Method and system for impedance synthesis and / or replication for use in hardware-in-the-loop testing of electrical systems

Abstract

To provide a method for impedance synthesis and / or replication for use in Hardware-in-the-Loop testing of electrical systems, which is versatile and can account for great dynamic ranges as well for oscillatory load, a method (100) for impedance synthesis and / or replication for use in Hardware-in-the-Loop testing, preferably Power Hardware-in-the-Loop testing, of electrical systems is proposed, comprising the steps of: a) Determining a frequency dependent reference impedance (10), b) Modelling, on a computing device (12), an electrical circuit network (11), the electrical circuit network (11) comprising adjustable parameters, c) Determining, on the computing device (12), an electrical equivalent circuit network from the electrical circuit network (11) by adjusting the adjustable parameters of the electrical circuit network (11), the electrical equivalent circuit network having a frequency dependent impedance matching the frequency dependent reference impedance (10) within a, preferably predetermined, first tolerance interval, d) Optimizing the electrical equivalent circuit network by iteratively conducting the steps of: e) Conducting a real-time simulation of the electrical equivalent circuit network, f) Controlling an amplifier (18) based on the real-time simulation of the electrical equivalent circuit network, g) Measuring a measured frequency dependent impedance at an amplifier output (19), and h) Adjusting the electrical equivalent circuit network by adjusting the adjustable parameters and / or by Adapting an inverse transfer function obtained from the measured frequency dependent impedance, so that the measured frequency dependent impedance matches the frequency dependent reference impedance (10).

Description

[0001] Method and system for impedance synthesis and / or replication for use in Hardware-in-the-Loop testing of electrical systems

[0002] The present invention relates to a method for impedance synthesis and / or replication for use in Hardware-in-the-Loop testing, preferably Power Hardware- in-the-Loop testing, of electrical systems. Furthermore, the present invention relates to a method for Hardware-in-the-Loop testing, preferably Power Hardware-in-the-Loop testing, of electrical systems and to a system for impedance synthesis and / or replication.

[0003] Technological Background

[0004] Impedance-based stability investigations play a crucial role in ensuring the reliable operation of power generation and / or distribution systems and in evaluating the performance of electrical systems and devices connected to the power generation and / or distribution system.

[0005] For example, the transition to a more environmentally friendly shipping industry calls for the integration of renewable energies, battery energy storage systems as well as fuel cells as a supplement or replacement for diesel engines. In this transition, considerations are made to shift the ship's main power distribution from an alternating current (AC) to a direct current (DC) system for easy integration of those technologies. When switching to a DC power distribution system, transformers from conventional AC systems have to be replaced by DC / DC converters for system decoupling and voltage level changes, and therefore, depending on the topology isolated microgrids are created in the system. Additionally, consumers in the grid which are mostly electrical machines and static switchable loads are coupled via variable frequency drives (VFD) and switching mode power supplies (SMPS). The biggest challenge in the transition of a system to DC is the resulting oscillatory distortion which is generated by fast switching devices such as VFD and SMPS. When considering the effects of high frequency oscillations in the grid, knowledge of the frequency dependent impedance of the grid and the connected devices are mandatory to perform a stability analysis. One approach known in the technical field is performing impedance simulations using physical R, L and C components connected to form discrete circuits. Furthermore, the use of dedicated impedance simulators is known.

[0006] However, only very specific impedances can be generated or synthesized with the discrete components since the components exist only in certain values. Also, no other impedances can be generated because the component values must be calculated to a specific simulation. The known impedance simulators can only simulate are very limited number of components, which means that replication of complicated impedance curves is not possible.

[0007] In both cases oscillatory pre-loads are not taken into account and a considerable amount of time is required to transfer measured impedances into an approximate simulation.

[0008] Disclosure of the Invention: Problem, Solution, Advantages

[0009] It is an object of the present invention to provide a method for impedance synthesis and / or replication for use in Hardware-in-the-Loop testing, preferably Power Hardware-in-the-Loop testing, of electrical systems, which is versatile and can account for great dynamic ranges as well as for oscillatory pre-loads.

