Reactive Power Reserve Assessment Scheme Considering Stochastic Wind Power Generation

10th IFAC Symposium on Control of Power and Energy Systems 10th IFAC Symposium on 4-6, Control Tokyo, Japan, September 2018of Power and Energy Systems Available www.sciencedirect.com Tokyo, Japan, September 2018of Power 10th IFAC Symposium on 4-6, Control andonline EnergyatSystems 10th IFAC Symposium on 4-6, Control Tokyo, Japan, September 2018of Power and Energy Systems Tokyo, Japan, September 4-6, 2018

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IFAC PapersOnLine 51-28 (2018) 492–497

Reactive Reactive Power Power Reserve Reserve Assessment Assessment Scheme Scheme Considering Considering Stochastic Stochastic Wind Wind Power Power Reactive Power Reserve Assessment Scheme Considering Stochastic Wind Generation Generation Reactive Power Reserve Assessment Scheme Considering Stochastic Wind Power Power Generation ` ` Generation E. E. El-Araby* E. E. El-Araby* ``Naoto Naoto Yorino** Yorino** E. E. El-Araby*  Naoto Yorino** E. E. El-Araby* Naoto Yorino** ** Department Port  Department of of Electrical Electrical Engineering, Engineering, Port Said Said University, University, Port Port Said, Said, Egypt Egypt  (Tel: 20-66-3426172; e-mail: [email protected]). * Department of Electrical Engineering, Port Said University, Port Said, Egypt (Tel: 20-66-3426172; e-mail: [email protected]). * Department of Engineering, Port Said University, University, Hiroshima, Port Said, Egypt ** Department ofElectrical System Cybernetics, Hiroshima Japan (Tel: 20-66-3426172; e-mail: [email protected]). ** Department of System Cybernetics, Hiroshima University, Hiroshima, Japan (Tel: 20-66-3426172; e-mail: [email protected]). (e-mail: [email protected]) ** Department of System Cybernetics, Hiroshima University, Hiroshima, Japan (e-mail: [email protected]) ** Department of System Cybernetics, Hiroshima University, Hiroshima, Japan (e-mail: [email protected]) Abstract: This paper presents a(e-mail: reactive power “VAR” reserve assessment tool considering the extended [email protected]) Abstract: This paper presents a reactive power “VAR” reserve assessment tool considering the extended

