Equivalent Single-input Single-output Research Articles

Voltage and active power local PI control of distributed energy resources based on the effective transfer function method

This paper presents the design of local PI regulators to control voltage and active power of the Distributed Energy Resources (DERs) in grid-connected Active Distribution Networks (ADNs). The design is developed based on the proposed Multiple-Input Multiple-Output (MIMO) model of ADN. Firstly, the Relative Gain Array (RGA) matrix is used to address the problem of input–output pairing and to show that the voltage control loops are coupled whereas the active power control loops are decoupled. Subsequently the method of the Effective Open-Loop Transfer Function (EOTF) is used to decompose the multi-loop voltage control system into a set of equivalent Single-Input Single-Output (SISO) loops. Then, each PI regulator is independently designed to fulfill some control objectives dictated by the designer. The proposed design procedure is simple and straightforward. The fixed-parameters PI regulators facilitate the integration of DERs into traditional distribution networks which are usually operated without or with limited communication infrastructure. The simulation results presented for various scenarios of two different ADN confirm that performance objectives and regulation at the desired set-points are achieved in a robust sense.

Control of Generalized Decoupled MIMO Systems Based on Linear Programming Method

In this work, a control method is suggested to generalize decoupled multi-input multi-output (MIMO) plant to get satisfactory results. The phenomena of decoupling converts a MIMO plant to number of equivalent single-input single-output (SISO) loops which enables one to control number of outputs independently even due to the effect of coupling present in control inputs and outputs. The effect of these cross-couplings causes the disturbances. The decoupler aim is to eradicate the effect of these disturbances on outputs. In order to achieve it, this work proposed a novel generalized decoupling technique on the basis of linear programming. Infinity norm method is considered to minimize the effect of decoupler gain of the cross-couplings of the MIMO system, over all frequencies, that minimizes undesired mutual couplings of the resulting decoupled plant also nullifying coupling effect completely at steady state as well. The proposed method of decoupling is compared with the relative gain array (RGA) and further modified RGA (MRGA) technique of decoupling which is also elaborated in this paper. To achieve the desired response from the decoupled plant proportional integral derivative (PID) control method is suggested using the Kharitonov theorem. The ensued technique is employed on different types of MIMO systems including square, non-square and time-delayed.

Impedance-Based Analysis and Stability Improvement of DFIG System Within PLL Bandwidth

In this article, we analyze the negative impact of phase-locked loop (PLL) on the stability of the doubly fed induction generators system. The small-signal disturbance of PLL mainly affects the coordinate transformation of the rotor current and introduces a negative resistance within PLL bandwidth. Two impedance reshaping methods are carried out to weaken this negative resistance. A virtual impedance in the conventional current control is added to the first reshaping method. The second reshaping method completely removes the coordinate transformation of the rotor current by switching the control target from current to power. The difference between these two reshaping methods is analyzed based on the equivalent single-input single-output impedance model. The experimental results validate the effectiveness of these two reshaping methods and the superiority of the second reshaping method at a lower short-circuit ratio.

Unified SISO Loop Gain Modeling, Measurement, and Stability Analysis of Three-Phase Voltage Source Converters

Frequency-domain modeling is an effective technique in the dynamic analysis of power electronic converters-based power systems. In this paper, a unified single-input single-output (SISO) loop gain modeling for the three-phase grid-tied voltage source converters (VSCs) under both symmetric and asymmetric AC grids is presented, which facilitates the physical measurement and stability analysis. Based on the linear-time-periodic (LTP) modeling technique, the harmonic admittance model of the three-phase grid-tied VSC is developed in the stationary ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">αβ</i> )-frame, which accurately captures the coupling dynamics. This model can be transformed into other existing models through coordinate transformations. According to the idea of mathematical induction, a two-by-two recursive admittance matrix (RAM) model is derived, which is easy to include frequency coupling components of arbitrary order. It is illustrated that the VSC admittance is coupled with the grid admittance due to the frequency coupling effect (FCE). Furthermore, the RAM is converted to its equivalent SISO models following the concept of loop gain. The system stability is thus assessed by the SISO stability criteria (e.g., Nyquist stability criterion). In addition, the loop gain allows the traditional SISO perturbation and measurement scheme to be used for detecting the stability margin information. Finally, simulation results verify the feasibility and correctness of the theoretical analysis presented above.

