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Dynamic vulnerability in standalone hybrid renewable energy system
Energy Conversion and Management 180 (2019) 258–268
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Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman
Dynamic vulnerability in standalone hybrid renewable energy system Shoki Kosai
T
Department of Mechanical Engineering, College of Science and Engineering, Ritsumeikan University, Shiga, Japan
ARTICLE INFO
ABSTRACT
Keywords: Redundancy Battery performance Energy security Reliance Diversification Zero energy building
Ensuring continuous power supply in the hybrid renewable energy and battery system is important because power utilization is fundamental to economy and human well-being. Earlier studies have been concerned with the ability to supply a desired amount of power in a long-term static condition in the context of system reliability. Meanwhile, short-term dynamic behavior and its relevant vulnerability in a hybrid system associated with a continuous power supply has been given less attention due to the modeling complexity of the problem. This study uses a parametric approach to assess the dynamic transition of vulnerabilities potentially leading to disruptions in electricity supply throughout a given day to identify a specific vulnerable time. The methodology of quantifying the dynamic vulnerability of power source components during a given day in a hybrid system is developed. Then, the temporal dynamic vulnerability and overall vulnerability in the system are presented by changing the capacity size in the case of a fictitious standalone house. Through the analysis, the approach developed in this study would potentially highlight the greater contribution of the battery to continuous power supply, compared with the solar PV in the hybrid system.
1. Introduction
In these applications of hybrid renewable energy and battery systems, ensuring a continuous power supply without disruption is significant because power utilization is crucial for stable economy and human well-being. A sustainable hybrid renewable energy and battery system can be achieved via thorough evaluation of vulnerabilities to disruptions of electricity supply. Particularly, vulnerability is highly related to facilities of power generation, including renewable energy sources and storage technology. Many studies have been concerned with the ability of hybrid renewables and batteries to supply a desired amount of power in a long-term static condition. The common vulnerability associated with power generation is insufficient capacity size [11]. Development of an adequate infrastructure containing redundant capacity would assist in the uninterrupted access of power products [12]. Reflecting the intermittent and stochastic characteristics of renewables, the probability of power disruption over a long period (e.g., one year) is, in many cases, assessed to quantify system reliability. Various reliability indices have been developed so far, including loss of power supply probability (LPSP) [13–20], loss of load expectation (LOLE) [21], and loss of load probability (LOLP) [22–27], and each index is computed under various options of capacity size. Additionally, earlier studies have also focused on the uncertainties potentially affecting long-term reliability. Uncertainties in intermittent renewable energy, such as wind speed and site [22,28] were analyzed using a design-space approach [21,29–32] and chance-constrained approach [33–36]. Uncertainties in consumption patterns were also
In last few decades, heavy reliance on fossil fuels has raised an alarming number of various energy-related issues, such as economic and environmental concerns, and energy security. To decrease the reliance on fossil fuels, renewable energy has been increasingly considered a panacea. Meanwhile, the use of renewable energy (e.g., solar PV) brings uncertainties of constant power supply due to the high dependency on weather conditions. The stochastic and intermittent nature of renewables require the installation of storage technology. Despite high capital costs and energy losses in the process of conversion [1,2], storage technology can contribute to power and load leveling, and the retention of power stability [3]. In addition, storage technology also operates as an energy source when the demand exceeds the power generated by renewables [4]. Because of its community-based nature, renewable energy is highly matched with the concept of local production for local consumption. It can be applied as a microgrid of a medium-sized power flow system in both rural and urban communities. Rural communities are often isolated communities in which the electrical support of a centralized power grid is not provided [5]. Urban communities are under the shift from a centralized to a distributed power system to establish a society more resilient to climate change and natural disasters [6–8]. Besides its application as a microgrid, the hybrid system can be used as a smallersized system for an individual building and house, named zero energy building (ZEB) and zero energy house (ZEH) (e.g., [9,10]).
E-mail address: [email protected]. https://doi.org/10.1016/j.enconman.2018.10.087 Received 30 August 2018; Received in revised form 26 October 2018; Accepted 27 October 2018 0196-8904/ © 2018 Elsevier Ltd. All rights reserved.
