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Sweeping power system stabilisation with a parametric fuzzy predictive control of a generalised energy storage device

2020; Institution of Engineering and Technology; Volume: 14; Issue: 25 Linguagem: Inglês

10.1049/iet-gtd.2020.0940

1751-8695

Hailiya Ahsan, Mairaj-ud-Din Mufti,

Frequency Control in Power Systems

IET Generation, Transmission & DistributionVolume 14, Issue 25 p. 6087-6096 Special Section: Extended Papers from the 9th Conference on Power and Energy Systems, 2019Free Access Sweeping power system stabilisation with a parametric fuzzy predictive control of a generalised energy storage device Hailiya Ahsan, Corresponding Author Hailiya Ahsan hailiya.ahsan@gmail.com orcid.org/0000-0002-6968-2260 Department of Electrical Engineering, National Institute of Technology, Srinagar, Jammu and Kashmir, 190006 IndiaSearch for more papers by this authorMairajud Din Mufti, Mairajud Din Mufti Department of Electrical Engineering, National Institute of Technology, Srinagar, Jammu and Kashmir, 190006 IndiaSearch for more papers by this author Hailiya Ahsan, Corresponding Author Hailiya Ahsan hailiya.ahsan@gmail.com orcid.org/0000-0002-6968-2260 Department of Electrical Engineering, National Institute of Technology, Srinagar, Jammu and Kashmir, 190006 IndiaSearch for more papers by this authorMairajud Din Mufti, Mairajud Din Mufti Department of Electrical Engineering, National Institute of Technology, Srinagar, Jammu and Kashmir, 190006 IndiaSearch for more papers by this author First published: 07 December 2020 https://doi.org/10.1049/iet-gtd.2020.0940Citations: 3AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract A control oriented approach is adopted for the implementation of a parametric fuzzy-predictive control on a compact model of a generalised energy storage device implanted in a multi-machine system. It is realised using a combination of a heuristic fuzzy logic control (HFLC) and a predictive step ahead control (PSAC) for energy storage reactive and real power modulation, respectively. While PSAC overcomes the computational burden innate to model predictive control, the HFLC with paramount simplicity lays down the design template for fuzzy control. Local bus measurements are translated into rate of change of frequency and voltage errors, while accommodating a second-order dynamics of a phase locked loop. To emphasise the computational simplicity and implementation speed of the proposed technique, all parameters of the problem are solved explicitly. These parameters account for the input–output mapping structure consisting of membership spreads and rule base in fuzzy domain. In predictive control, while approximating the storage-converter dynamics by a second-order system, relevant expressions are derived for the parameters involved in the loop. Umbrella power system stabilisation, viz., high oscillation damping with quicker settling times, frequency-nadir curtailment, power and voltage smoothing is assured with the parametric fuzzy-predictive controlled energy storage. Nomenclature E d d component of alternator transient emf E q q component of alternator transient emf E f d alternator field voltage r s alternator stator resistance X d d component of alternator reactance X q q component of alternator reactance X d ′ d component of alternator transient reactance X q ′ q component of alternator transient reactance θ bus voltage angle δ rotor/machine angle D damping constant T q o i d- axis alternator transient time contant T d o i q- axis alternator transient time contant ω angular speed ω s alternator rotor speed H inertia constant P m mechanical power output K E AVR excitation gain S E E f d AVR exciter saturation function V R regulator voltage T E AVR exciter time constant R f regulator voltage K F stabiliser's gain T F time constant of stabiliser circuit K A gain of regulator T A time constant of regulator circuit V ref reference voltage V d q s dq components of DFIG's stator voltage V d q r dq components of DFIG's rotor voltage ψ d q s dq components of DFIG's stator side flux ψ d q r dq components of DFIG's rotor side flux I d q s dq components of DFIG's stator side currents I d q r dq components of DFIG's rotor side currents R s DFIG's stator resistance R r DFIG's rotor resistance X s DFIG's stator reactance X r DFIG's rotor reactance X m magnetising reactance X ′ fictitious reactance P s stator power output P ∗ reference active power Q ∗ reference reactive power C d c dc link capacitance D chopper duty ratio R bat effective battery resistance R uc effective ultracapacitor resistance C