capability curvepaper of the doubly fed induction generator (DFIG) based tool windconsidering farm. Thethe problem is Abstract: This presents a reactive power “VAR” reserve assessment extended capability curvepaper of the doubly fed induction generator (DFIG) based tool windconsidering farm. Thethe problem is Abstract: This presents areserve reactive poweris“VAR” reserve assessment extended formulated such that the VAR amount determined taking into account the wind power forecast capability curve of the VAR doubly fed induction generator (DFIG) based wind the farm. The problem is formulated such that reserve amount is determined taking into account wind power forecast capability curve of their the doubly fed induction generator (DFIG) based wind farm. The disturbance. problem is errors by addressing possible scenarios both the base caseinto andaccount a presumed severe formulated such that the VAR reserve amountfor is determined taking the wind power forecast errors by addressing their possible scenarios for both the base case and a presumed severe disturbance. formulated such that the reserve amount is determined taking into account the wind three powerobjective forecast The is stated as VAR an optimization problem, aiming to optimize errorsmodel by addressing scenarios for both the base case and asimultaneously presumed severe disturbance. The is stated their as anpossible optimization problem, aiming to optimize three objective errorsmodel by addressing their possible scenarios for both thecost base case and asimultaneously presumed severe disturbance. functions representing the expected values of the energy corresponding to the base case, corrective The modelrepresenting is stated astheanexpected optimization aiming optimize simultaneously three corrective objective functions valuesproblem, of the energy costto to the base case, The model is stated an severe optimization problem, aiming tocorresponding optimizefrom simultaneously three objective control cost under the as most contingency, the VAR reserve the committed conventional functions representing the expected values of theand energy cost corresponding to the base case, corrective control cost under the most severe contingency, and the VAR reserve from the committed conventional functions representing theThe expected values of function the energy cost corresponding to the base case, corrective synchronous generators. total objective is achieved while satisfying, for each addressed control cost under the most and the reserve from the committed conventional synchronous generators. Thesevere total contingency, objective function is VAR achieved while satisfying, for each addressed control under the most severe contingency, and the VAR from the committed conventional scenario,cost a set of operating constraints including explicitly thereserve probable active power output of DFIG synchronous generators. The total objective function is achieved while satisfying, for each addressed scenario, a set of operating constraints including explicitly the probable active power output of DFIG synchronous generators. TheVAR totalcapability objective limits function is achieved while satisfying, for each addressed wind turbine and its relevant as well as voltage stability margin. scenario, a set ofitsoperating constraints including explicitly the probable active power output of DFIG wind turbine and relevant VAR capability limits as well as voltage stability margin. scenario, a set of operating constraints including explicitly the probable active power output of DFIG wind turbine and its relevant VARerrors, capability limits as wellDFIG asHosting voltage © 2018, IFAC (International Federation of voltage Automatic Control) Elseviermargin. Ltd. All rights reserved. Keywords: VAR reserve, forecast security, windbystability generator, capability curve. wind turbine and its relevant VARerrors, capability limits as wellDFIG as voltage margin. Keywords: VAR reserve, forecast voltage security, wind stability generator, capability curve. Keywords: VAR reserve, forecast errors, voltage security, DFIG wind generator, capability curve.  Keywords: VAR reserve, forecast errors, voltage security, DFIG wind generator, capability curve.  conventional synchronous generator (Lund et al. (2007)). The  conventional synchronous generator (Lund et al. (2007)). The 1. INTRODUCTION  current practice in many generator utilities imposes wind farmsThe to 1. INTRODUCTION conventional synchronous (Lund et al. (2007)). current practice in many generator utilities imposes wind farmsThe to 1. INTRODUCTION conventional synchronous (Lund et al. (2007)). regulate the power factor within a specified range (0.95 Because of the continuous evolution of the load demand and practice in many utilities imposes wind farms to 1. INTRODUCTION regulate the power factor within a specified range (0.95 Because of the continuous evolution of the load demand and current current practice in many thereby utilities the imposes wind farms to leading tothe0.95 lagging), benefit of the extra the tied of allocated investment of transmission, many power regulate power factor within a specified range (0.95 Because the continuous evolution of the load demand and leading lagging), thereby the benefit of the (0.95 extra the tied of allocated investment of transmission, many power regulate to the0.95 power factor within curve a specified range Because the continuous evolution ofunder the load demand and reactive power of the capability of DFIG units is system grids all over the world operate heavily stressed leading to 0.95 of lagging), thereby curve the benefit of the extra the tiedgrids allocated investment transmission, manystressed power reactive power the capability of DFIG units is system all over the world of operate under heavily leading to 0.95Several lagging), thereby the benefit of the extra the tied allocated investment of transmission, many power underutilized. researchers have investigated the conditions. This situation raises considerably the effective reactive power Several of the capability curve ofinvestigated DFIG unitsthe is system gridsThis all over the world operate under heavily stressed underutilized. researchers have conditions. situation raises considerably the effective of the capability of DFIG is system allreactive over the power world operate under stressed impact ofpower the Several extended capabilitycurve curve DFIG units on the role ofgrids theThis in heavily power system reactive underutilized. researchers have of investigated conditions. situation raisesreserve considerably the effective impact of the extended capability curve of DFIG on the role of the reactive power reserve in power system underutilized. Several researchers have investigated the conditions. This situation raises considerably theagainst effective power system operation (Konopinski et al. (2009)). The operational planning in safeguarding the system the impact system of the extended curve on The the role of theplanning reactivein safeguarding power reserve power system operation capability (Konopinski et of al. DFIG (2009)). operational the in system against the power impact of of these the extended capability curve of DFIG on the role of the reactiveinstability power that reserve in power system works demonstrate that occurrence of voltage could emerge following power of system operation (Konopinski etthe al.unutilized (2009)). extra The operational planning in safeguarding the system against the results results these works demonstrate that the unutilized extra occurrence of voltage instability that could emerge following power system operation (Konopinski et in al. enhancing (2009)). The operational planning in safeguarding the system against of DFIG units isthat vital the critical disturbances. an adequate amount of the reactive ofcapacity these works demonstrate occurrence of voltage Preserving instability that could emerge following reactive of DFIG units isthat vitalthe inunutilized enhancingextra the critical disturbances. Preserving an adequate amount of the results results system ofcapacity theseperformance. works demonstrate the unutilized extra occurrence of voltage instability that could emerge following power The extended capability curve of reactive power reserve to immediately be employed in this capacity of DFIG The unitsextended is vital capability in enhancing the critical disturbances. Preserving an adequate amount in of this the reactive power system performance. curve of reactive power reserve to immediately be employed reactivecancapacity of DFIG units is reserve vital inproblem enhancing the critical disturbances. Preserving an adequate amount of the DFIG be exploited in the VAR since it emergency events to keep the voltage security is one power system performance. The extended capability curve of reactive power reserve to immediately be employed in this DFIG can be exploited in the VAR reserve problem since it emergency events to keep the voltage security is one of the power system performance. Thefast extended capability curve of reactive power reserve to immediately bebyemployed in this mainly relies on the available dynamic VAR sources in primary duties that must be satisfied power system DFIG can be on exploited in the VAR reserve problem since in it emergency eventsthat to keep the voltage security is onesystem of the mainly relies the available