Optimal Design Model for a Residential PV Storage System an Application to the Spanish Case
Round 1
Reviewer 1 Report
Authors partly addressed the previous reported issues. The heating issue was not clarified. The authors declare that heating is included in the winter months energy demand. Is it true? The household is heated with an average power below 200W during a December night? (considering that all the other appliances are off). More details related to the considered residential house must be included in the paper (at least the heated surface, number of users, thickness of the thermal insulation etc.).
L47: all acronyms and symbols used in the manuscript must be included here
L47: both acronyms and symbols must be alphabetically arranged;
L47: the acronym HAD is not consistent with its definition “Hourly Discrimination Tariff”;
L47: the description of the Ch must be consistent with that in the manuscript;
L271: please include some details in the manuscript related to “the acquisition cost of new devices in the year t”;
L373: “The PV panels are made of modules manufactured from crystalline silicone” must be corrected;
L374: please explain what means “with a losing in the energy production of 18%”;
L408: please include in table 5 more details related to the PV panel: number of the PV panels installed, efficiency of the PV panel, surface of a PV panel etc.;
L427: according to Fig.8, the PV production is able to fully cover the energy demand until 14:00, not to 15:00; please correct;
L427 and 430: 15:00 p.m. is redundant, please delete p.m.;
Author Response
REVIEWER 1
Comments and Suggestions for Authors
Authors partly addressed the previous reported issues. The heating issue was not clarified. The authors declare that heating is included in the winter months energy demand. Is it true? The household is heated with an average power below 200W during a December night? (Considering that all the other appliances are off). More details related to the considered residential house must be included in the paper (at least the heated surface, number of users, thickness of the thermal insulation etc.).
The data are referred to a household located at Seville, where winter is relatively warm, with a minimum temperature not lower than 5 ºC (ref. https://es.climate-data.org/europe/espana/andalucia/sevilla-2933/). So, warming at night is not normally done with electrical devices, but using blankets and winter pyjamas –gas, fuel oil or electric heating are rarely used at night–. We have removed from the paper the comment on heating and energy consumption to avoid any misunderstanding.
L47: all acronyms and symbols used in the manuscript must be included here
All the equations have been reformulated and symbols changed (following the suggestion of another reviewer). Regarding the acronym IRENA, it has been included in the table of acronyms.
L47: both acronyms and symbols must be alphabetically arranged;
They were arranged by definition. They are now arranged alphabetically according to acronyms and symbols.
L47: the acronym HAD is not consistent with its definition “Hourly Discrimination Tariff”
HAD has been replaced by HDT in the table and in section 2.2.2.
L47: the description of the Ch must be consistent with that in the manuscript;
Ch has been changed to ECH and defined as “Energy from PV panels used to charge the battery”.
L271: please include some details in the manuscript related to “the acquisition cost of new devices in the year t”;
The following text has been included at the end of section 3 “The shelf life of the BESS corresponds to 5000 charge cycles. If we assume one charge cycle per day, it would be necessary to replace the BESS after the thirteenth year. However, we have decided to replace it in year twelve in order to avoid battery malfunction problems. Note that the investment produced in that year will negatively affect its corresponding cash flow (eq. 8).”
L373: “The PV panels are made of modules manufactured from crystalline silicone” must be corrected;
The sentence has been corrected in section 2.2.3. The new sentence is as follow: “The facilities assessed in this research are composed of several PV panels (made from crystalline silicone) [11], an inverter and a BESS to store the surplus energy”.
L374: please explain what means “with a losing in the energy production of 18%”;
This comment has been removed from the paragraph involved (the one of L374). The reason is that we wanted to explain the components of the facility in that paragraph, and not their technical characteristics. These technical attributes are shown in Table 4 of the new version of the paper. In any case, the sentence means that the energy lost by the PV panels is 18%, defined this loss as the ratio between the solar energy they receive and the electrical energy they generate. This loss is not considered in our study, since we only need the data of the energy delivered by the panels.
L408: please include in table 5 more details related to the PV panel: number of the PV panels installed, efficiency of the PV panel, surface of a PV panel etc.;
Currently, the peak power of a (1.9m x 1.3m; 2.5 m2) PV panel is around 500Wp (0.5 kWp) –source: https://www.rebacas.com/paneles-solares-24-voltios/1155-panel-solar-500w-bluesun.html–. So, each step of 0.5 kWp in the facility involves installing one more panel. Thus, a facility of 1.0 kWp has two panels; a 1.5 kWp facility has three panels and so on. Likewise, the panel efficiency is given by “1 – system loss (%)”. All this information has been included in Table 4 of the new version of the paper.
Notice that some information has been omitted from the new table 4 at the request of another reviewer. In any case, it must be taken into account that our standard panel enters the mathematical model only through the energy it provides to the battery.
L427: according to Fig.8, the PV production is able to fully cover the energy demand until 14:00, not to 15:00; please correct;
Thank you! It has been corrected in the text.
L427 and 430: 15:00 p.m. is redundant, please delete p.m.;
Thank you! It has been corrected in the text.
Author Response File: 
Author Response.docx
Reviewer 2 Report
Find enclosed my report as well as the commented PDF.
Comments for author File: 
Comments.pdf
Author Response
REVIEWER 2
Summary of the manuscript and general comments.
