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  • Journal article
    Scarciotti G, Astolfi A, 2017,

    Nonlinear Model Reduction by Moment Matching

    , Foundations and Trends in Systems and Control, Vol: 4, Pages: 224-409, ISSN: 2325-6818

    Mathematical models are at the core of modern science and technology. An accurate description of behaviors, systems and processes often requires the use of complex models which are difficult to analyze and control. To facilitate analysis of and design for complex systems, model reduction theory and tools allow determining “simpler” models which preserve some of the features of the underlying complex description. A large variety of techniques, which can be distinguished depending on the features which are preserved in the reduction process, has been proposed to achieve this goal. One such a method is the moment matching approach.This monograph focuses on the problem of model reduction by moment matching for nonlinear systems. The central idea of the method is the preservation, for a prescribed class of inputs and under some technical assumptions, of the steady-state output response of the system to be reduced. We present the moment matching approach from this vantage point, covering the problems of model reduction for nonlinear systems, nonlinear time-delay systems, data-driven model reduction for nonlinear systems and model reduction for “discontinuous” input signals. Throughout the monograph linear systems, with their simple structure and strong properties, are used as a paradigm to facilitate understanding of the theory and provide foundation of the terminology and notation. The text is enriched by several numerical examples, physically motivated examples and with connections to well-established notions and tools, such as the phasor transform.
  • Journal article
    Merlin MMC, Soto-Sanchez D, Judge PD, Chaffey G, Clemow P, Green TC, Trainer DR, Dyke KJet al., 2017,

    The extended overlap alternate arm converter: a voltage source converter with DC fault ride-through capability and a compact design

    , IEEE Transactions on Power Electronics, Vol: 33, Pages: 3898-3910, ISSN: 1941-0107

    The Alternate Arm Converter (AAC) was one ofthe first modular converter topologies to feature DC-side faultride-through capability with only a small penalty in powerefficiency. However, the simple alternation of its arm conductionperiods (with an additional short overlap period) resulted in(i) substantial 6-pulse ripples in the DC current waveform,(ii) large DC-side filter requirements, and (iii) limited operatingarea close to an energy sweet-spot. This paper presents a newmode of operation called Extended Overlap (EO) based onthe extension of the overlap period to 60◦which facilitates afundamental redefinition of the working principles of the AAC.The EO-AAC has its DC current path decoupled from the ACcurrent paths, a fact allowing (i) smooth DC current waveforms,(ii) elimination of DC filters, and (iii) restriction lifting on thefeasible operating point. Analysis of this new mode and EO-AAC design criteria are presented and subsequently verifiedwith tests on an experimental prototype. Finally, a comparisonwith other modular converters demonstrates that the EO-AACis at least as power efficient as a hybrid MMC (i.e. a DC faultride-through capable MMC) while offering a smaller converterfootprint because of a reduced requirement for energy storagein the submodules and a reduced inductor volume.
  • Journal article
    Singh AK, Pal BC, 2017,

    Decentralized nonlinear control for power systems using normal forms and detailed models

    , IEEE Transactions on Power Systems, Vol: 33, Pages: 1160-1172, ISSN: 1558-0679

    This paper proposes a decentralized method fornonlinear control of oscillatory dynamics in power systems. Themethod is applicable for ensuring both transient stability as wellas small-signal stability. The method uses an optimal control lawwhich has been derived in the general framework of nonlinearcontrol using normal forms. The model used to derive the controllaw is the detailed subtransient model of synchronous machinesas recommended by IEEE. Minimal approximations have beenmade in either the derivation or the application of the controllaw. The developed method also requires the application ofdynamic state estimation technique. As the employed control andestimation schemes only need local measurements, the methodremains completely decentralized. The method has been demon-strated as an effective tool to prevent blackouts by simulating amajor disturbance in a benchmark power system model and itssubsequent control using the proposed method.
  • Journal article
    Mylvaganam T, Sassano M, Astolfi A, 2017,

    A differential game approach to multi-agent collision avoidance

    , IEEE Transactions on Automatic Control, Vol: 62, Pages: 4229-4235, ISSN: 0018-9286