fast dynamic VAR sources primary duties must be satisfied by power DFIG can beTherefore, exploited this in the VAR reserve problem since it emergency events to keep the voltage is one of system. paper focused on developing operators.duties Various research havesecurity been in the the mainly reliesTherefore, on the available fastis dynamic VAR sources inaa primary that must studies be satisfied by proposed power system the system. this paper is focused on developing operators. Various research studies have been proposed in the mainlyformulation relies on thethat available fast dynamic VAR the sources in primary duties that must be satisfied by power properly incorporate DFIG literatures to quantify the studies required of thesystem VAR the system. Therefore, paper is focused on developing operators. Various research haveamount been proposed the new new formulation thatthis properly incorporate the DFIGaa literatures to quantify the studies required amount of the in VAR the system. Therefore, this paper is focused on developing operators. Various research have been proposed in the curve intothat the conventional VAR reserve reserve in real time operation and planning stageof(Choi et al. capability new formulation properly incorporate theproblem DFIG literatures to quantify the required amount the VAR curve intothat the conventional VAR reserve problem reserve in real time operation and planning stageof(Choi et al. capability new formulation properly incorporate the DFIG literatures to quantify the required amount the VAR to examine its effect on the system security and operating (2013)). They have commonly (2011), Leonardi and Ajjarapu capability curve into the conventional VAR reserve problem reserve in real time operation and planning stage (Choi et al. to examine its effect on the system security and operating (2013)). They have commonly (2011), Leonardi and Ajjarapu capability curve into the conventional VAR reserve problem reserve in real time operation andthe planning stage (Choi et the al. costs. emphasized the crucial role of VAR reserve from to examine its effect on the system security and operating Theyreserve have commonly (2011), Leonardi and Ajjarapu emphasized the crucial role of(2013)). the VAR from the costs. to examine its effect on the system security and operating (2013)). have commonly (2011), Leonardi and Ajjarapu conventional synchronous generators in They protecting the system costs. emphasized the crucial role of the VAR reserve from the conventional synchronous generators in protecting the system emphasized the crucial role of thetheVAR reserve from the costs. The paper aims to develop a VAR reserve assessment against voltage collapse. Although power system utilities conventional synchronous generators protecting the utilities system The present present paper aims to develop a VAR reserve assessment against voltage collapse. Although thein power system conventional synchronous generators inpower protecting the system The and management considers the capability curve of have increased the level of the wind to a significant paper tool aimsthat to develop a VAR reserve assessment against voltage collapse. the power power system utilities and present management tool that considers the capability curve of have increased the level Although of the wind a significant assessment The present paper aimsThe to develop a VAR reserve against voltage collapse. Although the power to system utilities the DFIG wind farm. active power of the DFIG and its value, the impact of the large-scale integration of wind power and management tool The that active considers theofcapability curve of have increased the level of the wind power toofawind significant the DFIG wind farm. power the DFIG and its value, the impact of the large-scale integration power and management tool that considers the capability curve of have increased the level of the wind power to a significant relevant reactive power limits defined by its capability curve on the VAR reserve problem has been rarely investigated in the DFIGreactive wind farm. The active power ofitsthe DFIG and its value, the impact of the large-scale integration of wind power relevant power limits defined by capability curve on the VAR reserve problem has been rarely investigated in the DFIG wind farm. The active power of the DFIG and its value, the impact of the large-scale integration of wind power been incorporated mathematical formulation of the previous publications. Thehasvariable-speed wind turbine relevant reactive power into limitsthe defined by its capability curve on the VAR reserve problem been rarely investigated in have have been incorporated into mathematical formulation of the previous publications. Thehasvariable-speed wind turbine relevant reactive power limitsthe defined by its capability curve on the VAR reserve problem been generators rarely investigated in the VAR reserve assessment tool developed by the authors’ equipped with doubly fed induction (DFIG) is haveVAR beenreserve incorporated into the mathematical formulation of the previous publications. The variable-speed wind turbine the assessment tool developed by the authors’ equipped with doubly fed induction generators (DFIG) is have beenwork incorporated into mathematical of the previous most publications. The variable-speed windinstalled turbine the currently common turbine technology ((2018)) .formulation The (El-Araby andthe Yorino VAR work reserve assessment tool developed by theuncertain authors’ equipped the with doubly fed wind induction generators (DFIG) is previous currently the most common wind turbine technology installed )) previous (El-Araby and Yorino 2018 . The uncertain VAR reserve assessment tool developed by the authors’ equipped with doubly fed induction generators (DFIG) is the in system. The feature of this type of wind turbine is its nature of work the wind power and output has been intouncertain account currently mostfeature common turbine installed (2018taken )). The (El-Araby Yorino in system.the The of wind this type of technology wind turbine is its previous nature of work the wind power and output has been taken intouncertain account currently mostand common wind turbine technology installed ability to the rapidly continuously control the reactive power ( 2018 )) . The previous (El-Araby Yorino by considering the possible outcomes “scenarios representing in system. The feature of this type of wind turbine is its ability to rapidly and continuously control the reactive power nature of the wind power output has been taken into account by considering the possible outcomes “scenarios representing in system.theTheintegration feature of of thispower-electronic type of wind turbine is its nature through converters. of power the wind powererrors” outputgenerated has been taken into of account wind forecast by means Latin ability to rapidly and continuously control the reactive power the through the integration of power-electronic converters. by considering the possible outcomes “scenarios representing the wind power forecast errors” generated by means of Latin ability to rapidly and continuously control thepenetration reactive power Therefore, the potential impact of high wind level by considering the possible outcomes “scenarios representing hypercube sampling (LHS) technique. The proposed through the integration of of power-electronic converters. Therefore, the potential impact high wind penetration level the wind power forecast errors” generated by means of Latin hypercube sampling (LHS) technique. The proposed through thereserve integration ofshould power-electronic converters. on the VAR problem be wind thoroughly addressed. the wind power forecast errors” generated by means of is deemed as an operational planning toolproposed thatLatin can Therefore, the potential impact of high penetration level approach on the VAR reserve problem should be thoroughly addressed. hypercube sampling (LHS) technique. The approach is deemed as an operational planning toolproposed that can Therefore, the potential impact of high wind penetration level The capability curve (PQ diagram) of DFIG turbine can be hypercube sampling (LHS) technique. The be used off line (hours ahead) to concurrently optimize the on the VAR reserve should be addressed. The capability curveproblem (PQ diagram) of thoroughly DFIG turbine can be be approach is line deemed as an operational planning tool that can used off (hours ahead) to concurrently optimize the on the VAR reserve problem should be thoroughly addressed. represented similarly as the one typically used for the approach is deemed as an operational planning tool that can The capability curve (PQ DFIG turbine can the be represented similarly as diagram) the one of typically used for used off line (hours ahead) to concurrently optimize the The capability curve (PQ diagram) of DFIG turbine can be be represented similarly as the one typically used for the be used off line (hours ahead) to concurrently optimize the 2405-8963 © IFAC (International of Automatic represented similarly as the oneFederation typically used for Control) the 492Hosting by Elsevier Ltd. All rights reserved. Copyright © 2018, 2018 IFAC Copyright 2018 responsibility IFAC 492Control. Peer review©under of International Federation of Automatic 10.1016/j.ifacol.2018.11.751 Copyright © 2018 IFAC 492 Copyright © 2018 IFAC 492