This works is about defining a model to find the optimal design for a PV system and a storage system for households in Spain. The authors first describe the model, then describe the case study and conduct the optimization. The topic is really interesting and could be of interest for readers of Sustainability however. I have serious concerns regarding this manuscript. First the introduction is difficult to follow and does not clearly motivate the novelty of the present work in regards to the current literature. The presentation of the model is difficult to read because of the choice of the notation and because of the way it is presented. (Que hacemos aqui??) Finally the case study uses market prices (for roof-mounted PV system) that seem particularly low (nearly three time lower than the market price, see the comment G6). Given that the objective of the optimization problem are economic. Either the author can provide a strong justification of the value used, or they need do redo their calculations with more realistic prices. I cannot recommend acceptation of the present paper in the present state unless significant work is done to the manuscript. I advise the author to rework and resubmit as I still think that their work can be of great interests.
To my belief the main directions for improvement are:
— What are the contribution of the work compared to the literature and other optimization models of self-consumption presented in the literature?
— Please rework in the notation and the presentation of your model. A summary of the problem could help the reader (objective functions, variables, constraints, optimization method)
— Rework on the hypothesis of your model (price of the components, lifetime) I provided comments below for the manuscript. You can also find additional comments on the commented PDF.
G1) English: It seems to me that there are very few typos of English. However there are many uncorrected grammatical construction which sometimes makes there and understanding very difficult. I underlined and quoted bellow some examples. I strongly suggest the authors rephrase these parts.
We have found and corrected some typos along the text. Likewise, we have corrected the grammar constructions indicated by the reviewer. Thank you very much for warning us about these mistakes.
G2) The introduction must be reworked. It is difficult to follow the progression of the introduction. I have trouble understanding where the authors want to bring the readers. Furthermore the paragraphs are very long. It would be clearer to have shorter paragraphs, and one main idea by paragraph. Here I can’t see which ideas are in which paragraphs. Introduction also lacks transition between the main ideas.
The literature review has been rewritten and divided into shorter paragraphs to facilitate reader understanding. It follows the next scheme:
1.- General legislative framework.
2.- Purpose of the study.
3.- PV energy regulation at the residential level.
4.- Literature review on profitability of the PV household facilities, with special attention to the Spanish case.
5.- The novelty of our research compared to other studies.
Moreover, there are no mentions of previous study that did similar work such as for example:
- Comparing demand response and battery storage to optimize self-consumption in PV systems, 2016, Applied Energy, Lorenzi et al.
- Photovoltaic self-consumption regulation in Spain: Profitability analysis and alternative regulation schemes, 2017, Energy policy, López Prol et al.
Could you also clarify how your model is different from these studies? What is the novelty of your approach compared to theirs?
The article by Lopez and Steininger (2017) is mentioned in our paper (as reference [8]) for its analysis of the impact of different regulation schemes on the profitability of the PV installation. Additionally, we have included the following paragraph in the introduction in order to clarify how our model is different to that proposed by these authors: “…Note that these authors do not consider energy storage in their study nor do they try to identify an optimal configuration of the PV installation (with storage) for a typical consumer; they also consider some charges on the prosumer that are not currently in force in Spain.”
Regarding the paper by Lorenzi and Santos (2016), the next paragraph has been introduced in the introduction section: “…These authors take a different approach than ours. Thus, they compare two different strategies to optimize self-consumption in PV systems (in Portugal): storage and demand response. According to them, the most advantageous alternative will be the one that minimizes the daily expenditure for electricity (they do not adopt an annual cash flow perspective). Moreover, to deal with peak hours, its storage model imposes a different behaviour on weekdays and weekends that is not necessary in our model; thus, they assume that, during weekdays, the majority of the time is constituted by peak hours, so the surplus PV energy is forced to be injected in the battery.”
The reviewer should note that previous studies which propose similar analyses have been commented in our paper, such as [15], [16], [18], [20], [21], [24].
G3) As your paper is about a model to optimize storage and production according to the consumption of an households. You should have a paragraph that discuss about those models and previous studies. Here the only reference about a model is the one of Zhu et al.
FIGURE 1 –Table from Branker et al.for usual Price of PV systems
Following the reviewer's advice, we have highlighted the novelty of our optimization model and described the main differences between our research and other studies in the last part of the literature review: “The aim of this paper is to provide a general model that, for a specific user profile and PV facility location, gives the optimal configuration of BESS capacity and PV panel peak power according to the financial indicators Net Present Value (NPV), Internal Rate of Return (IRR) and Return of Investment (IR). Given that the financial indicators depend on the BESS and PV panel costs, and that these costs are falling in recent years, an analysis is carried out to measure the effect of the decreasing trend of these two costs on those financial indicators. In our opinion, this paper presents at least two main contributions: the data sources and the flexibility of the model of energy generation, sales and self-consumption. We use data from the Spanish market: the production of photovoltaic energy has been obtained from PVGIS (a specialized software), while the domestic energy demand comes from the hourly data of the user smart meters. Notice that our demand data is not the result of a simulation process, as is usually the case in the literature in this field; for this reason, the results obtained from our analysis are more accurate than those based on demand algorithms or simulations. As for the flexibility of the model, it is remarkable that, unlike those studies based on mathematical simulation, which are the majority in this field (see, for example, Ghiassi et al. [12]), Zhu et al. 18], Colmenar et al. [21], Bernal and Dufo [22] and Sarassa et al. [23]), our empirical financial model can easily be extended to other locations or pricing schemes.”