Robust semiactive control of a half‐car vehicle suspension system with magnetorheological dampers: Quantitative feedback theory approach with dynamic decoupler

AbstractThis article presents the quantitative feedback theory (QFT) based multivariable controller for the vertical and the pitch angle motion of a half‐car suspension system. A coupled half‐car system with significant uncertainty, due to sprung masses variation, poses a challenging control problem. Multi‐input multi‐output (MIMO) QFT method is used for this purpose which involves converting the actual MIMO system into an equivalent single‐input single‐output (SISO) system so that the design problem is carried out using the SISO QFT principles. The proposed idea is centered on by converting the coupled MIMO system into a decoupled one using the dynamic decoupler where in controllers are designed independently based on the equivalent SISO system. The designed QFT‐based controllers with the decoupler use the semiactive suspension strategy (realized using the magnetorheological (MR) damper) to reduce the vibration of the half‐car suspension system (in vertical/pitch angular motion) and hence to increase the ride comfort and the vehicle road holding. The feedback cost is less in the proposed design than the sequential QFT design. In this study, the MR damper dynamics is captured by the first‐order model which is realistic, efficient, and simple form. Extensive comparative simulation studies are carried out to illustrate the effectiveness of the proposed design over the existing methods such as passive and skyhook control under different road excitation.

High-Frequency Resonance Analysis and Reshaping Control Strategy of DFIG System Based on DPC

Direct power control (DPC) can reduce the complexity of a controller and enhance the dynamic response for doubly fed induction generators (DFIG) system. The high-frequency resonance (HFR) issues will be analyzed for the DFIG system based on DPC under inductive weak grid in this article. Based on the simplified high-frequency impedance model of the DFIG system based on DPC and the Bode diagram of equivalent single-input single-output impedance, it is found that a strong frequency coupling related to the components of system delay in off-diagonal admittance will cause the high-frequency phase to change periodically for the DFIG system. Therefore, the DFIG system will show capacitive or even negative resistance to introduce potential risk of HFR at high frequency. The stability of a DFIG system will be further deteriorated as the system delay increases. An impedance reshaping control strategy is proposed to reduce the degree of frequency coupling at high frequency for eliminating the negative effects of system delay, so that HFR can be suppressed. The experimental results validate the availability of the proposed reshaping control strategy.

Impedance Characteristic Analysis and Reshaping Method of DFIG System Based on DPC Without PLL

The phase locked loop (PLL) will introduce the negative resistance near the fundamental frequency, which deteriorates the stability of doubly fed induction generators (DFIG) system under the inductive weak grid. This article develops the impedance model of the DFIG system based on direct power control without PLL, and analyzes the frequency coupling characteristic of established impedance model. The phase margin around the fundamental frequency is enhanced after cancelling the PLL. However, there will be a high-frequency resonance issue related to the frequency coupling characteristic. Based on the simplified high-frequency impedance model and the Bode diagram of equivalent single-input single-output impedance, it can be found that the DFIG system is more prone to have stability issues when the degree of frequency coupling is enhanced. An impedance reshaping control strategy is proposed to reduce the degree of frequency coupling at high frequency and suppress the high-frequency resonance. The experimental results validate the availability of the proposed reshaping control strategy.

Small-Signal Stability Enhancement Approach for VSC-HVDC System Under Weak AC Grid Conditions Based on Single-Input Single-Output Transfer Function Model

The voltage source converter (VSC) system has stability issue under weak AC grid conditions. In this paper, the multi-input multi-output (MIMO) transfer function model of VSC system in frequency-domain is derived. Then, the individual channel analysis and design (ICAD) approach is employed to develop the equivalent single-input single-output (SISO) feedback control model for stability analysis. On that basis, the stability of VSC system and the coupling interaction intensity among the multiple control loops, including the active power control (APC), reactive power control (RPC) and phase-locked-loop (PLL) are investigated. The results show that larger PLL bandwidth increases the coupling degree of active power control (APC) and reactive power control (RPC) closed loops, resulting in the instability of the system under weak AC grid conditions. Finally, a derivative feedback compensation (DFC) approach is proposed to enhance the stability margin for VSC system connected to weak AC grid. The results based on MATLAB-based theoretical analysis and electromagnetic transient (EMT) simulations show that the proposed DFC approach can effectively suppress the instability of VSC system due to the close coupling of APC and RPC closed loops caused by the large PLL bandwidth, thus effectively improve the stability margin of the system.