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expected energy losses at the base case and guarantee that the amount of the VAR reserves is sufficient to maintain system voltage security under a severe disturbance. All the VAR control devices including DFIG VAR outputs are effectively applied in the anticipated normal state to ensure economical utilization of these devices in minimizing the energy losses. The uncertain VAR output of the DFIG turbine, synchronous condensers, conventional generators reactive power reserves and load shedding are used in post contingency state to ensure that the voltage stability margins are satisfied at a minimum control cost, even if the VAR reserve is insufficient. The participation of each generator on the reactive power reserve is determined using the sensitivity of the voltage stability margin with respect to the generator VAR output to reflect its worthy in maintaining voltage stability margin. As the problem formulation includes several simulated scenarios at the base case and corrective state, the problem size is considered very large to be solved straightforwardly by the classical methods. Therefore, a hybrid method based on particle swarm optimization (PSO) and conventional method is employed to solve the problem.

max maximum VAR ( Qgi ) of the generator minus its VAR

b output ( Qgi ) employed at the base case as shown in Fig.1. max b Qgi res  (Qgi  Qgi ) 

The DFIG is generally employed in variable-speed wind turbines. It is interconnected to the grid through powerelectronic converter that enables the DFIG turbines to adjust the net reactive power output, so as to control the terminal voltage or to satisfy a desired certain power factor. The net real power supplied to the grid can be approximately stated as a function of the slip of the machine and stator active power while its associated delivered net reactive power is approximately equal to the stator reactive power. The detailed explanation of the fundamental steady state equations characterizing the relationship of the rotor and stator voltages and currents as well as the net power delivered to the grid are given in (Lund et al. (2007)). These equations have been exploited to derive a set of steady-state equations that model the PQ capability curve of DFIG turbine, which is identical to the conventional synchronous generators. The derived capability curve denoted that when the wind turbine operates below its rated power, it provides considerable additional VAR support over the conventionally specified power factor range. As the wind plants are expected to operate most of the time below its rated power, the available additional VAR could be fully utilized to enhance power system performance. Since the present mandatory provisions in many utilities for the grid interconnection compel wind farms to keep power factor within the range of 0.95 leading to 0.95 lagging, significant extra VAR output of the wind plants in this operation is extremely unutilized. The operation of DFIG turbine over the mandated power factor limits at no additional converter costs has been confirmed in (Konopinski et al. (2009)). It has been demonstrated that, when the capability curve of DFIG parks are implemented and fully utilized, the extra VAR output of the turbine impacts significantly the system costs, reduces the amount of committed conventional reactive reserve and improves voltage security following large disturbances. These results encourage the authors to reformulate the VAR reserve problem incorporating DFIG capability curve in order to examine its effect on the required VAR reserve amount and total operating costs that essentially rely on all the available VAR sources in the system.

The amount of the remained VAR of the conventional synchronous generators at the base case affects considerably the occurrence of voltage collapse that could be taken place following sudden serious outages. Consequently, preserving adequate amount of VAR reserve from the most worthy dynamic VAR sources is indispensable to appropriately and quickly adjust their VAR outputs for keeping voltage stability. The well-known PQ capability curve shown in Fig. 1 is usually used to clarify the conventional generator’s VAR reserve. The maximum reactive power Qgmax can be determined according to its active power dispatch Pgsch using (1). Rotor limit

Qgmax

Turbine limit

Pgsch

Armature limit

Qgb

PR

Pg (MW )

Stator limit

Fig.1 Generator capability curve

max 2 Qg ( Pgsch )  Vg /

Xs 

Vg2 I 2f max X s2

(2)

3. DFIG WIND TURBINE MODEL

2. FUNDEMANTALS OF VAR RESERVES

Qg (MVAR)

493

3.1 Analysis of Wind Power Forecast Errors 2  Pgsch

, Pgsch  PR

As the wind power cannot be accurately anticipated, the prospective errors associated with the current existing forecasted tools have be taken into consideration in the proposed model. To realize the expected errors of a specific forecasted value of wind power, normal distribution has been commonly used in the literatures. In this paper, the wind power is assumed to comply with the normal distribution

(1)

Where Vg is the generator terminal voltage, X s is the synchronous reactance, PR is the generator’s rated active power, I f max is the maximum field current.