G4) The nomenclature is appreciable but the authors should significantly rewrite the way they introduce the model. It is very difficult to follow as all the equation and parameters are introduced at once. I would suggest introducing one equation, defining the variables and notations of your equations and then moving to the next one. See some examples that find pretty clear:
— Comparing demand response and battery storage to optimize self-consumption in PV systems, 2016, Applied Energy, Lorenzi et al.
— Photovoltaic self-consumption regulation in Spain: Profitability analysis and alternative regulation schemes, 2017, Energy policy, López Prol et al.
Taking the references proposed by the reviewer, we have rewritten the mathematical model; all the equations have been introduced step by step. Moreover, the nomenclature of variables has been revised and reformulated in all the paper and, at the same time, the suffix “hdt” has been removed from the model. We appreciate the reviewer's suggestion; the model is clearer now.
Could you also clarify how your model is different from these studies? What is the novelty of your approach compared to theirs?
The answer to this comment can be found in point G2 of this review.
G5) About your economic model: Did you considered the Operation and maintenance costs? If yes where? Did you consider the price of the inverter? If yes how?
The objective of the paper is not the optimal design of the technical equipment, the objective is to define a tool that determines the optimal combination of storage and PV generation for a given user (based on his hourly consumption). For this reason, and in order not to extend the paper too much, a breakdown of the components of the installation has not been considered, although these components are included in the two main sections of investment (BESS and PV facility).
Did you consider the fact that you have to change your battery after 12 years? If yes where?
It negatively affects the cash flow of year 12 (see eq. 8, component It).
Did you consider a nonlinear variation of the systems (battery and PV) with respect to the size (economy of scale)? If not could you justify why?
The existence of fixed installation costs (which would justify the existence of economies of scale) would only affect the NPV in the initial period investment, I0. These costs have not been considered in our model for the sake of simplicity; note that they are relatively small in relation to the whole project and that in many municipalities in Spain these costs are offset by subsidies granted by local administrations –in Seville, for example, the prosumer is entitled to pay only half of the real estate tax over a 5-year period–.
G6) l.382 The authors consider a price of Photovoltaic system (all inclusive, including the installation etc) of 900 €/kWp. This value only applies for very large PV farms. For utility scale (2-5kWp) the price is more around 3000 €/kWp. Furthermore, the author justifies this price with ref Branker et al. "A review of solar photovoltaic levelized cost of electricity" [31], however in this work the prices are more around 5000 €/kWp (the smallest price they gave was of 3500C/kWp). The second reference the author gives (G. del Coso et al. "The impact of silicon feedstock on the PV module cost") is about price of Silicium. It is therefore irrelevant as it does not include all the cost related to a roof mounted PV system. If you used a value of 900 €/kWp and you cannot justify it better, I am afraid all your results are irrelevant...
The price of the PV system in our paper is the result of current offers made by local contractors –in an increasingly competitive market, the higher the competition between the companies that offer this type of systems, the lower the price of the system–.
The values mentioned by the reviewer were reasonable until not long ago. The survey of Branker et al. (2011) was published in 2011 (9 years ago), and it analyses studies from the period 2003-2011. In the recent contribution by Dorr and Seba (2020): “RethinkX Energy Disruption Methodology”, it can be appreciated the amazing cost reduction that this technology has had in recent years, more than 80% between 2010 and 2020. Observe the figure used by these authors:
In our opinion, the PV costs described by Branker et al. (2011) are compatible with the reduction rate presented by Door and Seba (2020), and with the price of 900 Euros/kWp that local constructors have recently offered us.
Specific comments
l.58: Authors say: "At the same time, all the administrative process has been simplified, only one notification being necessary to the Administration in order to sell". Not sure to understand. Maybe this is something common in Spain but make this clearer for internal readers.
The sentence has been corrected to make it clearer: “At the same time, all the administrative process has been simplified; thus, currently, a seller only has to present to the Spanish Public Administration a formal declaration (endorsed by an engineer) indicating that technical and administrative requirements for sale of energy are met.
l.61: And? What is the purpose of this sentence here?
l.64: Reference?
We have linked in a more correct way all the information concerning Dusonchet and Telaretti (2010): “Dusonchet and Telaretti [4] presented an economic analysis of a photovoltaic (PV) facility without BESS in western EU countries in the year 2009. They pointed out that most of the countries analyzed (14 out of 17) have introduced policies to support PV household facilities, but the saving in tariffs did not cover the expenses of the facility in five of them (Netherlands, Luxembourg, Finland, Ireland and Sweden).”
l.65: I think you mean ’the countries’ instead of ’those countries’. If you use ’those country, it refers to those you just talked about which are Netherlands, Luxembourg, Finland, Ireland.