[0010] To solve the object the present invention proposes a method for impedance synthesis and / or replication for use in Hardware-in-the-Loop testing, preferably Power Hardware-in-the-Loop testing, of electrical systems, comprising the steps of: a) Determining a frequency dependent reference impedance, b) Modelling, on a computing device, an electrical circuit network, the electrical circuit network comprising adjustable parameters, c) Determining, on the computing device, an electrical equivalent circuit network from the electrical circuit network by adjusting the adjustable parameters of the electrical circuit network, the electrical equivalent circuit network having a frequency dependent impedance matching the frequency dependent reference impedance within a, preferably predetermined, first tolerance interval, d) Optimizing the electrical equivalent circuit network by iteratively conducting the steps of: e) Conducting a real-time simulation of the electrical equivalent circuit network f) Controlling an amplifier based on the real-time simulation of the electrical equivalent circuit network, g) Measuring a measured frequency dependent impedance at an amplifier output, and h) Adjusting the electrical equivalent circuit network by adjusting the adjustable parameters and / or by Adapting an inverse transfer function obtained from the measured frequency dependent impedance, so that the measured frequency dependent impedance matches the frequency dependent reference impedance.

[0011] Hardware-in-the-Loop simulation is a technique that is used in development and testing of electrical systems connected to complex external system. The complexity of the external system, to which the electrical system is coupled, is included in testing and development by adding a mathematic representation of all related dynamic systems. The electrical system to be tested interacts with this simulation. A particular category of Hardware-in-the-Loop testing methods are Power Hardware-in-the-Loop testing methods which relate to methods in which a real-time simulator uses a power amplifier to mirror a connection point into the real world and thus allowing for the connection of real hardware, i.e. the electrical system, to the simulation.

[0012] In open-loop Hardware-in-the-Loop testing methods no feedback from real devices into the simulation is provided. In closed-loop Hardware-in-the-Loop testing methods feedback from real devices is provided to the simulation so that the simulation can respond to events from the real devices.

[0013] Preferably, the method for impedance synthesis and / or replication for use in Hardware-in-the-Loop testing, preferably Power Hardware-in-the-Loop testing, is configured for closed-loop Hardware-in-the-Loop testing method, or for a closed- loop Power Hardware-in-the-Loop testing method.

[0014] The determined frequency dependent reference impedance can also be called spectral reference impedance.

[0015] The electrical systems that can be subject to the in Hardware-in-the-Loop testing, preferably to the Power Hardware-in-the-Loop testing, can be embedded systems, integrated circuits, electrical networks, electrical equipment. The electrical systems can have power ranges from a few Watts up to Megawatts.

[0016] The frequency dependent reference impedance can be the impedance of an external system measured in response to excitations at the corresponding frequencies. The external system can be any power generation and / or distribution system. In particular, the external system can be a power generation and / or distribution system of a ship, a car, an airplane or the like. The external system can also be a power grid or wind park or a solar park.

[0017] The frequency dependent reference impedance can also be a completely generic predetermined frequency dependent reference impedance.

[0018] In the method an electrical circuit network is modelled on a computing device, the electrical circuit network comprising adjustable parameters. By adjusting the adjustable parameters an electrical equivalent circuit network is obtained which has a frequency dependent impedance which closely matches the frequency dependent reference impedance. A particularly important aspect of the present invention is the implementation of a feedback loop for optimizing the electrical equivalent circuit network. In particular for Power Hardware-in-the-Loop testing an amplifier has to be used to provide a connection point for the electrical system to be tested. In general, an amplifier distorts the simulated impedance such that deviations are noticeable. With the feedback loop of steps d) to h) a self-correction function is provided. Each time a frequency dependent impedance is measured at an amplifier output the measured frequency dependent impedance is fed back to the computing device. Using the computing device the parameters of the electrical equivalent circuit network are adjusted further so that in a following real-time simulation the measured frequency dependent impedance at the amplifier output matches the frequency dependent reference impedance more closely.

[0019] Because the distortions on the measured frequency dependent impedance introduced by the amplifier are comparatively small, only a few iteration steps are required to provide a frequency dependent impedance at the amplifier output that matches the frequency dependent reference impedance up to a selected quality measure.

