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A Chance Constrained Programming Approach to theIntegrated Planning of Electric Power Generation,

Natural Gas Network and StorageBabatunde Odetayo, Student Member, IEEE, Mostafa Kazemi, John MacCormack, Member, IEEE,

W. D. Rosehart, Senior Member, IEEE, Hamidreza Zareipour, Senior Member, IEEE, Ali Reza Seifi, Member IEEE

Abstract—Natural gas is increasingly becoming the preferredchoice of fuel for flexible electricity generation globally resultingin an electricity system whose reliability is progressively dependenton that of the natural gas transportation system. The cascadedrelationship between the reliabilities of these system necessitatesan integrated approach to planning both systems. This paperpresents a chance constrained programming approach to minimizethe investment cost of integrating new natural gas-fired generators,natural gas pipeline, compressors and storage required to ensuredesired confidence levels of meeting future stochastic power andnatural gas demands. The proposed model also highlights the role ofnatural gas storage in managing short time uncertainties in devel-oping a long-term expansion plan for both the electric and naturalgas systems. A two-stage chance constrained solution algorithmis employed in solving the mix-integer non-linear programmingoptimization problem and illustrated on a standard IEEE 30 bustest system superimposes on the Belgian high-calorific gas network.

Index Terms—Integrated planning, Chance constrained pro-gramming, Natural gas transmission system, Natural gas-firedelectricity generators;

I. NOMENCLATUREA. Indicesb, r Index of source and demand electricity busesc Index of NG compressor stationsi, j Index of source and demand NG nodesp Index of NG pipeline typess Index of NG storage sizest Index of planning time horizon, t = 0,1,...T% Index of NG-fired generator sizesB. Binary Variablesyp,i,j,t 1 if a pipeline y is installed between NG nodes

i, j in time t. 0 otherwisezi,j,t 1 when there is NG flows from node i to j in

time t and 0 otherwise.λb,t 1 if a new NG-fired generator (NGG) is con-

nected to b in time t. 0 otherwiseψi,j,t 1 when compressor is installed between nodes i

to j in time t. 0 otherwise.φi,t 1 when the upper limit of NG sources is increasedC. VariablesP

(n)b,t Power generation from new(n) NGG connected

to bus b in time tP

(e)b,t Generation from existing (e) NGG at bus b in tflb,r,t Power flow from bus b to r in time tΘi,t,Θj,t Square of NG nodal pressure at source i and sink

j NG nodes in time t

Φi,j,t NG flow rate between NG nodes i, j in time tΓi,t NG pressure at source NG nodes i in time tD. Random Variablesξ1 Electricity demand forecast uncertaintyξ2 NG demand uncertaintyE. Chance constraint variable/parametersα Desired confidence-level for electricity systemβ Desired confidence-level for the NG systemγ Desired confidence level for the entire systemF. ParametersC

(I)% Overnight investment (I) cost of NGG of size %

C(I)p Overnight investment (I) cost of NG pipeline p

C(I)c The overnight investment (I) cost of compressor

(c) stationC

(o)% Operating cost (o) of NGG %

C(o)p Operating cost (o) of NG pipeline p

C(o)c Operating cost (o) of NG compressor c

d(e)i,t NG demand by existing (e) NGG at node i in

time td

(n)i,t NG demand by new (n) NGG at node i in time td

(h)i,t NG demand for non-electric power generation at

node i in time tir Interest rate on capitalLi,j Length of existing and candidate pipeline con-

necting NG nodes i and jM1 Large number equivalent to maximum possible

NG flow in a pipeline in time tM2 Large number used to limit the square of the

nodal pressureM3 A large value greater or equal to the maximum

acceptable pressurengsi,t NG supply at node i in time tngs

i,tLower limit on NG supply at node i in time t

ngsi,t Upper limit on NG supply at node i in time tP

(L)b,t Electricity demand at bus b in time tXb,r Reactance of the transmission line connecting

buses b, r.θb,t Voltage phasor angle at bus b in time t∆i,j Diameter of existing and candidate pipeline con-

necting nodes i and jΓi,t Lower limit on the NG nodal pressure in time tΓi,t Upper limit on the NG nodal pressure in time tκ Maximum pressure increase multiplier at a com-

pressor station

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σ discretized storage and inflow/outflow rate usedto linearize the properties of the NG storage

G. SetsΩb Set of electricity buses (indexed by (b,r))Ω

()c Sets of NG compressor nodes

Ωdn Set of NG demand nodesΩn Set of NG nodesΩp Set of all pipe typesΩs Set of NG storage sizesΩsn Set of NG supply nodesΩ(tr) Set of transhipment nodesΩ% Set of NGDG sizes

II. INTRODUCTION

The worldwide electric power generation capacity is expectedto grow by 69% from 21.6 trillion kilowatt-hours (kWh) in 2012to 36.5 trillion kWh by 2040. In the same period, electricitygeneration from natural gas (NG) is expected to grow by 110%from 4.8 trillion kWh to 10.1 trillion kWh. [1]. This trendis driven by the availability of relatively cheap NG supply,environmentally responsible regulations, and the improved effi-ciencies, competitive investment cost, relatively short ramp rates,modularity and scalability of NG-fuel generators (NGGs) [2]–[4]. Increasing electricity generation from NG, however, exposesthe electricity grid to reliability concerns on the NG trans-portation system [5]. Potential reliability concerns on the NGtransmission system includes outages resulting from componentfailures, malicious attacks, competing NG demand from othersectors such as transportation and extreme weather conditionsas experienced in the northeast of the USA during 2013/1014polar vortex [4], [6]. These risks make the long-term planningof both systems challenging as the planner is constantly facedwith the tough decision between the high cost of overbuildingthe system as a result of building redundancies and the cost ofoutages.

To some extent, energy utilities can manage some of thesereliability concerns by utilizing NG storage and employing anintegrated approach to the long-term planning of the electricityand NG systems. NG storage can provide contingent NG supplyin the advent of an outage on NG transmission network, a spikein power demand or a sudden drop in power generation from re-newable energy resources. Integrated planning of the electricityand NG systems is challenging because of the traditional plan-ning culture of the individual systems, non-collusion concernsbetween them, the overall reliability of the cascaded systems,the computational complexities of planning and managing bothsystems for uncertain power and NG demands.

