electrical power system dynamics

The (future) electrical power system dynamics: A systems theoretical point of view

Christoph Hackl Head of Research Group “Control of Renewable Energy Systems (CRES)”, TUM www.cres.mse.tum.de

07.06.2017 CREATE Tower, Singapore

Outline

1

Why will dynamics become more important?

2

What should we do about it?

3

What are we doing about it?

C. Hackl

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07.06.2017

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Why will dynamics become more important? The future power system: A likely guess

‚ more distributed generation / renewable energy systems ‚ diminishing mechanical inertia ‚ hybrid grid and transmission topologies (e.g. AC & DC) ‚ more unbalanced faults (ą 75% of faults already today) ‚ more loosely-coupled & unbalanced micro-grids ‚ more power electronics

ùñ Faster dynamics/transients, more harmonics & weaker overall grid! ùñ Stationary models considering fundamental only not sufficient! ùñ Multi-phase multi-wire state-space models crucial! C. Hackl

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Why will dynamics become more important? The dynamics of the (future) power system

Coupled, time-varying partial differential algebraic system (PDAS): ´ f

B B Bt zpt, xq, Bx zpt, xq, zpt, xq, . . . , t

where

¯ “ 0n

ωptq ˚ δptq ‹ zpt, xq :“ ˝ vpt, xq‚ ¨

˛

ipt, xq

Several simplifying assumptions have to be RE-considered, e.g. ‚

B zpt, xq Bx

‚

B zpt, xq Bt

“ 0m , i.e. Π- or T -models (?) “ jωZpxqe

‚ losses (?) C. Hackl

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jωt

, ω ą 0 (?)

‚ time-variance (?) ‚ detailed low-level models (?) ‚ ...


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Why will dynamics become more important? 2

Built on many assumptions: The swing equation M

200

d 2δ dt

d ` Dd dt δ “ pt ptq ´ pˆel sinpδq

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: REGULAR PAPERS, VOL. 56, NO. 1, JANUARY 2009

Improved Swing Equation and Its Properties in Synchronous Generators Jun Zhou and Yasuharu Ohsawa, Member, IEEE 2016 IEEE 55th Conference on Decision and Control (CDC) ARIA Resort & Casino December 12-14, 2016, Las Vegas, USA

Abstract—Modeling single-machine (synchronous-generator) existence and stability; 2) clarify what dynamic features and to infinite-bus (SMIB) systems with what we call the improved swing what degree may have been neglected or ignored when convenequations is considered in this paper. The existence and proper- tional swing equations, or simplified swing equations [1] and ties of local solutions to the improved swing equations are then classical swing equations [2], are used; and 3) investigate nuexamined. Furthermore, the local stability of the SMIB systems Pooya Monshizadeh, Claudio De Persis, Nima Monshizadeh, and Arjan J van der Schaft is scrutinized. By interpreting the improved swing equations with meric differences between the improved swing equations and Taylor expansions, approximate linear time-invariant improved the conventional ones.2016 ICSEE International Conference on the Science of Electrical Engineering swing equations are derived, with which the dynamics of the SMIB To achieve the aims, the improved swing equation for SMIB systems can be estimated pointwisely. Comparisons between the In this paper,solution we provide a nonlinear analysis for an improved Abstract— In this systems paper, weisinvestigate an then, introducedthe in properties Section II,ofand its local improved and conventional swing equations are made through improved swing equation model for synchronous generators. swing equation to fulfill higher accuracy in existence is examined rigorously by meansyet of easy-to-use the fixed-point illustrative examples. This model is derived by omitting the main simplifying asanalysis and modeling of the synchronous generator that can theory, together with ourWe observations sumption the conventional swing equation. carry out a about solution properIndex Terms—Equilibrium, local solution, stability, swingofequaalso exploited in small-scale networks. We first explicate nonlinear analysis forties the and stability and frequency regulation and equilibrium distribution. Equipped withbethe improved tion, synchronous generator. the contradicting assumptions in obtaining the conventional provide region of attraction estimates the for local two scenarios. First swing equations, stability of the SMIB systems around swing equation and elaborate deriving the improved model. we study the case that a synchronous generator is connected to a their equilibria dealt with in Section III. Equivalent improved constant load. Second, we inspect the is case of the single machine In Section III, as the first scenario, we look into the properties swing in terms of Taylor expansions are considered in 2015 IEEE 54th Annual Conference on Decision and Control (CDC) I. INTRODUCTION connected to an infinite bus.equations Finally, the different behaviors of Elad Venezian of the model when the December generator 15-18, is connected to a constant George Weiss 2015. Osaka, Japan the conventional andSection improved equations are depicted IV, swing and approximate linear time-invariant (LTI) swing School Tel Aviv School of EE, Tel Aviv University load of andEE, provide an University estimate of the region of attraction by simulations. LTERNATIVE current (ac) power systems are compli- equations are suggested as well. We will see that the dynamics