Thank you! The sentence has been corrected in the text as follow: “…that the countries with net-metering and active self-consumption in 2013 (Italy and Greece) have the highest profitability indexes for PV facilities”.
l.89: What is the facility life time? Is it in year? To me LCOE=Cost / (energy production), and not ’cost/ facility lifetime’ See e.g. Sommerfeldt et al. 2017 RSER, Revisiting the techno-economic analysis process for building-mounted, grid-connected solar photovoltaic systems: Part one–Review.
Part of the sentence has been removed in order not to mislead the readers: The corrected sentence is: “The levelized cost of energy (LCOE) was reviewed by Zhang et al. [11] in the year 2014 for the European electrical market.” Please, note that the LCOE indicator is not part of our mathematical model.
l.91 : I do not understand the two part of the sentence. Does the authors mean ’... and THAT the feed-in tariffs ...’.
Indeed, the sentence is ambiguous. It has been rewritten as follow: “They observed that the LCOE for PV facilities decreases as a consequence of technological evolution, and that the feed-in tariffs to support the PV deployment were reduced or even eliminated”.
l.101: Authors say: "Nowadays in Spain, with more mature technology and more suitable policies, it is considered that net-metering is an excellent way to improve the profitability and sustainability of PV pa- nels, which should be commissioned according to the best renewable energy resource available in each location. End of the sentence is unclear to me.
This part of the sentence has been removed because the commissioning of renewable energy supply is not the purpose of this research, which focuses only on solar energy at the residential level. The corrected sentence is as follow: “Nowadays in Spain, with more mature technology and more suitable policies, it is considered that net-metering is an excellent way to improve the profitability and sustainability of PV panels.”
l.109 Please define. There are many way energy efficiency can be defined with PV systems. To me the most common being the ’Energy/production/Irradiation received". I do not think you mean this energy efficiency in your example.
Sorry, the right word used in the mentioned paper (Chiacchio et al. [15]) is “performance”: “Chiacchio et al. [17] determined the performance (in terms of plant and services availability) of a PV facility of 4.32 kWp located at Catania”.
l.121-126: You should talk about your contribution in a dedicated paragraph (like the one that you start at l.156). You cannot just make some statements ("Unlike our study ...’", "... while we used ...") here and there. Moreover then you don’t talk about your work until l. 156.
To follow the reviewer's suggestion, we have emphasized the purpose of our paper in the first paragraph of the introduction, and concluded the literature review with a paragraph on the novelty and relative contribution of our study. Likewise, we introduce a reflection on the social and private benefits of this type of generation business.
l.159: Authors say: "As the BESS and PV panels prices are falling due to technological progress, a sensitivity analysis is performed based on technical parameters and equipment (panel and BESS) costs." How does the ’falling price’ relates to the sensitivity analysis? I do not understand this sentence.
The sentence has been rewritten as follow to make it clearer: “Given that the financial indicators depend on the BESS and PV panel costs, and that these costs are falling in recent years, an analysis is carried out to measure the effect of the decreasing trend of these two costs on those financial indicators”. Note that the word “sensitivity”, which can be ambiguous, has been removed from the text to avoid confusion.
l.162-163: Authors say: "Regarding the data, it must be borne in mind that we use real data (not simulated) from the Spanish case:" Data are data. The fact that they are simulated makes not them ’unreal’. Please rephrase. Furthermore, what you mean here is that your data are not simulated. I may disagree with that. Indeed I thought that PVGIS was extrapolating data from weather stations. The data you using are likely to be an interpolation of data in nearby weather stations. However they are likely to be different from data you would obtain from direct measurements using parameters.
The reviewer is right (we wanted to refer to demand data). The commented sentence has been rewritten as follow: “We use data from the Spanish market: the production of photovoltaic energy has been obtained from PVGIS (a specialized software), while the domestic energy demand comes from the hourly data of the user smart meter. Notice that our demand data is not the result of a simulation process, as is usually the case in the literature in this field…”
Table.1 what is ’Theme’? You distinguish ’Economic Analysis’ from LCOE. To me LCOE is an economic indicator for economic analyses. Please clarify. What is the purpose of Table 1? Your paper is not a review paper. Here to me it looks like you did a small review of related paper but without a clear goal.
You are totally right, LCOE is an economic indicator.
Following your recommendation, Table 1 has been removed from the paper. The rest of the tables have been renumbered, as well as their references in the text.
l.236-248: Here the author introduce the model. However 8 equations and 18 parameters are introduced at once without any explanations and descriptions. It is therefore nearly impossible (except by taking a considerable amount of time) to understand what was done. You should introduce each equation by saying what this equation represents (For ex : the storage equation for eq 1 the cash flow for eq. 8). This makes the reading very difficult and It is also difficult to check the equations. I suggest a rewriting of this part. The use of ’hdt’ is very weird for me. Why not removing them (since they are everywhere).
We have rewritten the model so that all the equations have been introduced and explained step by step. Likewise, the suffix “hdt” has been removed from the model. We appreciate the reviewer's suggestion; the model is clearer now.
Your naming of the variable is also unclear. For energy sometime you use E, sometime D and sometime C. But you also use C for costs. This makes the reading and understanding difficult. Another example E is for Energy sold to the market and P for energy price, therefore EP can be the multiplication of both those terms. However you used EP as the Energy production... (To me a clearer way of naming data would be like Comparing demand response and battery storage to optimize self-consumption in PV systems, 2016, Applied Energy, Lorenzi et al.).