The integrated planning of electricity and NG system hasbeen approached from an operational [5], [7]–[13] and long-terminvestment [3], [4], [14], [15] point of view. In the operationalplanning, the prevalent objective is ensuring adequate NG fordaily variations in electric power generation. The integratedoperational planning problem is modelled as a Mixed-IntegerLinear Programming (MILP) security-constrained optimal powerand NG flow in [10], while [11] employed steady-state analysisbased on the Newton-Raphson method to solve the coordinatedoperation of both systems. In [12], a multi-stage stochasticmodel for the integrated operation of both systems considering

the uncertainties of electric and NG supply was presented, while[16] proposes a single-stage linear optimization model for thecoordinated operation of the NG and power system

In contrast to the short-term adequacy objective of the inte-grated operation planning problem, the chief goal of the long-term investment plan is the adequacy of electric power genera-tion, NG transportation capacity for both electric power gener-ation and non-electric power generation considering stochasticfuture power and NG demands. Recent studies have modelled thelong-term planning problem as electricity Generation ExpansionPlanning (GEP) - NG planning problem [2], [17], [18], GEP-NG-electric transmission planning problem [3], [19] and GEP-NG planning problem considering resilience constraints enhanc-ing grid resiliency [20].

NG storage is usually employed by utilities to augmentNG supplies and improve supply reliability. The operationalcharacteristic of NG storage for contingency management wasintroduced in [21], while its value for energy supply securitywas discussed in [9]. Models for the constraints associated withthe effective operation of an NG storage is presented in [9], [17]while the inflow /outflow rates to and from the NG storage aremodelled in [22].

The long-term integrated planning problem is often mod-elled as a cost minimization mixed integer non-linear problem(MINLP) which is usually difficult to solve [4]. A number ofapproaches have been employed to manage this challenge. Forinstance, [3], [23] employed a sequential approach where theelectricity system is planned first and then the NG system. In[19], [24], the complexities of the integrated planning prob-lem was managed by decomposing it into manageable units,while [25] employed an Elitist non-dominated Sorting GeneticAlgorithm to solve the integrated planning problem. The costof implementing a very reliable integrated plan can becomeastronomical as the level of dependency increases because of thecascaded relationship between the reliabilities of both systems.This is because the reliability of the entire system is a functionof the product of the reliabilities of the constituent systems.Probabilistic planning approach such as Chance Constrained pro-gramming (CCP) [26], [27], allows the planner to minimizes theinvestment and operation cost of the system within acceptableconfidence levels of electric and NG power supplies.

In this paper, the objective of the long-term integrated plan-ning problem is the minimization of investment cost of NG-firedgenerators, NG pipelines, and NG storage while ensuring theuncertain power and NG demands are met with desired levelsof confidence. The proposed model extends previous models [3],[14], [17], [28] for the integrated long-term planning of electricand NG systems to include NG compressors, storage and thedynamics of NG flow in and out of the storage for managingstochastic power and NG demand. Furthermore, compared to [3],[4], [14], [17], the proposed model accommodates the cascadedrelationship between the reliabilities of the electric and NGsystems in the long-term planning of both systems.

The CCP framework is employed in solving the proposed inte-grated planning model in two stages. First, a non-convex MINLPdeterministic planning problem is solved. Based on the solutionof the deterministic problem a convex NLP operational problemis solved for optimality. The operational solution accommodates

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the stochasticity of the electric power and NG demand by testingthe solution from the deterministic expansion plan for sufficientscenario sets of the uncertain demand pairs. The contribution ofthis paper is summarized as follows.• A CCP long-term integrated planning model that accom-

modates the interactions between the confidence levels ofmeeting the stochastic power and NG demands is presented.The proposed model allows the system operator or operatorof a vertically integrated utility accommodate the expansionof the NG system in the planning of a reliable powersystem. This planning approach that can be valuable whenplanning under tight budgetary constraints.

• Secondly, the proposed model incorporates the dynamicsof NG compressors, NG inflow and outflow from an NGstorage and its role in managing short-term demand uncer-tainties when developing a long-term integrated expansionplan. This can help reduce investment cost, size NG storageand develop operational policies for NG storage.

The rest of this paper is structured as follows. The integratedplanning problem is described in Section III, while the mathe-matical representation of the problem is presented in Section IV.The solution methodology is presented in Section V, in sectionVI, the solution methodology is implemented on a test systemand Section VI concludes the paper.

III. THE INTEGRATED PLANNING PROBLEM WITH NATURALGAS STORAGE

The power system planner is often tasked with ensuring ade-quate electric power supply from NGG, other power generators,and the interties. NGG as a power source is however dependenton the adequacy and reliability of the NG supply system asshown in Fig. 1. NG storage offers an option for substituteinvestment in new production and transportation capacity, pro-vide high security of supply, and bridging the gap between peakNG demand and supply. For example, NG storage can provideprompt NG boost supply to NGGs in the advent of a spike inelectricity demand or a dip in power output from renewableenergy resources. This might be more effective in comparisonto increasing NG supply at the source and transporting it atcirca 20 miles/hour to the NGG. The prevalent NG storagesare abandoned oil and gas, salt caverns, aquifers, LNG-storagesand pipeline line-pack. Abandoned oil and gas, salt caverns,aquifers are less flexible because they are naturally occurring orbase on naturally occurring geological formations. LNG-storagesis not dependent on naturally occurring factors hence, it offerssignificant location and size flexibilities [22].

The operational characteristic of an NG storage includes thebase (cushion) gas, working gas, injection and extraction rangeand cycling as illustrated in Fig. 2. The base gas is a permanentNG inventory required to maintain adequate NG pressure andoutflow rate. The amount of base gas required is dependenton the engineering of the storage, contractual obligations andregulatory requirements.The working gas i.e. the NG availablefor cushioning the effects of extensive competing NG demand istied to the contractual obligation, injection and extraction rate.The proposed model considers the operation characteristic in thedevelopment of a long-term expansion plan for the electric andNG systems.

Fig. 1. Schematic of a coupled NG and electric power system

Fig. 2. A illustration of the operational characteristic of NG storage

IV. INTEGRATED PLANNING MODEL

The objective of the integrated planning problem is to mini-mize the investment and operational cost of electric and naturalgas systems as modeled in (1).

min z =

T∑t

[CC

(n)t +OC

(n/e)t + CCt

+ CC(ς)t +OCςt + CC

(ϕ)t +OC

(ϕ)t

](1)

Where CC(n)t in (1) is the present value (PV) of the capital cost

of building new (n) NGG. CC(n)t is further defined in (2).

CC(n)t =

∑b∈Ωb

∑%∈Ω%

δtλb,%,tC(I)% (2)

δt = ir1−(1+ir)−t . The operating cost of electric power generation

from both existing and new generators i.e., the second term of(1) is modeled in (3). This cost constitute the fixed and variableoperating cost of the electric power generator.

