Modeling and stability analysis of a simulation–stimulation interface for hardware-in-the-loop applications

Abstract

This paper presents the stability evaluation of a Simulation–Stimulation (Sim–Stim) interface that integrates hardware to software to perform Hardware-In-the-Loop (HIL) studies for testing and developing electrical equipment. Modeling issues of such an interface are discussed and a practical Sim–Stim interface model whose parameters are sampling rate and time delay is developed for the theoretical evaluation of the stability. The developed Sim–Stim interface model is applied to a low power DC system and closed-loop stability of the resulting HIL system is studied analytically in terms of time delay and sampling rate. A prototype of Sim–Stim interface is designed and realized to validate theoretical stability results using HIL simulation.

Introduction

Hardware-in-the-loop (HIL) simulation is an effective method to design, develop and test new hardware and/or systems. Within HIL environment, a real hardware to be tested interacts with a virtual system (i.e., a simulation based mathematical model) that replaces part of a real system or component. The main advantage of using the HIL approach is that the critical equipment can be tested in a variety of scenarios of operation without: (i) The need to build an actual or scale down version of the system in which the equipment will be installed; (ii) the need to develop a validated model of the equipment for inclusion in a computer simulation. Hence, HIL techniques can provide lower cost and faster implementation than the conventional ways of testing equipment. Because of these advantages, the HIL simulation has been extensively used as a design step in a wide range of fields such as: traction control and anti-lock braking system [1], testing the controls for an electrical locomotive system [2], performance evaluation of a commercial motor used for drive-train of hybrid vehicles [3], automatic synchronization of generators in power systems [4], testing and controlling for power electronics equipment [5], [6], designing a real-time test bed for power quality assessment [7], digital control system for magnetic levitation system [8].

The key element of HIL simulation is the interface between the simulation model and hardware. Although the applications may vary, a commonality of HIL approaches is that there is only signal coupling (low-level control signals) between the hardware and the virtual system. In this way, the monitoring and controlling hardware can be easily achieved. In order to take the advantage of virtual prototyping in the design and testing of power hardware, some recent studies have extended the HIL concept to a more interesting and challenging case where a real power must be virtually exchanged between the simulation and the actual hardware [9], [10], [11]. We denote this HIL by Power-Hardware-in-the-Loop (PHIL) system to differentiate it from the signal based HIL systems. The PHIL system can evaluate the performance of power hardware components (Hardware-Under-Test, HUT) as if they were operating in an actual power system environment. The objective of the PHIL is to test/diagnose power components (such as RL-load, induction motor, generator, power converter, uninterruptible power supplies, UPS, etc.) as if they were connected to a real system represented by a simulation model.

The key to an effective PHIL is the interface called Simulation–Stimulation (Sim–Stim) interface (shown in Fig. 1) that connects the Hardware-Under-Test (HUT) with the Virtual Electrical System (VES). The VES is a computer program that simulates the electrical system in which the HUT will be implemented in an actual operation. The interface consists of sensors plus Analog-to-Digital Converters (ADC) in the feedback part and Digital-to-Analog Converters (DAC) plus a power source/sink in the feedforward part. Since the VES output will be either a current or voltage, the power source must be a current- or voltage-source inverter/converter. It must be noted that the Sim–Stim interface must be able to both deliver and absorb real power depending on the type of the HUT. If the HUT is a load such as a micro-grid or induction motor, then the VES models the power generation and distribution system, and the Sim–Stim interface delivers power. On the other hand, if the HUT is a source such as a generator, battery, fuel cell, or distribution system, then the Sim–Stim interface absorbs power.

The Sim–Stim interface translates the computed VES power information output (e.g. voltage, current, frequency, phase, harmonics, etc.) via the DAC and power source/sink into real energy which powers to the HUT (feedforward). Moreover, the Sim–Stim interface also monitors HUT and supplies information on its operating states to the VES via the sensors and ADC (feedback), thus allowing closed-loop, real-time interaction between the HUT and the VES as if the HUT were connected to a real system. The requirement to deliver power to HUT differentiates PHIL from the traditional HIL systems that deal only with low-level control signals (e.g. small voltages/currents) for digital logic purposes or servo-control.

Ideally, the HUT should perform the same whether it is a part of a real system or connected to the PHIL system. In other words, from the HUT’s point of view, it should be unable to distinguish between being connected either to the VES via the Sim–Stim interface or to a real system. This means that the interface should not introduce any characteristics that might alter the operation of the HUT. For the PHIL system of Fig. 1 to perform electrically in the same manner as the original system (without the interface), the Sim–Stim interface must be seamless in terms of real-time performance of the power system for various operating conditions such as steady-state operation (i.e., load flow, power transfer, and power quality) and dynamic operation (i.e., stability, on and off switching, etc.). That is, the Sim–Stim interface must be lossless to maintain the same power quality, have unity gain, and infinite bandwidth and dynamic range, and not introduce additional dynamics. However, in the actual hardware implementation of the interface using a power converter, a certain level of power loss will occur. If not properly quantified, this loss can affect the designed PHIL experiment. For a seamless operation of the interface during the actual realization, any power loss encountered must be compensated for within the VES. In addition, the presence of the Sim–Stim interface in the PHIL system can introduce additional dynamics and time delays into the system both in the feedforward and feedback paths. Time delays and other interface parameters such as sampling rate, quantization and saturation may adversely affect the stability performance of the PHIL system [12]. Thus, in an actual implementation, to provide a matched performance of the HUT as compared to when it is connected to a real system, certain measures must be accounted within the VES to account for these additional effects. For example, to account for quantifiable delays in the Sim–Stim interface, optimal control schemes may be utilized that use receding horizon schemes for improved predictive control inputs [13].

But before this actual implementation it is necessary to understand this novel PHIL system in terms of its operational limits or its stability. Since an ideal Sim–Stim interface cannot be realized, there is a need to develop a mathematical model of the PHIL system (VES plus Sim–Stim interface) and a method of evaluating its stability. This study concentrates on the closed-loop stability of PHIL system of Fig. 1 and how the stability of such a hybrid system will be affected by the newly introduced Sim–Stim interface parameters. Similar to the networked control systems, time delays and sampling rate are the most significant interface parameters that could degenerate the stability performance of the system [14], [15], [16], [17]. The Sim–Stim interface is the key component of the PHIL system that needs to be modeled for stability analysis. Therefore, this paper first gives an overview of modeling issues for such an interface and then discusses the parameters that must be included in the model depending on the phenomenon of interest. A realizable Sim–Stim interface model whose main parameters are sampling rate and time delay is developed for theoretical evaluation of stability using sampled-system theory [14]. The PHIL application of the proposed Sim–Stim interface is illustrated for a low power DC system. An RL load is chosen as being the HUT that is connected to a virtual model of DC source through the Sim–Stim interface. In order to evaluate the stability performance, a two-step approach is adopted. In the first step, a discrete-time model of the PHIL system is determined to investigate the stability analytically by means of stability regions in terms of sampling rate and time delay. The characterization of the stability using regions in the Sim–Stim interface parameter space (that is, sampling rate vs. time delay) is useful since it offers a set of acceptable interface parameters for which the PHIL system is stable. In the second step, a prototype of the Sim–Stim interface is designed and realized to validate theoretical stability results. Differences between theoretical and experimental stability results are also discussed in details.