Journal of Modern Power Systems and Clean Energy

ISSN 2196-5625 CN 32-1884/TK

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Expansion Planning for Renewable Integration in Power System of Regions with Very High Solar Irradiation  PDF

  • Musfer Alraddadi 1
  • Antonio J. Conejo 2
  • Ricardo M. Lima 3
Department of Electrical and Computer Engineering, The Ohio State University, Columbus, OH 43210, USA; Department of Integrated Systems Engineering and the Department of Electrical and Computer Engineering, The Ohio State University, Columbus, OH 43210, USA; King Abdullah University of Science and Technology, Thuwal 23955-6900, Kingdom of Saudi Arabia

Updated:2021-05-19

DOI:10.35833/MPCE.2019.000112

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Abstract

In this paper, we address the long-term generation and transmission expansion planning for power systems of regions with very high solar irradiation. We target the power systems that currently rely mainly on thermal generators and that aim to adopt high shares of renewable sources. We propose a stochastic programming model with expansion alternatives including transmission lines, solar power plants (photovoltaic and concentrated solar), wind farms, energy storage, and flexible combined cycle gas turbines. The model represents the long-term uncertainty to characterize the demand growth, and the short-term uncertainty to characterize daily solar, wind, and demand patterns. We use the Saudi Arabian power system to illustrate the functioning of the proposed model for several cases with different renewable integration targets. The results show that a strong dependence on solar power for high shares of renewable sources requires high generation capacity and storage to meet the night demand.

Nomenclature
A. Indices
δ Scenario
b Storage unit
d Demand
j Combined cycle gas turbine (CCGT)
l Transmission line
n Node
o Day
r(l) Receiving-end node of transmission line l
s Solar unit
s(l) Sending-end node of transmission line l
t Time period
w Wind unit
B. Sets
ΩnB Storage units located at node n
ΩnD Demands located at node n
ΩnJ CCGTs located at node n
ΩL Prospective transmission lines
ΩnS Solar units located at node n
ΩnW Wind units located at node n
Ωr Reference nodes
C. Parameters
αo Weight of day o
βδ Probability of scenario δ
ηb Energy efficiency of storage unit b
σj The minimum power output coefficient of CCGT j
φEA Per unit factor regarding average renewable energy
φEE Per unit factor regarding renewable energy per scenario
φC Per unit factor regarding renewable power
Bl Susceptance of transmission line l
CdU Load-shedding cost of demand d
CjJ Production cost of CCGT j
CsS Production cost of solar unit s
CwW Production cost of wind unit w
E¯bB,max The maximum energy capacity that can be built of storage unit b
Flmax Capacity of transmission line l
Fδ,s,o,tS Solar capacity factor of solar unit s in scenario δ at hour t of day o
Fδ,w,o,tW Wind capacity factor of wind unit w in scenario δ at hour t of day o
IbB Annualized investment cost of storage unit b
IG,max Investment budget for building gas, wind, solar, and storage units
IjJ Annualized investment cost of CCGT j
IlN Annualized investment cost of prospective transmission line l
IL,max Investment budget for building transmission lines
IsS Annualized investment cost of solar unit s
IwW Annualized investment cost of wind unit w
M Large enough positive constant
pbBP,max Charging capacity of storage unit b
pbBT,max Discharging capacity of storage unit b
Pδ,d,t,oD Load of demand d in scenario δ at hour t of day o
P¯jJ,max The maximum capacity that can be built of CCGT j
P¯sS,max The maximum capacity that can be built of solar unit s
P¯wW,max The maximum capacity that can be built of wind unit w
RjD Ramping-down limit of CCGT j
RjU Ramping-up limit of CCGT j
D. Binary Variables
xl Binary variable that is equal to 1 if prospective transmission line l is built and 0 otherwise
yδ,j,o,t Binary variable that is equal to 1 if CCGT j is on-line in scenario δ at hour t of day o, and 0 otherwise
E. Continuous Variables
θδ,n,o,t Voltage angle at node n in scenario δ at hour t of day o
EbB,max Energy capacity of storage unit b
Eδ,b,o,tB Energy in storage unit b in scenario δ at the beginning of hour t of day o
Fδ,l,o,tL Power flow through transmission line l in scenario δ at hour t of day o
pδ,b,o,tB,T Discharging power from storage unit b in scenario δ at hour t of day o
pδ,b,o,tB,P Charging power to storage unit b in scenario δ at hour t of day o
pδ,d,o,tD,U Load shed of demand d in scenario δ at hour t of day o
PjJ,max Capacity of CCGT j
pδ,j,o,tJ Power produced by CCGT j in scenario δ at hour t of day o
PsS,max Capacity of solar unit s
pδ,s,o,tS,spill Spilled power of solar unit s in scenario δ at hour t of day o
PwW,max Capacity of wind unit w
pδ,w,o,tW,spill Spilled power of wind unit w in scenario δ at hour t of day o
xδ,j,o,t Product of binary variable yδ,j,o,t and continuous variable PjJ,max in scenario δ at hour t of day o
zδ,j,o,t Positive slack variable of CCGT j in scenario δ at hour t of day o
Pδ,d,t,oD Load of demand d in scenario δ at hour t of day o