OC(n/e)t =

∑b∈Ωb

∑%∈Ω%

δtP(n/e)b,t C(o)

% (3)

The cost of building new or extending existing pipelines to newNG demand nodes, i.e., the third term of (1) is modelled in (4)

CCt =∑

(i,j)∈Ωn

∑p∈Ωp

δtC(I)p Li,j(yp,i,j,t+1 − yp,i,j,t) (4)

The capital cost of the NG pipeline constitutes the cost of thepipeline material and installation per diameter per length. Theoperating cost of NG pipeline a small fraction of the cost of NG

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hence it is ignored. Compressors stations increase NG flow rateby increasing pressure differential along a pipeline segment. ItsPV and operation costs are modeled in (5) and (6) respectively.

CC(ς)t =

∑(i,j)∈Ωn

∑c∈Ωc

δtC(I)c (ψi,j,t+1 − ψi,j,t) (5)

OC(ς)t =

∑(i,j)∈Ωn

∑c∈Ωc

δtψi,j,tC(o)c (6)

The capital and operation cost of NG storage is modeled in(7) and (8), where S is the capacity of the NG storage. Thecost of refrigeration/liquefaction accounts for the majority ofthe operating cost NG storage [29].

CC(ϕ)t =

∑s∈Ωs

∑j∈Ωn

δtφs,j,tC(I)s (7)

OC(ϕ)t =

∑s∈Ωs

δtSs,tC(o)s (8)

The minimization of the investment and operating cost of theelectric and NG system is constrained by the physical and oper-ating constraints on the electric and NG system and the couplingconstraint between them. These constraints are discussed next.

A. Physical and operating constraint on the electricity networkThe physical and operating constraints on the electricity

system presented in (9) [30] .

P(e)b,t + P

(n)b,t = PLb,t(ξ1) +

∑r∈Ωb

flb,r,t ∀b, r ∈ Ωb, t ∈ T (9a)

Pb,t = P(e)b,t + P

(n)b,t ∀b ∈ Ωb, t ∈ T (9b)

flb,r,t =1

Xb,r,t(θb,t − θr,t) ∀(b, r) ∈ Ωb, t ∈ T (9c)

θb,t = 0 ∀b = slackbus ∀b ∈ Ωb, t ∈ T (9d)0 ≤ Pb,t ≤ λb,%,tPG% ∀b ∈ Ωb, t ∈ T (9e)

fl ≤ flb,r,t ≤ fl ∀(b, r) ∈ Ωb (9f)Constraint (9a) is the kirchhoff’s flow conservation nodal

balance constraint. Constraint (9b) ensures that total electricpower generation is always the sum of up existing (e) and new(n) power generations. The approximate power flow betweenconnected electricity buses is modeled in (9c). Constraint (9d)sets the angle of the voltage phasor of the slack bus to zero.Constraints (9e) and (9f) models the limits on the capacity ofnew and existing generators and power flow in the transmissionlines. PG% is the name place capacity of NGG type %.

B. Physical and operational constraint on the NG systemNG flow through the pipeline system is constrained by a

number of physical, operation and contractual constraints asmodeled in (10). [3], [31]–[33].

Γi,t = Γi ∀i ∈ Ωsn, t ∈ T (10a)

Γi,t ≤ Γi,t ≤ Γi,t ∀i ∈ Ωdn, t ∈ T (10b)

Φi,j,t ≤M1zi,j,t ∀(i, j) ∈ Ωn, t ∈ T (10c)ngs

i,t≤ ngsi,t ≤ (ngsi,t + 5φi,t) ∀i ∈ Ωsn, t ∈ T (10d)

di,t = d(e)i,t + d

(n)i,t + d

(h)i,t ∀i ∈ Ωd ∪ Ωc, t ∈ T (10e)

ngsi,t +∑j∈Ωn

Φj,i,t −∑j∈Ωn

Φi,j,t = di,t(ξ2)

∀(i, j) ∈ Ωn, t ∈ T (10f)∑j∈Ωn

Φi,j,t −∑j∈Ωn

Φj,i,t = 0 ∀i ∈ Ω(tr), t ∈ T (10g)

(Γ2i,t − Γ2

j,t)−Ψi,jΦ2i,j,t ≥M2(zi,j,t − 1)

∀(i, j) ∈ Ωn, t ∈ T (10h)

(Γ2i,t − Γ2

j,t)−Ψi,jΦ2i,j,t ≤M2(1− zi,j,t)∀(i, j) ∈ Ωn, t ∈ T (10i)

Ψi,j =

(1

1.1494× 10−3

)2GTfLi,jZf

∆5i,j

(PbTb

)2

(10j)

zi,j,t + zj,i,t ≤ 1 ∀(i, j) ∈ Ωn, i < j, t ∈ T (10k)

zi,j,t + zj,i,t ≤∑p∈Ωp

yp,i,j,t ∀(i, j) ∈ Ωn, i < j (10l)

yp,i,j,t ≤ yp,i,j,t+1 ∀(i, j) ∈ Ωp, t = 1, ...|T | − 1 (10m)ψi,j,t + ψj,i,t ≤ 1 ∀(i, j) ∈ Ωc, i < j, t ∈ T (10n)

Γj,t − κΓi,t ≤M3(2− zi,j,t − ψi,j,t)∀(i, j) ∈ Ωc, t ∈ T (10o)

Γj,t − κΓi,t ≥M3(zi,j,t + ψi,j,t − 2)

∀(i, j) ∈ Ωc, t ∈ T (10p)Γj,t − Γi,t ≤M3(1− zi,j,t + ψi,j,t)

∀(i, j) ∈ Ωc, t ∈ T (10q)Γj,t − Γi,t ≥M3(zi,j,t − ψi,j,t − 1)

∀(i, j) ∈ Ωc, t ∈ T (10r)ςψi,j,t − Φi,j,t ≤M1(ψi,j,t − 1)∀(i, j) ∈ Ωc, t ∈ T (10s)ψi,j,t ≤ ψi,j,t+1 ∀(i, j) ∈ Ωc, t = 1, ..|T | − 1 (10t)∑

j

Φj,s,t ≤∑σ

ν(in)σ,s,tΠ

(in)σ ∀s ∈ Ωs ∪ Ωn, t ∈ T (10u)

∑j

Φs,j,t ≤∑σ

ν(out)σ,s,t Π(out)

σ ∀s ∈ Ωs ∪ Ωn, t ∈ T (10v)∑σ

ν(in)σ,s,t +

∑σ

ν(out)σ,s,t = 1 ∀s ∈ Ωs ∪ Ωn, t ∈ T (10w)

(ν(in)σ,s,t + ν

(out)σ,s,t )χσ−1 ≤ xσ,s,t ≤ (ν

(in)σ,s,t + ν

(out)σ,s,t )χσ (10x)

Ss ≤ xs,t ≤ Ss ∀s ∈ Ωs, t ∈ T (10y)

xs,t = xs,t−1 +∑i∈i(s)

Φi,s,t −∑i∈i(s)

Φs,i,t

∀s ∈ Ωs, i ∈ Ωp, t ∈ T (10z)

Constraint (10a) sets the NG pressure at the source nodes tothe maximum. Constraints (10b) sets the limits on the square ofthe NG pressure at the demand nodes. Constraint (10c) limitsthe NG mass flow rate on each segment of the pipeline, whereM1 is large number that indicates the maximum possible flow.