    A multi-agent system consisting of N agents is considered. The problem of steering each agent from its initial position to a desired goal while avoiding collisions with obstacles and other agents is studied. This problem, referred to as the multi-agent collision avoidance problem, is formulated as a differential game. Dynamic feedback strategies that approximate the feedback Nash equilibrium solutions of the differential game are constructed and it is shown that, provided certain assumptions are satisfied, these guarantee that the agents reach their targets while avoiding collisions.
  • Journal article
    Djapic P, Strbac G, McKenna R, Weinand J, Fichtner Wet al., 2018,

    Assessing the implications of socioeconomic diversity for low carbon technology uptake in electrical distribution networks

    , Applied Energy
  • Conference paper
    Fatouros P, Konstantelos I, Papadaskalopoulos D, Strbac Get al., 2017,

    A stochastic dual dynamic programming approach for optimal operation of DER aggregators

    , IEEE PowerTech 2017, Publisher: IEEE

    The operation of aggregators of distributed energy resources (DER) is a highly complex task that is affected by numerous factors of uncertainty such as renewables injections, load levels and market conditions. However, traditional stochastic programming approaches neglect information around temporal dependency of the uncertain variables due to computational tractability limitations. This paper proposes a novel stochastic dual dynamic programming (SDDP) approach for the optimal operation of a DER aggregator. The traditional SDDP framework is extended to capture temporal dependency of the uncertain wind power output, through the integration of an n-order autoregressive (AR) model. This method is demonstrated to achieve a better trade-off between solution efficiency and computational time requirements compared to traditional stochastic programming approaches based on the use of scenario trees.
  • Conference paper
    Ye Y, Papadaskalopoulos, Moreira, strbacet al., 2017,

    Strategic Capacity Withholding by Energy Storage in Electricity Markets

    , 12th IEEE PES PowerTech Conference, Publisher: IEEE

    Abstract:Although previous work has demonstrated the ability of large energy storage (ES) units to exercise market power by withholding their capacity, it has adopted modeling approaches exhibiting certain limitations and has not analyzed the dependency of the extent of exercised market power on ES operating properties. In this paper, the decision making process of strategic ES is modeled through a bi-level optimization problem; the upper level determines the optimal extent of capacity withholding at different time periods, maximizing the ES profit, while the lower level represents endogenously the market clearing process. This problem is solved after converting it to a Mathematical Program with Equilibrium Constraints (MPEC) and linearizing the latter through suitable techniques. Case studies on a test market quantitatively analyze the extent of capacity withholding and its impact on ES profit and social welfare for different scenarios regarding the power and energy capacity of ES.
  • Conference paper
    Trovato V, Tindemans S, Strbac G, 2017,

    Understanding aggregate flexibility of thermostatically controlled loads

    , 12th IEEE Power and Energy Society PowerTech Conference 2017, Publisher: IEEE

    Thermostatically controlled loads (TCLs) are an attractive source of responsive demand. This paper aims to provides a better understanding of the relation between thermal properties of TCLs and their suitability to provide energy arbitrage and frequency services. An approximate analysis on the basis of dimensionless parameters is used to visualise the relative abilities of eight classes of TCLs. The results are compared to those obtained from a formal optimisation approach, in the context of a GB case study. Additional studies are performed to investigate the impact of increasingly flexible frequency services and physical variations of TCL thermal models (thermal conductance and temperature deadband).
  • Conference paper
    Scarciotti G, Teel AR, 2017,

    Model Order Reduction for Stochastic Nonlinear Systems

    , 56th IEEE Conference on Decision and Control, Publisher: IEEE
  • Software
    Gu Y, Bottrell, Green, 2017,

    Reduced-Order Models for Representing Converters in Power System Studies

    Matlab codes of reduced-order models for representing power electronic converters in power system analyses.
  • Conference paper
    Padoan A, Astolfi A, 2017,

    Eigenvalues and Poles of a Nonlinear System: a Geometric Approach

    , 56th IEEE Conference on Decision and Control, Publisher: IEEE
  • Journal article
    Tindemans S, Strbac G, 2017,

    Robust estimation of risks from small samples

    , Philosophical Transactions A: Mathematical, Physical and Engineering Sciences, Vol: 375, ISSN: 1471-2962