I. Introduction

IN this paper, we propose a generation and transmission expansion model motivated by an energy transition in regions with very high solar irradiation. These regions are strong candidates for a transition from a power system based on thermal generation to the one based on solar power. Examples of regions with very high solar irradiation include southwest USA, the Arabian Peninsula, north of Africa, Inner Mongolia and Tibet in China, north of Mexico, western and central Australia, western Pakistan, western South Africa, and north Chile. However, a number of challenges exist to incorporate solar power in power systems [

1]. The aforementioned regions have a strong and widespread availability of solar resources, but integrating these resources requires technical and economic analyses of viable percentages of different technologies including energy storage. In addition, it is relevant to assess the operation complementarity of solar and other renewable sources. Overall, these analyses are relevant to support decision-makers on where and when to install renewable sources.

We propose a stochastic programming model to address the generation and transmission expansion planning that involves the selection of alternative generation plants, energy storage, and transmission lines to install. We adopt a greenfield perspective for the generation plants, but not for the transmission lines. Planning new transmission lines is important to avoid congestions due to the integration of renewable sources, which is spatially conditioned by the locations of resources. We model both long- and short-term uncertainties. Long-term uncertainty pertains to demand growth patterns across the region of interest and it is represented using a number of scenarios. Short-term uncertainty refers to the daily variation of the electricity demand and the power production of solar and wind facilities and it is represented using a number of typical days. The objective of the model is to minimize total costs, and a number of case studies are considered with increasing renewable integration targets, from business as usual (BAU) to 100% renewable sources, and the outcome is analyzed in terms of generation mix, energy storage, investment costs, and operation costs.

Generation and transmission expansion planning models have been evolving to accommodate reliability targets, renewable generation plants, environmental concerns, and others. This planning problem can be analyzed and studied from multiple perspectives, depending on the objectives and context of the considered power system. The relevance to the society and the economy of this problem has originated a large number of works. Therefore, we limit our review to those related to our work, and refer the reader to [

2]-[4] for comprehensive reviews on different perspectives. Reference [5] focuses on generation and transmission expansion planning, where wind power investments and associated transmission reinforcements are determined to minimize consumer payments. A relevant perspective in planning is the value of storage to facilitate the integration of renewable sources. In this regard, [6] discusses the benefits of energy storage systems to integrate weather-dependent renewable sources. Also, in [7], a number of case studies in renewable integration are discussed in detail and relevant suggestions are made to achieve better integration of renewable sources in the USA. Regarding generation and transmission expansion, [8] proposes an integrated formulation that accounts for a probabilistic reliability criterion. Reference [9] focuses on the generation expansion problem considering the uncertainty in the load and wind power output and uses a two-stage stochastic programming formulation. The alternative renewable policy scenarios and their impact on CO2 emissions are studied. Reference [10] focuses on long-term uncertainties such as carbon and fuel prices, demand, and renewable penetration at the European level. A power system involving multiple regions with transmission limits between regions is considered. A relevant topic in these models is the characterization of the short-term uncertainty of hourly wind and solar power output, and of the demand. Reference [11] proposes an optimization-based approach to select representative days, which shows that their approach decreases the computation resources required to solve generation expansion planning problems. Reference [12] focuses on the generation expansion problem for the integration of large amounts of wind, which proposes a multi-stage stochastic programming formulation where some decisions affect future uncertainties. Reference [13] proposes a generation expansion planning model with investments occurring at different years and involving various energy sources (wind, solar, coal, natural gas, and nuclear). A nested Benders decomposition algorithm is developed to address the computation challenges of large instances. However, long-term uncertainty and transmission constraints are not considered. Reference [14] describes a generation and transmission expansion planning model to support investment decisions to move to a fully renewable power system from a thermal dominated one. Reference [15] analyzes the impact of considering detailed unit commitment constraints on investment results related to generation capacity and energy storage, which shows that ignoring those constraints leads to building less storage in the system, but as expected, the complexity of the model increases substantially due to the number of binary variables introduced by the commitment of thermal units. As a final reference, we mention [16], a book regarding models for the integrated expansion of generation and transmission facilities based on mixed-integer linear programming (MILP) models.