[0020] It is also possible that in step h) the electrical equivalent circuit network is adjusted by Adapting an inverse transfer function obtained from the measured frequency dependent impedance, so that the measured frequency dependent impedance matches the frequency dependent reference impedance. The Adapting the inverse transfer function allows to compensate for the system dynamics.

[0021] Preferably, steps a) to c) can be designated as impedance synthesis. Further preferably, steps c) to h) of optimization step d) can be designated as impedance replication.

[0022] Preferably, the real-time simulation of the electrical equivalent circuit network can be carried out using a real-time simulator. The real-time simulation of the electrical equivalent circuit network can be a CPU-based real-time simulation or an FPGA-based real-time simulation. FPGA-based real-time simulations allow for significantly higher simulation bandwidths.

[0023] Preferably the optimization of the electrical equivalent circuit network is stopped, when the measured frequency dependent impedance at the amplifier output is equal to the frequency dependent reference impedance within a, preferably predetermined, second tolerance interval.

[0024] The first and second tolerance intervals define quality measures to evaluate the frequency dependent impedance of the electrical equivalent circuit network and the measured frequency dependent impedance at the amplifier output, respectively, in comparison with the frequency dependent reference impedance.

[0025] Preferably, the first tolerance interval is equal to the second tolerance interval. However, it is also possible that the second tolerance interval is smaller or greater than the first tolerance interval.

[0026] Preferably, in steps c) and / or h) the parameters are adjusted using a heuristic optimization method, preferably a particle swarm algorithm or a generative algorithm.

[0027] In a particle swarm algorithm a population of particles represents potential solutions in a search space. In the method for impedance synthesis and / or replication, each solution is a set of values of the adjustable parameters. Each particle adjusts its position iteratively based on its own best solution and the best solution found by any particle in the swarm. This iterative process aims to explore the search space and converge towards an optimal solution. Using a heuristic optimization method the determination and / or optimization of the electrical equivalent circuit network can be sped up by several orders of magnitude.

[0028] Preferably the heuristic optimization method is carried out using a CPU and / or a GPU and / or a TPU, and / or a FGPA. Preferably the electrical circuit network is a LC electrical circuit network, or a PI electrical circuit network, or a T electrical circuit network.

[0029] An LC electrical circuit network is an electrical circuit comprising of parallel resonant circuits consisting of an inductor, represented by the letter L, and a capacitor, represented by the letter C, connected together. A parallel resonant circuit can act as an electrical resonator oscillating at the circuit resonant frequency. The LC electrical circuit network may also comprise a resistance R.

[0030] The electrical circuit network may comprise a predetermined number n of electrical components.

[0031] The number n of electrical components is preferably predetermined and is chosen to find a compromise between accuracy of the synthesis of the frequency dependent reference impedance and speed of the determination of the electrical equivalent circuit network and / or of the optimization of the electrical equivalent circuit network.

[0032] For example, n maybe between 10 and 100, preferably between 20 and 50, further preferably between 25 and 35.

[0033] The electrical components may be parallel resonant circuits and / or resistors, wherein the electrical components, in particular the parallel resonant circuits and / or resistors, are arranged in series and / or in parallel.

[0034] Depending on the choice of the electrical components and the arrangement in the electrical circuit network the electrical circuit network can be configured as a LC electrical circuit network, a PI electrical circuit network or a T electrical circuit network.

[0035] Furthermore preferably, the electrical circuit network comprises at least one voltage source. Further preferably, the adjustable parameters comprise resistances Rnand / or inductivities Lnand / or capacitances Cn, and / or voltages Vnand / or frequencies fn, preferably for each of the n electrical components.

[0036] For example, if the electrical circuit network is a LC electrical circuit network it may comprise n parallel resonant circuits l...n, preferably arranged in series. Each of the n parallel resonant circuits has for adjustable parameters an inductivity Lnand a capacitance Cnand preferably a resistance Rn. The LC electrical circuit network may also have an additional resistance Ro. These parameters are adjusted during determination and / or optimization of the electrical equivalent circuit network.