N (  ,  2 ) with an expected value  and standard deviation  standing for its volatility. The Latin hypercube sampling (LHS) method is selected to produce multiple scenarios by

For a given active power schedule, the technical VAR reserve of generator i ( Qgi res ) is defined by (2) which is equal to the 

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discretizing of the continuously normal distribution shape of wind power forecast errors (Wang et al. (2008)). Each scenario stands for a random output of wind power and is given a particular probability value. LHS technique has been validated to be more accurate than simple Monte Carlo simulation. In general, in order to accurately represent the uncertainties, the number of generated scenarios will be very large affecting the computation time of the simulation. Thus due to computational burden and time limitation, scenario reduction techniques are usually applied to select a reduce number of scenarios so that the relative distance between the original ones and selected-scenarios is within predefined limit (Dupacova et al (2003)).

Where subscripts b, c, s refer to the base case, contingency state, and scenario number respectively. s=(1,2…,ns) stands for the generated scenarios. Eloss is the base case energy losses, Fcont is the corrective control cost, Qg is the VAR output of generator g, Qg is the generator VAR output at the nose point for the addressed contingency, Psh is the load shedding value at load bus i associated with the contingency state , Cm is the reactive power corresponding to FACTS device m,  b is the occurrence probability corresponding to the base case,  c is the occurrence probability of the examined contingency,  s is the probability of scenario s,

4. PROPOSED METHOD This section is devoted to reformulate the VAR reserve problem so as to take into account the capability curve of DFIG wind farm. First, we suppose that the forecasted active power of a wind park is provided by any of the existing forecasted tool. Then, in order to consider the variability of wind power output, the above LHS technique is used to generate a set of discrete values of active power with their corresponding probabilities. The VAR limits associated with each discrete value is then determined using the capability curve as formulated in (Lund et al. (2007)). The obtained discrete values of active power and VAR limits with the corresponding probabilities are incorporated into the VAR reserve problem, and consequently, enabling the assessment of VAR reserve and operating cost in the presence of extended capability curve of DFIG. The prime goal in the proposed formulation is assumed to simultaneously optimize three objective functions, specifically, minimizing the expected values of the energy cost corresponding to the normal state and corrective control cost under the most sever contingency as well as maximizing the expected value of the VAR reserve from the committed conventional synchronous generators. The goal is supposed to be achieved while satisfying, for each addressed state, a set of the equality and inequality constraints representing load flow equations and physical limits of the system variables. The objective function and the operating constraints have been stated to consider all the generated scenarios relevant to forecasted wind power output. The active power and its reactive power limits “determined based on the capability curve of DFIG” have been incorporated into the equality and inequality constraints. This treatment increases substantially the size of the problem, which becomes very large to be solved straightforwardly by the conventional methods. The objective function is chosen to minimize the following:

Ftotal  F1  F2  F3

s 1

m , are the weighting factors of energy loss, VAR reserve, generator VAR control, load shedding and VAR control of FACTS devices respectively, ns is the number of investigated scenarios, ng is the number of the generators, nsh is the number load buses assigned for load shedding and mc is the number of FACTS devices. The first objective function F1 in (3) represents the expected energy loss cost. The second objective F2 stands for the expected costs relevant to the readjustment of the fast VAR devices and load shedding required to maintain the voltage stability margin following the investigated severe contingency. The third objective F3 represents the expected cost of effective reactive power reserve of the conventional generators considering their relative effect of voltage stability margin after contingency. All the expected costs are evaluated for all the generated scenarios standing for the forecasted errors of the wind park. Note that the objective function F3 excludes the reserve amount of the DFIG wind turbine since its value is uncertain. The impact of the supplied VAR of the wind turbine is considered in the problem constraints and in turn will affect the reserve amount from the controlled dynamic VAR sources. Consequently, the aforementioned objective function is selected so that the amount of the generators VAR reserve is provided only from the committed conventional synchronous generators. The total objective function has been built so that the VAR reserve amount can be rationally obtained satisfying simultaneously the minimum expected energy loss cost and control cost while guaranteeing the desired security level following the addressed severe outage. This handling encloses that the excessive VAR reserve for the conservative system security is avoided and its value is decided properly taking into account not only the system security, but also its influences on the expected operating costs. In order to simulate the real system conditions, we suppose that each generator will proportionally contribute on the total VAR reserve reflecting its relative worth on the voltage stability margin, where the participation factor’ value of each committed generator will be varied with the system

ns

b, s F1  we *  b   s Eloss ,

F3   c * wg 

scenario s under the contingency state , we , wg ,  g , i ,

(3)