The contractual limits of NG supply is modelled in constraint(10d). This limit can be physical or contractual, therefore (10d)is modelled such that the contractual limit increases by multiplesof 5Mm3/day when such an increase does not violate the phys-ical limits of the system. A multiple of 5Mm3/day is selectedrandomly to allow easy tractability of the result. Constraint(10e) models the NG demand for electricity and non-electricity

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purposes. The NG flow conservation equation at NG demandand supply nodes i is modeled in constraint (10f). Constraint(10g) is conservation equation at the transhipment nodes i.e.,nodes where where there are no local NG demans.

Constraints (10h) and (10i) models the NG pressure dropbetween two nodes of pipeline segment assuming isothermalflow through a horizontal pipeline such that the effect of kineticenergy is negligible [3], [31]–[33]. (10h), (10i) and (10c) ensurethat NG only flows from higher to lower pressure nodes.Constraint (10h) and (10i) is formulated such that it is only tightwhen there is NG flow between two nodes i.e. when za,j,i,t = 1.M2 is a large value close to Γi,t

2. The pipeline resistance Ψi,j

is modeled in (10j) - ∆i,j and Li,j (km) are the diameterand length of the pipeline segment connecting nodes i and jrespectively. Where f , Pb, Tb, G, Z, and Tf are the frictionalfactor, base pressure, base temperature, NG gravity, gas com-pressibility factor and flow temperature respectively. Constraint(10k) ensures a unidirectional flow of NG per time [31] whileconstraint (10l) ensure that for NG flow to be possible, a pipelinemust be present. yi,j,t is a unique identifier for installed pipeline.Constraint (10m) ensures that new pipelines remain installed forthe entire planning period.

Constraint (10n) ensure that the compressor only increases NGpressure in one direction. Constraints (10o) and (10p) ensure theNG pressure increase through a compressor is less or equal toκ. Constraint (10o) and (10p) are only tight when a compressorexists and there is a positive NG flow i.e. when ψi,j,t = 1 andzi,j,t = 1. Constraints (10q) and (10r) ensures the pressure atthe inlet and outlet of the compressor are equal in the absenceof compression i.e. when ψi,j,t = 0, consequently treating thepipeline as a passive pipeline. In addition, constraints (10q)and (10r) dissociates Γi,t and Γj,t when there are no NG flowbetween nodes i and j i.e. when zi,j,t = 0 in the presenceor absence of a compressor [31]. In addition, constraints (10l),(10o) - (10r) ensures that a compressor can only be installedbetween two nodes connected via a pipeline. Constraint (10s)ensures that flow rate of NG through a pipeline connected to acompressor station is less or equal to the total flow capacity ofthe compressor station. In this constraint, when a compressor ispresent between nodes i, j i.e., ψi,j,t = 1 the difference betweenthe flow capacity of the compressor ς and the flow rate in theconnecting pipe is less than zero. Otherwise, the flow rate in apipeline without a compressor is less than M1. Constraint (10t)ensures that an installed compressor remains installed for theplanning period.

The maximum rate of NG flow rate in and out of NG storageis limited by the capacity of the connecting pipes and NG level inthe storage. The maximum inflow and outflow of NG into storageare strictly decreasing and increasing convex function of the NGstorage level. The level of NG in the storage is discretized by aset of constant x1, ....xσ , corresponding inflow Π

(in)1 , ... Π

(in)σ

and outflow Π(out)1 , ... Π

(out)σ rates, and variables ν1, .....νσ is

a convex combination of discretized storage and NG injection(in)/extraction (out) flow rate employed in linearizing the NGstorage characteristic as shown in Fig. 4 [22], [34].

The characteristic of NG flow in and out of the NG storages is constrained constraints (10u) - (10z). Constraints (10u) and(10v) limits the NG injection (in)/extraction (out) from the

Fig. 3. Illustration of the linearization of the inflow and outflow rate of a NGstorage system

NG storage in time t. Constraint (10w) ensures a uni-direction(in)/(out) NG flow per time. Constraint (10x) ensures that theNG levels between two point of approximation is constrainedby the sum of the convex combination of the net NG flow to orfrom the storage. On the flip side, constraint (10x) ensures thediscrete representation of the inflow or outflow is constrained bythe level of the storage at a given time. Constraint (10y) place acapacity limit on the NG storage. Constraint (10z) ensures thatthe difference between storage levels at two given times is afunction of the net NG inflow and outflow.

a) Non-linear constraint approximation: The flow equa-tion i.e. constraints (10h) and (10i) introduces non-linearity intothe integrated planning model because of Γ2 and Φ2. To improvethe linearity of the model Γ2

i is replaced with Θi and (10h) and(10i) are reformulated as (11).

(Θi,t −Θj,t)−Ψi,jΦ2i,j,t ≥M2(zi,j,t − 1)

∀(i, j) ∈ Ωn, t ∈ T (11a)

(Θi,t −Θj,t)−Ψi,jΦ2i,j,t ≤M2(1− zi,j,t)∀(i, j) ∈ Ωn, t ∈ T (11b)

Γi,t2 ≤ Θi,t ≤ Γi,t

2 (11c)where (11c) is the limit on the square of the nodal pressureΘi. The planning remains non-linear because of Φ2

i,j,t, however,recent improvements in computational methods have providedacceptable solutions to similar MINLP problems [31], [35].

C. Coupling constraint

The NG required by the existing (e) and new (n) NGGs asa function of the electric power injected into the electricity net-work at time t is computed with the relaxed coupling constraintpresent in (12) [4], [28].

d(n/e)i,t ≥ ai+biP (n/e)

b,t +ci(P(n/e)b,t )2 ∀b ∈ Ωb,∀i ∈ Ωdn (12)

Constraint (12) is the relaxed non-convex equality couplingconstraint [4]. ai,bi,bi are the gas fuel rates coefficients of theNGG. For simplicity purposes all candidate NGGs are assumedto have similar fuel rate coefficients.