The nomenclature of variables has been reformulated and grouped by class (energy, costs, etc.) Thanks for the reference (Lorenzi and Santos, 2016).
l.256-258: I thought you used data from PVGIS? In PVGIS the weather conditions are already taken into account, then why modelling them with a random noise? Moreover, how did you define this random noise?
It is true that in PVGIS the weather conditions are already taken into account, but this does not allow controlling for certain disturbances that may affect PV production, such as an unexpected cloudiness, an unexpected failure of the PV installation, measurement errors, etc. This kind of random events are controlled by an error term in our model.
l.265: What is Dhdt – Eq:(5). Please rewrite.
Sorry, D is not an hourly variable. It is the annual demand of the household. It should be denoted as “D”. It has been corrected in the paper.
l.284: Typo in equation, see PDF.
Thank you. Equations corrected.
Figure 3. Hour instead of month see PDF.
Thank you. Figure corrected.
Table 6: You considered that the investment price of the PV system varies linearly with its capacity. This may be true, but the costs for installing the system are nearly a fixed cost (given that you consider a small installation). Therefore I seriously doubt that I0=(Cost of the PV system + cost of the installation + cost of the inverter) is linear with the size if the system. Could you comment on this point?
As we discussed earlier, the existence of fixed installation costs would only affect the NPV in the initial period investment, I0. These costs have not been considered in our model for the sake of simplicity; note that they are relatively small in relation to the whole project and that, in many municipalities in Spain, these costs are offset by subsidies granted by local administrations –in Seville, for example, the prosumer is entitled to pay only half of the real estate tax over a 5-year period–.
Table 4: How did you consider the round trip efficiency of the battery in your model?
This parameter had been taken into account in the calculations but not in the description of the model. We have corrected equation (1) to account for this efficiency (η). Observe that it enters the model by reducing the energy supplied by the PV panel that the battery is capable of managing (η = 0.92 (92%)).
TYPOS
l.56: Authors say: "In particular, this Decree allowed households to sell the surplus energy to the market, being the energy company in charge of compensating the income earned on the electricity bill" The market is the energy company? Please check English.
Thank you! The sentence has been rewritten as follow: “In particular, this Decree allowed households to inject the surplus energy into the electricity market, being the company with which the user has contracted the electricity supply the one in charge of offsetting the income earned by the prosumer on the electricity bill”.
Author Response File: Author Response.docx
Round 2
Reviewer 1 Report
Authors addressed the previous reported issues.
The paper can be considered for publication after a minor revision addressing the following issue.
L460: according to the authors’ response, the 18% seems to be actually the efficiency of the photovoltaic modules, not their loss. Thus, efficiency must appear in Table 4 instead of loss
Author Response
REVIEWER 1
Authors addressed the previous reported issues.
The paper can be considered for publication after a minor revision addressing the following issue.
L460: according to the authors’ response, the 18% seems to be actually the efficiency of the photovoltaic modules, not their loss. Thus, efficiency must appear in Table 4 instead of loss.
Thank you very much. Table 4 has been modified as follows:
Table 4. Location and parameters for the PV panels. Source: PVGIS [34].
|
Item |
Value |
|
Location (Seville) (º) : |
37.389, -5.995 (Seville) |
|
Database used: |
PVGIS-SARAH |
|
PV technology: |
Crystalline silicon |
|
PV installed (kWp): |
1.0 |
|
Surface (m2) |
5.0 |
|
Number of panles |
2 |
|
System efficiency (%): |
18 |
|
Slope angle (°): |
34 |
|
Azimuth angle (°): |
2 |
|
Yearly PV energy production (kWh): |
1599.92 |
|
Yearly in-plane irradiation (kWh/m2): |
2 187.31 |
Author Response File: Author Response.pdf
Reviewer 2 Report
Dear Authors,
Please find attached the comments. I still have major issues regarding the economical hypothesis and the setting of the optimisation problem.
Comments for author File: Comments.pdf
Author Response
REVIEWER 2
- General comment
Authors provided great effort into rewording and better presenting and explaining the model which is greatly appreciated. Work has also been made on the introduction.
We want to thank the reviewer for his/her review, the paper is improving remarkably thanks to his/her contributions.
I still have two major concerns regarding the hypothesis about the solar system cost and the optimization problem. Without a clear and sounded rebuttal to my issues I cannot recommend acceptance.
- Optimisation Problem
Author said: "The objective of the paper is not the optimal design of the technical equipment; the objective is to define a tool that determines the optimal combination of storage and PV generation for a given user (based on his hourly consumption)." I did not really understand the difference.
Sorry, really, the sentence is confusing. The idea we want to convey is that we do not intend to optimize the PV facility for a particular user with a specific consumption profile, but to define a general tool that is capable of optimizing the facility for any consumer (based on their consumption profile).
If you are doing optimization please clearly state: What is your objective(s) functions (what are the values that you minimize/maximize), what are the variables (optimization parameters), what are your constraints. I have still some trouble identifying these in your problem. In the figure 1 is the example of Zhu et al. We can here clearly understand their optimization problem.