Modelling and analysis of equivalent SISO d-q impedance of grid-connected converters

Small-signal stability of three-phase grid-connected converters can be analysed by using the impedance-based method in d-q frame. Based on this approach, the d-q impedance models of both source and load subsystems are represented with 2-by-2 matrices, and their ratio (known as the return ratio matrix) is used for stability assessment. This, however, requires to apply the generalized Nyquist criterion (GNC), due to the intrinsic multi-input multi-output (MIMO) property of the d-q system. During the process, some complexities are inevitably caused because of the need to calculate the ratio of the impedance matrices, and to obtain the eigenvalues of the return ratio matrix. In this context, this paper presents an equivalent single-input single-output (SISO) model for the d-q impedance of three-phase grid-connected converters, which leads to two scalar impedance ratios of d- and q-axis, instead of the conventional 2-by-2 return ratio matrix. Consequently, the stability of the two SISO systems can be analysed by using the classic Nyquist stability criterion (NC), resulting in a much simpler and more intuitive analysis process than GNC. The equivalence between the original MIMO d-q impedance model and the proposed SISO model in stability assessment is verified by comparing their stability conditions. As an example of applying this approach, the effects of PLL, grid impedance, and power control on a grid-connected converter are investigated. The performed analysis is finally validated by Matlab/Simulink simulations.

Single-Input–Single-Output Feedback Control Model and Stability Margin Analysis for Hybrid Dual-Infeed HVDC System

To quantitatively investigate the system stability margin and provide systematic design guidance for the hybrid dual-infeed high-voltage direct current (HVdc) system, this article develops a dynamic multi-input–multi-output (MIMO) transfer function model for the hybrid dual-infeed HVdc system, consisting of a line-commutated converter-based HVdc (LCC-HVdc) link and a modular multilevel converter-based HVdc (MMC-HVdc) link located in close mutual proximity at the receiving side. Then, based on the individual channel analysis and design (ICAD) theory, the equivalent single-input–single-output (SISO) feedback control model is developed without structural information loss, which has the advantage of quantitative evaluation for the system stability margin. Then, the impacts of the ac system strength and control system on the system stability margin are quantitatively evaluated by gain margin (GM) and phase margin (PM) indexes based on the derived SISO model. Moreover, the coupling effect between the ac system strength and the control parameters is also studied. The obtained results from the theoretical analysis and the detailed electromagnetic transient (EMT) simulation in PSCAD/EMTDC validate the accuracy of the derived SISO feedback control model and the correctness of the theoretical findings.

Performance improvement of MIMO FSO systems against destructive interference

Although multiple-input multiple-output (MIMO) technique is used in free space optical (FSO) systems to reduce the effect of atmospheric turbulence, however, employing this technique without sufficient attention to the interference of laser beams not only does not reduce the effect of atmospheric turbulence, but also it can significantly degrade the performance of the FSO system. This study investigates that the average intensity of laser beams at the receiver aperture of MIMO FSO systems is very sensitive to small variations of path lengths between the transmitter and receiver. Therefore, the destructive interference that degrades the performance of MIMO FSO systems compared to equivalent single-input single-output (SISO) FSO ones is due to the difference in path lengths of laser beams between transmitter and receiver apertures. For this reason and in order to mitigate the interference effect, the authors compensate small changes of path lengths through adjusting the sending times and the initial parameters of laser beams in the transmitter apertures. The authors' analysis supported by numerical results show that the adjustment of laser parameters could increase the chance of peak intensity of MIMO-FSO systems to be higher than the peak intensity of equivalent SISO-FSO ones.

