Profitability of Concentrated Solar-Biomass hybrid power plants: Dataset of the stochastic techno-economic assessment

Abstract

An increasing share of dispatchable renewable generation is required to achieve energy decarbonisation goals and ensure a reliable supply to power grids. Concentrating solar power (CSP) plants hybridised with biomass boilers are promising alternatives to replace part of the peaking and baseload power generated from fossil fuel-based systems. This paper includes data related to the design variables, equations, valuation parameters and detailed results that support the research article “Market profitability of CSP-Biomass hybrid power plants: Towards a firm supply of renewable energy.” The profitability assessment is based on integrating the hourly variation of electricity prices in the Iberian day-ahead market (MIBEL) to the results of the techno-economic model through a novel economic metric named Profitability Factor. In addition, stochastic simulations were conducted to capture the uncertainty of relevant input variables on the profitability of the proposed hybrid plants. The resulting datasets presented in this paper will provide insights for researchers looking to address the economic performance of renewable generation concepts from a market profitability approach. Furthermore, the data can be used by investors and policymakers to better understand the risks and implications associated with the profitability potential of these systems.

Nomenclature

A_sf

solar field reflection area (m²)

HHV_Biomass

biomass high heating value (MWh_th/tonne)

I_sf

solar field incident power (MWh/m²/year)

M_Biomass

biomass feed flow (tonnes/year)

NC_system

system installed capacity (kW_e)

Ƞ_e

net electric efficiency (%)

Ƞ_(boiler)

biomass boiler global efficiency to electricity (% HHV)

Ƞ_(PB)

power cycle efficiency (%)

Ƞ_(Q)

part-load efficiency (%)

Ƞ_(T)

temperature variation efficiency (%)

Ƞ_{th (boiler)}

biomass boiler thermal efficiency (% HHV)

Q_n

plant power output (MWh/year)

Q_sf

solar field power output (MWh/year)

Q_TES

thermal energy storage power output (MWh/year)

SM

solar multiple

TES_hours

thermal energy storage capacity (hours)

TGE_Biomass

biomass gross thermal energy (MWh_th/year)

Specifications Table

Subject	Renewable Energy, Sustainability, and the Environment
Specific subject area	Hybrid renewable power systems
Type of data	Table Raw data Equation Figure
How data were acquired	An annualised dataset of solar irradiation was used to predict the energy yield of the CSP system. In addition, the historical market electricity price dataset was used in the economic model for the profitability assessment. A novel evaluation metric called Profitability Factor was proposed. The resulting datasets related to the profitability assessment were obtained using self-constructed probability distributions for some relevant design parameters of the techno-economic analysis and the Monte-Carlo simulations of the stochastic model (10 000 iterations).
Data format	Raw Analysed Filtered
Description of data collection	The criteria for collecting data on solar irradiation and electricity prices in the market was based on matching both data series on an hourly resolution for the same year. At the same time, the techno-economic design parameters were obtained from current best practices in the sizing of CSP-biomass hybrid plants. 1.Data on solar irradiation and other climatic variables were obtained from the meteorological station of the engineering school (ETSI) of the University of Seville. 2.For modelling the CSP generation system, technical design parameters widely accepted in the literature were used, as well as the specialised software System Advisor Model (SAM) property of the National Renewable Laboratory. 3.The annual electricity price data series was obtained from the Iberian electricity market operator (MIBEL) and “Red Eléctrica de España (REE)”. 4.For modelling the biomass block integration and the economic analysis, a proprietary calculation tool was used, in which the market prices of electricity were also included. Monte-Carlo simulations were carried out through Crystal Ball software.
Data source location	Country: Spain Primary dataset: “Iberian Electricity Market Operator”, data “Hourly day-ahead market price (EUR/MWh)” from 01 January 2017 to 31 December 2017. Link: https://www.omie.es/es/market-results/daily/daily-market/daily-hourly-price
Data accessibility	Repository name: HARVARD Dataverse Data identification number: 10.7910/DVN/ZD2LFV Direct link to the dataset: https://doi.org/10.7910/DVN/ZD2LFV
Related research article	R. Gutiérrez-Alvarez, K. Guerra, P. Haro, Market profitability of CSP-Biomass hybrid power plants: Towards a firm supply of renewable energy, Appl. Energy. 335 (2023) 120754. https://doi.org/10.1016/j.apenergy.2023.120754.