We have included the following table in the paper to clarify the optimisation model:
|
Given: |
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1) An hourly PV energy generation . |
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2) The hourly demand profile, . |
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3) The energy price (PE) and access tariff (AT). |
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4) The round trip efficiency of the BESS (η). |
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5) The daily peak hours and off-peak hours. |
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Find: PV panel peak power () and battery capacity () for different scenarios of investment costs () and annual residential demand (D). |
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Maximize: The financial indicators (optimised separately): |
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where:
|
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Subject to: |
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1) BESS level constraint: |
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2) PV outflow constraints: |
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3) Self-consumption constraints: |
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4) Surplus energy constraint: |
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5) Hourly demand constraints:
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- Hypothesis on investment cost.
Please make clear if you consider the module price (which indeed in 2020 can be as low as 900C/kWp). Or the total price of an installed roof mounted PV system (as your footnote suggests) including: Inverters, wires, installation cost.
Please be clear about what is included in this price, and provide a suitable reference for this price (For example average market prices in Spain).
The paragraph on the PV system cost has been modified: “In this research, the unitary cost of the PV system () is 900 €/kWp [31], [32], [33] 1. An important aspect to take into account is that this cost refers to the total price of an installed roof mounted PV system, including Engineering Procurement and Construction (EPC), Balance of Systems (BoS), inverter, PV modules and others. The only cost that have not been considered in this total is the fixed installation cost (permitting and other legal issues), since in many Spanish municipalities there are equivalent subsidies that offset these costs –note also that this assumption simplifies the programming of the model.”
In footnote 1 you can read: “ 1 In addition to these references, the unitary cost of the PV system has been contrasted with a real offer made by a local contractor in Spain; the offer includes EPC, BoS, inverter, PV modules and others.”
Indeed, I am sorry but the references you provided are not sufficient, the first reference [8] is about the price of silicons in 2010, the second (Dorr and Seba (2020) : “RethinkX Energy Disruption Methodology”) is about a Think Tank doing some prospective projections. In your review report you show a Figure of these authors (Figure 3 to justify the price of 900C/kWp. This figure is problematic for several reasons:
— First the unit is in $=kW which does not mean much. They probably mean $=kWp
— They say that the original data comes from the NREL.
— We do not know what is included in this price (is it just the module or the module + all the other cost inherent to a roof mounted PV system).The NREL is indeed a reference in PV system. However I could not find these data. Instead on the NREL website you can find the following figure 4.
In the NREL database (see 4) the price for installed cost of residential PV in 2018 was of 2700 $=kWp (nearly 2200C/kWp) which is still more than twice higher than the author hypotheses of 900 C/kWp... Moreover either considering a cost decrease between 2018 and 2020, we are still very far from 900C/kWp. This work needs to be done by the author not the reviewer...
Being not fluent in Spanish I could not look for those prices in Spain but here is what I found: March 2020 : [GreenTechMedia] : Around 2C/Wp (2000C/kWp) [Idealista] : ’between 600 and 800 euros per square metre’ which make it roughly around 3000-4000C/kWp...
Even if you claim (and I agree with you) that price should keep on falling in the future, I cannot agree with your hypothesis. Moreover given that all your indicators (NPV, IR and IRR, which are the objective functions to be minimized) are highly dependant on this investment price, therefore you must be more convincing about the economical hypothesis.
We fully understand all your comments and concerns. We will try to clarify them below. First of all, we want to point out the significant difference between the USA and Europe in terms of the price of roof mounted PV systems, an issue that has always been controversial. In this regard, a report recently prepared by the Joint Research Centre (JRC, 2019, page 51, Figure 12) shows that the cost of a residential roof mounted PV installations in the USA is three times the cost in Germany –Jäger-Waldau, A., PV Status Report 2019, Publications Office of the European Union, Luxembourg, 2019, ISBN: 978-92-76-12608-9, doi:10.2760/326629–.
In this report you can read the following: "Please note that customers in the USA still receive a 30% federal tax credit (until 2021), which in parts is responsible for the overall higher prices. The price increase in 2018 and 19 is attributed to higher module prices due to the import tariffs as well as a high demand”.
It appears that fiscal policies and market tensions are behind the higher prices in the USA, explaining the difference between the price published by NREL and the one used in our work. Moreover, Figure 12 of the JRC report includes all installation costs for a residential rooftop facility: Engineering Procurement & Construction, Balance of Systems, Inverter, PV Module and others (pages 50 and 53). In the case of Germany, in 2018, those costs were around 1,000 Euros/kWp, compared to approximately 3,500 Euros/kWp in the American case.
The cost considered in our work, 900 Euros/kWp, is somewhat lower than that mentioned for Germany (1,000 Euros/kWp). It must be taken into account that: (a) the labour cost in Spain is lower than in Germany, so that the PV installation price in Spain will be reduced compared to the German case; (b) the decreasing trend of costs would justify lower prices for the year 2020.