ns

s 1 ns

prgc, s is the participation factor of generator gi relevant to

c, s F2   c   s Fcont ,

s

s 1

ng

 prgc,s *(Qgc,s  Qgb,s ) g 1

ng

nsh

mc

g 1

i 1

m 1

c, s c, s c, s b, s Fcont    g Qgc, s  Qgb, s   i Psh ,i   m Cm  Cm

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conditions (El-Araby and Yorino (2018)). The objective function is subjected to a set of operating constraints represent each investigated scenario generated by LHS method for both of the base case and the investigated severe contingency. This implies that, for the base case, we have stated a set of equality and inequality constrains standing for generated scenarios. In same manner, these constraints have been also incorporated into the examined contingency for each studied scenario. As demonstrated in (El-Araby and Yorino (2010)), under the contingency state, the constraints should be identified for both of the nominal load operating point and its corresponding voltage collapse point to explicitly involve the load power margin into the problem formulation for the purpose of keeping its value within the desired level. The constraints can be stated as follows:

mismatch, Psh,i and Qsh ,i are the shedding values of the active and reactive power at load bus i respectively, x is the state variables vector “voltage magnitudes and angles”, u is the control variables vector “ slow and fast VAR devices” excluding the predefined reactive power control parameters of the wind turbine, generators and load shedding, Notation “  ” stands for nose point for each scenario, wl is the left eigenvector “row vector”.

f p,q is power flow Jacobian

“singular at nose point”.  is the load parameter value. 5. SOLUTION ALGORITHIM

1- Base case constraints   b, s b, s b b, s b, s  Qg ,i  Qw,i  Qd ,i  f q,i ( x , u )  0   s=1,2,..., ns  ,  xmin  xb, s  xmax , umin  u b, s  umax   i=1,2,..., nbus   b, s max min b, s max Qwmin ,i  Qw,i  Qw,i , Qg ,i  Qg ,i  Qg ,i   …………………………………………………..(4) 2- Contingency state constraints Pgb,i

495

 Pwb,,is  Pdb,i  f p,i ( xb, s , u b, s )  0

Operating constraints at the nominal load operating point c, s c, s c, s  Pgc,i  Pwc,,is  Pdc,i  Psh ,i  f p ,i ( x , u )  0  c, s c, s c c, s c, s c, s Qg ,i  Qw,i  Qd ,i  Qsh,i  f q,i ( x , u )  0    s=1,2,..., ns  xmin  xc, s  xmax , umin  u c, s  umax  ,  i=1,2,..., nbus     c, s c, s 0  Psh,i  Psh max , 0  Qsh,i  Qsh max  c, s c, s max  max min Qwmin ,i  Qw,i  Qw,i , Qg ,i  Qg ,i  Qg ,i  ……………………………………………………………..(5) Operating constraints at the nose point

The problem described by the objective function (3) and constraints (4-6) is classified as a large-scale highly nonlinear optimization problem. The performance of the classical optimization methods in solving directly this type of problem is inefficient. The decomposition approaches are preferred in this situation since the intact problem can be divided into several smaller problems to be solved eaisly as a stand-alone problems by the available conventional tools. The hybrid methods compromise heuristic techniques and conventional methods have been validated to be very effective in such optimization problems as they have been successfully applied to several challenging problems as the problem at hand. Consequently, this paper presents a hybrid method based on PSO and conventional method to avoid the difficulties associated with the straightforward conventional techniques. Particle 1

S=1 0

S=2

S=2

S=1

S=ns

0

 ns

1

S=ns

 ns

Base case (F1) b

Base case (F1) b





(Slow control )

(Slow control )

Contingency state (F2)  c

Contingency state c (F2) 

VAR reserve (F3)

c, s c, s c, s Pgc,i  Pwc,,is  Pdc,i  Psh )0  ,i  f p ( x , u  c, s c,s c,s  Qgc ,i  Qwc,,si  Qdc ,i  Qsh  f ( x , u )  0 q ,i

Particle n

Particle 2

VAR reserve (F3)

VAR reserve (F3)

Evaluate Particle 1 equation (5),F

Evaluate Particle 2 equation (5),F

VAR reserve (F3)

VAR reserve (F3)

VAR reserve (F3)

Evaluate Particle n equation (5),F

 store best previous positions and global position in a solution set  w( x c, s , u c, s ,  c, s ) f p,q ( x c,s , u c ,s ,  c ,s )  0   s=1,2,..., ns  update velocity and position for each particle  ,  i=1,2,..., nbus  wl  0    next iteration  umin  u c, s  umax ,  c, s  min , Fig.2 Proposed solution algorithm  c, s c, s 0  Psh  ,i  Psh max , 0  Qsh,i  Qsh max The first step of the proposed solution method is to define the c, s max min c, s max  Qwmin  ,i  Qw,i  Qw,i , Qg ,i  Qg ,i  Qg ,i variables that represent candidate solution in the PSO ……………………………………………………………..(6) algorithm. In this paper, the particles of PSO have been Where P is the active power generated at bus i, P is the selected so that their agents are limited solely to generators’ g ,i

d ,i

maximum VAR Qmax p , which in turn makes the search space

active power demand at bus i, Pw ,i and Qw,i are the

significantly small. The computational processes of the developed method are depicted in Fig.2. The proposed algorithm commences with a random swarm consisting of a number of particles, particle 1, particle. 2.,…., particle m, as shown in Fig. 2. Each particle stands for a potential solution,

generated active and reactive power of wind turbine at bus i respectively, f p ,i is the power flow equation at bus i associated with the active power mismatch, f q,i is the power flow equation at bus i associated with the reactive power 495