    Data-driven risk analysis involves the inference of probability distributions from measured or simulated data. In the case of a highly reliable system, such as the electricity grid, the amount of relevant data is often exceedingly limited, but the impact of estimation errors may be very large. This paper presents a robust non-parametric Bayesian method to infer possible underlying distributions. The method obtains rigorous error bounds even for small samples taken from ill-behaved distributions. The approach taken has a natural interpretation in terms of the intervals between ordered observations, where allocation of probability mass across intervals is well specified, but the location of that mass within each interval is unconstrained. This formulation gives rise to a straightforward computational resampling method: Bayesian interval sampling. In a comparison with common alternative approaches, it is shown to satisfy strict error bounds even for ill-behaved distributions.
  • Conference paper
    Zhou Y, Boem F, Parisini T, 2017,

    Partition-based Pareto-optimal state prediction method for interconnected systems using sensor networks

    , 2017 American Control Conference, Publisher: IEEE, Pages: 1886-1891

    In this paper a novel partition-based state prediction method is proposed for interconnected stochastic systems using sensor networks. Each sensor locally computes a prediction of the state of the monitored subsystem based on the knowledge of the local model and the communication with neighboring nodes of the sensor network. The prediction is performed in a distributed way, not requiring a centralized coordination or the knowledge of the global model. Weights and parameters of the state prediction are locally optimized in order to minimise at each time-step bias and variance of the prediction error by means of a multi-objective Pareto optimization framework. Individual correlations between the state, the measurements, and the noise components are considered, thus assuming to have in general unequal weights and parameters for each different state component. No probability distribution knowledge is required for the noise variables. Simulation results show the effectiveness of the proposed method.
  • Conference paper
    Scarciotti G, Teel AR, Astolfi A, 2017,

    Model reduction for linear differential inclusions: robustness and time-variance

    , 2017 American Control Conference, Publisher: IEEE, ISSN: 2378-5861

    This paper deals with the problem of modelreduction by moment matching for linear differential inclusions.The problem is formally formulated and the notions of moment-set, perturbed moment trajectory, approximate reduced ordermodel and robust reduced order model are introduced. Twosets of results are presented. The first part of the paper dealswith robustness of the reduced order models with respect toinput perturbations. Exploiting this result an enhanced modelreduction scheme for linear differential equations is presented.In the second part of the paper we focus on the problem ofmodel reduction by moment matching for time-varying systemsdriven by time-varying signal generators. Finally, these two setsof results are used to solve the problem of model reductionfor linear differential inclusions. The results are illustrated bymeans of numerical examples.
  • Conference paper
    Padoan A, Astolfi A, 2017,

    Moments of random variables: a system-theoretic interpretation

    , 2017 American Control Conference (ACC), Publisher: IEEE

    Moments of continuous random variables with aprobability density function which can be represented as theimpulse response of a linear time-invariant system are studied.Under some assumptions, the moments of the random variableare characterised in terms of the solution of a Sylvester equationand of the steady-state output response of an interconnectedsystem. This allows to interpret well-known notions and resultsof probability theory and statistics in the language of systemtheory, including the notion of moment generating function, thesum of independent random variables and the notion of mixturedistribution.
  • Conference paper
    Padoan A, Astolfi A, 2017,

    Model reduction by moment matching at isolated singularities for linear systems: a complex analytic approach

    , 20th IFAC 2017 World Congress, Publisher: Elsevier

    The model reduction problem by moment matching for continuous-time, single-input, single-output, linear, time-invariant systems is studied at isolated singularities (in particular, at poles). The notion of moment at a pole of the transfer function is defined. Exploiting this notion a one-to-one correspondence between moments at a pole of the transfer function and the “limit solution” of a family of Sylvester equations is established. Finally, a family of reduced order models is defined. A simple example illustrates the theory.
  • Conference paper
    Mylvaganam T, Astolfi A, 2017,

    Zero finding via feedback stabilisation

    , IFAC 2017 World Congress, Publisher: Elsevier, Pages: 8133-8138, ISSN: 1474-6670