Performance Analysis of Nonlinear SFBC OFDM Systems Over TWDP Fading Channel

In this paper, the practical performance of space-frequency block code (SFBC)-based multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) system in the presence of nonlinear power amplifier with imperfect channel state information (CSI) over two-wave with diffuse power (TWDP) channel is analyzed. In the performance analysis, we first introduce the equivalent single-input single-output (SISO) scalar model with nonlinear power amplifier and then the SISO model is used to construct a model for the nonlinear MIMO-OFDM system. Considering the channel estimation error at the receiver, we study the effects of MMSE channel estimation error on the channel capacity. What is more, based on inter modulation product (IMP) analysis, we study the BER performance of nonlinear SFBC MIMO-OFDM systems, considering M-ary phase shift keying (MPSK) and M-ary quadrature amplitude modulation (MQAM). And the effects of channel estimation error on the BER performance are studied. Finally, this paper also derives the closed-form expressions of the system optimal operating point. The numerical results and comparisons are provided for several forms of SFBC MIMO-OFDM. From these analysis results, it is found that the analytical interpretation of the observed behavior in the simulation can be advanced, and the actual analysis of the performance optimization of the nonlinear MIMO-OFDM system is also provided.

A Novel Cross-Feedback Notch Filter for Synchronous Vibration Suppression of an MSFW With Significant Gyroscopic Effects

To effectively suppress the synchronous vibration torques for a magnetically suspended rotor (MSR) with significant gyroscopic effects and serious coupling dynamics, a novel cross-feedback notch filter is proposed in this paper. First, the coupled multi-input-multi-output active magnetic bearing rotor system is converted into an equivalent complex single-input single-output (SISO) system. The equivalent transformation aims at easing the controller design and extending the classical stability criterion to the complex coefficient frequency domain. Then, the principle and implementation of the proposed scheme used for synchronous vibration suppression over an entire rotational speed range is analyzed in details. The performance compared with the conventional decentralized notch filter is investigated. Moreover, the closed-loop stability, which based on the equivalent complex SISO system and complex-coefficient stability criterion is given. Experimental results on a magnetically suspended flywheel demonstrate the significant effect of the proposed method on both synchronous vibration suppression and stability preservation.

A Practical Analysis of Performance Optimization in OSTBC Based Nonlinear MIMO-OFDM Systems

This paper presents a practical performance analysis of an orthogonal space-time block code (OSTBC) based multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) system in the presence of nonlinear power amplifiers (PAs). The equivalent single-input single-output (SISO) scalar model is introduced and this then is used to construct a model for the nonlinear MIMO-OFDM system. Based on an unique inter-modulation product (IMP) analysis, it is shown how the receiver signal-to-noise ratio (SNR) may be derived to a polynomial based function of the system operating point. It is also shown that expressions for the asymptotical behavior of this SNR, when the linear and highly nonlinear PA operations are applied, may also be derived. Based on these derivations, it is further shown that the optimal system operating point, which corresponds to the maximum receiver SNR and SEP lower bound, can be identified and be derived to a polynomial based expression. Additionally, a general expression for the different integral expressions of SEP for the phase shift keying (PSK) and quadrature amplitude modulation (QAM) signals is found. By means of these analytical results, it was found possible to advance analytical explanations of observed behaviour in simulations and also to provide a practical analysis of performance optimization of nonlinear MIMO-OFDM systems.

Bounds on the Information Rate for Sparse Channels with Long Memory and i.u.d. Inputs

In this paper we propose new bounds on the achievable information rate for discrete-time Gaussian channels with intersymbol interference (ISI) and independent and uniformly distributed (i.u.d.) channel input symbols drawn from finite-order modulation alphabets. Specifically, we are interested in developing new bounds on the achievable rates for sparse channels with long memory. We obtain a lower bound which can be achieved by practical receivers, based on MMSE channel shortening and suboptimal symbol detection for a reduced-state channel. An upper bound is given in the form of a semi-analytical solution derived using basic information theoretic inequalities, by a grouping of the channel taps into several clusters resulting in a newly defined single-input multiple-output (SIMO) channel. We show that the so obtained time-dispersive SIMO channel can be represented by an equivalent single-input single-output (SISO) channel with a significantly shorter channel memory. The reduced computational complexity allows the use of the BCJR algorithm for the newly defined channel. The proposed bounds are illustrated through several sparse channel examples and i.u.d. input symbols, showing that the upper bound significantly outperforms existing bounds. Performance of our lower bound strongly depends on the channel structure, showing best results for minimum-phase and maximum-phase systems.

