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.
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 [
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 [
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.
The proposed model has the form as follows.
(1) |
s.t.
(2) |
(3) |
(4) |
(5) |
(6) |
(7) |
(8) |
(9) |
(10) |
(11) |
(12) |
(13) |
(14) |
(15) |
(16) |
(17) |
(18) |
(19) |
(20) |
(21) |
(22) |
(23) |
(24) |
(25) |
(26) |
(27) |
(28) |
(29) |
(30) |
where .
The terms included in objective function (1) are as follows.
1) is the annualized investment cost of new transmission lines.
2) is the annualized investment cost of new solar units.
3) is the annualized investment cost of new wind units.
4) is the annualized investment cost of new combined cycle gas turbines (CCGTs).
5) is the annualized investment cost of new storage units.
6) is the operation cost of all units.
7) is the load-shedding cost.
Both terms 6 and 7 are multiplied by the weight of the day type and the weight of the corresponding scenario .
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 . 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 . 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 . Constraint (29) defines binary variable . Finally, constraint (30) defines binary variable .
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.
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 [
The generation and load data of the Saudi Arabian power system are obtained from [

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) [
We apply the capital recovery factor 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 [
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.
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 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 [
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 . 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.
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) renewable energy per scenario: in this case, up to of the total energy per scenario can be produced using thermal units ( in (24)).
3) renewable power: in this case, only of the total power capacity built can be thermal ( in (25)).
4) average renewable energy for the three scenarios: in this case, up to of the total average energy for the three scenarios can be produced using thermal units ( in (26)).
We pay particular attention below to case 2 due to its practical relevance.
To solve these cases, we use CPLEX [
The investment, operation, and total costs for cases 1 and 2 are shown in
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.

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 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 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 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 . Exceeding in case 2 requires high investment cost and the system would have a large amount of lightly used capacity.
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).
The worst operation condition (day) in case 3 with corresponds to day 3 and scenario 3 (peak demand of 73 GW).

Fig. 4 Newly built generator and transmission facilities in case 3 with X = 60.
EIA [
We analyze how the investment and operation costs change as a function of a high pathway cost 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
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.

Fig. 6 Increment in investment and operation costs 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.
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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