    Two iterative algorithms for solving systems of linear and nonlinear equations are proposed. For linear problems the algorithm is based on a control theoretic approach and it is guaranteed to yield a converging sequence for any initial condition provided a solution exists. Systems of nonlinear equations are then considered and a generalised algorithm, again taking inspiration from control theory, is proposed. Local convergence is guaranteed in the nonlinear setting. Both the linear and the nonlinear algorithms are demonstrated on a series of numerical examples.
  • Conference paper
    Scarciotti G, Teel AR, 2017,

    Model order reduction of stochastic linear systems by moment matching

    , 20th IFAC World Congress, Publisher: IFAC Secretariat, Pages: 6332-6337, ISSN: 2405-8963

    In this paper we characterize the moments of stochastic linear systems by means of the solution of a stochastic matrix equation which generalizes the classical Sylvester equation. The solution of the matrix equation is used to define the steady-state response of the system which is then exploited to define a family of stochastic reduced order models. In addition, the notions of stochastic reduced order model in the mean and stochastic reduced order model in the variance are introduced. While the determination of a reduced order model based on the stochastic notion of moment has high computational complexity, stochastic reduced order models in the mean and variance can be determined more easily, yet they preserve some of the stochastic properties of the system to be reduced. The differences between these three families of models are illustrated by means of numerical simulations.
  • Conference paper
    Khusainov B, Kerrigan EC, Suardi A, Constantinides GAet al., 2017,

    Nonlinear predictive control on a heterogeneous computing platform

    , IFAC World Congress 2017, Publisher: IFAC / Elsevier, Pages: 11877-11882

    Nonlinear Model Predictive Control (NMPC) is an advanced control technique that often relies on computationally demanding optimization and integration algorithms. This paper proposes and investigates a heterogeneous hardware implementation of an NMPC controller based on an interior point algorithm. The proposed implementation provides flexibility of splitting the workload between a general-purpose CPU with a fixed architecture and a field-programmable gate array (FPGA) to trade off contradicting design objectives, namely performance and computational resource usage. A new way of exploiting the structure of the Karush-Kuhn-Tucker (KKT) matrix yields significant memory savings, which is crucial for reconfigurable hardware. For the considered case study, a 10x memory savings compared to existing approaches and a 10x speedup over a software implementation are reported. The proposed implementation can be tested from Matlab using a new release of the Protoip software tool, which is another contribution of the paper. Protoip abstracts many low-level details of heterogeneous hardware programming and allows quick prototyping and processor-in-the-loop verification of heterogeneous hardware implementations.
  • Conference paper
    Boem F, Reci R, Cenedese A, Parisini Tet al., 2017,

    Distributed clustering-based sensor fault diagnosis for HVAC systems

    , 20th IFAC World Congress, Publisher: IFAC / Elsevier, Pages: 4197-4202

    The paper presents a distributed Sensor Fault Diagnosis architecture for Industrial Wireless Sensor Networks monitoring HVAC systems, by exploiting a recently proposed distributed clustering method. The approach allows the detection and isolation of multiple sensor faults and considers the possible presence of modeling uncertainties and disturbances. Detectability and isolability conditions are provided. Simulation results show the effectiveness of the proposed method for an HVAC system.
  • Conference paper
    Shukla H, Khusainov B, Kerrigan EC, Jones CNet al., 2017,

    Software and hardware code generation for predictive control using splitting methods

    , IFAC World Congress 2017, Publisher: IFAC / Elsevier, Pages: 14386-14391

    This paper presents SPLIT, a C code generation tool for Model Predictive Control (MPC) based on operator splitting methods. In contrast to existing code generation packages, SPLIT is capable of generating both software and hardware-oriented C code to allow quick prototyping of optimization algorithms on conventional CPUs and field-programmable gate arrays (FPGAs). A Matlab interface is provided for compatibility with existing commercial and open-source software packages. A numerical study compares software, hardware and heterogeneous implementations of splitting methods and investigates MPC design trade-offs. For the considered testcases the reported speedup of hardware implementations over software realizations is 3x to 11x.
  • Journal article
    Bachtiar V, Manzie C, Kerrigan EC, 2017,

    Nonlinear model-predictive integrated missile control and Its multiobjective Tuning