[0037] In a non-limiting example, the electrical circuit network may be an LC electrical circuit network, as shown in Fig. 3 comprising n parallel resonant circuits with inductivities Ln, capacitances Cnand resistance Rn. The parallel resonant circuits are arranged in series. Each of the parallel resonant circuits n has an impedance Zn. The LC electrical circuit network of Fig. 3 further comprises a resistance Roand a voltage source Uo.

[0038] In a heuristic optimization method, preferably a particle swarm algorithm, the goal is to minimize the objective function for the parameter vectors is the frequency dependent reference impedance at each frequency point i. x) represents the frequency dependent impedance of the electrical circuit network during determination of the electrical equivalent circuit network or the measured frequency dependent impedance at the amplifier output during optimization of the electrical equivalent circuit network.

[0039] In order to ensure that the electrical equivalent circuit network remains within valid operating ranges of the component values the optimization may be subject to the following constrains:

[0040] Rmax- Ro > 0, R0-Rmin > 0

[0041] Rmax- Rn > 0, Rn—Rmin > 0

[0042] Lmax—Ln > 0, Ln—Lmin > 0

[0043] Cmax- Cn > 0, Cn—Cmin > 0

[0044] Preferably, high frequency oscillatory pre-loads are incorporated by simulating the voltage source.

[0045] The simulation of the voltage source to incorporate high frequency oscillatory pre-loads is in particular advantageous, when the electrical circuit network is a PI electrical circuit network or a T electrical circuit network.

[0046] Still further preferably the frequency dependent reference impedance is a measured frequency dependent reference impedance of a power generation and / or distribution system, preferably of a ship.

[0047] The power generation and / or distribution system can be any power and / or distribution system, for example a power grid or a wind farm or a solar farm.

[0048] The frequency dependent reference impedance can also be a frequency dependent reference impedance of any type of electrical network in three-phase alternating current and / or direct current. Furthermore, the method is applicable independent of transformations of the electrical network, such as With-against- zero sequence (symmetrical components 012), dq-transformations, alpha- betatransformations. It is also possible that the frequency dependent reference impedance is a generic frequency dependent impedance, preferably determined using a software-based editor.

[0049] Thus, already during the development process of an external system different setups of the external system and, therefore, different expected frequency dependent reference impedances can be tested.

[0050] Furthermore, determining and / or changing the frequency independent reference impedance, for example using a software-based editor, allows for testing possible changes within an existing external system.

[0051] Furthermore preferably, the method further comprises the steps of: i) Modifying the frequency dependent reference impedance, and j) Repeating steps c) to h).

[0052] Thus, an on-the-fly adjustment of the frequency dependent reference impedance is possible to simulate and / or test different operating points of the external system.

[0053] A further solution to the problem is a method for Hardware-in-the-Loop testing, preferably Power Hardware-in-the-Loop testing, of electrical systems, wherein an amplifier is controlled by a real-time simulation of an electrical equivalent circuit network, wherein the electrical equivalent circuit network is determined by a method as described above.

[0054] The electrical equivalence circuit network may comprise at least one voltage source, wherein effects of, preferably high frequency, oscillatory pre-loads are incorporated by adjusting the parameters of the voltage source in the real-time simulation of the electrical equivalent circuit network.

[0055] Thus, during Hardware-in-the-Loop testing of electrical systems, high frequency oscillatory pre-loads and their effects on the frequency dependent reference impedance of the external system can be incorporated in the Hardware-in-the- Loop simulations and, therefore, the response of the external system and / or the system to be tested, i.e. the electrical system, to the oscillatory pre-loads can be determined.

[0056] Furthermore preferably, the Hardware-in-the-Loop testing method is a method for Power Hardware-in-the-Loop testing.

[0057] Thus, the method is not only limited to Hardware-in-the-Loop testing procedures where control signals are exchanged between the external system and the electrical system. In particular, the method can also be used for simulating power generation and / or distribution systems, for example of a ship.

