered. The structure of the decoupled iq current inner loop is shown in Figure 4. Ts is the sampling period of the current inner loop (which is also the PWM switching period), and KPWM is the equivalent gain of the bridge PWM. To simplify the analysis, the perturbation of uq is not considered, and the PI regulator transfer function is written as a pole-zero form, as shown in Equation (1).
The small time constants 0.5TS and TS are combined to produce a simplified current inner loop structure, as shown in Figure 5. Due to the high switching frequency of power electronics, the switching period is very short. The transfer function is approximately equivalent to 1. Since the current inner loop responds faster than the outer loop, the response time scale is small. Therefore, the simplified model ignores the dynamic process of the current inner loop in the double loop control, where the input value of the inner loop is equal to the output value, and the converter is replaced with the controlled power sources. The simplified model structure and control system are shown in Figure 6. T s is the sampling period of the current inner loop (which is also the PWM switching period), and K PWM is the equivalent gain of the bridge PWM. To simplify the analysis, the perturbation of u q is not considered, and the PI regulator transfer function is written as a pole-zero form, as shown in Equation (1).
The small time constants 0.5T S and T S are combined to produce a simplified current inner loop structure, as shown in Figure 5.
Electronics 2020, 9, x FOR PEER REVIEW 4 of 10 Due to the symmetry of the two current inner loops, iq is taken as the object of discussion. The delay of the current inner loop signal sampling and the small inertia characteristics of the Pulse Width Modulation (PWM) control are considered. The structure of the decoupled iq current inner loop is shown in Figure 4. Ts is the sampling period of the current inner loop (which is also the PWM switching period), and KPWM is the equivalent gain of the bridge PWM. To simplify the analysis, the perturbation of uq is not considered, and the PI regulator transfer function is written as a pole-zero form, as shown in Equation (1).
The small time constants 0.5TS and TS are combined to produce a simplified current inner loop structure, as shown in Figure 5. Due to the high switching frequency of power electronics, the switching period is very short. The transfer function is approximately equivalent to 1. Since the current inner loop responds faster than the outer loop, the response time scale is small. Therefore, the simplified model ignores the dynamic process of the current inner loop in the double loop control, where the input value of the inner loop is equal to the output value, and the converter is replaced with the controlled power sources. The simplified model structure and control system are shown in Figure 6. Due to the high switching frequency of power electronics, the switching period is very short. The transfer function is approximately equivalent to 1. Since the current inner loop responds faster than the outer loop, the response time scale is small. Therefore, the simplified model ignores the dynamic process of the current inner loop in the double loop control, where the input value of the inner loop is equal to the output value, and the converter is replaced with the controlled power sources. The simplified model structure and control system are shown in Figure 6.
Electronics 2020, 9, 358 5 of 10 Electronics 2020, 9, x FOR PEER REVIEW 5 of 10 The input stage is simplified to a controlled voltage source. The voltage reference signal Udc1ref is compared with the capacitor voltage Udc1, the error of which is processed by the PI regulator to output a current inner loop reference signal. Since the current inner loop is simplified, the actual value of the inner loop current signal is considered to be equal to the reference value, which multiplies the proportional coefficient k to generate the controlled current source reference signal Idc_1s, so that the capacitor voltage is stabilized at the reference value. The current signal Idc1 from the DC terminal to the isolation stage is obtained from dividing the grid power signal by the voltage signal. The isolation stage simplification method is similar to that of the input stage, which is simplified to a controlled voltage source supplying for a DC load. The output stage is simplified to a three-phase controlled voltage source. The voltage outer loop reference signals Udref and Uqref are compared at actual values Ud and Uq, respectively, the errors of which are processed by the PI (proportional-integral) regulator to generate the output current inner loop reference signal. The inner loop output value, which gets the coordinate inverse, transforms to obtain the reference signal of the three-phase controlled voltage source and is equivalent to the input reference signal value. The stages are connected by the power balance relationship.