D. Chance constrained model of the stochastic constraints

The CCP modelling approach restricts the feasible region of astochastic constraint so that the confidence level of the solutionis greater or equal to a set value. The stochastic constraints (9a)and (10f ) are modelled as chance constraints in (13).

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P[⋂b

(P

(e)b,t + P

(n)b,t −

∑r∈Ωb

flb,r,t ≥ P (L)b,t

)]≥ α (13a)

P[⋂i

(ngsi,t +

∑j∈Ωn

Φj,i,t −∑j∈Ωn

Φi,j,t ≥ di,t)]≥ β (13b)

γ = α× β (13c)0 ≤ α ≤ 1, 0 ≤ β ≤ 1 (13d)

Equation (13a) states that the joint probability that the powergeneration, less the net power flow is greater or equal to thestochastic power demand must be greater or equal to a desiredconfidence level α. Similarly, (13b) ensures NG supply matchesthe stochastic NG demand with a confidence level β. Due tothe cascaded relationship between these systems, the confidencelevel of meeting the system energy demand γ is a productof α and β as modelled in (13c). Assuming the power andNG demand follow a normal distribution, (13a) and (13b) isapproximated to (14a) and (14b) [36]–[38].

P(e)b,t + P

(n)b,t −

∑r∈Ωb

flb,r,t = µP(L)b,t + σP

(L)b,t Zα (14a)

ngsi,t +∑j∈Ωn

Φj,i,t −∑j∈Ωn

Φi,j,t = µdi,t + σdi,tZβ (14b)

where Zα and Zβ are the inverse cumulative distributions of therandom power and NG demands. µP

(L)b,t and µdi,t are the means

of the power and NG demands respectively. While, σP(L)b,t and

σdi,t are their respective standard deviations.

V. SOLUTION METHODOLOGY

The MINLP long-term integrated planning of the electricityand NG systems is challenging to solve, a challenge furthercomplicated by the stochasticity of the power and NG demands.The CCP solution algorithm accommodates these challenges byiteratively solving the planning in two main stages illustratedin Fig. 4. First, an approximation of the stochastic long-termplanning problem is solved. Based on the solutions of this de-terministic problem, a convex Non-Linear Programming (NLP)operation problem i.e. the Natural Gas constrained OptimalPower Flow (NGOPF) is then solved for Ntimes samples ofNG and power demands. Should the confidence levels be lessthan the desired values, the expected demand pairs in thedeterministic problem are updated using by updating Zα and Zβin (14) and re-evaluated. The details of this solution algorithmis discussed in the following subsections.

A. The deterministic integrated planning model

The deterministic approximation of the stochastic long-termintegrated planning problem modelled in (14) is solved for arandomly selected sets of inverse cumulative distributions Zαand Zβ [36]–[38]. The output of interest includes the locationand size of NGGs, NG pipelines, compressors and storages arethen passed to feasibility check sub-model as shown in Fig. 4

B. The feasibility check model

The solution from section V-A might be a local optimum sinceit only accommodates a set of expected power and NG demand

Fig. 4. Flowchart of the implemented CCP

scenario. To ensure the desired confidence levels is achieved inthe presence of stochastic demand pairs, the solution is testedfor feasibility by solving a NGOPF modelled in (15), for Ntimesscenario of NG and power demands sets in t ∈ T . Scenarios ofpower demand, P (L)

b,t and NG demand for heat d(h)i,t are generated

via Monte Carlo simulation. The uncertainties in NG demand forpower generation is determined from P

(L)b,t . The accuracies of

this feasibility check increases with the value of Ntimes.

min z∗ =

T∑t

( ∑b∈Ωb

∑%∈Ω%

P(n/e)b,t C(o)

%

+∑

(i,j)∈Ωp

∑c∈Ωc

ui,j,tC(o)c +

∑s∈Ωs

Ss,tC(o)s

)(15a)

s.t. P(e)b,t + P

(n)b,t −

∑r∈Ωb

flb,r,t = P(L)b,t ∀b ∈ Ωb (15b)

ngsi,t +∑j∈Ωn

Φj,i,t −∑j∈Ωn

Φi,j,t = di,t ∀i, j ∈ Ωn (15c)

Pb ≤ P(n)b,t ≤ min

[ di,tHR

,Pb]∀b ∈ Ωb, i ∈ Ωd (15d)

0 ≤ Φi,j,t ≤M1 ∀i, j ∈ Ωp, (15e)ngsi,t ≤ ngsi,t ≤ ngsi,t ∀i ∈ Ωs ∪ Ωd, (15f)

Θi,t −Θj,t = Ψi,jΦ2i,j,tzi,j,t ∀i, j ∈ Ωp (15g)

Θi,t −Θj,t = −Ψi,jΦ2i,j,tzi,j,t ∀i, j ∈ Ωc (15h)

Γj,t − κΓi,t = 0 ∀(i, j) ∈ Ωc, (15i)(9b− 9f), (10a, 10b, 10e, 10j, 10u− 10z), (12) (15j)

Constraint (15a) minimize the operation cost of generators,compressors, and storages. ui,j,t indicates the presence of acompressor. Constraints (15b) and (15c) ensures a nodal balanceof electric power and NG flow. Constraint (15d) set the capacitylimits on electricity generation based on the nameplate capacityand the Heat-rate (HR) of the generators. Constraints (15e)and (15f) sets the capacity limits NG flow rates and supply.

7

Constraints (15g) and (15h) models the NG flow conservationequation in the passive and active pipelines, while (15i) modelsthe flow conservation at a compressor station. zi,j,t indicatesthe direction of Φi,j,t. zi,j,t is the known variable from thedeterministic problem sent to the lower level problem and treatedas a constant. With the direction of Φi,j,t determined fromthe solution to the deterministic model, the NGOPF modelis convex [39]. The components of (15j) are defined abovein section IV. The average feasible cases i.e. pfeas of theNtimes set of scenarios indicates the confidence level of thesolution computed in the deterministic model. If pfeas ≥ γ,the solution to the deterministic model guarantees the desiredconfidence levels i.e. optimality. If the condition does not hold,the approximations in the deterministic model are updated usingthe Z-update algorithm [37], [40].