bat equivalent battery capacitance C uc equivalent ultracapacitor capacitance C e q equivalent charge separation capacitance V bat voltage across C bat V uc voltage across C uc V e q voltage across C eq 1 Introduction Energy storage systems (ESS) are characterised by a quick response to the control signals, making them an increasingly expedient option of power stability improvement as well as retention. They are able to inject/store huge amounts of real and/or reactive powers in a very minuscule time, to render the system free of large damping excursions [[1]]. As tenable sources/sinks of power, ESS like superconducting magnetic energy storages, flywheel energy storages, battery energy storages, supercapacitor energy storages, static synchronous compensators and so on; they facilitate robust mitigation of power system intermittences with dedicated disturbance rejection, easier control, reduced converter ratings and even a dynamic storage potentiality [[2], [3]]. ESS which have been articulated to be the holy grail of modern power systems (New York Times, November 2010) are mostly economically not viable. Had the scenario of renewable power penetration not assumed the power system stage, the call for ESS would still have been far away! A Californian independent service operator, S. Berberich referred to ESS as, 'It's good stuff, but it's expensive, and we've to find business cases'. A large chunk of researchers are still sceptical about the oddly high cost of ESS units. However, with incoming efforts from certain power and energy monographs of the 2017 IEEE magazine issues, which are devoted to opening the door to energy storage-challenges on future power systems, the acceptance of such support systems is gaining importance. Despite the heated discussions rooted at a Switzerland seminar in the dawn of 2017, this ongoing decade has witnessed colossal burgeoning of ESS implementation and experimentation. Witnessing anomalously high installations in large pockets of the world, wind is carving its way from a support dependent technology to an economically independent renewable source. The recent years have certainly faced a paradigm shift, due to the 'greening' image wind energy deployment creates by reducing CO 2 emission footprints altogether, in an era of disturbingly fluctuating fossil costs. 2017 showed a role reversal with a handsome number of wind markets emerging in parts of Africa, Europe and Latin Americas. With the promise of blowing down all competition around cost, reliance and performance delivery, wind power is taking the path of around 70–100 GW annually in the coming years. However, the addition of wind energy whether through simple asynchronous generator aggregates serving as wind farms or even doubly fed induction generators (DFIGs) coming to the stage, this point of grid interconnection seems to be the most vulnerable. The expansive thriving of wind farms weakens the synchronising coupling in power systems with intermittent wind power injection [[4]]. In addition, the wind farm voltage dip is drastically more when the grid is struck with a short circuit, increasing the line impedance, making the grid situation even worse, eventually leading to grid asynchronisation [[5]]. With conventional induction generators drawing reactive power during normal as well as fault conditions, the DFIG however, inject reactive current as per stable grid codes. With increasing doubly fed IG based wind generation, it often results in loss of synchronism between the WF and grid, even when met with a relatively benign transient situation/perturbation. Quite a lot of work can be traced, which study the stability margin enhancement and fault ride through augmentation of multi-machine power systems with embedded WF's [[6], [7]]. A plethora of literature is available on the modelling and control of ESS [[8]–[10]]. The control techniques covered by this group are H α control, sliding mode control, virtual inertia emulation and others. Recently, model predictive control has assumed charge as an advanced adaptive control technique in many power system control applications, enhancing comprehensive stability of the same [[11]]. MPC has favoured the load frequency control of large interconnected power systems as highlighted in [[12], [13]]. The only catch in the said works is the absence of AGC and AVR loops. In [[14]], MPC controlled ESD operation is presented for an IEEE 5 bus system. The authors prefer locating the storage at the wind farm bus and THD inferring Simscape based simulation studies are performed for situations of sag-swell only. MPC has been hugely applied for