Value of the Data

• •These data provide a detailed description of the technical and economic parameters used in modelling various configurations of Concentrated Solar-Biomass hybrid plants for electricity generation. The design parameters, equations and relationships obtained from optimisation analyses and presented in this paper provide valuable insights for researchers and technology developers studying the feasibility of hybrid technologies in other locations beyond the sunbelt.
• •This article presents for the first-time datasets of stochastic calculations (probability distributions) for the Profitability Factor, a novel economic metric applicable to assess the economic feasibility of renewable generation systems from a market profitability approach. These data help to understand the Profitability Factor's construction by facilitating its calculations' reproducibility.
• •These data can be useful to policymakers as a basis for developing new financial support mechanisms to encourage investment in baseload renewable power systems. In addition, data can be used to assess the effect of targeted subsidies to reward ancillary services supplied to the grid by dispatchable technologies (e.g., stability and rotational inertia).
• •These data also serve as a reference for researchers seeking to include electricity price variability in feasibility analyses of new energy systems. Accounting for the variations of electricity prices in a day-ahead market (hourly datasets) extends the scope of traditional techno-economic studies towards an approach of profitability and competitiveness under real conditions.
• •Although these data are specific to Seville (Spain), they serve as a guide for researchers and investors who want to assess the performance of hybrid CSP-biomass systems in other locations. Furthermore, the datasets provide a framework for extending the application of the Profitability Factor to analyse other renewable technologies and their participation in other electricity markets.

1. Objective

Given the progressive withdrawal of feed-in tariff subsidies for newly constructed renewable systems, it is crucial to assess their performance when participating as free bidders in electricity markets. The data included in this paper plot the hourly coupling between the generation of a dispatchable renewable system (i.e., CSP-biomass hybrid plant) and the variation in market electricity prices. Due to the probabilistic approach and the diversity of assessed cases (30 in total), a large number of results (300 000) were generated in the original research study [1]. The datasets included in this paper reflect in detail the iterative process conducted to account for the uncertainty linked to relevant economic design variables and their effect on the profitability of each case. Therefore, allowing for the reproducibility of the methodology used in the study and its potential extension to assess the profitability of other renewable generation concepts.

2. Data Description

This paper includes data that supports the profitability assessment of CSP-biomass hybrid power plants and their potential to participate in the electricity market as price-taking technologies. For the calculation of market profitability, a new economic metric proposed by the authors called "Profitability Factor" has been used, whose detailed description and calculation procedure are presented in [1]. Thirty cases were assessed considering different combinations between two CSP technologies (i.e., Parabolic Trough (PT) and Solar Tower (ST)), three operating strategies and five levels of thermal storage. Data of the normal direct irradiation (DNI) for Seville and the data series of hourly electricity prices in the Iberian market have been included. Besides, deterministic and stochastic results (e.g., Monte-Carlo simulations) related to the techno-economic performance of the addressed plant configurations are presented. The data are grouped into several categories, which are summarised as follows:

Section 2.1. shows the generation profiles for different thermal energy storage (TES) and biomass capacities, including the effect of the day-dependent DNI variations. Data related to the annual deterministic performance are presented in Section 2.2, while the probability distributions related to the profitability factor for all the assessed cases are summarised in Section 2.3. Finally, a thorough description of the dataset included in a public repository [2] with all the runs performed in the Monte-Carlo simulations is provided in Section 2.3.

2.1. Generation profiles

The intensity of biomass and TES participation in the electricity generation profiles of the entire system are shown using ST technology as an example. Figs. 1 and 2 show the hourly electricity price profiles for operating strategies 1 and 2 (medium and high biomass share), respectively. The variable participation of generation sources is shown for each operation strategy, considering two TES capacities (0 and 20 hours) for three different days according to their DNI level (P0%, P50% and P100%), as detailed in Table 1.