C. The Z-update Algorithm

The approximation of the stochastic demand pairs modelledwith a mean, µ, and standard deviation, σ , in (14a) and (14b),can be updated by updating the inverse cumulative distributionof the demands i.e. Zα or Zβ . The Z-update algorithm providesa framework to update the Zα or Zβ in terms of the initial,computed (pfeas) and expected (γ) sets of confidence levels.If pfeas ≤ γ, γ is updated by either updating α or β or bothbased on (13c). The approximate power demand is updated byupdating Zα in (14a) using (16) [36]–[38].

Zα = ZLo +[Z( γ

β

) − Z2

Z1 − Z2

(ZHi − ZLo

)](16)

where, ZHi and ZLo are the inverse distribution of the lower(P1) and upper (P2) limits on the confidence levels search space.Z1 and Z2 are the inverse distribution of the Pfeas associatedwith ZHi and ZLo respectively. Z( γ

β

) is the minimum Zα

required for achieving a system confidence level γ.

VI. TEST SYSTEM AND RESULT

The proposed model is illustrated by developing a 20 yearsintegrated expansion plan based on a ieee 30 bus test systemsuperimposed on the Belgium calorific gas network. The roleof the NG storage in accommodating short-time uncertaintieswhen developing the long-term expansion plan is investigatedby considering the following scenarios:

1) Scenario 1: No NG storage - In this scenario, it is assumedthat there is no NG storage in the system

2) Scenario 2: Low NG supply constraint - In this scenario,the long-term plan is expected to accommodate a maximumof 1 day of complete NG storage depletion annually

3) Scenario 3: Extensive NG supply constraint - this scenariorequires a plan capable of accommodating a maximum of3 days of continuous depletion of the NG storage. Forexamples an outage on a major NG transmission pipeline.

A. The test system and basic assumptions

A summary of the modified test system is presented TableII. The NG nodes and electric buses are labelled G1- G29 andE1-E30 respectively.

The following assumptions were made in our illustration

TABLE ISUMMARY OF THE TEST SYSTEM [39], [41], [42]

IEEE 30-bus system Belgian NG system

Buses 30 Total nodes 20Generators 6 Existing compressors 3Base lines 41 Base pipelines 24Candidate transmission lines 41 Candidate pipes 30Existing gas generators 2 Candidate nodes 29Demand bus 20 Existing NG Storage 4Bus voltages 132/33kV Norminal nodal pressure 80 bar

NG source (ngs) 2 ( ngsG1, ngsG8)

1) The overnight investment cost of candidate generators,compressors, storage, and pipelines are shown in Table II

TABLE IICHARACTERISTIC AND CAPITAL COST OF CANDIDATE GENERATORS AND

PIPELINE [43]–[45]

Generator Compressor LNG storage NG pipeline

MW 100 200 4974kW 1Mm3/day ∆(mm) 890 590 315

Capital Cost$M 90 170 11.42 2.17 $M/km 2.18 1.45 0.96

$2, 450 per millimeter of diameter per kilometer [43]

2) The desired system reliability γ is set to 96% while theminimum acceptable reliability of the constituent systemi.e. α and β are set to 98% for illustrative purpose

3) The cost associated with increasing the upper limit of NGsupply is assumed to be negligible

4) f , Pb, Tb, G, Z, and Tf are taken to be 0.012, 1 bar, 288oK,0.66, 0.805, and 283oK respectively [31]

5) The long-term integrated planning model is explored for aplanning horizon of 20 years

6) The locations and capacities of existing NG storages are:G2 -12.6Mm3; G5 - 7.2Mm3; G13 -1.8Mm3; G14 -1.44Mm3 [39], [41], [42].

7) The power and NG demand growth is assumed to be 3%and 2% respectively

8) For the sake of simplicity, candidate power generators areassumed to be NG fired. The proposed model could beextended to include other types of generations such asrenewable energy resourcesby treating them as negativeloads [46]

9) In this illustration, we assumed a utility with large NGgenerators where the system operator or planner mustaccommodate future constraints in the NG network in otherto ensure reliable power supply in the future

10) The non-convex MINLP deterministic integrated planningmodel is solved using the Branch-And-Reduce Optimiza-tion Navigator (BARON) [47] solver available in GAMS24.2 [48]. The solution of the deterministic model is testedfor optimality by solving the convex NGOPF over 1000samples i.e., Ntimes = 1000 of power and NG demandpairs using the DIscrete and Continuous OPTimizer (DI-COPT) [49] solver also available GAMS 24.2.

B. Results and explanation

First, the role of the NG storage in managing the short-term stochasticity of NG demand is investigated. Secondly, the

8

reliability and cost of the CPP long-term planning model iscompared to a deterministic model. Finally, the sensitivities ofthe expansion plan to the confidence levels is illustrated.

1) NG storage and the long-term planning model: The pro-posed expansion plans for the three storage scenarios indentifiedin Section VI are presented in Table III. The computed plansillustrate the role of NG storage in the long-term integratedplanning of electric power and NG system while consideringextensive constraint on NG supply. The result shows that acombination of investments in both NGG, NG compressors,NG pipeline and a possible increase in NG supply contractis required to accommodate extensive constraint on the NGtransportation system.

The time and location of the proposed NGG’s remain thesame for most of the three scenarios as shown in Table III,this is because the electrical demand remains the same and theNG system allows for cheaper means of mitigating against theconstraints on NG supply. Increasing supply from Norwegiangas was preferred over Algerian gas because the price ofthe NG from Norwegian gas was 26% cheaper. It should bepointed out that these solutions are unique to the test system’sability to accommodate increased NG flow in the existing NGtransportation system, existing NG storages and an assumptionthat the NG supply from Algerian gas and Norwegian gas canbe increased. The difference between the plans for each of thescenarios is discussed in the following sub-sections.

a) Scenario 1: When there are no NG storages in the testsystem, the confidence level of 96% is unachievable/infeasiblefrom year 4 as shown in Table III. This is due to the inability ofthe NG network to transport enough NG to meet both power andnon-power NG demands with the desired confidence level. Thishighlight the ease with which reliability concerns can propagatebetween the two cascaded systems.

b) Scenario 2: As shown in Table III, the expansion planassuming scenario 2 constitute a combination of NGG, NGcompressor, NG pipeline, and an increase in the upper limitsof potential NG import from Algerian and Norwegian gas.The presence of daily depletable NG storage that can supportcomplete daily depletion ensures that the power and NG demandare always meet the desired confidence levels. This is becausethe NG storage is able to provide NG boost that is required tocompensate for short time increase in NG demand.