IFAC CPES 2018 496 Tokyo, Japan, September 4-6, 2018

E.E. El-Araby et al. / IFAC PapersOnLine 51-28 (2018) 492–497

active power and employed VAR limits. The VAR limits indicated in the table stand for both of the regulated power factor range and the limits of the capability curve. The probability of each scenario is also provided in the table. In order to evaluate the developed approach, the base case of the two addressed cases is stressed first to 140 % of the primer load. Then, the most severe contingency has been adopted for the examinations, where the load margin value and bus voltage magnitudes violate pre-specified limits. The following parameters are used for the simulations: vmin=0.90,

i.e., a pattern of generators’ maximum VAR Qmax p . The generated value of each agent Qmax p of the particle stands for the maximum reactive power of generator to be employed at the base case for each generated scenario. Note that, each agent of the particle is limited by the generator VAR production mode, i.e. ( 0  Qmax p  Qgmax ). This candidate pattern is used commonly for each addressed scenario associated with the base case and contingency state. Namely, assume that particle 1 is being evaluated during PSO iteration. This particle will be proceeded to the wind power scenario at the base case where each scenario is solved individually by the conventional method to evaluate the expected energy cost F1 by considering the occurrence

vmax=1.05,

min =0.25,

I f max =2,

X s =0.9,

 c =0.06,

 b =0.94,  gi =1.0, m =1.0, i =10^9, we =10^3, wg = 10^4.

probabilities “  b ,  s ” of both of the base case and individual scenario. Then, based on the results obtained for each scenario at the base case, the same particle “particle 1” is forwarded to all scenarios under the investigated contingency to evaluate the expected control cost F2 taking

Table 1. Wind power scenarios (active power and VAR limits)

into account the probabilities of the contingency  c and each scenario  s . According to the results obtained at the base case and contingency state, the expected effective VAR reserve F3 of the generators taken into consideration their relative impact on voltage stability margin is computed. Finally, the total objective function Ftotal (3) for particle 1 is evaluated. The same computational procedures will be repeated for each particle in the swarm updating the swarm to next iteration. These procedures are repeated till a termination criterion is satisfied.

Table 2. Generators’ maximum VAR and optimal pattern Qmax p Wind power (MW)

Generator number 3 4 5

1

2

0.50

0.69

0.25

2.00

0.09

1.79

regulated pf

0.00

0.69

0.25

2.00

0.09

1.09

Qgmax

6

(20, 50 MW) 20

6. SIMULATION RESULTS In order to validate the performance of developed method, it has been tested on IEEE-57 bus system. In the following simulation, we consider that the system has only one wind farm located at bus 5 with a rated power of 60 MW representing an aggregate multiple DFIG turbines “1.5x40 turbines”, where the technical parameters of 1.5 MW DFIG wind generator are given in (Konopinski et al. (2009)). Two cases has been investigated to demonstrate the impact of the extended capability curve of DFIG on the VAR reserve problem. In case 1, the reactive power output of DFIG wind turbine is assumed to be regulated within the power factor range 0.95 leading to 0.95 lagging, while in case 2, the VAR limits of DFIG capability curve are fully utilized. The two cases have been addressed for two forecasted wind park output levels, namely 20 and 50 MW, respectively. To consider the wind power forecast errors, LHS method is applied to generate 300 scenarios for each investigated forecasted wind power where its output is used as the mean value and 10% of the forecasted power is employed as the standard deviation. To decrease the execution time of the analysis, 10 scenarios standing for the average values of each 30 scenarios are selected to approximately represent the simulated cases. Table 1 shows the respective values (simulated scenarios) of the wind farm outputs in terms of the

50

PQ limits

0.00

0.18

0.25

2.00

0.09

1.09

regulated pf

0.00

0.41

0.25

2.00

0.09

1.09

PQ limits

0.00

0.14

0.25

2.00

0.09

1.09

max Table 2 indicates the maximum reactive power Qgi and the

acquired optimal pattern of the maximum VAR Qmax p for the two wind power levels with the regulated power factor range and the capability curve limits. The table demonstrates that the optimal pattern is almost the same for all generators except generator 2, where its obtained value for the regulated power factor range is higher than the capability curve limits. These results reflect the impact of the extra VAR provided from the wind power park when its capability curve model is utilized as its VAR output has been exploited at the base case and in turn leading to keep more reactive power revere from the conventional reactive power sources. The results of scenario 10 for the forecasted 20 MW wind park output is presented in Table 3. The table indicates the obtained optimal values of the base case generators’ VAR output Qgb as well as the VAR reserve and participation factor corresponding to each generator for both of the regulated power factor and capability curve limits cases. It is 496

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clear that, due to the extra VAR provided in the capability

regulated power factor case, reflecting the substantial impact of exploiting the excessive VAR capacity of DFIG turbine.

b

curve model case, Qg is lower than the regulated power factor case. As presented in the table, for regulated power factor case, the VAR reserve associated with generators 1, 4 and 6 are higher than the reserve amount relevant to the other generators. The obtained results signify that generators 1, 4 and 6 are considered more worthy to be employed at the corrective state to fulfil the required security limits. The significant importance of generators 1, 4 and 6 is confirmed