Fig. 1.

Power output profile for Solar Tower with medium biomass operation for various day types according DNI level. (a) P0% without TES, (b) P50% without TES, (c) P100% without TES, (d) P0% with 20 hours of TES, (e) P50% with 20 hours of TES, (f) P100% with 20 hours of TES.

Fig. 2.

Power output profile for Solar Tower with full biomass operation for various day types according DNI level. (a) P0% without TES, (b) P50% without TES, (c) P100% without TES, (d) P0% with 20 hours of TES, (e) P50% with 20 hours of TES, (f) P100% with 20 hours of TES.

Table 1.

Days sorted by DNI level.

	Day 1	Day 2	Day 3
DNI (kWh/m2-day)	0.01	6.33	11.69
Percentile	P0%	P50%	P100%
Date for 2017	18th January	25th November	16th May
Day type	Working day	Non-Working day	Working day

2.2. Annualised deterministic results

Table 2, Table 3, Table 4, Table 5, Table 6, Table 7, Table 8 show the annualised deterministic results according to the fixed point techno-economic input parameters for all the cases included in the study (BC - NB: Base case - No biomass, OS1 - MB: Operation strategy 1 - Medium biomass, OS2 - FB: Operation strategy 2 - Full biomass).

Table 2.

Capacity factor results for PT and ST.

	Capacity factor (%)
	No-TES	5h	10h	15h	20h
Parabolic Trough
BC - NB	21.31%	32.51%	42.78%	52.97%	59.37%
OS1 - MB	59.80%	66.82%	72.29%	77.00%	80.04%
OS2 - FB	99.77%	100.00%	100.00%	100.00%	100.00%
Solar Tower
BC - NB	23.66%	38.99%	51.82%	63.15%	71.44%
OS1 - MB	61.71%	71.30%	78.29%	84.45%	88.97%
OS2 - FB	100.00%	100.00%	100.00%	100.00%	100.00%

Table 3.

Solar share results for PT and ST.

	Solar share (%)
	No-TES	5h	10h	15h	20h
Parabolic Trough
BC - NB	100.00%	100.00%	100.00%	100.00%	100.00%
OS1 - MB	35.63%	48.65%	59.17%	68.80%	74.18%
OS2 - FB	21.36%	32.11%	42.08%	52.52%	59.07%
Solar Tower
BC - NB	100.00%	100.00%	100.00%	100.00%	100.00%
OS1 - MB	38.34%	54.68%	66.19%	74.77%	80.29%
OS2 - FB	23.55%	37.75%	49.60%	59.84%	67.20%

Table 4.

Biomass use results for PT and ST.

	Biomass use (kt/year)
	No-TES	5h	10h	15h	20h
Parabolic Trough
BC - NB	0	0	0	0	0
OS1 - MB	118.76	105.84	91.02	74.08	63.74
OS2 - FB	215.25	188.14	161.15	131.06	112.57
Solar Tower
BC - NB	0	0	0	0	0
OS1 - MB	111.12	94.32	77.27	62.19	51.20
OS2 - FB	199.20	166.53	136.37	109.74	90.28

Table 5.

Net electric efficiency for PT and ST.

	Net electric efficiency (%)
	No-TES	5h	10h	15h	20h
Parabolic Trough
BC - NB	14.48%	14.72%	14.53%	14.40%	13.45%
OS1 - MB	19.89%	18.68%	17.55%	16.60%	15.28%
OS2 - FB	23.45%	21.81%	20.22%	18.77%	17.12%
Solar Tower
BC - NB	15.48%	16.03%	15.96%	15.90%	15.50%
OS1 - MB	20.81%	19.52%	18.44%	17.68%	16.88%
OS2 - FB	24.48%	22.53%	20.85%	19.57%	18.41%

Table 6.

Investment per capacity for PT and ST.