process control tasks in the industry, voltage stability control, transient stability and oscillation damping [[15]]. The computational burden of MPC implementation for real-time applications is a cause of concern. Fuzzy logic control (FLC) of ESS can be found in [[3], [16]–[22]]. The only lacunae behind FLC is that it is highly dependent on the designer's expertise and no systematic methodology is available, as far as the design, development and application of FLC goes. No doubt Taj et al. [[3]] present an amalgamation of fuzzy-neuro adaptive control of ES devices like the flywheel, but the rule bases and membership functions are attained monotonously as per the designers expertise. There is scope for improvement in this sphere. The industry oriented proportional–integral–derivative controllers do not suffice for multifariously constrained systems. Energy storage devices (ESDs) find considerable attention for power utility applications and stability augmentation, especially with fluctuating renewable power portions. It becomes imperative to consider a generalised detailed modelling of these devices, which imbibe/capture the dynamics of the storage side as well as the grid side converters, in addition to the mathematical modelling of the intermediate dc link [[23]]. The control strategies presented in [[23]] are selectively applied in combination in this treatise. In addition, the generalised energy storage device (GESD) model synthesis has been confirmed with flywheel energy storage, superconducting magnetic energy storage and ultrabattery energy storage inherent dynamic loops. The main contributions of this paper are: The use of a generalised ESD for real and reactive power exchange, to facilitate umbrella power system oscillation alleviation in a multi machine power system. Highlighting a novel predictive and fuzzy control combination with explicit parametric computations. Step ahead predictions are made on a control oriented model, by parametrically solving the problem. Systematic development of a heuristically tuned FLC is delineated, where the optimal fuzzy template is dispatched using mixed integer mathematics. To stress on the accuracy of approximating the inner loop dynamics of a GESD by a first-order system, the inherent dynamic loops of flywheel energy storage, superconducting magnetic energy storage and ultrabattery energy storage are described. 2 System model A benchmark power system model is developed using essential dynamic components and regulators and an elaborate network structure model. A Western Systems Coordinating Council (WSCC) which emerged around the late 1960s, and was later referred to as the Western Electricity Coordinating Council (WECC) after the merger of some additional transmission bodies in 2002, is considered as the test bed system in this treatise for performing extensive stability studies. The old connotation of the system as WSCC is preferred here. As of now, synchronous generation is akin to power systems. Alternators include inertia and therefore heavily impact the initial dynamics of the system during the first few seconds post-contingency. On the other hand, a non-synchronous generation, which is dependent on stochastic parameters, and is mostly configured using power electronic support, might not be able to recover a system with power deficits during the first few seconds of any random imbalance hit. It can be said hypothetically, that a total synchronous machine deficient system has zero coupling between frequency and power mismatch. In light of this, as of now, a completely synchronous generation deficient system is not a practical concept. A few federal governments have settled on certain thresholds for non-synchronous generation penetration around 60–75 %. 2.1 Machine modelling While accounting the transient effects, the alternators are modelled using the two axis model, given in [[24]–[26]]. I d I q = − r s − X q ′ X d ′ − r s { V sin ⁡ ( δ − θ ) V cos ⁡ ( δ − θ ) − E d ′ E q ′ } E d . E q . + E f d 0 = − E d / T q o − E q / T d o + − X d d 0 0 X q q I d I q T E d E f d d t = − ( K E + S E ( E f d ) ) E f d + V R T F d R f d t = − R f + ( K F / T F ) E f d d V R d t = − V R + K A R f − ( K A K F ) / T F E f d + K A ( V ref − V ) T A (1) All synchronous generators are supported by respective automatic voltage controls (AVRs), using the IEEE-Type I excitation standard [[27], [28]]. Kron's reduction is applied to include all machines as current injection sources in the power system network [[28]]. Novel mathematical modelling of a DFIG is performed using a group of differential algebraic state equations, as given