[0058] Still a further solution to the problem is the provision of a system for impedance synthesis and / or replication configured for conducting one of the methods described above, the system comprising a computing device for modelling an electrical circuit network and for determining an electrical equivalent circuit network, a Real-Time Simulator for conducting a real-time simulation of the electrical equivalent circuit network, an amplifier, and an impedance measuring device for measuring a measured frequency dependent impedance at an amplifier output and / or for determining, preferably for measuring, a frequency dependent reference impedance of a power generation and / or distribution system, preferably of a ship.

[0059] The system is further configured for feeding back a measured frequency dependent impedance at an amplifier output to the computing device for modelling and / or optimizing the electrical equivalent circuit network.

[0060] All steps, features and advantages of the methods describes above can be analogously applied to the system for impedance synthesis and / or replication.

[0061] Preferably the computing device is a computer, comprising a CPU and / or a GPU and / or a TPU, and / or a FGPA. Preferably, the real-time simulator can be a CPU-based real-time simulator or an FPGA-based real-time simulator.

[0062] Brief description of the figures

[0063] The present invention is described in more detail with reference to the accompanying figures.

[0064] Fig. 1 shows a flowchart of a method for impedance synthesis and / or replication, Fig 2 shows the magnitude and phase of frequency dependent reference impedance,

[0065] Fig. 3 shows an electrical circuit network,

[0066] Fig. 4 shows a system for impedance synthesis and / or replication, and

[0067] Fig. 5 shows a flowchart of a method for Hardware-in-the-Loop testing of electrical systems.

[0068] Detailed description of the figures

[0069] Fig. 1 shows a flowchart of a method 100 for impedance synthesis and / or replication for use in Hardware-in-the-Loop testing of electrical systems in accordance with the present invention.

[0070] In a first step a) a frequency dependent reference impedance 10 is determined. An example of a frequency dependent reference impedance 10 is shown in Fig. 2 The frequency dependent reference impedance 10 is the impedance of an external system measured in response to excitations at the corresponding frequencies. In Fig. 2a) the magnitude of the frequency dependent reference impedance 10 is shown as a function of the frequency. Fig. 2b shows the phase of the frequency dependent reference impedance 10 as a function of the frequency. The frequency dependent reference impedance 10 can be determined by measuring a frequency dependent impedance of an existing external system, such as a power generation and / or distribution system of a ship.

[0071] In a second step b) an electrical circuit network 11 is modelled on a computing device 12. The electrical circuit network 11 comprises adjustable parameters. The computing device 12 is part of a system 200 for impedance synthesis and / or replication shown in Fig. 4.

[0072] An example of a possible electrical circuit network 11 is shown in Fig. 3. The electrical circuit network 11 is a LC electrical circuit network 11a. The electrical circuit network 11 comprises n electrical components 13 which are configured as parallel resonant circuits 14 with component impedance ZNand a resistor 15 with resistance Ro. Each of the parallel resonant circuits 14 has as adjustable parameters its inductivity Ln, its capacitance Cnand its resistance Rn. The parallel resonant circuits 14 and the resistor 15 are arranged in series. The electrical circuit network 11 further comprises a voltage source 16.

[0073] In a third step c) an electrical equivalent circuit network is determined, in particular calculated, by the computing device 12 from the electrical circuit network 11 by adjusting the parameters Ro, Ln, Cnand Rn, until the frequency dependent impedance of the electrical equivalent circuit network matches the frequency dependent reference impedance 10 within a predetermined first tolerance interval.

[0074] For determining the adjustable parameters, a heuristic optimization method, for example a particle swarm algorithm, can be used.