Other references that are in line with the JRC report are:
Keiner, D., Ram, M., Barbosa, L. D. S. N. S., Bogdanov, D., & Breyer, C. (2019). Cost optimal self-consumption of PV prosumers with stationary batteries, heat pumps, thermal energy storage and electric vehicles across the world up to 2050. Solar Energy, 185, 406-423. [Table A.1]
Ram, M.; Bogdanov, D.; Aghahosseini, A.; Oyewo, S.; Gulagi, A.; Child, M.; Breyer, C.; Caldera U.; Sadovskaia K.; Farfan J.; Barbosa LSNS.; Fasihi M.; Khalili S.; Dalheimer B.; Gruber G.; Traber T.; De Caluwe F.; Fell H. Global Energy System based on 100% Renewable Energy – Power, Heat, Transport and Desalination Sectors; Study by Lappeenranta University of Technology and Energy Watch Group, Lappeenranta. Berlin, Germany, 2019.
Consequently, in order to avoid misunderstanding, we have removed the following references on the cost of PV installation:
Del Coso, G.; Del Canizo, C.; Sinke, W. C. The impact of silicon feedstock on the PV module cost. Solar Energy Materials and Solar Cells. 2010, 94, 345-349, doi:10.1016/j.solmat.2009.10.011.
Dorr, Adam; Seba, Tony; RethinkX Energy Disruption Methodology. Available on line: https://static1.squarespace.com/static/585c3439be65942f022bbf9b/t/5faae0da798b066250710f7f/1605034238811/Energy+Reports+-+Methodology.pdf (accessed on 09 December 2020).
Instead, we have included the following references:
[31] Jäger-Waldau A. PV Status Report 2019, EUR 29938 EN. Publications Office of the European Union, Luxembourg, 2019, doi:10.2760/326629.
[32] Keiner, D; Manish, R.; Barbosa, L; Bogdanov, D; Breyer, C. Cost optimal self-consumption of PV prosumers with stationary batteries, heat pumps, thermal energy storage and electric vehicles across the world up to 2050. Solar Energy. 2019, 185, 406-423, doi.org/10.1016/j.solener.2019.04.081.
[33] Ram, M.; Bogdanov, D.; Aghahosseini, A.; Oyewo, S.; Gulagi, A.; Child, M.; Breyer, C.; Caldera U.; Sadovskaia K.; Farfan J.; Barbosa LSNS.; Fasihi M.; Khalili S.; Dalheimer B.; Gruber G.; Traber T.; De Caluwe F.; Fell H. Global Energy System based on 100% Renewable Energy – Power, Heat, Transport and Desalination Sectors; Study by Lappeenranta University of Technology and Energy Watch Group, Lappeenranta. Berlin, Germany, 2019.
Then, the sentence on the average cost of the PV system is as follows: “In this research, the unitary cost of the PV system () is 900 €/kWp [31], [32], [33]…”
In any case, we would like to emphasize that the price adopted in our study does not come directly from an academic source, but from a real PV facility installed in the home of one of the members of our research group, who has provided us with the project budget and the invoice from his PV installation –see footnote number 1–.
Regarding the references you mention about the Spanish market, we would like to mention the following:
- GreenTechMedia: https://www.greentechmedia.com/articles/read/spain-goes-from-zero-to-hero-on-solar-self-consumption. The source of information is an interview with the CEO of Ecovatios:
“According to Carlos García Buitrón, CEO and founder of the Madrid-based green power retailer Ecovatios, the cost of commercial-scale PV arrays in Spain is currently under €1 ($1.10) per watt for systems above 50 kilowatts, and as low as €0.70 ($0.77) above 500 kilowatts. This can result in a payback of as little as five years in some parts of the country, he said.
For residential systems, which tend to be between 1.5 kilowatts and 2 kilowatts in size, the cost is less than €2 ($2.22) per watt without storage, “but you can find much more aggressive offers in the market,” García said”
Note that, although Mr. Garcia says that the cost is less than 2 euros per watt (we guess Wp), he also says: “..but you can find much more aggressive offers in the market”. Since we do not really know this company, we have been searching for its activities, and we have found that it is a company of five employees (https://www.linkedin.com/company/ecovatios/, https://ecovatios.com) which has developed a business model based on building self-consumption plants at a high cost, assuring prosumers a price for their surplus energy of 85 euros/kWh, which is almost twice the regulated price. It doesn't seem like a reliable source or a long-term sustainable business.
- https://www.idealista.com/en/news/lifestyle-in-spain/2020/08/04/7760-how-much-does-it-cost-to-install-solar-panels-on-a-property. The ‘Idealista’ website is dedicated to the sale and rental of properties between individuals and companies. It offers, as an added service, contractors for painting, reforms, plumbing or electricity. In our opinion, it should not be considered a solvent source to analyse the costs of the residential PV rooftop market in Spain, and even more after our real experience with a contractor in our city.
The authors say ‘The existence of fixed installation costs (which would justify the existence of economies of scale) would only affect the NPV in the initial period of investment, I0. These costs have not been considered in our model for the sake of simplicity; note that they are relatively small in relation to the whole project and 2/4 2020/11/26 that in many municipalities in Spain these costs are offset by subsidies granted by local administrations –in Seville, for example, the prosumer is entitled to pay only half of the real estate tax over a 5-year period–.’
You define the NPV as such 5. How can these costs [I0] have not been considered in our model? You explicitly included I0 in the NPV definition (and therefore in IR and IRR...).
Furthermore the NPV is defined over the lifetime of the project, so that it must include the initial investment. You cannot just disregard them for the sake of simplicity.