below: V d q s = − R s I d q s + 1 ω s d ( − X s I d q s − X m I d q r ) d t + j ( − X s I d q s − X m I d q r ) ⏟ ψ d q s (2) V d q r = − R r I d q r + 1 ω s d ( − X r I d q r − X m I d q s ) d t + j s ( − X r I d q r − X m I d q s ) ⏟ ψ d q r (3) M d ω r d t = ( ω s ω r ) P m − P s (4) The stator transients just like grid transients are classified as high frequency changes unnecessarily complicate the model study. Inclusion of such terms would call for minute integral steps to picture the dynamics fully [[29]]. As such transients are irrelevant in DFIG model based stablility studies, these are ignored and a third-order system is arrived at. Neglecting the stator transients (i.e. the differential terms entirely in (2)–(3)) to obtain a simpler state-space representation, and the simultaneous solution of the above three equations, we get E d . = 1 T o [ − X s X ′ E d + s ω s T o E q + X s − X ′ X ′ V d s − T o ω s X m X r V q r ](5) E q . = 1 T o [ − X s X ′ E q − s ω s T o E d + X s − X ′ X ′ V q s + T o ω s X m X r V d r ](6) I d r . = 1 T o [ − X s X ′ I d r + s ω s T o I q r ] − X s X ′ X m ω s [ − − s ( X s − X ′ ) X s V d s + X m X r V d r ] (7) I q r . = 1 T o [ − X s X ′ I q r − s ω s T o I d r ] − X s X ′ X m ω s [ − − s ( X s − X ′ ) X s V q s + X m X r V q r ] (8) As a simplified representation, the DFIG's stator is expressed as a reactance X' behind emf E X ′ = X s − X m 2 X r In terms of the stator voltage and current, transient emf, E can be penned down as E d s E q s = V d s V q s + 0 X m 2 − X m X s X r X r − X m 2 − X m X s X r X r 0 I d s I q s (9) For detailed dynamic modelling of wind turbine aerodynamics and DFIG integration with the multi-machine WSCC, the reader is referred to [[29], [30]]. A reoriented wind farm integrated MATLAB/Simulink model is developed for the exemplar WSCC as shown in Fig. 1. Notably, the re-orientations in the prototype WSCC are as follows: (1) To facilitate a 50 MW share of renewable power, a DFIG run wind plant is placed at the 4th bus. Fig. 1Open in figure viewerPowerPoint Re-oriented test system (2) The load of the system is also randomly increased by 50 MW at the 7th bus to match the generation-demand curve. (3) A 60 MW GESD is connected at the third bus of the network. All basic details about the benchmark WSCC can be found in [[28], [30]]. 2.2 GESD modelling A compact ESD model is developed and proposed for dynamic and stability pre-requisite conditions in terms of frequency and voltage regulation. Separate active and reactive power loops translate rate of change of frequency (RoCoF) and voltage errors using two distinct control strategies. To account for an immediate influence on frequency deviation reduction when a transient strikes the system, an intrinsic frequency-active power coupling is endorsed [[31]]. It not only supervises the frequency of the centre of inertia of the network machines but the dc link connecting the storage side converter and grid side converter is also monitored for a ripple free voltage profile [[32]]. Phase locked loop dynamics is also incorporated to contemplate the measurement delays. With second-order dynamics, it assures appropriate synchronisation between the converter and the grid [[33]]. To render the system stable, especially when a contingency strikes any node/machine of the network, the inclusion of an ESD prevents the machines from accelerating by offering immediate relief through voltage recovery as an effective fault ride through support. This is facilitated by the voltage regulation loop of the GESD, which prevents the generators in drawing huge reactive VAR's from the grid. However, the dc link voltage of the power conditioning support system is rendered smooth using a simple error regulating loop (PI controlled, in this paper), in simultaneous supervision with the active power exchange control. Mathematically C link V dclink d t = [ I grid − P gesd V dclink ](10) Primarily, the dc link capacitor design intends to fulfil either of the two objectives: (1) Ripple curtailment due to fast switching (2) Providing a short circuit ride over ability To sustain a short circuit voltage sag, a good t C dc design entails a support of atleast half a cycle ( t half ), for cent percentage of dip. Mathematically, the steady-state dc voltage is assumed as the rated value. The relation between the converter rated power ( P conv ), dc link capacitance ( t C dc ) and the steady state voltage V dcnom ) can be ascertained as P conv t half = 1 2 C dc ( V dc nom 2 − V dc min 2 )(11) Here, V dcmin is the voltage reached by the capacitor, at which the converter operation is stopped. As a