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  • 1.
    Andreasson, Martin
    et al.
    KTH, Skolan för industriell teknik och management (ITM). KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Sjödin, Emma
    KTH, Skolan för industriell teknik och management (ITM). KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Sandberg, Henrik
    KTH, Skolan för industriell teknik och management (ITM). KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Johansson, Karl H.
    KTH, Skolan för industriell teknik och management (ITM). KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Coherence in Synchronizing Power Networks with Distributed Integral Control2017Ingår i: 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017, IEEE , 2017, s. 6683-6688Konferensbidrag (Refereegranskat)
    Abstract [en]

    We consider frequency control of synchronous generator networks and study transient performance under both primary and secondary frequency control. We model random step changes in power loads and evaluate performance in terms of expected deviations from a synchronous frequency over the synchronization transient; what can be thought of as lack of frequency coherence. We compare a standard droop control strategy to two secondary proportional integral (PI) controllers: centralized averaging PI control (CAPI) and distributed averaging PI control (DAPI). We show that the performance of a power system with DAPI control is always superior to that of a CAPI controlled system, which in turn has the same transient performance as standard droop control. Furthermore, for a large class of network graphs, performance scales unfavorably with network size with CAPI and droop control, which is not the case with DAPI control. We discuss optimal tuning of the DAPI controller and describe how internodal alignment of the integral states affects performance. Our results are demonstrated through simulations of the Nordic power grid.

  • 2. Govindarajan, Nithin
    et al.
    Arbabi, Hassan
    van Blargian, Louis
    Matchen, Timothy
    Tegling, Emma
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik.
    Mezic, Igor
    An operator-theoretic viewpoint to non-smooth dynamical systems: Koopman analysis of a hybrid pendulum2016Ingår i: 2016 IEEE 55th Conference on Decision and Control, CDC 2016, Institute of Electrical and Electronics Engineers (IEEE), 2016, s. 6477-6484, artikel-id 7799266Konferensbidrag (Refereegranskat)
    Abstract [en]

    We apply an operator-theoretic viewpoint to a class of non-smooth dynamical systems that are exposed to event-triggered state resets. The considered benchmark problem is that of a pendulum which receives a downward kick at certain fixed angles. The pendulum is modeled as a hybrid automaton and is analyzed from both a geometric perspective and the formalism of Koopman operator theory. A connection is drawn between these two interpretations of a dynamical system by establishing a link between the spectral properties of the Koopman operator and the geometric properties in the state-space.

  • 3.
    Sjödin, Emma
    et al.
    KTH, Skolan för elektro- och systemteknik (EES).
    Gayme, D. F.
    Topcu, U.
    Risk-mitigated optimal power flow for wind powered grids2012Ingår i: 2012 American Control Conference (ACC), IEEE Computer Society, 2012, s. 4431-4437Konferensbidrag (Refereegranskat)
    Abstract [en]

    Increased penetration of renewable energy sources poses new challenges to the power grid. Grid integrated energy storage combined with fast-ramping conventional generation can help to address challenges associated with power output variability. This paper proposes a risk mitigating optimal power flow (OPF) framework to study the dispatch and placement of energy storage units in a power system with wind generators that are supplemented by fast-ramping conventional back-up generators. This OPF with storage charge/discharge dynamics is solved as a finite-horizon optimal control problem. Chance constraints are used to implement the risk mitigation strategy. The model is applied to case studies based on the IEEE 14 bus benchmark system. First, we study the scheduling of spinning reserves and storage when generation and loads are subject to uncertainties. The framework is then extended to investigate the optimal placement of storage across different network topologies. The results of the case studies quantify the need for storage and reserves as well as suggest a strategy for their scheduling and placement.

  • 4.
    Sjödin, Emma
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. Johns Hopkins University, USA.
    Gayme, Dennice F.
    The Johns Hopkins University, USA.
    Transient losses in synchronizing renewable energy integrated power networks2014Ingår i: American Control Conference (ACC), 2014, IEEE , 2014, s. 5217-5223Konferensbidrag (Refereegranskat)
    Abstract [en]

    This paper quantifies the transient power losses incurred in re-synchronizing a network of generators and loads. The power system is represented using a network preserving model with loads and asynchronous generators modeled as frequency dependent power injections, which we refer to as ‘first-order oscillators’. Coupling these models with the swing equations of traditional generators leads to a mixed-oscillator system. The power flows used to maintain network synchronization induce resistive (real power) losses in the system, which we quantify through an H2 norm that is shown to scale with network size. Our results also show that given a fixed network size, this H2 norm is the same for first-order, second-order and mixed-oscillator systems, provided that the damping coefficients are all equal. Therefore, if the renewable power generators being added to a power network can be controlled so that their effective dampings match those of the existing generators, they will not increase transient power losses in the system.

