1. Introduction
2. Interface Algorithms of Power HardwareInTheLoop Systems
2.1. Ideal Transformer Method
2.2. Advanced Ideal Transformer Method
2.3. Partial Circuit Duplication
2.4. Damping Impedance Method
2.5. IA Extendible Feedback Current Filter
2.6. Summary
3. Comparison of Power Amplifier with Power HardwareintheLoop Systems
3.1. Switching Amplifier
3.2. Linear Amplifier
3.3. Comparison of Power Amplifiers
4. Preliminary Simulations of Power HardwareintheLoop Systems
4.1. Simulation of the Ideal Transformer Method
4.2. Simulation of the Advanced Ideal Transformer Method
4.3. Simulation of the Damping Impedance Method
4.4. Conclusion of the IA Simulation Studies
5. Verification of IA in Real PHIL Systems
 
 Reduce electromagnetic influences by using screened and short wires, especially for the lowlevel signals;
 
 Reduce delays by using fast components and short connections;
 
 All devices have to be in the same emergency circuit;
 
 Integrate error detectors and protection devices (i.e., in the realtime simulator and power amplifier [17]);
 
 Ensure the safety of the experiment setup, especially when using hardware like batteries and rotating machines.
5.1. Testing the Ideal Transformer Method
5.1.1. Ideal Transformer Method with Linear Amplifier
5.1.2. Ideal Transformer Method with Switching Amplifier
5.1.3. Conclusion of the ITM Experiments
5.2. Testing the Damping Impedance Method
5.2.1. Damping Impedance Method with Linear Amplifier
5.2.2. Damping Impedance Method with Switching Amplifier
5.2.3. Conclusion of the DIM Experiments
6. Experimental Investigation of ITM and DIM
6.1. Test Case 1: ITM
6.2. Test Case 2: DIM
7. Conclusions
Acknowledgments
Conflicts of Interest
References
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Interface Algorithm  Mathematical Expression  Pro and Contra 

Ideal Transformer Method  ${\mathrm{Z}}_{\mathrm{S}}\left(\mathrm{s}\right)/{\mathrm{Z}}_{\mathrm{H}}\left(\mathrm{s}\right)$  + best accuracy for PHIL + easy implementation − low stability 
Advanced Ideal Transformer Method  ${\mathrm{Z}}_{\mathrm{S}}\left(\mathrm{s}\right)/({\mathrm{Z}}_{\mathrm{C}}\left(\mathrm{s}\right)+{\mathrm{Z}}_{\mathrm{H}}\left(\mathrm{s}\right))$  + high accuracy + easy implementation + good stability 
Partial Circuit Duplication  ${\mathrm{Z}}_{\mathrm{S}}\left(\mathrm{s}\right)\cdot {\mathrm{Z}}_{\mathrm{H}}\left(\mathrm{s}\right)/$ $\left(\left({\mathrm{Z}}_{\mathrm{S}}\left(\mathrm{s}\right)+{\mathrm{Z}}_{\mathrm{SH}}\left(\mathrm{s}\right)\right)\cdot \left({\mathrm{Z}}_{\mathrm{H}}\left(\mathrm{s}\right)+{\mathrm{Z}}_{\mathrm{SH}}\left(\mathrm{s}\right)\right)\right)$  + extreme high stability − additional hardware required − low accuracy 
Damping Impedance Method  ${\mathrm{Z}}_{\mathrm{S}}\left(\mathrm{s}\right)\cdot \left({\mathrm{Z}}_{\mathrm{H}}\left(\mathrm{s}\right){\mathrm{Z}}^{*}\left(\mathrm{s}\right)\right)/$ $\left(\left({\mathrm{Z}}_{\mathrm{S}}\left(\mathrm{s}\right)+{\mathrm{Z}}_{\mathrm{SH}}\left(\mathrm{s}\right)\right)\left({\mathrm{Z}}_{\mathrm{H}}\left(\mathrm{s}\right)+{\mathrm{Z}}_{\mathrm{SH}}\left(\mathrm{s}\right)+{\mathrm{Z}}^{*}\left(\mathrm{s}\right)\right)\right)$  + great stability + good accuracy − additional hardware required 
Feedback Current Filter  ${\mathrm{T}}_{\mathrm{FCF}}\left(\mathrm{s}\right)\cdot {\mathrm{Z}}_{\mathrm{S}}\left(\mathrm{s}\right)/{\mathrm{Z}}_{\mathrm{H}}\left(\mathrm{s}\right)$  + Extendible feature for IA + easy implementation − accuracy depending on f_{C} 
System Parameter  Linear Amplifier  Switching Amplifier  Current Probe  Voltage Probe 

Model  S & S PAS 90000  Ametek RS 270  LEM HTA 1000  LEM CV 3–100 V 
Power  3 × 30 kVA  3 × 3 × 30 kVA  1000 A  1000 V 
Bandwidth  DC … 5 kHz  DC … 2 kHz  DC … 50 kHz  DC … 800 kHz 
Swell rate  >52 V/µs  >0.5 V/µs  >50 A/µs  0.4 µs to 90% V_{N} 
ITM  System A  System B 