	Investment per capacity (USD/kWe)
	No-TES	5h	10h	15h	20h
Parabolic Trough
BC - NB	3010.39	4904.76	6799.13	8693.50	10587.86
OS1 - MB	4180.10	6074.46	7968.83	9863.20	11757.57
OS2 - FB	5326.41	7220.78	9115.14	11009.51	12903.88
Solar Tower
BC - NB	3936.89	5271.57	6524.11	7694.53	8782.81
OS1 - MB	5127.67	6462.35	7714.90	8885.31	9973.59
OS2 - FB	6294.63	7629.31	8881.86	10052.27	11140.55

Table 7.

LCOE for PT and ST.

	LCOE (USD/kWh)
	No-TES	5h	10h	15h	20h
Parabolic Trough
BC - NB	0.214	0.223	0.231	0.236	0.253
OS1 - MB	0.128	0.152	0.174	0.195	0.217
OS2 - FB	0.105	0.126	0.148	0.171	0.194
Solar Tower
BC - NB	0.242	0.198	0.185	0.178	0.179
OS1 - MB	0.142	0.148	0.155	0.161	0.169
OS2 - FB	0.114	0.126	0.138	0.150	0.160

Table 8.

Profitability factor for PT and ST.

	Profitability factor (USD/kWh)
	No-TES	5h	10h	15h	20h
Parabolic Trough
BC - NB	-0.143	-0.152	-0.161	-0.167	-0.184
OS1 - MB	-0.060	-0.084	-0.106	-0.126	-0.149
OS2 - FB	-0.037	-0.058	-0.080	-0.103	-0.126
Solar Tower
BC - NB	-0.172	-0.127	-0.115	-0.110	-0.111
OS1 - MB	-0.074	-0.079	-0.087	-0.093	-0.101
OS2 - FB	-0.046	-0.058	-0.070	-0.082	-0.092

2.3. Profitability factor probability distributions

This section presents the datasets associated with the results of the profitability analysis under uncertainty for CSP-biomass hybrid power plants. PT and ST technologies were considered, each with three operating strategies (no biomass, medium and full biomass) and five cases according to their thermal storage capacity (no storage, 5, 10, 10, 15 and 20 hours). Figs. 3 and 4 show the cumulative distribution functions for all PT and ST cases, respectively.

Fig. 3.

Cumulative distribution function of the profitability factor for Parabolic Trough plants. (a) Base Case, (b) Including biomass. BC: base case (no biomass), OS1: operation strategy 1 (medium biomass); OS2: operation strategy 2 (full biomass).

Fig. 4.

Cumulative distribution function of the profitability factor for Solar Tower plants. (a) Base Case, (b) Including biomass. BC: base case (no biomass), OS1: operation strategy 1 (medium biomass); OS2: operation strategy 2 (full biomass).

In total, 30 Monte-Carlo simulations were run (1 per case), each with 10 000 trials. The raw datasets are included in the Harvard repository. The datasets are contained in an Excel file, freely accessible at [2] and consisting of thirteen datasheets. The first sheet (Index) presents a general table of contents to describe the corresponding abbreviations and the order presentation of the other datasheets. Two sheets have been included for each of the six assessed configurations (i.e., considering two technologies and three operating strategies), which individually encompass the five cases according to TES capacities. The first one presents the datasets related to the random combinations of stochastic input variables and the corresponding results of the Profitability Factor. The second sheet shows each case's probability density and cumulative distribution functions.

3. Experimental Design, Materials and Methods

3.1. Meteorological data and biomass properties

For the study located in Seville – Spain, a single year (2017) solar data with a 10-minute resolution is used. This dataset was provided by the meteorological measurement station of the Universidad de Sevilla (University of Seville) [3]. These data are computed using NREL's System Advisor Model (SAM) software to obtain datasets related to the performance of the solar block (e.g., net generated electricity, thermal power captured in the reflection field, charging and discharging of the thermal storage, among others). General information related to the measuring station and a summary of the main parameters for the assessed single-year and the typical meteorological year (TMY) datasets is shown in Table 9. The TMY series was constructed and provided by the thermodynamics and renewable energy group of the University of Seville from data collected at the station during the period 2000-2012 [3]. Table 10 compares accumulated incidence, and daily DNI means for each month of the year regarding both datasets (i.e., this study's selected year and TMY). Finally, the properties of the feed biomass for the grate boiler included in the model are shown in Table 11 [4].