    , Journal of Guidance Control and Dynamics, Vol: 40, Pages: 2961-2970, ISSN: 1533-3884
  • Journal article
    Majumdar A, Agalgoankar YP, Pal BC, Gottschalg Ret al., 2017,

    Centralized volt-var optimization strategy considering malicious attack on distributed energy resources control

    , IEEE Transactions on Sustainable Energy, Vol: 9, Pages: 148-156, ISSN: 1949-3037

    The adoption of information and communication technology (ICT) based centralized volt-var control (VVC) leads to an optimal operation of a distribution feeder. However, it also poses a challenge that an adversary can tamper with the metered data and thus can render the VVC action ineffective. Distribution system state estimation (DSSE) acts as a backbone of centralized VVC. Distributed energy resources (DER) injection measurements constitute leverage measurements from a DSSE point of view. This paper proposes two solutions as a volt var optimization-distribution system state estimation (VVO-DSSE) malicious attack mitigating strategy when the DER injection measurements are compromised. The first solution is based on local voltage regulation controller set-points. The other solution effectively employs historical data or forecast information. The concept is based on a cumulant based probabilistic optimal power flow with the objective of minimizing the expectation of total power losses. The effectiveness of the approach is performed on the 95-bus UK generic distribution system (UKGDS) and validated against Monte Carlo simulations.
  • Journal article
    Puthenpurayil Kunjumuhammed L, Pal BC, Gupta R, Dyke KJet al., 2017,

    Stability analysis of a PMSG based large offshore wind farm connected to a VSC-HVDC

    , IEEE Transactions on Energy Conversion, Vol: 32, Pages: 1166-1176, ISSN: 1558-0059

    This paper presents modal analysis of a large offshore wind farm using PMSG type wind turbines connected to a VSC-HVDC. Multiple resonant frequencies are observed in the ac grid of offshore wind farms. Their control is crucial for the uninterrupted operation of the wind farm system. The characteristics of oscillatory modes are presented using modal analysis and participation factor analysis. Sensitivity of critical modes to wind turbine design parameters and their impact on closed loop stability of the system are discussed. A comparison between a full wind farm model and an aggregated model is presented to show differences in the characteristics of critical modes observed in the models, and implication of using the models for stability studies. It is concluded that robust control design is important for reliable operation of the system.
  • Conference paper
    Scarciotti G, 2017,

    Discontinuous phasor model of an inductive power transfer system

    , IEEE Wireless Power Transfer Conference (WPTC 2017), Publisher: IEEE, ISSN: 2474-0225

    Recently, a new discontinuous phasor transform has been introduced. The discontinuous phasor can represent the steady-state quantities of electrical circuits powered by discontinuous sources (e.g. square waves) without approximations. In this paper we provide a discontinuous phasor model of a two-coil inductive power transfer system. We validate this model studying the relation between the maximum power dissipated by the load and the frequency of the square wave. The simulations show that the new model correctly describes the steady-state behavior of the circuit for any quality factor and for any frequency.
  • Conference paper
    Huyghues-Beaufond N, Jakeman A, Tindemans S, Strbac Get al., 2017,

    Enhancing distribution network visibility using contingency analysis tools

    , International Conference on Resilience of Transmission and Distribution Networks (RTDN 2017), Publisher: IET

    The East Kent area in the South East of England is the good example of how the uptake of distributed generation is changing the way electricity networks operate. This paper identifies the technical and operational challenges facing transmission and distribution networks in the East Kent area. It introduces the Kent Active System Management (KASM) project, which develops an online contingency analysis solution designed to assist UK Power Networks (UKPN) in maximising asset utilisation while maintaining the network security.
  • Conference paper
    Jamieson M, Strbac G, Tindemans S, Bell Ket al., 2017,

    A simulation framework to analyse weather-induced faults

    , RTDN 2017: International Conference on Resilience of Transmission and Distribution Networks, Publisher: IET