magnetic ESS, an SMES absorbs/delivers real power to (or from) the network, depending on the voltage applied across the magnetic coil. It is a dc current driven device, in which the duty ratio determines the nature of the applied voltage (positive/negative) across the coil. By virtue of a substantial power conditioning support, which comprises of a voltage source converter and a two-quadrant dc–dc chopper, it also ensures a bidirectional reactive and active power control, respectively [[28]]. Typically, as a source/sink of huge power bursts, an SMES is characterised by a significantly low discharge time ( <80 s). A typical model of an SMES system can be seen in Fig. 2a. It comprises an inner loop dynamics, which encompasses a duty ratio determining chopper action and the magnetic coil voltage scenario. Mathematically 2 0.5 + I dc − dc I dcsmes ⏟ Duty ratio (D) − 1 V dclink = L smes d I dcsmes d t (12) To maintain an effectively longer time span of the power conditioning support, the dc link voltage is also monitored to yield a smooth link voltage profile I dc − dc + C link d V dclink d t = I grid (13) Fig. 2Open in figure viewerPowerPoint Inner loop dynamics (a) SMES, (b) FESS, (c) UbESS Time and again, flywheels have been reported in power system literature to mitigate frequency issues, voltage sags and to ensure power levelling. A flywheel ESS (FESS) employs a spinning disc mechanism to exchange energy with the connecting grid. Its power conditioning support consists of cascaded converters, interfacing the grid with the flywheel through a machine connected dc link [[30]]. The active power regulation performed by the FESS is facilitated by the machine side converter, which modulates the charging/discharging of the unit by enabling the machine to act in motor/generator mode with speed up or deceleration of the rotor. The instantaneous permanent magnet machine action is given in (14), which is the steady-state reduction of an equivalent machine-flywheel single mass model [[34]]. The flywheel inner loop modelling equations can be deduced from Fig. 2b. 2 H fess = d ω r fess d t = T e fess (14) By supervising the FESS current share ( I fess ) and the grid injected current ( I grid ), the power exchange through the link is governed C link d V dclink d t + P fess V dclink = I grid (15) An ultrabattery ESS (UbESS) on the other hand is an amalgamation of the technologies of lead acid battery and supercapacitor, sharing a mutual electrolyte. A dc–dc converter controlled UbESS is linked to the network through a voltage source converter and transformer assembly. The UbESS model is developed using the following set of equations [[35]] (see Fig. 2c): L d I U b d t = V C U b − V U b (16) [ 1 R bat + 1 R uc ] V U b − I U b = V e q R bat + V bat R bat + V uc R uc (17) C bat d V bat d t + V bat ( 1 R bat + 1 R s d ) = V U b R bat − V e q R bat (18) C uc d V uc d t = V U b R uc − V uc R uc (19) C e q d V e q d t + V e q 1 R bat = V U b R bat − V bat R bat (20) Here, all capacitances and resistances of the battery and ultracapacitor are considered as lumped parameters. 3 Parametric fuzzy predictive control Parametric fuzzy predictive control as the name suggests is a selective combination of predictive and fuzzy approaches. The parameters are explicitly obtained with reduced computational effort and less memory requirement. Predictive step ahead control (PSAC) is designed and applied for real power modulation of GESD and heuristic FLC (HFLC) caters to Volt-Var control (or reactive power modulation). Fig. 3 gives the control architecture of a GESD being run using PFPC. Apropos comments are included while detailing the control. Fig. 3Open in figure viewerPowerPoint GESD parametric fuzzy predictive control (a) PFPC control architecture depicting reactive and active power control of GESD, (b) GESD compact model with inner loop dynamics appoximated by a first-order delay and PI control based dc link voltage regulation 3.1 Heuristic fuzzy logic control The attempt is to relax the constraints of conventional fuzzy logic application, by allowing an intelligent control method by using an evolutionary algorithm to optimally dispatch the fuzzy template. Genetic algorithms (GAs) are particularly suited to problems with variables, either integer valued or continuous, being constrained within some upper and lower thresholds. Also, the ability of GAs to surf the search paradigm in parallels, without any requirement of the optimisation function to be differentiable or smooth, makes it the most amenable option for our problem [[36]]. A custom GA function is coordinated with mixed integer