Nonlinear Analysis of an Improved Swing Equation

A warning about the use of reduced models of synchronous generators

A

Ramatnonlinear Aviv 69978, IsraelFurther in Section IV, the second Ramat Aviv 69978, Israel through analysis. cated networks consisting of interconnecting generators, of the approximate LTI improved swing equations can be emscenario which is mainly referred to as Single Machine I. I NTRODUCTION transmission equipment such as transformers, distributed power ployed for estimating those of the improved swingBus equations. Infinite (SMIB) is investigated. We provide Usesanalytical and Abuses of the Swing Equation Model sources, and miscellaneous loads, and so on. InDriven an ac by power environmental and technical motivations, re- the Section IV collects examples to illustrate numericofefficacy estimates the region of attraction for both conventional structuring classical power networks has equations, been undertogether vast and system, all synchronous generators must operate at the the same Abstract—Synchronous are an essential component phase difference of the improved swing withgenerators brief comparimproved swing models in this case. Finally, simulationsbetween it and the grid is constant. Therefore, of the electric grid. Recently, the stability of the electric grid it is desirable to knowSina attention recent decades. theand goals are system frequency in order to keep electric power supplyduring safely theisons if forY.a Caliskan given grid and which contains SGs Paulo Tabuada between the Among improved conventional equations. areswing provided as a verification of the results. hasdistributed become an area of high interest and intensive research. We and a loads, the SGs tend to synchronize (for initial states in a energy losses by moving and stably. If generators lose synchronism duedecreasing to disturbances Conclusions are towards sketched in SectiongenV. discuss the stability of aII. single generator connected to an infinite C ONVENTIONAL AND I MPROVED S WING E QUATIONS and preventing In fault through building up like short circuits and abrupt load variationseration amid incidents, thepropagation literature, conventional swing are modeled bus, and show thatequations certain reduced models fail to predict the reasonably large region) and if yes, if the grid frequency and microgrids. are small power network areas power flows remains stable. To simplify the stability analysis, electricity quality in the power system may smart deteriorate, and Microgrids behavior of trivial this system. mechanical dynamics of theThe synchronous generator after neglecting some seemingly factorsThe of synchronous Abstract— swing equation model is widely used in the equation for stability analysis under small oscillations we which can be seen as single entities from the large power is common to use the Park transformation of the voltages power supply even comes to a complete halt in worst cases. generators to surmount nonlinearities and singularities reads as [3]–[7] literature to study aitlarge class problems, including stability obtain results contradicting a more detailed FP model. I. I NTRODUCTION grids. In such small-scale the energy consumption generators. currents, that maps sinusoidal positive sequence signals power We show(1) in this paper, by compariTherefore, it is unavoidable to consider synchronization of relatednetworks, J ω˙ + Ddanalysis (ω − ω ∗of )= τm −systems. τand to the dynamics of synchronous In general, e , andtransmission. production uncertainty increases to a great extent acprinciples theinswing equation model The AC electricity wasdynamics developed atsonthewith enda first of the into amodel, fixed that point the state space. generators, which is related closely to power conventional swing equations focus on slowgrid swing + II. as S YNCHRONOUS G ENERATOR M ODELS maytotal lead totoday. erroneous conclusions when performing stability where J ∈ R the of The inertia of common the cording to the fewer number of consumers XIXth and unpredictable century, has remained very issimilar untilmoment most reduced model, which is known the Synchronism of generators can be lost due to swing phenomena when SMIB systems are running under and operational power level. 2 analysis ofmpower under small oscillations. turbinecomplex and generator rotor ), ω systems, ∈ classical R+ iseven the rotor is power injections of renewables such as wind turbines The grid is anand enormously nonlinear and(kg randomly model, a second order non linear model. The occurring in-between generators. Possible discrepancies have not been clarified when high-speed ∗ + In this section, we review two synchronous generator shaftrigorous velocity stability (mechanical rad/s), ω ∈ Rreference the angular solar panels. Designing controllers for the varying electrical sources system for which analysis is impos[10] argues that this model is not realistic enough I. isI NTRODUCTION This paper is devoted to modeling single-machine infinite-bus swings are involved and/or the SMIB areassociated poweredwith the nominal frequency models. The first model is derived from first principles while velocity ((2π)60Hz), under such perturbations and abrupt power variations, calls systems sible. Many techniques and models that have been and model that a more complicated (but of stillthe reduced) model, which The developed