Simulation Time and Accuracy Analysis
In order to verify the correctness of the simplified model, the micro-grid electromagnetic transient detailed model and simplified model were built on the PSCAD software platform to analyze. The input stage was connected to a 10kV/50 Hz AC grid, which is considered an infinite system with a constant output voltage. The DC voltage on the input stage side was 18 kV. The frequency of the high frequency square wave of the isolation stage was 10 kHz, where the high frequency transformer transformation ratio was 18 kV:0.75 kV. The DC voltage on the output stage side was 0.75 kV, the output of which was 0.38 kV/50 Hz AC. The AC load was 0.09 MW and the DC load was 0.2 MW. The simulation steps were 5 and 20 μs, respectively, and the simulation duration was 2 s. The corresponding time-consumption comparison results are shown in Table 1.  The input stage is simplified to a controlled voltage source. The voltage reference signal U dc1ref is compared with the capacitor voltage U dc1 , the error of which is processed by the PI regulator to output a current inner loop reference signal. Since the current inner loop is simplified, the actual value of the inner loop current signal is considered to be equal to the reference value, which multiplies the proportional coefficient k to generate the controlled current source reference signal I dc_1s , so that the capacitor voltage is stabilized at the reference value. The current signal I dc1 from the DC terminal to the isolation stage is obtained from dividing the grid power signal by the voltage signal. The isolation stage simplification method is similar to that of the input stage, which is simplified to a controlled voltage source supplying for a DC load. The output stage is simplified to a three-phase controlled voltage source. The voltage outer loop reference signals U dref and U qref are compared at actual values U d and U q , respectively, the errors of which are processed by the PI (proportional-integral) regulator to generate the output current inner loop reference signal. The inner loop output value, which gets the coordinate inverse, transforms to obtain the reference signal of the three-phase controlled voltage source and is equivalent to the input reference signal value. The stages are connected by the power balance relationship.

Simulation Time and Accuracy Analysis
In order to verify the correctness of the simplified model, the micro-grid electromagnetic transient detailed model and simplified model were built on the PSCAD software platform to analyze. The input stage was connected to a 10kV/50 Hz AC grid, which is considered an infinite system with a constant output voltage. The DC voltage on the input stage side was 18 kV. The frequency of the high frequency square wave of the isolation stage was 10 kHz, where the high frequency transformer transformation ratio was 18 kV:0.75 kV. The DC voltage on the output stage side was 0.75 kV, the output of which was 0.38 kV/50 Hz AC. The AC load was 0.09 MW and the DC load was 0.2 MW. The simulation steps were 5 and 20 µs, respectively, and the simulation duration was 2 s. The corresponding time-consumption comparison results are shown in Table 1. As shown in Table 1, under the same simulation step conditions, since the simplified model replaces the converter with controlled sources and simplifies the control loop, the time consumption was significantly shorter than that of the switch model. The finer the simulation step size was, the more obvious the time-consumption reduction effect was.
At T = 1 s, the 0.09 MW AC load was input, and the 0.1 MW DC load was cut off at 1.5 s. The dynamic characteristics and accuracy of the model are shown in Figure 7 and Table 2.
Electronics 2020, 9, x FOR PEER REVIEW 6 of 10 was significantly shorter than that of the switch model. The finer the simulation step size was, the more obvious the time-consumption reduction effect was. At T = 1 s, the 0.09 MW AC load was input, and the 0.1 MW DC load was cut off at 1.5 s. The dynamic characteristics and accuracy of the model are shown in Figure 7 and Table 2  As shown in Figure 7, the dynamic curve of the simplified model proposed in this paper was basically consistent with that of the detailed model. The AC load power PloadAC_sim curve of the simplified model and the AC load power PloadAC curve of the detailed model were almost identical, both of which increased due to the input of the AC load. The DC voltage Udc2 of the detailed model fluctuated slightly due to the switching of the load, and the DC voltage Udc2_sim of the simplified model was always constant because the reference signal remained constant. At T = 1 s, when the AC load was input, the DC load power PloadDC of the detailed model also had a small fluctuation due to the small fluctuation of the DC voltage Udc2. Since the DC voltage Udc2_sim of the simplified model remained stable, the DC load power PloadDC_sim of the simplified model also remained stable. At T = 1.5 s, due to the cut off of the DC load, the DC load power of both the detailed model and the simplified model decreased. At T = 1 s, due to the input of AC load, the grid power increased. At T = 1.5 s, the DC load was cut off, and the grid power decreased.  Table 2 show that the output steady state errors between the simplified model and detailed model were within 5%, which meets the requirement of engineering calculation precision [21].  As shown in Figure 7, the dynamic curve of the simplified model proposed in this paper was basically consistent with that of the detailed model. The AC load power P loadAC_sim curve of the simplified model and the AC load power P loadAC curve of the detailed model were almost identical, both of which increased due to the input of the AC load. The DC voltage U dc2 of the detailed model fluctuated slightly due to the switching of the load, and the DC voltage U dc2_sim of the simplified model was always constant because the reference signal remained constant. At T = 1 s, when the AC load was input, the DC load power P loadDC of the detailed model also had a small fluctuation due to the small fluctuation of the DC voltage U dc2 . Since the DC voltage U dc2_sim of the simplified model remained stable, the DC load power P loadDC_sim of the simplified model also remained stable. At T = 1.5 s, due to the cut off of the DC load, the DC load power of both the detailed model and the simplified model decreased. At T = 1 s, due to the input of AC load, the grid power increased. At T = 1.5 s, the DC load was cut off, and the grid power decreased.
Since the simplified model replaces the converter with controlled sources, there was no loss of the grid power, but there were slight errors. The data in Table 2 show that the output steady state errors between the simplified model and detailed model were within 5%, which meets the requirement of engineering calculation precision [21].