programming, employing intcon as the integer constrained vector prompt. In this study, the problem is set up and defined in MATLAB. Standard fuzzy template is obtained using mixed integer programming based mathematics, which is optimally tuned using GA. The target lies in establishing the component values for the control strategy to yield a structured approach for the fuzzy controller. Practically, infinite possible outcomes of chromosome strings carrying encoded fuzzy information are possible which may vary with the variations in the system operating state. The target is to find the best values of the bits in the chromosome array/string to accord all-inclusive favourable results matching the steady-state values. In an optimisation sense, it is attempted to minimise the height of the area under the curve of an integral squared quantity. As it is, an integer constrained optimisation problem comes at hand, because the fuzzy rule base features crisp quantified levels, emanating from a pre-defined universe of discourse. However, the other share of the string is clearly not integer constrained due to the flexibility granted to membership function spreads as well as the series aligned fuzzy weights. Thence, a mixed integer constrained chromosome string is to be tackled to yield an optimised fuzzy template [[37]]. A few points worth noting here are, (1) The absence of non-linear and linear equality constraints in the problem facilitates mixed integer optimisation, as the equality and integer constraints cannot co-exist for mixed integer programming. (2) A dichotomy exists between the fitness and penalty function concerning the non-feasibility of the search variables based on integer constraints, in which case the penalty function retains the value of the highest fitness function among the search variables of the population. The dichotomy seizes if and only if the search variable is feasible [[37]]. (3) Tightly binding the upper and lower thresholds, for all the search variables so as to reduce the heuristic search space and quick convergence of GA. (4) The integer constraints of the mixed integer optimisation are met by GA built creation, crossover and mutation. An encoded chromosome string is designed with the chromosome apices representing the input as well as output membership spread, symmetric fuzzy logic rules and series fuzzy weights. A compact chromosome string template is designed using six membership value bits (four inputs, two outputs) and 13 mirror image logic rules. In this study, symmetric trapezoidal membership functions are chosen as fuzzy system inputs, while symmetric singletons are designated as output membership spreads. This is primarily done to restrict the chromosome string to a smaller order of 19. A triangular cum trapezoidal symmetric membership function is characterised by five distinct nodes as [( −b, −a, 0, a, b); ( −d, −c, 0, c, d)] for the two inputs. Similarly, the output singletons are classified along ( −f, −e, 0, e, f) as crisp locus points. In this work, a medium sized universe of discourse for all input/output selections is adhered to and classified under five labels, viz., negative big (NB), negative (N), zero (Z), positive (P) and positive big (PB). The linguistic labels NB, N, Z, P, PB are operated as 1, 2, 3, 4 and 5, respectively, in numerical denominations (see Fig. 4a). These 5 × 5 rules are split symmetrically along the mid-locus as mirror images, thereby reducing the length of the encoded string to 13 only. Fig. 4b illustrates the chromosome structure chosen as the design template. Fig. 4Open in figure viewerPowerPoint HFLC organization (a) Input–output fuzzy mapping template, (b) Fuzzy chromosome structure First the designing summons certain bounds on each of the template variables. Our variables will be the indices for the fuzzy rule base vector, hence fixing the lower bound always to 1 (i.e. the lowest possible index for the vectors). The upper bounds at the same time shall be the length of the available bit options. As we are interested in a symmetric rule base, a mirror image segregation shall create a space for 13 possible rule loci, out of a spectrum of 25 distinct options. Clearly, each of the first 13 entries of the vector shall have the upper bounds set to 5 and are constrained to have integer values, due to the available options from the universe of discourse. The other sections of the vector however, enjoy all real values, defined within realistic upper and lower bounds. The cost function is chosen as a convenient modification of the integral squared errors (ISEs) of the frequency of centre of inertia and the storage