7. CONCLUSIONS This paper introduces a security-constrained reactive power reserve scheme taking into account the extended reactive capability curve of DFIG wind generator and its output variability. The technique is supposed to be employed as an operational planning tool aiming to maintain the voltage security for the both of base case and the most severe contingency considering the possible scenarios relevant to the forecasted wind power errors. Since the problem is stated as a large scale non-linear programming problem, a hybrid PSO and conventional method is applied to solve the overall problem. The proposed approach has been successfully tested on IEEE 57 bus test system. The obtained results demonstrate the positive impact of the extended DFIG capability curve on the VAR reserve amount required from the conventional sources to maintain the security limits. A remarkable saving in the operating cost has been also achieved compared with the current practice of the regulated power factor range.

by their participation factors “ prgi ” as they are higher compared to generators 2, 3 and 5. The same conclusion can be extracted for the PQ limits case except that the VAR reserve of generator 2 is increased due to the extra power supplied by the wind park. This extra VAR has been fully utilized at the base case, enabling generator 2 to maintain more VAR reserve to be employed at the corrective state. Table 3. VAR reserve and participation factor (scenario 10, 20 MW)

Regulated pf

PQ limits

Generator number 3 4 5

2

0.00

0.69

0.25

1.73

0.09

1.09

0.24

0.08

Qgres

0.5

0.00

0.00

0.37

0.00

0.70

-

-

prg10

0.48

0.06

0.13

0.39

0.05

1.00

-

-

Qgb

0.00

0.18

0.25

1.66

0.09

1.09

0.24

0.40

Qgres

0.5

0.51

0.00

0.44

0.00

0.70

-

-

prg10

0.59

0.44

0.00

0.36

0.04

1.00

-

-

Qgb

6

Wind power P Q

1

REFERENCES Choi, Y. H., Kang, S., and Lee, B. (2011). Justification of Effective Reactive Power Reserves With Respect to a Particular Bus Using Linear Sensitivity. IEEE Transactions on Power Systems, 26 (4), 2118-2124. Leonardi, B. and Ajjarapu, V. (2013). An Approach for Real Time Voltage Stability Margin Control via Reactive Power Reserve Sensitivity. IEEE Transactions on Power Systems, 28 (2), 615-625. Lund, T., Sørensen, P. and Eek, J. (2007). Reactive power capability of a wind turbine with doubly fed induction generator. Wind Energy, 10 (4), 379–394. Konopinski, R.J., Vijayan, P. and Ajjarapu,V. (2009). Extended Reactive Power Capability of DFIG Wind Parks for Enhanced System Performance. IEEE Transactions on Power Systems, 24(3), 1346-1355. El-Araby, E. E. and Yorino, N. (2018). Reactive Power Reserve Management Tool for Voltage Stability Enhancement. Proc. of IET Transaction on Generation, Transmission and Distribution, Available on line, http://digitallibrary.theiet.org/content/journal/10.1049/ietgtd.2017.1356. Wang, J. Shahidehpour, M. and Li, Z. (2008). SecurityConstrained Unit Commitment with Volatile Wind Power Generation. IEEE Transactions on Power Systems, 23 (3), 1319-1327. Dupacova, J., Gröwe-Kuska, N. and Römisch, W. (2003). Scenario Reduction in Stochastic Programming an Approach Using Probability Metrics. Mathematical Programming, Ser. A 95, 493-511. El-Araby, E. E. and Yorino, N. (2010). A hybrid PSO Technique for Procuring VAR Ancillary Service in the Deregulated Electricity Markets. International Journal of Electrical Power & Energy Systems, 32 (6), 664-670.

Table 4. VAR reserve and participation factor (scenario 10, 50 MW)

Regulated pf

0.00

0.406

0.25

1.69

0.09

1.09

0.59

0.19

Qgres

0.5

0.282

0.00

0.41

0.00

0.70

-

-

prg10

0.23

0.42

0.12

0.59

0.04

1.00

-

-

0.00

0.14

0.25

1.66

0.09

1.09

0.59

0.23

Qgres

0.5

0.55

0.00

0.35

0.00

0.70

-

-

prg10

0.24

0.37

0.02

0.63

0.04

1.00

-

-

Qgb

Qg

6

Wind power P Q

2

b

PQ limits

Generator number 3 4 5

1

Table 5. Expected total cost, Ftotal Wind power 20 MW

Wind power 50 MW

Regulated pf

PQ limits

Regulated pf

PQ limits

1.3295e+003

1.2009e+003

1.2287e+003

1.1567e+003

497

Table 4 shows the results of scenario 10 for the forecasted 50 MW wind farm output. As shown in the table, the VAR limits of the wind park for both cases are approximately the same. Accordingly, the VAR reserve associated with generators 1, 2, 4 and 6 for PQ limits have been changed slightly compared with the regulated power factor case. The obtained results still signify the worthy of generators 1, 2, 4 and 6 in achieving the required security limits following the contingency. The worthy of generators 1, 2, 4 and 6 have been also validated since their participation factors are higher compared to the other generators. Table 5 depicts the expected total cost required to achieve the desired security level. It is clear that the total costs of PQ limits for the two wind power levels have been decreased compared to the 497