A novel CDD-OFDM scheme with pilot-aided channel estimation

Cyclic delay diversity (CDD) is a low-complexity standard-conformable transmit diversity scheme for coded orthogonal frequency division multiplexing (OFDM) systems. However, it makes channel estimation more challenging due to the increased frequency-selectivity of the equivalent single-input single-output channel. In this paper, we propose a novel CDD-OFDM scheme with pilot-aided channel estimation for any number of transmit antennas. By alternating and optimizing the cyclic delay parameter over adjacent OFDM symbols, we design a simple yet efficient channel estimation scheme and illustrate its excellent performance for the DVB-T application.

Performance analysis on LDPC-Coded systems over quasi-static (MIMO) fading channels

In this paper, we derive closed form upper bounds on the error probability of low-density parity-check (LDPC) coded modulation schemes operating on quasi-static fading channels. The bounds are obtained from the so-called Fano-Gallager's tight bounding techniques, and can be readily calculated when the distance spectrum of the code is available. In deriving the bounds for multiple-input multiple-output (MIMO) systems, we assume the LDPC code is concatenated with the orthogonal space-time block code as an inner code. We obtain an equivalent single-input single-output (SISO) channel model for this concatenated coded-modulation system. The upper bounds derived here indicate good matches with simulation results of a complete transceiver system over Rayleigh and Rician MIMO fading channels in which the iterative detection and decoding algorithm is employed at the receiver.

Exact error probability of Orthogonal Space-Time Block Codes over flat fading channels

Space time block coding is a modulation scheme recently discovered for the transmit antenna diversity to combat the effects of wireless fading channels. Using the equivalent Single-Input Single-Output (SISO) model, this paper presents closed-form expressions for the exact Symbol Error Rate (SER) and Bit Error Rate (BER) of Orthogonal Space-Time Block Codes (OSTBCs) with M-ary Phase-Shift Keying (MPSK) and M-ary Quadrature Amplitude Modulation (MQAM) over flat uncorrelated Nakagami-m and Ricean fading channels.

Independent Design of Multi-Loop Controllers Considering Multivariable Interactions.

In this paper, a simple independent design method for multi-loop controllers is proposed which exploits process interactions for the improvement of loop performance. Unlike many other methods that emphasize suppression of interactions for decoupling purposes, our method is developed to channel the effect of interactions to individual loops for speeding up loop responses. This is achieved by regarding each loop together with its corresponding interactions from all other loops as an equivalent single-input single-output (SISO) plant, and designing an independent SISO controller for it. Once an objective transfer function is specified for each of these equivalent processes, a set of simultaneous equations is formed and separated into independent ones, each of which contains one controller element only. They are then solved to obtain exact solutions, which are usually irrational. The exact solutions can be well approximated by rational functions. The popular multi-loop PID controllers can naturally be obtained as a special case of rational approximation, and they give a reasonable trade-off between loop and decoupling performance. Simulation examples are provided to show the effectiveness of the proposed method, and comparisons are made with the BLT method.

Multiloop Version of the Modified Ziegler−Nichols Method for Two Input Two Output Processes

In this paper, a multiloop version of the modified Ziegler−Nichols method1 is proposed for two input two output (TITO) processes. The key idea is to regard each loop together with its corresponding interactions from all other loops as an equivalent single input, single output (SISO) plant and design for it a SISO controller by shifting a given point on the Nyquist curve of the equivalent SISO plant to a desired position. This is, however, a nonlinear problem because the equivalent plants depend on unknown controllers. A novel approach is thus presented to obtain the controller parameters which achieve the above design objective. Unlike many other methods that emphasize the suppression of interactions, our method is developed to channel the effect of interactions to individual loops to increase the speed of loop responses. Simulation examples are provided to show the effectiveness of the proposed method and comparisons are made with the biggest log modulus tuning (BLT) method.