Table 9.

Meteorology station and solar datasets.

Meteorology station
Location	Seville
Time zone	GMT-1
Altitude above sea level (m)	15
Latitude (°)	37.41
Length (°)	-6.01
Station Owner	ETSI
Data provider	GTER
Meteorology data
Type	Single year	TMY
Data resolution	10-minute	10-minute
Global horizontal irradiance (kWh/m2/day)	5.11	4.99
Direct normal irradiance (kWh/m2/day)	5.92	5.67
Diffuse horizontal irradiance (kWh/m2/day)	1.58	1.57
Mean temperature (°C)	18.3	18.3
Mean wind speed (m/s)	2.6	2.6

ETSI: Escuela Técnica Superior de Ingeniería (University of Seville).

GTER: Group of Thermodynamics and Renewable Energy (University of Seville).

Table 10.

DNI comparative between the selected single-year and TMY dataset.

	Single year		TMY
	Monthly DNI (kWh/m2)	Mean daily DNI (kWh/m2)	Monthly DNI (kWh/m2)	Mean daily DNI (kWh/m2)
January	160.3	5.17	123.78	3.99
February	133.1	4.75	126.05	4.50
March	184.2	5.94	146.86	4.74
April	153.6	5.12	167.48	5.58
May	246.1	7.94	218.05	7.03
June	240.9	8.03	232.49	7.75
July	287.3	9.27	272.15	8.78
August	201.2	6.49	241.02	7.77
September	184.6	6.15	176.42	5.88
October	98.3	3.17	139.17	4.49
November	168.8	5.63	117.35	3.91
December	102.0	3.29	107.54	3.47
TOTAL	2160.4	5.92	2068.37	5.67

Table 11.

Biomass feedstock properties [4].

Component	% wt, dry basis
Carbon	50.90
Hydrogen	6.05
Oxygen	41.92
Nitrogen	0.17
Sulphur	0.04
Ash	0.92
Moisture	30% wt
High heating value	20.18 MJ/kg

3.2. Baseline design parameters

The optimal solar multiple (SM) at design for each TES capacity is calculated according to Eqs. 1 and 2 for PT and ST configurations, respectively [5]. Parametric optimisation analysis was conducted by varying the SM from 1.0 to 3.0 with a step of 0.4 and the TES capacity from 0 (implies no TES) to 18 hours with a step of 2 hours as in [6]. The parametric analysis results were used as input variables for the sizing of the hybrid systems. Correlations were obtained from the combinations between SM and TES where the minimum LCOE is obtained. The results are shown in Fig. 5.

$$SM=0.100\left(TE{S}_{hours}\right)+1.000$$ (1)

$$SM=0.106\left(TE{S}_{hours}\right)+1.122$$ (2)

Fig. 5.

Variation of LCOE and Capacity factor based on TES hours at various SM levels for CSP conventional plants. (a) Parabolic trough; (b) Solar tower.

Parameters such as total absorbed power, TES capacity and total reflection area, among others, vary depending on the correlations mentioned above. In addition, other input variables such as tower height (i.e., for ST configurations), receiver area and solar field geometry are calculated using the optimisation algorithm of the System Advisor Model (SAM) software based on the SM and DNI values at design. Details of the specifications used in the sizing of the PT and ST systems according to each TES level are presented in Table 12, where the summary shown in [1] is extended.

Table 12.

Technic parameters per storage capacity.