    A framework for simulating weather-induced dependent faults across networks is proposed and demonstrated on a truncated GB network representative of the Scottish and Northern English network. Different weather scenarios are simulated on the test network considering location and wind-speed intensity, analysed using Monte-Carlo simulation. The sensitivity of the network to co-occurrence of faults is simulated by changing the sensitivity of network assets to wind speed via an exponential function. Greater sensitivity to wind speed induces a significant increase in outages, as reflected by risk metrics, specifically Expected Energy Not Served and Expected Maximum Load Shed.
  • Journal article
    Ameli H, Strbac, Qadrdan, 2017,

    Value of gas network infrastructure flexibility in supporting cost effective operation of power systems

    , Applied Energy, Vol: 202, Pages: 571-580, ISSN: 1872-9118

    The electricity system balancing is becoming increasingly challenging due to the integration of Renewable Energy Sources (RES). At the same time, the dependency of electricity network on gas supply system is expected to increase, as a result of employing flexible gas generators to support the electricity system balancing. Therefore the capability of the gas supply system to deliver gas to generators under a range of supply and demand scenarios is of a great importance. As potential solutions to improve security of gas and electricity supply, this paper investigates benefits of employing flexible multi-directional compressor stations as well as adopting a fully integrated approach to operate gas and electricity networks. A set of case studies for a GB gas and electricity networks in 2030 have been defined to quantify the value of an integrated operation paradigm versus sequential operation of gas and electricity networks. The results indicate there are significant overall system benefits (up to 65% in extreme cases) to be gained from integrated optimization of gas and electricity systems, emphasizing the important role of gas network infrastructure flexibility in efficiently accommodating the expected expansion of intermittent RES in future power systems.
  • Journal article
    Moreira A, strbac G, Moreno R, Street A, Konstantelos Iet al., 2017,

    A Five-Level MILP Model for Flexible Transmission Network Planning under Uncertainty: A Min-Max Regret Approach

    , IEEE Transactions on Power Systems, Vol: 33, Pages: 486-501, ISSN: 0885-8950

    The benefits of new transmission investment significantly depend on deployment patterns of renewable electricity generation that are characterized by severe uncertainty. In this context, this paper presents a novel methodology to solve the transmission expansion planning (TEP) problem under generation expansion uncertainty in a min-max regret fashion, when considering flexible network options and n 1 security criterion. To do so, we propose a five-level mixed integer linear programming (MILP) based model that comprises: (i) the optimal network investment plan (including phase shifters), (ii) the realization of generation expansion, (iii) the co-optimization of energy and reserves given transmission and generation expansions, (iv) the realization of system outages, and (v) the decision on optimal post-contingency corrective control. In order to solve the fivelevel model, we present a cutting plane algorithm that ultimately identifies the optimal min-max regret flexible transmission plan in a finite number of steps. The numerical studies carried out demonstrate: (a) the significant benefits associated with flexible network investment options to hedge transmission expansion plans against generation expansion uncertainty and system outages, (b) strategic planning-under-uncertainty uncovers the full benefit of flexible options which may remain undetected under deterministic, perfect information, methods and (c) the computational scalability of the proposed approach.
  • Journal article
    Teng F, Mu Y, Jia H, Wu J, Zeng P, Strbac Get al., 2017,

    Challenges on primary frequency control and potential solution from EVs in the future GB electricity system

    , Applied Energy, Vol: 194, Pages: 353-362, ISSN: 0306-2619

    System inertia reduction, driven by the integration of renewables, imposes significant challenges on the primary frequency control. Electrification of road transport not only reduces carbon emission by shifting from fossil fuel consumption to cleaner electricity consumption, but also potentially provide flexibility to facilitate the integration of renewables, such as supporting primary frequency control. In this context, this paper develops a techno-economic evaluation framework to quantify the challenges on primary frequency control and assess the benefits of EVs in providing primary frequency response. A simplified GB power system dynamic model is used to analyze the impact of declining system inertia on the primary frequency control and the technical potential of primary frequency response provision from EVs. Furthermore, an advanced stochastic system scheduling tool with explicitly modeling of inertia reduction effect is applied to assess the cost and emission driven by primary frequency control as well as the benefits of EVs in providing primary frequency response under two representative GB 2030 system scenarios. This paper also identifies the synergy between PFR provision from EVs and “smart charging” strategy as well as the impact of synthetic inertia from wind turbines.

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