swing isτ a∈perfect example (SMIB) systems by what we will call the improved swing equa- heavily or insufficiently. There are numerousτ efforts simplify the second is the traditional swing equation model that is ∈ R+togrid, is theusing net rigorous mechanical shaftequation torque (N m), for rethinking about the accuracy of the to models were ofma power e assessthat the stability modelling they call improved swing equation (ISE), should be used. In famous line by George Norman Draper in [2]: “All widely used in the literature. After introducing these models, tions for describing swing phenomena more fully and exactly. nonlinearities and surmount singularity to the swing equaR+ is counteracting electromagnetic torqueBox (N and m), (mostly) valid for the classical electrical systems. and system theoryrelated techniques mixed with practical paper weand show thatPower even engineers the model proposed in [10] is models shortcuts arecoefficient wrong, this but some useful.”. 1 It is well known that swing phenomena can beDespite depictedthebyextensive the tions. we show how to recover the swing equation model from the For instance, [8]–[10] and [11] Dd ∈modelings R+driven is thethat damping-torque (Nreliable m s) are . The advances in extracting energy fromsuggest and simplifying assumptions by experience, see used for this not predict an successfully modelBearing inforthestability past toanalysis, describebecause syn- itFPcan’t model by making several assumptions: neglect of reactive so-called conventional swing equations, in which some highly may reflect swing more precisely multimachine rotational loss due to friction is unstable ignored. renewables, synchronous generators areprocesses still the main supinstance [1], [2], [3], mechanical [4],in[5]. behavior that is predicted by a more faithful model chronous a large class Pm nonlinear and complicated dynamics of generators power systems. Great suchUnder as in [1], [2], [12]–[19] τe generators = Pe we in can the of power engineering power (Assumption 2.1 in Section II-B), and an angular that τhave plierareofneglected the implemented microgrids (seeefforts e.g. [1]). m = In recent years, duein tomind the increasing penetration renewthe model same system. ω and of problems [1], ω[3]. of Notwithstanding being stated in most velocity in the vicinity of ωs (Assumption 2.5). or merely approximately treated. By this study, we introduce alsoinbeen made stability analysis and stabilization in SMIB synchronous generator as unpredictable changes loads and inrenewable generations, able energy resources, which connect to thepowers grid via powerbooksThe this equation paper is organized systems thatrest the of swing is not validas follows. In Section nonlinear and singular differential equations for SMIB systems through the conventional swing power output, and to assure of the and/or stabilitymultimachine and frequencysystems regulation of the converters and produce an intermittent it is II, a fourth order model of a SG connected to infinite bus ∗ Jω ω˙ + D away ω(ω −from ω ) equilibrium, = Pm − Pe the , long track (2) of success in using this without significant approximations so that dynamics A. First Principles Model equations. power and grid,strucit appears crucial to investigate accuracy of the traditional models dand methods for nottheclear whether having constant field currentresulted is presented. The reduction model for solving a and broad spectrum of applications tural facts about SMIB systems can be reflected better. The the electrical and dynamical models of these machines. controlling the power where grid will control Therefore, Pmsucceed and Pto thea it. mechanical input) andmodel from above to themodel second described in generator is composed of a moving come are in biased focus(physical on the the “usefulness” of this at order the ISEAis synchronous San WING EQUATIONS II. exploited IMPROVED study about the improved swing equations has the afollowing While large number of articles have the classical there is increasing interest in(physical the fundamental mathematical electrical output) power III. Simulations and local stability shows and a fixed frame. The electrical windings expense of respectively. blurring Section the boundaries of the region where the analysis ponent, that the rotor, swing equation as the model for the synchronous aims: 1) Develop a more accurate dynamic modeling for SMIB stability analysis for the grid, see for equation, instance [5], In Section II.A, we models derivegenerator, aand class ofa nonlinear singular In the and conventional swing Jω Dd ω behavior are different of the our models are given Section IV. swing equation canand be applied. In apthis paper, objective is in connected to the fixed frame are called stator windings, and ∗ ∗ recently brought up doubts about[6], its [7], accuracy and systems and examine its major characteristics,few suchhave as solution [8],for [9], [10]. proximated constants M= andback A =toDclarifying state-space differential equations the SMIB systemwith shown dω . to shift theJω focus this boundary by askingTO INFINITE they are BUS denoted by the subscripts a, b, and c. The field II. M ODELING SG CONNECTED validity, and proposed models of higher accuracy [2]–[8]. generator The approximation, synchronous is the main power source in Fig. 1 without significant i.e., we(SG) are going