	No-TES	5 hours	10 hours	15 hours	20 hours
Parabolic Trough
Solar multiple (-)	1.0	1.5	2.0	2.5	3.0
Gross power output (MWe)	55.0
Alternator efficiency (-)	90%
Net power output at design (MWe)	49.5
Power cycle efficiency (-)	39%
Reference optical efficiency (-)	78%
Reference thermal efficiency (-)	72%
Power cycle thermal power (MWth)	141.0
Total power absorbeda (MWth)	141.0	211.5	282.1	352.6	423.1
TES thermal capacity (MWth)	0.0	705.15	1410.3	2115.45	2820.6
Collector type	EuroTrough ET150
Solar collector array (SCA) assemblies per loop	4.0
SCA length (m)	150
SCA aperture (m)	5.75
Required number of loops (-)	91.0	136.0	181.0	226.0	271.0
Total reflection area (m2)	295428	443142	590857	739020	886170
Solar Tower
Solar multiple (-)	1.1	1.7	2.2	2.7	3.2
Gross power output (MWe)	55.0
Alternator efficiency (%)	90%
Net power output at design (MWe)	49.5
Power cycle efficiency (-)	41.2%
Reference optical efficiency (-)	54%b
Reference thermal efficiency (-)	91%b
Power cycle thermal power (MWth)	133.5
Total power absorbed (MWth)	146.8	226.9	293.7	360.4	427.2
TES thermal capacity (MWth)	0.0	667.5	1335.0	2002.5	2670.0
Heliostat focusing method	IDEAL
Heliostat canting method	On-axis
Required number of heliostats (-)	2125	3382	4515	5523	6407
Total reflection area (m2)	306797	488276	651852	797382	925009
Tower height (m)	97	116	132	148	164
Receiver height (m)	9.5	11.8	13.3	14.4	15.3
Receiver diameter (m)	9.0	10.6	12.2	13.9	15.8

^aCalculated at DNI design point (850 W/m²).

^bAnnualised value.

The biomass block global efficiency can vary in the range of 20% to 40% depending on its size, plants of more than 100 MW_e reach the highest yields [7]. The influence of variable load operation on the biomass boiler thermal efficiency is included in the model, according to correlations 3 and 4. Logarithmic growth is assumed for operation at loads between 5 and 100 MW_e. Fig. 6 shows the biomass boiler's thermal efficiency variation as a load-level function. The applicable limits for the nominal capacities used in the study (i.e., 25 MW_e for operating strategy 1 (OS1) and 49.5 MW_e for operating strategy 2 (OS2)), including their minimum operating load, are highlighted. Further details are presented in [1].

$${\eta }_{th\left(boiler\right)}=0.134·\ln \left(OL\right)+0.285$$ (3)

$${\eta }_{\left(boiler\right)}={\eta }_{th\left(boiler\right)}·{\eta }_{\left(PB\right)}$$ (4)

Fig. 6.

Biomass boiler efficiencies as a function of the load level.

The variation of the turbine efficiency due to the system part-load operation and ambient temperature changes can be modelled according to Eqs. 5 and 6 [8]. For the temperature variation adjustment, the dataset of wet bulb temperature is used.

$${\eta }_{\left(Q\right)}=F_0+F_1·T_{norm}$$ (5)

$${\eta }_{\left(T\right)}=F_0+F_1·T_{norm}$$ (6)

Where:

$${\mathrm{Q}}_{norm}=Q_{actual}/Q_{design}$$

$${\mathrm{T}}_{norm}=T_{actual}-T_{design}$$

$${\eta }_{\left(Q\right)}\to F_0=0.9|F_1=0.1$$

$${\eta }_{\left(T\right)}\to F_0=1|F_1=-0.002$$

3.3. Market electricity price dataset

Iberian electricity day-ahead market (MIBEL) hourly prices for 2017 were used to analyse the profitability of the CSP-biomass hybrid systems. The dataset was obtained from the website of the Iberian trade system operator [9,10,11]. The data were processed to differentiate between working and non-working days, including in the latter the days that corresponded to local holidays in 2017 (Spain and Andalusia) [12]. Fig. 7 shows the annual average electricity prices for each hour. In addition, the mean annual price, calculated from all annual data according to each type of day, is included. Finally, Table 13 shows the summary of the dataset, including the minimum and maximum prices for each hour.

Fig. 7.

Hourly average electricity price in MIBEL.

Table 13.

Hourly electricity prices in the Iberian market.