c) Scenario 3: In comparison to scenario 2, there a largerincrease of the upper limits of NG supply is proposed. Thisis to accommodate the expected extensive utilization of theNG storages for NG supply compensation in the presence ofextensive NG supply constraints. Another significant differencebetween the proposed plan in scenario 2 and 3 is the locationand integration timing of NG compressors. The integration of acompressor was recommended earlier in the scenario 3 focusedexpansion plan. A compressor ψ(G14,G15) between NG demandnodes G14 and G15 is recommended mainly to boost NG flowrate to France. The compressor recommended in scenario 2 i.e.ψ(G11,G12) is mainly required to increase NG pressure to allowincreased NG supply from G8. This helps to compensate forextensive demand from the storage connected to G13 and G14.The extensive constraint on NG supply influenced the locationof NGG i.e. 100E16 in year 20 in comparison to the previous

scenario. The NGG is sited closer to the NG sources i.e. E16 toavoid potential pressure drop that might result from the depletionof the NG storages connected to G13 and G14. The minimaldifference between scenario 2 and 3 is attributed to the abilityof the existing test system to accommodate the increase in NGsupply and negligible cost associated this increase.

2) Deterministic model vs chance constrained programmingmodel: A comparison of the solution to the deterministic andstochastic long-term integrated planning model for scenario 2 ispresented in Table IV. As expected the proposed expansion planresulting from the deterministic model is cheaper than that of theCCP model. Although the investment cost is lower, the reliabilitycost is higher as captured by the frequency with which theelectric power nodal balance constraint is violated. This alignswith intuitive expectations i.e. investment cost typically increaseswith an increase in the reliability of of satisfying the stochasticelectric demand. The computational time for the deterministicand CCP solution is presented in Table V. Although there existssignificant difference in the computation time of both solutionalgorithms, both times are sufficient for long-term planning.

3) Sensitivity of the integrated plan to the confidence levels ofcascaded constituent systems: Thus far, α and β are set to 98%each in order to meet the system wide energy demand with aconfidence level, γ of 96%. However, an 0.96 γ can be achievedwith other combinations of different α’s and β’s. A sensitivityof the outputted expansion plan to the values of a and is shownin Table VI.

As shown in Table VI, the selected α and β combinationcan affect the cost of the expansion plan. In this specific case, ahigher confidence level on the NG system, β results in an overallcheaper expansion plan. However, there is no cost differencewhen the confidence level of the electric system, α is sethigher. The influence of the individual confidence levels on theexpansion plan is dependent on the level of integration betweenthe systems, the ratio of the NG demand used for electricitygeneration and time horizon under consideration. A higher β,for example, results in a cheaper plan because NG demand forelectricity is a small part of the total NG demand, thereforethe main contributor to the system-wide reliability violation isthe non-electric NG demand. This collaborates earlier resultswhere the expansion plans were infeasibility because of theviolation of adequacy constraint on the NG system. In addition,since the electric system in the test system is highly dependenton the NG system considering that all candidate generation isassumed to be NG fired, increasing the reliability of the NGsystem significantly influences the increase in the system-widereliability. Finally, as shown in Table VI, if the planning horizonhad been 9 years, the three combinations of confidence levelsconsidered would have resulted in similar solution from a costperspective.

VII. CONCLUSION

In conclusion, the increasing dependency of the electricsystem on NG systems has necessitated an integrated planningapproach towards planning both systems. Due to the cascadedrelationship between the power and NG system, the expansioncost of ensuring reliable energy supply can become financiallyunattainable. A planner can manage this potential challenge

9

TABLE IIICOMPUTED ELECTRICITY GENERATION AND NG SYSTEM EXPANSION PLANS

Scenario 1 Scenario 2 Scenario 3

Year (t) P(n)b (MW) yi,j / ψi,j P

(n)b (MW) yi,j / ψi,j P

(n)b (MW) yi,j / ψi,j

1 100E24 y(G8→E24) 100E24 y(G8→E24) 100E24 y(G8→E24)

ngsG8 :↑ 15∗ ngsG8 :↑ 15∗

ngsG1 :↑ 10∗ ψ(G11,G12)

ψ(G11,G12)

3 - ngsG1 :↑ 10∗ - - - -4 infeasible - ngsG1 :↑ 5∗ - ngsG1 :↑ 5∗

6 infeasible - -7 infeasible 100E10 y(G18→E10) 100E10 y(G18→E10)

8 infeasible ngsG1 :↑ 5∗ - ngsG1 :↑ 5∗

11 infeasible ψ(G14,G15) - ngsG8 :↑ 5∗

12 infeasible - ngsG8 :↑ 5∗ - -14 infeasible 100E21 y(G8→21) 100E21 y(G8→21)

ngsG8 :↑ 5∗

17 infeasible - ngsG8 :↑ 5∗ - ngsG1 :↑ 5∗

18 infeasible 100E17 y(G17→E17) 100E17 y(G17→E17)

19 infeasible - - ngsG8 :↑ 5∗

20 infeasible 100E12 y(G15→E12) 100E16 y(G13→E16)

ngsG1 :↑ 5∗ ngsG1 :↑ 5∗

27km 57km 52kmSummary 100 ngsG8 :↑ 15∗ 500 ngsG8 :↑ 15∗ 500 ngsG8 :↑ 25∗

ngsG1 :↑ 20∗ ngsG1 :↑ 15∗ ngsG1 :↑ 20∗

1× ψ(G11,G12) 1× ψ(G14,G15) 1× ψ(G11,G12)

* Mm3/day

TABLE IVCOMPUTED ELECTRICITY GENERATION AND NG EXPANSION TARGETS

Expectation integrated CCP model - Scenario 2

Year P(n)b yi,j / ψi,j Violation P

(n)b yi,j / ψi,j Violations

(t) (MW) (per 1000) (MW) (per 1000)

1 - - 23 100E24 y(G8→E24) 22 100E24 y(G8→E24) 3 - - 83 - - 8 - - 94 - 24 - ngsG1 :↑ 5∗ 95 - - 42 - - 136 - - 73 - - 197 - - 113 100E10 y(G18→E10) 38 - - 154 - ngsG1 ↑ 5∗ 49 - ngsG1 ↑ 5∗ 203 - - 810 - - 263 - - 1311 - - 312 - ψ(G14,G15) 1012 - ngsG1 ↑ 5∗ 366 - ngsG8 ↑ 5∗ 913 - - 423 - - 1814 100E21 y(G8→E21) 40 100E21 y(G8→21) 2