“. . . the results in this paper call into question the scientific foundations upon which the current power grid has been built.” [1] C. Hackl

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What should we do about it? Interdisciplinary research: A lot of collaboration required!

...

...

s tic a emdynamics

material ...

science circuit

th ma

e:

g ua

systems

science

mathematicsr g an theory we l o n social information p sociology y: mo g m engineering theory co olo political n ... climatologych te science architecture y ke... ...

...

C. Hackl

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philosophy

ics... n ro

computer

engineering theory

multi-body

chemistry

biology

physics

t

c ele...

economics

...

urban planing


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What should we do about it? Interdisciplinary research: Bottom-up approach (and, meanwhile, top-down approach)

simulation

control

optimization

monitoring

laboratory

(model reduction / model simplification) ¨

´ f

¯

B B Bt zpt, xq, Bx zpt, xq, zpt, xq, t

sources

lines

“ 0n

loads

where

˛ ωptq ˚ δptq ‹ ‹ zpt, xq :“ ˚ ˝vpt, xq‚ ipt, xq

storage

actuators

Unbalanced multi-phase multi-wire AC & DC power system dynamics C. Hackl

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What are we doing about it? CRES: Running projects (third-party funding ą 2 million e) and ą 40 publications (since 2014) Large-scale WTS

Small-scale WTS

Model predictive control for RES

Airborne Wind Energy

Efficiency+Reliability

Reluctance SM

Real-time applicability

Fault-tolerant control

Geothermal energy

Wave energy (SinnPower)

Electric vehicles (BMW)

Fault-tolerant control


C. Hackl

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Electrical power system

Three-phase four-wire system dynamics 8/10

What are we doing about it? Activities at TUM-CREATE

‚ Lecture on each Thursday (May-July) TUM CREATE Scientific Lecture: Modeling and Control of Renewable Energy Systems Dates (Thursdays, 13 sessions) 4 May 25 May 15 Jun 6 Jul 27 Jul

11 May 1 Jun 22 Jun 13 Jul

Time 10:00 am to 12:15 pm

18 May 8 Jun 29 Jun 20 Jul

Venue Theatrette, Level 2, CREATE Tower

Lecture Synopsis

 Introduction and motivation the "Energiewende" ‚ Seminar “Selected topics inforenergy research” on each Friday (May-July) 

Overview of renewable energy systems

 Mathematical preliminaries ((un-)balanced three-phase systems, space ‚ Unbalanced modeling of four-wire three-phase systems (collaborative research)  vector theory, etc.) 

Modeling of renewable energy systems

‚ Refinement of the swing equation research) o Power electronic devices (converter,(collaborative inverter, modulation ‚ ... C. Hackl

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07.06.2017

o strategies) o Electrical machines, etc.  Goal: Derivation of physical and dynamical models  Control of renewable energy systems | o The (future) electrical power system dynamics: A systems theoretical point of view Current control system

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References I

[1] Sina Y. Caliskan and Paulo Tabuada. Uses and abuses of the swing equation model. In 2015 54th IEEE Conference on Decision and Control (CDC). IEEE, dec 2015.

C. Hackl

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