In this paper, we propose a stochastic programming model that includes relevant features for a region with very high solar irradiation that aims at the transition to a power system based on solar and wind power. A two-stage decision framework that enables investment decisions at the first stage and operation decisions at the second stage. The uncertainty characterization includes long- and short-term uncertainties to capture demand growth, but also the uncertain output of weather dependent sources. The generation technologies include solar power plants (photovoltaic (PV) and concentrated solar), wind farms, energy storage, and flexible combined cycle gas turbines. Energy storage is considered as a component of concentrated solar power (CSP) plants, but also as independent plants.

Considering the literature review above, the contribution of this paper are threefold.

1) A generation and transmission expansion planning model is developed for power systems of regions with very high and stable solar irradiation. We illustrate such model through a comprehensive study pertaining the particular case of Saudi Arabia.

2) A number of case studies are analyzed in which increasing levels of renewable penetration are imposed in advance. Since we consider regions with very high and stable solar irradiation, very high integration of solar resources is a natural choice. We analyze the economic and technical consequences of such integration levels.

3) Policy observations are derived from our analysis and case study, which are generally applicable to power systems of regions with very high and stable solar irradiation.

The rest of this paper is organized as follows. Section II describes the formulation of the proposed generation and transmission expansion planning model. Section III applies this model to the Saudi Arabian power system and analyzes the outcomes obtained. Finally, Section IV provides conclusions and recommendations.

II. Formulation

The proposed model has the form as follows.

minΔlΩLIlNxl+sΩSIsSPsS,max+wΩWIwWPwW,max+jΩJIjJPjJ,max+bΩBIbBEbB,max+δβδoαot=124jΩJCjJpδ,j,o,tJ+sΩSCsSFδ,s,t,oSPsS,max+wΩWCwWFδ,w,t,oWPwW,max+dΩDCdD,Upδ,d,o,tD,U (1)

s.t.

0PjJ,maxP¯jJ,max    j (2)
0PsS,maxP¯sS,max    s (3)
0PwW,maxP¯wW,max    w (4)
0EbB,maxE¯bB,max    b (5)
jΩJIjJPjJ,max+sΩSIsSPsS,max+wΩWIwWPwW,max+bΩBIbBEbB,maxIG,max (6)
lΩLIlNxlIL,max (7)
σj xδ,j,o,tpδ,j,o,tJxδ,j,o,t    j,o,t,δ (8)
xδ,j,o,t=PjJ,max-zδ,j,o,t    j,o,t,δ (9)
0xδ,j,o,tP¯jJ,maxyδ,j,o,t    j,o,t,δ (10)
0zδ,j,o,tP¯jJ,max(1-yδ,j,o,t)    j,o,t,δ (11)
pδ,j,o,tJ-pδ,j,o,t-1JRjU    j,o,t,δ (12)
pδ,j,o,t-1J-pδ,j,o,tJRjD    j,o,t,δ (13)
0pδ,d,o,tD,UPδ,d,t,oD    d,o,t,δ (14)
Eδ,b,o,t+1B=Eδ,b,o,tB+pδ,b,o,tB,Pηb-pδ,b,o,tB,T    b,o,t,δ (15)
0pδ,b,o,tB,TpbBT,max    b,o,t,δ (16)
0pδ,b,o,tB,PpbBP,max    b,o,t,δ (17)
0Eδ,b,o,tBEbB,max    b,o,t,δ (18)
Fδ,l,o,tL=Bl(θδ,s(l),o,t-θδ,r(l),o,t)    l,lΩL,o,t,δ (19)
-FlL,maxFδ,l,o,tLFlL,max    l,lΩL,o,t,δ (20)
-xlFlL,maxFδ,l,o,tLxlFlL,max    l,lΩL,o,t,δ (21)
-(1-xl)MFδ,l,o,tL-Bl(θδ,s(l),o,t-θδ,r(l),o,t)(1-xl)M                                             l,lΩL,o,t,δ (22)
jΩnJpδ,j,o,tJ+sΩnSFδ,s,t,oSPsS,max-sΩnSpδ,s,t,oS,spill+wΩnWFδ,w,t,oWPwW,max-wΩnWpδ,w,t,oW,spill+bΩnBpδ,b,o,tBT-l|s(l)=nFδ,l,o,tL+l|r(l)=nFδ,l,o,tL=dΩnD(Pδ,d,t,oD-pδ,d,o,tD,U)+bΩnBpδ,b,o,tBP    n,o,t,δ (23)
φEEoαot=124sΩnSFδ,s,t,oSPsS,max+wΩnWFδ,w,t,oWPwW,max+jΩnJpδ,j,o,tJoαot=124sΩnSFδ,s,t,oSPsS,max+wΩnWFδ,w,t,oWPwW,max    δ (24)
φCjΩJPjJ,max+sΩSPsS,max+wΩWPwW,maxsΩSPsS,max+wΩWPwW,max (25)
φEAδβδoαosΩnSFδ,s,t,oSPsS,max+wΩnWFδ,w,t,oWPwW,max+jΩnJpδ,j,o,tJδβδoαot=124sΩnSFδ,s,t,oSPsS,max+wΩnWFδ,w,t,oWPwW,max (26)
-πθδ,n,o,tπ    n,o,t,δ (27)
θδ,n,o,t=0    nΩr,o,t,δ (28)
yδ,j,o,t{0,1}    j,o,t,δ (29)
xl{0,1}    lΩL (30)