	Working days electricity prices (USD/kWh)			Non-Working days electricity prices (USD/kWh)
	Mean	Max	Min	Mean	Max	Min
00:00	0.064	0.118	0.041	0.065	0.107	0.043
01:00	0.060	0.110	0.027	0.061	0.098	0.035
02:00	0.058	0.102	0.022	0.059	0.091	0.025
03:00	0.057	0.098	0.016	0.057	0.090	0.024
04:00	0.057	0.096	0.014	0.056	0.088	0.021
05:00	0.061	0.097	0.024	0.056	0.091	0.020
06:00	0.067	0.099	0.034	0.057	0.092	0.021
07:00	0.073	0.115	0.049	0.059	0.090	0.022
08:00	0.076	0.120	0.057	0.062	0.095	0.025
09:00	0.075	0.122	0.054	0.064	0.103	0.029
10:00	0.076	0.123	0.049	0.066	0.103	0.025
11:00	0.075	0.123	0.047	0.065	0.098	0.025
12:00	0.075	0.121	0.046	0.066	0.097	0.020
13:00	0.073	0.118	0.047	0.065	0.097	0.019
14:00	0.071	0.116	0.046	0.062	0.097	0.017
15:00	0.070	0.114	0.045	0.060	0.093	0.017
16:00	0.071	0.113	0.046	0.059	0.088	0.019
17:00	0.073	0.126	0.050	0.063	0.094	0.023
18:00	0.076	0.134	0.051	0.069	0.115	0.030
19:00	0.078	0.129	0.053	0.073	0.117	0.037
20:00	0.078	0.129	0.058	0.075	0.115	0.045
21:00	0.075	0.127	0.056	0.073	0.113	0.038
22:00	0.071	0.121	0.052	0.070	0.107	0.027
23:00	0.068	0.118	0.047	0.067	0.104	0.027

3.4. Stochastic input variables

Some input variables of the stochastic model fluctuate according to the probability distributions associated with their annual scaling rates. The probability distributions and the variation limits of all stochastic variables are thoroughly described in [1]. Fig. 8 shows the variation of the feed biomass cost by applying the high-end and low-end of its escalation rate (i_n) to the annual values within the economic analysis range. Regarding the electricity price, its annual escalation rate limits are applied to all hourly values of typical days (working and non-working), as shown in Fig. 9.

Fig. 8.

Biomass cost boundaries by annual escalation rate variation (i_n).

Fig. 9.

Electricity price boundaries by annual escalation rate variation (i_n). (a) Working days and (b) Non-working days.

The possibility of accentuating the trend of the peaks and troughs for daily electricity prices is also included in the model by considering a specific price variation (V_d) for the high-end (V_d = +25%) and the low-end (V_d= -50%) boundaries. This variation allows for the simulation of stretches or contractions of the critical points while maintaining the trend of the rest values concerning the annual average. The variation zones for the maximum and minimums daily prices are shown in Fig. 10.

Fig. 10.

Electricity price peak and trough boundaries by daily variation (V_d). (a) Working days and (b) Non-working days.

3.5. Technical valuation parameters and simulation procedure

The technical valuation parameters used to complement the economic assessment are calculated according to Eqs. 7 to 10.

$$CF=\frac{Q_n}{N{C}_{system}·8760}$$ (7)

$$Solarshare=\frac{Q_{sf}+Q_{TES}}{Q_n}·100$$ (8)

$$M_{Biomass}=\frac{TG{E}_{Biomass}}{HH{V}_{Biomass}}$$ (9)

$${\eta }_e=\frac{Q_n}{M_{Biomass}·HH{V}_{Biomass}+I_{sf}·A_{sf}}$$ (10)

Ethical Statement

This study meets all the requirements in Elsevier's publication ethics policy. It did not involve humans or animals and did not use data from social media platforms.

CRediT authorship contribution statement

R. Gutiérrez-Alvarez: Conceptualization, Methodology, Data curation, Formal analysis, Software, Writing – original draft. K. Guerra: Investigation, Writing – review & editing. P. Haro: Conceptualization, Methodology, Validation, Supervision, Writing – review & editing.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships which have or could be perceived to have influenced the work reported in this article.

Data Availability

• Profitability assessment of CSP-biomass hybrid power plants: Monte-Carlo simulations results (Original data) (Harvard dataverse).