[0075] When the electrical equivalent circuit has a frequency dependent impedance which matches the frequency dependent reference impedance 10 within the first tolerance interval, the electrical equivalent circuit network is optimized in a feedback loop of step d). The feedback loop comprises in a first step e) a real-time simulation of the electrical equivalent circuit network on a real time simulator 17 (cf. Fig. 4). In step f) an amplifier 18 is controlled based on the real time simulation of the electrical equivalent circuit network. In step g) a measured frequency dependent impedance is measured at an amplifier output 19. In general, an amplifier 18 will distort the impedance such that deviations are noticeable. Thus, in step h) the measured frequency dependent impedance measured at the amplifier output 19 is fed back to the computing device 11 for further adjustment of the parameters of the electrical equivalent circuit network, if the measured frequency dependent impedance does not match the frequency dependent reference impedance 10 within a second tolerance interval in a comparison step hl). In this case steps e), f), and g) are repeated. If in the comparison hl) the measured frequency dependent impedance does match the frequency dependent reference impedance 10 within the second tolerance interval, the method 100 stops.

[0076] Fig. 4 shows a system 200 suitable for use in the method 100 shown in Fig. 1.

[0077] The system 200 comprises a computing device 12 configured as a computer 20. The computer 20 comprises a CPU 21 and a GPU 22. The computer 20 is configuring for modelling an electrical circuit network 11 and for determining an electrical equivalent circuit network. The system 200 further comprises a realtime simulator 17 for conducting a real time simulation of the electrical equivalent circuit network and an amplifier 18, having an amplifier output 19. Furthermore, the system 100 comprises an impedance measuring device 23 for measuring a measured frequency dependent impedance at the amplifier output 19 and / or for determining, preferably for measuring, a frequency dependent reference impedance of a power generation and / or distribution system, preferably of a ship.

[0078] Fig. 5 shows a flowchart for a method 300 for Hardware-in-the-Loop testing of electrical systems in accordance with the present invention. In a first step SI a method 100 for impedance synthesis and / or replication according to Fig. 1 is carried out. The electrical equivalent circuit network resultingfrom step SI is then simulated in a second step S2 by a real-time simulator 17. The real-time simulation by the real-time simulator 17 is used to control an amplifier 18 in step S3, to which a system to be tested is connected.

[0079] In a further step S4 high frequency oscillatory pre-loads are incorporated in the method 300 for Hardware-in-the-Loop testing by adjusting the parameters of the voltage source 16 of the electrical equivalent circuit network in the real time simulation to determine the effects of such oscillations on the system to be tested.

[0080] List of reference numerals

[0081] 100 Method for impedance synthesis and / or replication

[0082] 200 System for impedance synthesis and / or replication

[0083] 300 Method for Hardware-in-the-Loop testing of electrical systems

[0084] 10 Frequency dependent reference impedance

[0085] 11 Electrical circuit network

[0086] 11a LC electrical circuit network

[0087] 12 Computing device

[0088] 13 Electrical component

[0089] 14 Parallel resonant circuit

[0090] 15 Resistor

[0091] 16 Voltage source

[0092] 17 Real-time simulator

[0093] 18 Amplifier

[0094] 19 Amplifier output

[0095] 20 Computer

[0096] 21 CPU

[0097] 22 GPU

[0098] 23 Impedance measuring device a) - h), hl) Method steps

[0099] S1 - S4 Method steps

Claims

Claims1. Method (100) for impedance synthesis and / or replication for use in Hardware-in-the-Loop testing, preferably Power Hardware-in-the-Loop testing, of electrical systems, comprising the steps of: a) Determining a frequency dependent reference impedance (10), b) Modelling, on a computing device (12), an electrical circuit network (11), the electrical circuit network (11) comprising adjustable parameters, c) Determining, on the computing device (12), an electrical equivalent circuit network from the electrical circuit network (11) by adjusting the adjustable parameters of the electrical circuit network (11), the electrical equivalent circuit network having a frequency dependent impedance matching the frequency dependent reference impedance (10) within a, preferably predetermined, first tolerance interval, d) Optimizing the electrical equivalent circuit network by iteratively conducting the steps of: e) Conducting a real-time simulation of the electrical equivalent circuit network, f) Controlling an amplifier (18) based on the real-time simulation of the electrical equivalent circuit network, g) Measuring a measured frequency dependent impedance at an amplifier output (19), and h) Adjusting the electrical equivalent circuit network by adjusting the adjustable parameters and / or by Adapting an inverse transfer function obtained from the measured frequency dependent impedance, so that the measured frequency dependent impedance matches the frequency dependent reference impedance (10).