VSS impedance ${\mathrm{R}}_{\mathrm{S}}$  1 Ω  2 Ω 
PPS impedance ${\mathrm{R}}_{\mathrm{H}}$  1 Ω  1 Ω 
Transfer function  ${\mathrm{e}}^{{\mathrm{T}}_{\mathrm{D}}}\cdot {\mathrm{T}}_{\mathrm{System}}\cdot {\mathrm{Z}}_{\mathrm{S}}/{\mathrm{Z}}_{\mathrm{H}}$  
Result  Stable  Unstable 
AITM  System A  System B 

VSS impedance ${\mathrm{R}}_{\mathrm{S}}$  3 Ω  4 Ω 
PPS impedance ${\mathrm{R}}_{\mathrm{H}}$  1 Ω  1 Ω 
Coupling imped. R_{SH}  3.5 Ω  3.5 Ω 
Transfer function  ${\mathrm{e}}^{{\mathrm{T}}_{\mathrm{D}}}\cdot {\mathrm{T}}_{\mathrm{System}}\cdot {\mathrm{Z}}_{\mathrm{S}}/({\mathrm{Z}}_{\mathrm{K}}+{\mathrm{Z}}_{\mathrm{H}})$  
Result  Stable  Unstable 
DIM  System A  System B  System C 

Virtual impedance ${\mathrm{R}}_{\mathrm{S}}$  2 Ω  5 Ω  6 Ω 
Coupling impedance ${\mathrm{R}}_{\mathrm{SH}}$  0.1 Ω  0.1 Ω  0.1 Ω 
Damping impedance ${\mathrm{R}}^{*}$  3 Ω  3 Ω  3 Ω 
Hardware impedance ${\mathrm{R}}_{\mathrm{H}}$  1 Ω  1 Ω  1 Ω 
Transfer function  ${\mathrm{e}}^{{\mathrm{T}}_{\mathrm{D}}}\cdot {\mathrm{T}}_{\mathrm{System}}\cdot {\mathrm{Z}}_{\mathrm{S}}\left(\mathrm{s}\right)\left({\mathrm{Z}}_{\mathrm{H}}\left(\mathrm{s}\right){\mathrm{Z}}^{*}\left(\mathrm{s}\right)\right)/\left(\left({\mathrm{Z}}_{\mathrm{S}}\left(\mathrm{s}\right)+{\mathrm{Z}}_{\mathrm{SH}}\left(\mathrm{s}\right)\right)\left({\mathrm{Z}}_{\mathrm{H}}\left(\mathrm{s}\right)+{\mathrm{Z}}_{\mathrm{SH}}\left(\mathrm{s}\right)+{\mathrm{Z}}^{*}\left(\mathrm{s}\right)\right)\right)$  
Simulation  Stable  Stable  Unstable 
Stable Case  ITM  AITM  DIM 

Virtual impedance ${\mathrm{R}}_{\mathrm{S}}$  1 Ω  5 Ω  6 Ω 
Hardware impedance ${\mathrm{R}}_{\mathrm{H}}$  1 Ω  1 Ω  1 Ω 
Ratio R_{S}/R_{H}  1  5  6 
Parameter of ITM Experiment with Linear Amplifier  

Voltage U_{init}  230 V at 50 Hz 
Virtual impedance R_{S}  variable 
Ratio of R_{S}/R_{H}  (0.9:0.1:1.8) 
Physical impedance R_{H}  105.90 Ω 
FCF f_{C}  (1:1:10) kHz 
Additional delay T_{D}  (0:25:400) µs 
Method  ITM with FCF 
Amplification system  Linear amplifier 
Realtime simulator  OP5600 from OPALRT 
Parameters of ITM Test with Switching Amplifier  

Voltage U_{init}  230 V at 50 Hz 
Virtual impedance R_{S}  variable 
Physical impedance R_{H}  31.8 Ω 
FCF f_{C}  (1:1:10) kHz 
Additional delay T_{D}  (0; 50; 500; 1000) µs 
Method  ITM with FCF 
Amplification system  Switched amplifier 
Realtime simulator  OP5600 from OPALRT 
Paramteres of DIM Experiment with Linear Amplifier  

Voltage U_{init}  230 V at 50 Hz 
Virtual impedance R_{S}  variable 
Damping impedance R*  variable 
Coupling impedance R_{SH}  variable 
Physical impedance R_{H}  105.90 Ω 
Additional delay T_{D}  (220) µs 
Method  DIM 
Amplification system  Linear amplifier 
Realtime simulator  OP5600 from OPALRT 
Parameters of DIM Experiment With Switching Amplifier  

Voltage U_{init}  230 V at 50 Hz 
Virtual impedance R_{S}  variable 
Damping impedance R*  variable 
Coupling impedance R_{SH}  0.23 Ω 
Physical impedance R_{H}  31.8 Ω 
Additional delay T_{D}  variable 
Amplification system  Switched amplifier 
Realtime simulator  OP5600 from OPALRT 
Test Case  1  2 

Description  Review of the ITM interface with resistive physical load.  Review the DIM interface with resistive physical load. 
Scenario 


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