ψ(G14,G15) ngsG8 ↑ 5∗

15 - - 91 - - 816 - - 169 - - 1617 - - 231 - ngsG8 ↑ 5∗ 1418 - ngsG8 ↑ 5∗ 312 100E17 y(G17→E17) 519 - - 398 - - 1620 - ngsG1 ↑ 5∗ 488 100E12 y(G15→E12) 2

ngsG1 :↑ 5∗

21km 57kmSummary 200 ngsG8 ↑ 10∗ 186.8 500 ngsG8 ↑ 15∗ 9.4

ngsG1 ↑ 10∗ ngsG1 ↑ 15∗

ψ(G14,G15) ψ(G14,G15)

* Mm3/day

TABLE VCOMPUTATIONAL TIME OF DETERMINISTIC AND STOCHASTIC MODEL

Solution algorithm Deterministic model Chance constrained programing model

Computational time 33sec 93.3min

by modelling the integrated planning problem in probabilisticterms that allows manageable violations of the nodal balanceconstraints. In this paper, we proposed a chance constrainedprogramming model of the integrated planning problem and

TABLE VISENSITIVITY OF INTEGRATED PLAN TO CONFIDENCE LEVELS TARGETS

α = 97%, β = 99% α = 98%, β = 98% α = 99%, β = 97%

Year P(n)b yi,j (km) / P

(n)b yi,j (km)/ P

(n)b yi,j (km) /

t (MW) ψi,j MW ψi,j (MW) ψi,j

1 - - 100E24 y(G8→E24) 100E24 y(G8→E24)

2 100E24 y(G8→E24) - - - -3 - ngsG1 ↑ 5∗ - - - -4 - ngsG1 :↑ 5∗ - ngsG1 :↑ 5∗

7 - - 100E10 y(G18→E10) 100E10 y(G18→E10)

8 - - - ngsG1 ↑ 5∗ - ngsG1 ↑ 5∗

9 100E10 y(G18→E10) - - - -ngsG1 ↑ 5∗

10 - ψ(G14,G15) - - - -ngsG1 ↑ 5∗

11 - - - ψ(G14,G15) - - ψ(G14,G15)

12 - - - ngsG8 ↑ 5∗ - ngsG8 ↑ 5∗

13 - - - - -14 - - 100E21 y(G8→21) 100E21 y(G8→21)

ngsG8 ↑ 5∗ - ngsG8 ↑ 5∗

15 - ngsG8 ↑ 5∗ - - - -16 100E21 y(G8→21) - - - -

ngsG8 ↑ 5∗ - - - -17 - - - ngsG8 ↑ 5∗ - ngsG8 ↑ 5∗

18 - ngsG8 ↑ 5∗ 100E17 y(G17→E17) 100E17 y(G17→E17)

19 100E17 y(G17→E17) - - - -20 - ngsG1 ↑ 5∗ 100E12 y(G15→E12) 100E12 y(G15→E12)

- - ngsG1 :↑ 5∗ ngsG1 :↑ 5∗

55km 57km 57kmSummary 400 ngsG8 ↑ 15∗ 500 ngsG8 ↑ 15∗ 500 ngsG8 ↑ 15∗

ngsG1 ↑ 20∗ ngsG1 ↑ 15∗ ngsG1 ↑ 15∗

1× ψ(G14,G15) 1× ψ(G14,G15) 1× ψ(G14,G15)

* Mm3/day

show that NG storages are efficient in managing short-timestochasticity of the demand pairs in the long-term integratedplanning of the electric and NG system and in achieving thedesired confidence levels of energy supply. In addition, we showhow the CPP model results in increased reliability in comparisonto a deterministic mode. Finally, we show that the sensitivity ofthe long-term expansion plan to the selected confidence levels isdependent on the level of integration between the systems, theratio of the NG demand used for electricity generation and time

10

horizon under consideration

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Babatunde Odetayo Babatunde Odetayo (S14) received the B.Sc. degreefrom Ladoke Akintola University of Technology, Ogbomoso, Oyo state, Nigeriain 2006, the M.Sc. degree from University of Nottingham, Nottingham, Not-tinghamshire UK in 2010 and the Ph.D. from University of Calgary, Calgary,AB, Canada. His research interests include power systems, natural gas systems,electricity markets, optimization, and its applications to energy systems.

Mostafa Kazemi Mostafa Kazemi received the B.Sc., M.Sc. and Ph.D. degreesin electrical engineering from Sharif University of Technology, Tehran, Iran, in2010, 2012 and 2016, respectively. He is currently an Assistant Professor inUniversity of Shahreza, Shahreza, Iran. His research interests include economicsand planning of restructured power systems.

John MacCormack John MacCormack received BSc. and MSc. degreesin electrical engineering from University of Saskatchewan, Saskatoon, SK,Canada in 1982 and 1988 respectively. In 2012 he received a PhD. in electricalengineering specializing in energy and environment from the University ofCalgary, AB, Canada. He is a practicing Professional Engineer with over 35years of experience in the electrical power industry and has appeared numeroustimes as an expert in front of the Alberta Energy and Utilities Board and itssuccessor the Alberta Utilities Commission.

William D. Rosehart William D. Rosehart (SM’05) received the B.Sc,M.Sc., and Ph.D. degrees in electrical engineering from the University ofWaterloo, Waterloo, ON, Canada. He is currently the Dean of Schulich Schoolof Engineering, University of Calgary, Calgary, AB, Canada. His main researchinterests include the areas of numerical optimization techniques, power systemstability, and modeling power systems in a deregulated environment.

Hamidreza Zareipour Hamidreza Zareipour (S’03-M’07-SM’09) received thePh.D. degree in electrical engineering from the University of Waterloo, Waterloo,ON, Canada, in 2006. He is currently a Full Professor with the Departmentof Electrical and Computer Engineering, University of Calgary, Calgary, AB,Canada. His research is focused on operation and planning of electrical energysystems in presence of various sources of uncertainty.

Ali Reza Seifi Ali Reza Seifi was born in Shiraz, Iran. He received his B.S.in Electrical Engineering from Shiraz University, Shiraz, Iran, in 1991, hisM.S. in Electrical Engineering from the University of Tabriz, Tabriz, Iran, in1993 and his Ph.D. in Electrical Engineering from Tarbiat Modarres University(T.M.U.), Tehran, Iran, in 2001. He is currently the Professor in Department ofPower and Control Engineering, School of Electrical and Computer Engineering,Shiraz University, Shiraz, Iran. In 2017-now, he works as a Visiting Professorin Department of Electrical and Computer Engineering, Schulich School ofEngineering, University of Calgary. His research interests include Energy, EnergyManagement, Power Plant Simulations, Power Systems, Electrical MachineSimulations, Power Electronics and Fuzzy Optimization.