Characteristic Analysis under Fault Conditions
In order to verify the effectiveness of the simplified model under fault conditions and to observe its dynamic characteristics under fault conditions, the action of the protection system was not considered, and the load did not change.

Characteristic Analysis under AC Load Side Fault Conditions
A single-phase ground fault occurred on the AC load side of the microgrid system at 1 s. The dynamic characteristics are shown in Figure 8.

Characteristic Analysis under Fault Conditions
In order to verify the effectiveness of the simplified model under fault conditions and to observe its dynamic characteristics under fault conditions, the action of the protection system was not considered, and the load did not change.

Characteristic Analysis under AC Load Side Fault Conditions
A single-phase ground fault occurred on the AC load side of the microgrid system at 1 s. The dynamic characteristics are shown in Figure 8. As shown in Figure 8, at 1 s, the a-phase voltage dropped to 0 due to the a-phase failure, and the b and c-phase voltages remained stable. The AC load voltage VloadAC_sim curve of the simplified model was able to maintain good consistency with that (VloadAC) of the detailed model.
When a three-phase asymmetric fault occurs on the AC side, the output power of the AC side contains a second-harmonic disturbance [22], as shown in Equation (2).
P0, Pc2, Ps2, Q0, Qc2, and Qs2 are AC power coefficients, which are related to voltage and current in a positive and negative sequence synchronous rotation coordinate system [14]. According to the principle of conservation of energy, there is also a second-harmonic disturbance equal to it on the DC side power, as shown in Equation (3).
where, Pdc2 is the DC power received by the output stage; Pac is the AC power flowing through the output stage; Pdc2' is the output DC power of the isolation stage; and Pac is the capacitor discharging power.
The capacitor discharging power is as shown in Equation (4): After the fault occurred, the AC load power dropped to around 0.06 MW containing a secondharmonic disturbance. The dynamic curves of the AC load power PloadAC_sim of the simplified model were almost the same as those (PloadAC) of the detailed model. The DC load voltage Udc2 also contained As shown in Figure 8, at 1 s, the a-phase voltage dropped to 0 due to the a-phase failure, and the b and c-phase voltages remained stable. The AC load voltage V loadAC_sim curve of the simplified model was able to maintain good consistency with that (V loadAC ) of the detailed model.
When a three-phase asymmetric fault occurs on the AC side, the output power of the AC side contains a second-harmonic disturbance [22], as shown in Equation (2).
P 0 , P c2 , P s2 , Q 0 , Q c2 , and Q s2 are AC power coefficients, which are related to voltage and current in a positive and negative sequence synchronous rotation coordinate system [14]. According to the principle of conservation of energy, there is also a second-harmonic disturbance equal to it on the DC side power, as shown in Equation (3).
where, P dc2 is the DC power received by the output stage; P ac is the AC power flowing through the output stage; P dc2' is the output DC power of the isolation stage; and P ac is the capacitor discharging power.
The capacitor discharging power is as shown in Equation (4): After the fault occurred, the AC load power dropped to around 0.06 MW containing a second-harmonic disturbance. The dynamic curves of the AC load power P loadAC_sim of the simplified model were almost the same as those (P loadAC ) of the detailed model. The DC load voltage U dc2 also contained a second-harmonic disturbance. The DC load voltage curves of the two models (U dc2 and U dc2_sim ) were also consistent with a very slight error. In conclusion, the dynamic characteristics of the simplified model maintain good consistency with those of the detailed model.