Ref : Sommerfeldt et al. 2017 RSER, Revisiting the techno-economic analysis process for building-mounted, grid-connected solar photovoltaic systems : Part one–Review For PV system + Battery storage, the Initial investment cost account for a very large part of the whole project cost.
Please be very clear about which cost you consider and justify them.
Note that this initial expenditure is included in the model through the variable I0. This initial investment includes both the cost of the PV facility (modules and its different components) and the cost of the storage system; only the fixed installation costs have been ignored (permitting and other legal issues) for the reasons already stated. In fact, the procedure followed in our work to calculate the NPV is consistent with that of Sommerfeldt et al. 2017.
I still suggest to check the English as many English typos are present in the revised version.
We have corrected the following typos:
L75 “…according to certain financial indicators; this outcome is especially useful for installers, prosumers and system regulators”
L136 “Zhu et al. [18] designed an algorithm to optimize a residential facility with PV panels and BESS based on an initial budget.”
Word “analyze” has been replaced by “analyse” along the text as for example:
L140 “There are some studies that analyse the deployment of PV energy in Spain…”
L152 ”For its part, Bernal and Dufo [21] analysed the economic viability of a residential PV facility located in Saragossa (Spain) in the year 2016…”.
Word “optimize” and “optimization” have been replaced by “optimise” and “optimisation” along the text as for example:
L70 “…that aims to optimise the power of the PV panels and the capacity of the BESS.”
L96 “Zhu et al. [10] presented in 2013 an optimisation analysis…”
L165 “…they consider some charges on the prosumer bill that are not currently in force in Spain”
L265 “…and not all the energy outflow is consumed by the household”
L271“…plus a random disturbance () which follows a normal distribution and allows controlling for certain unexpected events”
L368 “The range of the total monthly montly total consumption is between 253 kWh…”
L406 “…there is a specific electricity tax of 5.11% on the for the net cost of consumption bill and contracted power”
L573 “The exception to in this behaviour is observed in the panel of the lowest peak power (0.5 kWp), whose IRR rate tends to fall with the size of the battery.
Author Response File: Author Response.pdf
Round 3
Reviewer 2 Report
I thank the authors for their patience and work.
The optimization problem is now clearly presented.
Furthermore the hypothesis about the price of rooftop PV is better justified. I would not personnaly use a similar hypothesis for such a problem in Spain, I would be much more conservative. But the authors provided sounded references.
This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.
Round 1
Reviewer 1 Report
The authors present a model for an optimal design for a residential PV storage system and a case study on Spanish households. The subject is worth investigating but the paper cannot be considered for publication due to the following issues.
The main concerns are related to the novelty and to the advantages offered by the proposed model. The authors must highlight these in comparison with existing models and dedicated software (e.g. PVSol, PVGIS etc.). Also, the correctness of the numerical simulations is uncertain.
In the evaluation of the initial costs, only the price of the PV modules and of the
battery energy storage systems without considering the price of the inverter, charger, mounting structure, interconnections, protection elements, energy meter/s and so on, as well as the installing costs.
The demand profile presented in section 2.2.1 must be checked, the authors declare that heating is included in the winter months. Is it true? The household is heated with an average power below 200W during a December night? (considering that all the other appliances are off)
Quality of the figures must be improved (e.g. Fig.4)
The energy production profile of 1 kWp in Seville on 21 June (Fig.6) cannot be the same with that produced in December (Fig.7). Moreover, the graph plotted in Fig.8 for June shows higher values than in Fig.6. Which one is correct?
Also, the daily profile of the energy demand presented in Fig.8 for June does not match the values presented in Fig.5
All the symbols used in the paper must be alphabetically included in Nomenclature and the symbol description in the manuscript must be consistent with the Nomenclature.
English and formulation must be revised, e.g.:
L19:”PV peak power panels”
L29: “improve and develop solar energies”
L131: „a photovoltaic panel”
….
The measurement units must be correctly used:
L25: the battery capacity is measured in Ah not in kWh,
L26: the measurement unit for power is not kWh
Reviewer 2 Report
The article is very long and hard to read. A lot of work has been done on the Optimal design model for a residential PV storage system. Authors should emphasize more whether their approach is innovative.
https://doi.org/10.3390/app9061138
DOI:10.7873/DATE.2014.154
DOI:10.1109/TSTE.2015.2456752
DOI:10.1109/ASPDAC.2013.6509670
Reviewer 3 Report
The manuscript by Gallardo et al. discusses the model that best describes the PV power generation capacity, self-consumption, storage, and marketing to optimize financial investments and profitability. The issue is highly relevant for PV producers, investors, consumers, and policymakers. The manuscript is well-written and is of interest.
While it seems intuitively obvious to have a BESS for better PV utilization, a mathematical formulation makes it more quantitative.
I have two concerns that are listed following -
(1) In Figure 9, the data for June energy production seems to be an outlier. Not sure how much it would affect the analysis and conclusion.
(2) Comparing NPV in Figure (11) - without BESS and Figure (15) - with BESS, why the HPV values are the same for given PV panel peak power? Why that would be the case? The additional BESS component should change the cash flow.
Lastly, the conclusion can be improved, given the introduction discusses LCOE at many instances but it's totally missing in the conclusion.