where Δ={pδ,j,o,tJ,Fδ,l,o,tL,pδ,d,o,tD,U,PjJ,max,PsS,max,PwW,max,pδ,w,t,oW,spill,pδ,s,t,oS,spill, pδ,b,o,tB,P,pδ,b,o,tB,T,EbB,max,Eδ,b,o,tB,yδ,j,o,t,xδ,j,o,t,zδ,j,o,t,xl,θδ,n,o,t}.

The terms included in objective function (1) are as follows.

1) lΩLIlNxl is the annualized investment cost of new transmission lines.

2) sΩSIsSPsS,max is the annualized investment cost of new solar units.

3) wΩWIwWPwW,max is the annualized investment cost of new wind units.

4) jΩJIjJPjJ,max is the annualized investment cost of new combined cycle gas turbines (CCGTs).

5) bΩBIbBEbB,max is the annualized investment cost of new storage units.

6) jΩJCjJpδ,j,o,tJ+sΩSCsSFδ,s,t,oSPsS,max+wΩWCwWFδ,w,t,oWPwW,max, o,t,δ is the operation cost of all units.

7) dΩDCdD,Upδ,d,o,tD,U,o,t,δ is the load-shedding cost.

Both terms 6 and 7 are multiplied by the weight of the day type αo and the weight of the corresponding scenario βδ.

Constraints (2)-(7) are investment constraints. Among them, constraints (2)-(4) impose bounds on the production capacity of each generation unit to be built. Likewise, constraint (5) imposes bounds on the storage energy capacity of each storage unit to be built. Constraints (6) and (7) specify the investment budgets for building new generation units (all technologies) and new transmission lines, respectively.

Constraints (8)-(29) are operation constraints. Among them, the sets of mixed-integer linear constraints (8)-(11) replace the nonlinear constraint σjPjJ,maxyδ,j,o,tpδ,j,o,tJPjJ,maxyδ,j,o,t. This constraint imposes power output bounds on any new CCGT. Constraints (12) and (13) define the ramping-up and ramping-down limits of CCGT. Constraint (14) bounds the load-shedding of demand. Constraints (15)-(18) impose charging and discharging limits for each storage unit. Constraint (19) gives the power flow through the existing transmission line. Constraint (22) is the linearization of the nonlinear constraint Fδ,l,o,tL=xlBl(θδ,s(l),o,t-θδ,r(l),o,t). This constraint gives the power flow through the prospective transmission line. Constraints (20) and (21) limit the power flows through any transmission line. Constraint (23) enforces the power balance at each node. Constraint (24) enforces a minimum level of renewable energy per scenario. Constraint (25) enforces a minimum level of renewable power. Constraint (26) enforces a minimum level of average renewable energy. Constraint (27) establishes bounds for voltage angles at each node. Constraint (28) sets the voltage angle to be 0 at the reference node n. Constraint (29) defines binary variable yδ,j,o,t,o,t,δ. Finally, constraint (30) defines binary variable xl.