Characteristic Analysis under DC Load Side Fault Conditions
A two-pole short circuit fault occurred on the DC load side of the microgrid system at 1s. The dynamic characteristics are shown in Figure 9.
Electronics 2020, 9, x FOR PEER REVIEW 8 of 10 a second-harmonic disturbance. The DC load voltage curves of the two models (Udc2 and Udc2_sim) were also consistent with a very slight error. In conclusion, the dynamic characteristics of the simplified model maintain good consistency with those of the detailed model.

Characteristic Analysis under DC Load Side Fault Conditions
A two-pole short circuit fault occurred on the DC load side of the microgrid system at 1s. The dynamic characteristics are shown in Figure 9. 16  When a two-stage short circuit fault occurs on the DC side due to the DC voltage dropping to zero and the freewheeling effect of the short-circuit reactance, it is equivalent to a three-phase short circuit occurring on the AC side [10]. Its equivalent circuit is shown in Figure 10. As shown in Figure 9, when a two-pole short-circuit fault occurred on the DC load side at 1 s, the DC load voltage Udc2 suddenly dropped, which also caused the fluctuation of the input-stage side DC voltage Ud1. The DC load voltage Udc2 waveform of the simplified model and that (Udc2_sim) of the detailed model almost overlapped. Although the waveform of Ud1 in the detailed model fluctuated, its steady-state value was consistent with that (Ud1_sim) of the simplified model. The AC load voltage VloadAC_sim curve of the simplified model maintained good consistency with that (VloadAC) of the detailed When a two-stage short circuit fault occurs on the DC side due to the DC voltage dropping to zero and the freewheeling effect of the short-circuit reactance, it is equivalent to a three-phase short circuit occurring on the AC side [10]. Its equivalent circuit is shown in Figure 10.
Electronics 2020, 9, x FOR PEER REVIEW 8 of 10 a second-harmonic disturbance. The DC load voltage curves of the two models (Udc2 and Udc2_sim) were also consistent with a very slight error. In conclusion, the dynamic characteristics of the simplified model maintain good consistency with those of the detailed model.

Characteristic Analysis under DC Load Side Fault Conditions
A two-pole short circuit fault occurred on the DC load side of the microgrid system at 1s. The dynamic characteristics are shown in Figure 9. 16  When a two-stage short circuit fault occurs on the DC side due to the DC voltage dropping to zero and the freewheeling effect of the short-circuit reactance, it is equivalent to a three-phase short circuit occurring on the AC side [10]. Its equivalent circuit is shown in Figure 10. As shown in Figure 9, when a two-pole short-circuit fault occurred on the DC load side at 1 s, the DC load voltage Udc2 suddenly dropped, which also caused the fluctuation of the input-stage side DC voltage Ud1. The DC load voltage Udc2 waveform of the simplified model and that (Udc2_sim) of the detailed model almost overlapped. Although the waveform of Ud1 in the detailed model fluctuated, its steady-state value was consistent with that (Ud1_sim) of the simplified model. The AC load voltage VloadAC_sim curve of the simplified model maintained good consistency with that (VloadAC) of the detailed As shown in Figure 9, when a two-pole short-circuit fault occurred on the DC load side at 1 s, the DC load voltage U dc2 suddenly dropped, which also caused the fluctuation of the input-stage side DC voltage U d1 . The DC load voltage U dc2 waveform of the simplified model and that (U dc2_sim )