2. Method (100) for impedance synthesis and / or replication according to claim 1, wherein the optimization of the electrical equivalent circuit network is stopped, when the measured frequency dependent impedance at the amplifier output (19) is equal to the frequency dependent reference impedance (10) within a, preferably predetermined, second toleranceinterval, wherein further preferably the first tolerance interval is equal to the second tolerance interval.

3. Method (100) for impedance synthesis and / or replication according to claim 1 or 2, wherein in steps c) and / or h) the parameters are adjusted using a heuristic optimization method, preferably a particle swarm algorithm or a generative algorithm, wherein further preferably the heuristic optimization method is carried out using a CPU (21) and / or a GPU (22) and / or a TPU, and / or a FGPA.

4. Method (100) for impedance synthesis and / or replication according to one of the preceding claims, wherein the electrical circuit network (11) is a LC electrical circuit network (11a), or a PI electrical circuit network, or a T electrical circuit network.

5. Method (100) for impedance synthesis and / or replication according to one of the preceding claims, wherein the electrical circuit network (11) comprises a predetermined number n of electrical components (13), wherein preferably the electrical components (13) are parallel resonant circuits (14) and / or resistors (15), wherein further preferably the electrical components (13), in particular the parallel resonant circuits (14) and / or resistors (15), are arranged in series and / or in parallel.

6. Method (100) for impedance synthesis and / or replication according to one of the preceding claims, wherein the electrical circuit network (11) comprises at least one voltage source (16).

7. Method (100) for impedance synthesis and / or replication according to one of the preceding claims, wherein the adjustable parameters comprise resistances Rnand / or inductivities Lnand / or capacitances Cnand / or voltages Vnand / or frequencies fn, preferably for each of the n electrical components8. Method (100) for impedance synthesis and / or replication according to claim 6 or 7 , wherein in step e) effects of, preferably high frequency, oscillatory preloads are incorporated by simulating the voltage source (16).

9. Method (100) for impedance synthesis and / or replication according to one of the preceding claims, wherein the frequency dependent reference impedance (10) is a measured frequency dependent reference impedance (10) of a power generation and / or distribution system, preferably of a ship, and / or wherein the frequency dependent reference impedance (10) is a generic frequency dependent impedance, preferably determined using a software-based editor.

10. Method (100) for impedance synthesis and / or replication according to one of the preceding claims, wherein the method further comprises the steps of: i) Modifying the frequency dependent reference impedance (10), and j) Repeating steps c) to h).

11. Method (300) for Hardware-in-the-Loop testing, preferably Power Hardware- in-the-Loop testing, of electrical systems, wherein an amplifier (18) is controlled by a real-time simulation of an electrical equivalent circuit network, wherein the electrical equivalent circuit network is determined by a method (100) according to any one of the preceding claims.

12. Method (300) for Hardware-in-the-Loop testing according to claim 11, wherein the electrical equivalent circuit network comprises at least one voltage source (16), wherein effects of, preferably high frequency, oscillatory pre-loads are incorporated by adjusting the parameters of the voltage source (16) in the real-time simulation of the electrical equivalent circuit network.

13. Method (300) for Hardware-in-the-Loop testing according to claim 11 or 12, wherein the method is a method for Power Hardware-in-the-Loop testing.

14. System (200) for impedance synthesis and / or replication configured for conducting a method (100) according to one of claims 1 to 10 and / or forconducting a method (300) according to one of claims 11 to 13, the system comprising a computing device (12) for modelling an electrical circuit network (11) and for determining an electrical equivalent circuit network, a Real-Time Simulator (17) for conducting a real-time simulation of the electrical equivalent circuit network, an amplifier (18), and an impedance measuring device (23) for measuring a measured frequency dependent impedance at an amplifier output (19) and / or for determining, preferably for measuring, a frequency dependent reference impedance (10) of a power generation and / or distribution system (200), preferably of a ship.

15. System (200) according to claim 14, wherein the computing device (12) is a computer (20) comprising a CPU (21) and / or a GPU (22) and / or a TPU, and / or a FGPA.

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