Overall, the proposed stochastic programming model is translated into a large-scale MILP problem that can be solved using commercially available solvers. Binary variables pertain to both investment decisions in transmission lines and unit commitment decisions for CCGTs. Note that binary variables to avoid the simultaneous charging and discharging of energy storage are not incorporated. Capacity additions are modelled as continuous variables. This constitutes a reasonable trade-off between modelling accuracy and computation tractability.

III. Case Study of Saudi Arabian Power System

In this section, we apply the proposed generation and transmission expansion planning model to the Saudi Arabian power system. This case study corresponds to a realistic description of the Saudi Arabian power system. Saudi Arabia benefits from very high solar irradiation and plans to introduce renewable sources in its generation mix, as defined in the Governmental Plan Vision 2030 [

17]. Besides this energy transition plan, the Saudi Arabian government has already started the building process of a new city, NEOM, that will be run on 100% renewable energy [18]. At a regional scale, the potential of solar power in Saudi Arabia is assessed in [19]. The cost of including PV technology in the Saudi Arabian power system is studied in [20], where the KAPSARC energy model is extended to include solar PV. They perform several cost and benefit analyses considering a maximum installation of 20 GW capacity of solar PV. Reference [21] analyzes the benefits of energy and water storage in a future 100% renewable energy power system in Saudi Arabia. Reference [22] gives an overview of renewable energy in Saudi Arabia and analyzes the potential of renewable energy in that country.

A. Data

The generation and load data of the Saudi Arabian power system are obtained from [

19], whereas the data of locations and transmission lines can be found in [23]. Figure 1 depicts a simplified version of Saudi Arabian 380 kV power system.

Fig. 1 Schematic diagram of simplified version of Saudi Arabian 380 kV power system.

Renewable energy data for Saudi Arabia are obtained from the system advisor model (SAM) [

24], and weather data for Saudi Arabia are obtained from the PV geographical information system website [25]. In addition, investment cost data for all generation units are obtained from National Renewable Energy Laboratory (NREL) website [26]. The operation costs for renewable technologies are obtained from the USA Energy Information Administration (EIA) website [27] except for CSP units, which are obtained from the SAM [24].

We apply the capital recovery factor r(1+r)x/[(1+r)x-1] to the investment cost data to compute the annualized investment, where r is the real interest rate, and x is the number of years for the depreciation period. We annualize the investment costs by assuming a 25-year depreciation period and a 9% real interest rate. This yields an 10% cost-annualization rate.

We use a greenfield approach with respect to generation facilities, but not with respect to transmission lines. The target planning year is 2040. Due to unattractive wind profiles across the Arabian peninsula, only 9 locations are selected as candidates for installing onshore wind power plants. These locations correspond to nodes 7, 6, 13, 23, 24, 30, 31, 32, and 33. The annualized investment cost of any onshore wind unit is 172200 $/MW and its operation cost is 2.8 $/MWh. We consider that it is possible to build up to 22 PV power plants, and up to 22 CSP power plants. The annualized investment cost of any PV power plant is 106900 $/MW and its operation cost is 2.5 $/MWh. PV power plants can be located at any node except nodes 9 and 12. The annualized investment cost of any CSP power plant is 371000 $/MW and its operation cost is 4.7 $/MWh. We assume that each CSP power plant has a thermal energy storage (TES) system with 12 hours of energy storage capacity. CSP power plants can be located at any node except nodes 9 and 12.

Regarding storage units, we consider compressed air energy storage (CAES) with an annualized investment cost of 48000 $/MW [

28]. The energy efficiency is assumed to be 0.7 p.u. and the energy capacity is considered to be 10 hours times the power capacity. Different types of storage technologies characterized by different investment costs and efficiencies can be represented in the proposed model. Storage units can be located at any node except nodes 9 and 12.

We consider the possibility of installing CCGTs, whose investment cost is 89500 $/MW and the variable cost is 35 $/MWh. CCGTs can be located at any node except nodes 9 and 12. Table I provides the characteristics of existing transmission lines including their capacities and Table II provides the characteristics of 12 prospective lines including their capacities as well. The annualized investment cost of AC transmission lines is assumed to be 24000 $/km.