  • 5.
    Tegling, Emma
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Reglerteknik.
    Fundamental Limitations of Distributed Feedback Control in Large-Scale Networks2018Doktorsavhandling, monografi (Övrigt vetenskapligt)
    Abstract [sv]

    Distribuerad reglering av nätverk går ut på att definiera lokala styrregler och kommunikationsprotokoll, som leder till att nätverket i stort uppvisar önskat beteende. Denna avhandling undersöker fundamentala begränsningar hos sådana distribuerade regulatorer, utifrån den prestanda som kan uppnås globalt i storskaliga nätverk.  

    Vi modellerar nätverk där den lokala dynamiken är en enkel- eller dubbelintegrator, och som regleras genom linjär återkoppling från ett begränsat antal grannsystem.  En sådan modell kan till exempel representera formationskörning med autonoma fordon eller frekvenssynkronisering i elnät. Vi antar att systemet utsätts för störningar och mäter dess prestanda utifrån systemets H2-normmed avseende på en lämplig utsignal. På det sättet kan vi mäta ett nätverks koherens, som är ett mått på hur stor varians noderna har i förhållande till nätverksgenomsnittet.  Vi visar också att den här metoden kan uppskatta de elektricitetsförluster som uppstår på grund av cirkulerande strömmar i synkroniseringstransienten hos elnät.

    Det är känt att det finns begränsningar hos distribuerad reglering som är proportionell mot relativa tillståndsmätningar mellan grannsystem. Dessa innebär en dålig skalning av koherensmåttet i nätverk med lågdimensionell gitterstruktur och leder till att en endimensionell fordonsformation inte kan uppvisa en stelkroppsliknande rörelse. Avhandlingen visar att dynamiska regulatorer med ett ytterligare regulatortillstånd generellt sett omfattas av samma begränsningar. Beviset bygger delvis på en fundamental begränsning hos relativ återkoppling i nätverk med tre eller fler lokala integratorer. Vi visar att sådana system alltid blir instabila om nätverket tillåts växa utöver en viss (ändlig) storlek.

    Ett undantag till resultatet ovan inträffar om regulatorn har tillgång till sitt eget lokala tillstånd med avseende på en absolut referensram. Det är till exempel fallet med frekvensreglering i elnät, där den lokala frekvensavvikelsen kan mätas. I dessa fall kan en dynamisk regulator innehålla en deriverande eller integrerande del som leder till en fundamental prestandaförbättring och ökar skalbarheten. Om den absoluta tillståndsmätningen är brusig tappar dock den integrerande regulatorn sina fördelar och försämrar istället skalbarheten. Vi visar att integralverkan i stora nätverk därför i princip måste vara centraliserad eller tillåta kommunikation mellan samtliga noder. 

    När det gäller synkronisering i elnät visar vi att de transientförluster som uppstår på grund av till exempel laststörningar ökar linjärt med antalet generatornoder. Prestandan kan dock inte, som tidigare, förbättras av att öka konnektiviteten hos nätverket. Vi diskuterar vad detta kan innebära för framtidens elnät med distribuerad kraftproduktion. 

     

  • 6.
    Tegling, Emma
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik.
    On performance limitations of large-scale networks with distributed feedback control2016Licentiatavhandling, monografi (Övrigt vetenskapligt)
    Abstract [en]

    We address the question of performance of large-scale networks with distributed feedback control. We consider networked dynamical systems with single and double integrator dynamics, subject to distributed disturbances. We focus on two types of problems. First, we consider problems modeled over regular lattice structures. Here, we treat consensus and vehicular formation problems and evaluate performance in terms of measures of “global order”, which capture the notion of network coherence. Second, we consider electric power networks, which we treat as dynamical systems modeled over general graphs. Here, we evaluate performance in terms of the resistive power losses that are incurred in maintaining network synchrony. These losses are associated with transient power flows that are a consequence of “local disorder” caused by lack of synchrony. In both cases, we characterize fundamental limitations to performance as networks become large. Previous studies have shown that such limitations hold for coherence in networks with regular lattice structures. These imply that connections in 3 spatial dimensions are necessary to achieve full coherence, when the controller uses static feedback from relative measurements in a local neighborhood. We show that these limitations remain valid also with dynamic feedback, where each controller has an internal memory state. However, if the controller can access certain absolute state information, dynamic feedback can improve performance compared to static feedback, allowing also 1-dimensional formations to be fully coherent. For electric power networks, we show that the transient power losses grow unboundedly with network size. However, in contrast to previous results, performance does not improve with increased network connectivity. We also show that a certain type of distributed dynamic feedback controller can improve performance by reducing losses, but that their scaling with network size remains an important limitation. 