Table I Technical Characteristics of Existing Transmission lines
lCorridorLength (km)Capacity (MW)lCorridorLength (km)Capacity (MW)
1 7-2 100 1610 17 20-21 186 1000
2 7-5 50 1610 18 20-22 127 1500
3 2-24 356 400 19 20-23 250 700
4 2-5 75 1610 20 22-31 480 600
5 5-6 150 1310 21 23-24 100 1300
6 6-24 180 700 22 31-30 270 700
7 7-8 41 1610 23 30-32 162 1300
8 8-10 20 1610 24 31-32 320 700
9 9-10 75 1450 25 21-22 100 800
10 9-14 100 1610 26 32-33 170 850
11 9-21 421 500 27 32-34 178 800
12 10-12 180 1260 28 33-34 70 1610
13 12-13 20 1000 29 33-35 52 1200
14 14-20 406 700 30 34-36 76 1610
15 19-31 400 700 31 34-35 80 800
16 19-20 274 700
Table II Technical Characteristics of Prospective Transmission Lines
lCorridorLength (km)Capacity (MW)Annualized investment cost (103 $)
32 7-8 41 1610 984
33 2-8 140 800 3360
34 2-10 160 1610 3840
35 32-33 170 900 4080
36 33-36 80 1610 1920
37 34-35 80 800 1920
38 32-34 178 900 4272
39 24-19 624 400 14976
40 31-32 320 600 7680
41 8-10 20 1610 480
42 33-35 52 1100 1248
43 2-24 356 700 8544

B. Scenarios and Representative Days

The electric power demand during the day and night is flat in Saudi Arabia, both during the winter and summer. A representative demand curve can be observed in Fig. 2. The demand is flat because its most important component is air conditioning, and since ambient temperature does not change significantly from day to night, the need for air conditioning remains rather stable. The demand level in the summer is higher than that in the winter, but both are rather flat. Under these conditions, a few days are sufficient to accurately represent the whole year.

Fig. 2 Unit commitment decisions in the worst case scenario in case 3 with X = 60.

The current peak demand of the Saudi Arabian power system is 49 GW [

23]. Regarding long-term uncertainty and based on historical trends, we consider three different future load scenarios. The weights of these three scenarios are 1.1, 1.3, and 1.5, respectively, and their probabilities are 0.2, 0.3, and 0.5, respectively βδ=1. Econometric models could be used to estimate such potential growths and their probabilities, which is outside the scope of our work. Needless to say, additional scenarios including extreme low-probability ones can be incorporated at the cost of increasing the computation burden of the proposed model.

Based on historical data, we use eight typical days to represent the target year (2040). We use two typical days (spanning 24 hours) for each season of the year. The weight of each representative day is the number of days in the corresponding season αo=365. Note that it is a good enough approximation as most days in a given season in Saudi Arabia are virtually identical in term of demand, wind- and solar-production patterns. This is also the most likely outcome of a k-means algorithm to cluster days.

C. Case Studies

Planning target refers to a future outcome objective, e.g., achieving at least 80% renewable energy production in 2040. The scenario refers to a realization of the future peak load (long-term uncertain parameter), e.g., 20% above the forecasting value. We consider four case studies, which are characterized as follows.

1) BAU: in this case, there are no restriction in building CCGTs.

2) X% renewable energy per scenario: in this case, up to 100%-X% of the total energy per scenario can be produced using thermal units (φEE=X/100 in (24)).

3) X% renewable power: in this case, only 100%-X% of the total power capacity built can be thermal (φC=X/100 in (25)).

4) X% average renewable energy for the three scenarios: in this case, up to 100%-X% of the total average energy for the three scenarios can be produced using thermal units (φEA=X/100 in (26)).

We pay particular attention below to case 2 due to its practical relevance.

To solve these cases, we use CPLEX [

29] under GAMS [30] on a Windows PC with an Intel Core i5/2.4 GHz processor and 8 GB of RAM. The computation time required is approximately 48 hours for each case. An instance of this model includes 4047 binary variables, 126064 continuous variables, and 193347 equations. The solution is obtained within a relative optimality gap below 0.001%. Analyzing very large systems, e.g., the China southern power grid or the power system of the East Coast of the USA, would require using powerful computers (not a personal computer), but the modelling framework would remain unchanged.

D. Results

1) Case Comparison

The investment, operation, and total costs for cases 1 and 2 are shown in Table III and for cases 3 and 4 are shown in Table IV, where Δ1, Δ2, Δ3 are the increments of the investment cost, operation cost and total cost with respect to BAU, respectively. Results for cases 1 and 2 of total capacity to be built for each technology are given in Table V and for cases 3 and 4 are given in Table VI. It can be observed that if thermal limits are imposed, PV increases significantly due to its comparatively low investment cost. Although the energy efficiency of a CSP power plant is higher than that of a PV or wind power plant, the high capital cost of CSP makes this technology comparatively unattractive. As expected, the wind capacity built is low since wind conditions are not attractive. The capacity of energy storage units increases with the renewable capacity to store the energy from solar power plants to meet the demand during the night.

Table III Investment, Operation, and Total Costs for Cases 1 and 2
CaseXInvestment cost (1010 $)Δ1 (%)Operation cost (1010 $)Δ2 (%)Total cost (1010 $)Δ2 (%)
1 1.0190 1.4000 2.4190
2 30 1.4491 42 1.2464 -11 2.6955 11
40 2.0174 98 1.0801 -23 3.0975 28
50 2.4708 142 0.9544 -32 3.4252 41
60 2.8807 183 0.7341 -48 3.6148 49
70 3.6902 262 0.6047 -57 4.2949 77
80 4.5250 344 0.4756 -66 5.0006 106
90 6.3954 528 0.2926 -79 6.6880 176
100 7.6509 651 0.1600 -89 7.8109 222
Table IV Investment, Operation, and Total Costs for Cases 3 and 4
CaseXInvestment cost (1010 $)Δ1 (%)Operation cost (109 $)Δ2 (%)Total cost (1010 $)Δ3 (%)
3 60 1.8562 82 9.169 -35 2.7732 14
4 60 2.6520 160 6.669 -52 3.3189 37
3 80 3.5324 247 5.877 -58 4.1201 70
4 80 4.0220 295 4.119 -71 4.4339 83
Table V Capacity of Each Technology Built for Cases 1 and 2
CaseXCapacity (MW)
CCGTPVCSPWindEnergy storageTotal
1 66280 10770 3012 0 8840 88902
2 30 65968 20939 8386 4275 11120 110688
40 64282 54249 13610 5980 11300 149421
50 61787 64525 18802 14350 12598 172062
60 57195 74895 28200 13300 13022 186612
70 46020 95660 34402 11200 34960 222242
80 34840 116400 40826 10064 56933 259063
90 12480 157860 73628 6625 77804 328397
100 0 201413 67774 2947 130341 402476
Table VI Capacity of Each Technology Built for Cases 3 and 4
CaseXCapacity (MW)
CCGTPVCSPWindEnergy storageTotal
3 60 60109 82794 5160 2210 9055 159328
4 60 57353 71290 23425 13538 12200 177806
3 80 42613 166091 922 3439 56982 270047
4 80 40400 98155 38037 12210 43990 232792

In case 1, the renewable power capacity is just 17% of the total power capacity. The total cost of case 1 is the lowest, and the highest total cost is that of the 100% renewable case. Since thermal units have the lowest investment cost and the highest operation cost, the operation cost of case 1 is the highest and the investment cost is the lowest.

Besides case 1, we observe that imposing a requirement based on renewable energy per scenario is the most expensive option. The lowest cost option is imposing a requirement based on renewable capacity.

Figure 3 shows the investment, operation, and total costs as a function of the renewable power built for cases 1 and 2 with X ranging from 30 to 100. The total cost increases significantly beyond X = 80.

Fig. 3 Investment, operation, and total costs as a function of renewable power.

Based on these results, it can be concluded that case 2 with X=60 is a competitive option. Indeed, it is possible to increase the percentage of renewable energy per scenario from 17% (BAU) to 60% with an increment in total cost of 49% with respect to BAU.

The case 3 with X=60 is a good compromise between cost and renewable integration over all options. It achieves comparatively low operation cost and results in 43% shift in total renewable energy with 14% increment in total cost with respect to BAU. The case 4 with X=80 achieves a high level of renewable penetration, but at a comparatively high cost. However, it is a much more attractive option in terms of cost than case 2 with X=80. Exceeding X=80 in case 2 requires high investment cost and the system would have a large amount of lightly used capacity.