  • 7.
    Tegling, Emma
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Andreasson, Martin
    KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Simpson-Porco, John W.
    Sandberg, Henrik
    KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Improving performance of droop-controlled microgrids through distributed PI-control2016Ingår i: 2016 AMERICAN CONTROL CONFERENCE (ACC), IEEE conference proceedings, 2016, s. 2321-2327Konferensbidrag (Refereegranskat)
    Abstract [en]

    This paper investigates transient performance of inverter-based microgrids in terms of the resistive power losses incurred in regulating frequency under persistent stochastic disturbances. We model the inverters as second-order oscillators and compare two algorithms for frequency regulation: the standard frequency droop controller and a distributed proportional-integral (PI) controller. The transient power losses can be quantified using an input-output H-2 norm. We show that the distributed PI-controller, which has previously been proposed for secondary frequency control (the elimination of static errors), also has the potential to significantly improve performance by reducing transient power losses. This loss reduction is shown to be larger in a loosely interconnected network than in a highly interconnected one, whereas losses do not depend on connectivity if standard droop control is employed. Moreover, our results indicate that there is an optimal tuning of the distributed PI-controller for loss reduction. Overall, our results provide an additional argument in favor of distributed algorithms for secondary frequency control in microgrids.

  • 8.
    Tegling, Emma
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik.
    Bamieh, Bassam
    Gayme, Dennice F.
    The Price of Synchrony: Evaluating the Resistive Losses in Synchronizing Power Networks2015Ingår i: IEEE TRANSACTIONS ON CONTROL OF NETWORK SYSTEMS, ISSN 2325-5870, Vol. 2, nr 3, s. 254-266Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    This paper investigates the resistive power losses that are incurred in keeping a network of synchronous generators in a synchronous state. These losses arise due to the transient power-flow fluctuations that occur when the system is perturbed from a synchronous state by a small transient event or in the face of persistent stochastic disturbances. We call these losses the "price of synchrony," as they reflect the real power-flow costs incurred in resynchronizing the system. In the case of small fluctuations at each generator node, we show how the total network's resistive losses can be quantified using an H-2 norm of a linear system of coupled swing equations subject to distributed disturbances. This norm is shown to be a function of transmission-line and generator properties, to scale unboundedly with network size, and to be weakly dependent on the network topology. This conclusion differentiates the price of synchrony from typical power systems stability notions, which show highly connected networks to be more coherent and, thus, easier to synchronize. In particular, the price of synchrony is more dependent on a network's size than its topology. We discuss possible implications of these results in terms of the design of future power grids, which are expected to have highly distributed generation resources leading to larger networks with the potential for greater transient losses.

  • 9.
    Tegling, Emma
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Gayme, D. F.
    Sandberg, Henrik
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Performance metrics for droop-controlled microgrids with variable voltage dynamics2015Ingår i: Decision and Control (CDC), 2015 IEEE 54th Annual Conference on, IEEE , 2015, s. 7502-7509Konferensbidrag (Refereegranskat)
    Abstract [en]

    This paper investigates the performance of a microgrid with droop-controlled inverters in terms of the total power losses incurred in maintaining synchrony under persistent small disturbances. The inverters are modeled with variable frequencies and voltages under droop control. For small fluctuations from a steady state, these transient power losses can be quantified by an input-output H2 norm of a linear system subject to distributed disturbances. We evaluate this H2 norm under the assumption of a dominantly inductive network with identical inverters. The results indicate that while phase synchronization, in accordance with previous findings, produces losses that scale with a network's size but only weakly depend on its connectivity, the losses associated with the voltage control will be larger in a highly connected network than in a loosely connected one. The typically higher rate of convergence in a highly interconnected network thus comes at a cost of higher losses associated with the power flows used to reach the steady state.

  • 10.
    Tegling, Emma
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik.
    Sandberg, Henrik
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik.
    On the Coherence of Large-Scale Networks With Distributed PI and PD Control2017Ingår i: IEEE Control Systems Letters, ISSN 2475-1456, Vol. 1, nr 1, s. 170-175Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We consider distributed control of double-integrator networks, where agents are subject to stochastic disturbances. We study performance of such networks in terms of coherence, defined through an H2 norm metric that represents the variance of nodal state fluctuations. Specifically, we address known performance limitations of the standard consensus protocol, which cause this variance to scale unboundedly with network size for a large class of networks. We propose distributed proportional integral and proportional derivative controllers that relax these limitations and achieve bounded variance, in cases where agents can access an absolute measurement of one of their states. This case applies to, for example, frequency control of power networks and vehicular formation control with limited sensing. We discuss optimal tuning of the controllers with respect to network coherence and demonstrate our results in simulations.

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