2) Representative Days

The demand throughout the hours of the day at different locations and the renewable production throughout the day at different production locations are “short-term” uncertain parameters that we model using 8 representative days. To assess the stability of the results, we have also run case 1 with 12 representative days. Note that in Saudi Arabia, the demand and the renewable production are rather stable throughout the winter and summer (the only seasons in this country). Table VII shows that the results of case 1 for 8 and 12 representative days have the similar renewable penetration levels and investment costs. The operation costs decrease as a result of incorporating less extreme operation conditions. Therefore, only a few representative days are required to accurately represent the whole year.

Table VII Costs of Case 1 for 8 and 12 Representative Days
Time (day)Investment cost (1010 $)Operation cost (1010 $)Total cost (1010 $)Renewable penetration level (%)
8 1.019 1.40 2.42 17
12 1.018 1.36 2.38 17

3) Worst Operation Condition (Day) in Case 3 with X = 60

The worst operation condition (day) in case 3 with X=60 corresponds to day 3 and scenario 3 (peak demand of 73 GW).

Figure 4 shows the newly built generator and transmission facilities in case 3 with X=60. Figure 2 depicts the hourly production of each technology to supply the demand. It can be observed that wind units do not produce power during the night when PV and CSP units cannot produce power, which forces the system to use thermal units with high ramping capabilities. Otherwise, the model results would include building additional solar units to cover daytime demand. It can be observed that the energy storage units help the system use solar energy more efficiently. Indeed, they allow the system to use 59 GWh of solar energy during the night.

Fig. 4 Newly built generator and transmission facilities in case 3 with X = 60.

4) Results of Transmission Line

Table VIII provides the number of transmission lines built in each case. Case 1 includes the lowest number of transmission lines built, where the highest corresponds to case 2 with X=80. If we consider the Saudi Arabian power system has no exsiting transmission lines,the number of the transmission lines built in case 3 with X=60 will be smaller than that in case 1.

Table VIII Number of Transmission Lines Built
CaseXNo. of transmission linesCaseXNo. of transmission lines
1 2 2 80 12
2 60 9 3 80 9
3 60 6 4 80 11
4 60 9

E. Cost Projections

EIA [

27] provides three future pathways of capacity cost for different types of power plants. Approximately, the low and medium pathways have very similar cost assumptions, but the high pathway has significantly higher cost assumptions.

1) High Cost Assumption

We analyze how the investment and operation costs change as a function of a high pathway cost assumption. Figure 5 shows the increase in investment and operation costs with respect to medium pathway assumption.

Fig. 5 Increment in investment and operation costs of high pathway assumption with respect to medium pathway assumption.

The cases considered include case 1 and case 3 with X ranging from 50 to 90. It can be observed that the increment in investment costs decrease as the renewable capacity increases. This is because the investment cost of case 1 is the smallest and increases as the renewable penetration level increases, as shown in Fig. 3.

2) Only PV Investment Cost is High

In the previous cases, PV dominated the renewable energy due to its low investment cost. Thus, we analyze the result if only PV investment costs are comparatively high and other technologies remain at the medium pathway assumption. Figure 6 shows the increment in investment and operation costs with respect to medium pathway assumption when only PV investment costs are comparatively high. The cases considered include case 1 and case 3 with X ranging from 50 to 90.

Fig. 6 Increment in investment and operation costs with respect to medium pathway assumption when only PV investment costs are comparatively high.

Figure 7 illustrates the difference of renewable and CCGT power built with respect to medium pathway assumption when only PV investment costs are comparatively high.

Fig. 7 Difference of renewable and CCGT power built with respect to medium pathway assumption when only PV investment costs are comparatively high.

Comparing the results, it can be observed that the renewable power capacity built in case 1 decreases from 17% to 10% of the total power capacity if we change the investment cost of PV technology from medium to high pathway assumption.

IV. Conclusion

This paper uses a long-term generation and transmission planning model to analyze the transition of the Saudi Arabian power system toward high penetration level of renewable sources. Considering the case studies carried out, the conclusions are drawn as follow.

1) Regarding a renewable penetration level of only 17% in case 1, we can conclude that it is important to actively promote the integration of renewable power in the Saudi Arabian power system if a high penetration level of renewable sources is desired.

2) Since a high renewable penetration level is achieved using PV and CSP, which do not operate during the night, high generation and storage capacities need to be installed. This is specific to Saudi Arabia since attractive wind sites are not available.

3) Our model and analyses are applicable to power systems in geographical areas with high solar irradiation and stable weather condition.

An out-of-sample analysis for assessing the comparative performance of alternative expansion plans is a fruitful area of additional research.

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