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Nomenclature
PV SD VIT VR ZEB ZEH
List of abbreviations LOLE LOLP LPSP NEDO OVI OVR
loss of load expectation loss of load probability loss of power supply probability New Energy and Industrial Technology Development Organization overall vulnerability index overall vulnerability rate
photovoltaic System Dynamics vulnerability at the assessed instant of time vulnerability rate zero energy building zero energy house
List of subscripts t x
assessed to evaluate the impact of demand side management [15,37]. The combination of both aforementioned uncertainties was also addressed to cover various characteristics of system uncertainties [18,26]. However, the existing approach used for long-term assessment cannot simply be used to reveal the vulnerability inherent in power supply generation in the short term. As the basic pattern of both power demand and generation changes with time, the state of vulnerabilities in the power system is dynamically altered. Assessing the dynamic change in vulnerabilities in the short term (e.g., one day) is of the utmost importance to identify the specific time when the hybrid renewable energy and battery system is most vulnerable to interruptions in continuous power supply. As for the short-term dynamic behavior of general power systems, many studies have assessed the ability of power grids to address sudden disturbances in the context of system security [38–41] and resilience [42–45]. Meanwhile, these existing approaches have shortcomings, including complications in computational modeling, high simulation cost, theoretical constraints, and insufficient data [46–48]. To overcome these issues, the author has proposed a simplified concept of dynamic behavior for the short term, using a parametric approach on the national scale [49,50], microgrid scale [51], and individual building scale [52]. However, the vulnerability associated with short-term behavior for the dynamic condition in the hybrid system has been scarcely analyzed. As such, the objective of this study is to assess the dynamic change in the vulnerability of a hybrid renewable energy and battery system in the short term. This paper is structured as follows. Section 2 develops the methodology of quantifying the vulnerability dynamically altered during a day. Section 3 explains the case study. Section 4 presents the dynamic vulnerability in the case study. Section 5 compares the dynamic vulnerability developed in this study with the existing approach for evaluating the reliance of the energy mix. Section 6 concludes this paper.
the assessed instant of time failure rate
The supply capability reflects a fundamental aspect of the ability of the hybrid system to withstand failures of power source components and to remain self-sufficient. The state of self-sufficiency depends on the magnitude and duration of failures. The hybrid power system remains self-sufficient within the maximum accepted magnitude and duration of failures. In other words, the combination of the greatest accepted magnitude of failure and the longest accepted duration of failure at a given instant leads to a hybrid system with the most resilient supply capability at an arbitrary time. The magnitude of failure represents the percentage of component trouble, named the failure rate in this paper. The failure rate is 0% when the power source components operate perfectly under normal conditions, and it rises to 100% when all components fail. The failure duration refers to the span in which the component failure lasts, measured on a time scale, named the failure duration. The failure duration is set to less than 24 h in this study, so the time scale of the assessment is limited to one day as the short term. It is assumed that the failure rate instantly increases, remains at the same level until recovery to measure the failure duration, and then instantly decreases at the recovery time. The relationship between the maximum accepted failure rate and the maximum accepted failure duration is evaluated at any instant of time to quantify the potential vulnerability inherent in each of the power source components of the hybrid system. In this case, the highlight is on the maximum accepted trouble duration corresponding to a particular trouble rate. A reverse interpretation of this graph is also possible, where the reading would be the maximum accepted failure rate corresponding to a certain failure duration at which the standalone system remains self-sufficient. This relationship graphically is known as the magnitude-duration curve. Flowchart of steps for quantifying the dynamic vulnerability is presented in Fig. 1. Power source component failures could be considered sudden disturbances, occurring in the flow of time. Addressing sudden disturbances leads to the evaluation of power systems under dynamic conditions [54]. In this study, sudden disturbances are parametrically induced in the system model, so the obtained outcomes indicate the dynamic behavior of the power system. In addition, this assessment is considered an uncertainty assessment since the concept of sudden disturbances in the form of failures is matched with uncertainties in the continuous supply.
2. Methodology 2.1. Concept of vulnerability in hybrid renewable energy and battery system The core analysis of this study corresponds to assessing the vulnerability of the hybrid renewable energy and battery system, which can lead to potential disruptions in power supply. This study focuses on vulnerabilities arising from the failures in facilities of renewable energy and storage technology in the hybrid system. The cause of failure might be human error; such as damage on the terminal base due to construction failure or screw loosening; technical error, such as burning due to the heat generation from the module, dirt and damage on the panel, or accidental connection; or environmental phenomena such as lightning, fallen trees, or weeds [53]. The potential risk of supply disruption depends on the physical supply capability determined under the dynamic condition of balance between demand and supply at a certain time. Therefore, vulnerability is based upon supply capability while avoiding supply disruptions and analyzing the supply capability at a given time highlights the dynamic change in potential vulnerability inherent in hybrid renewables and battery systems.
2.2. Quantification of vulnerability To quantitatively assess the vulnerability of the hybrid renewable energy and battery system, this study develops an index dedicated to the vulnerability based on the proposed relationship between magnitude and failure duration. The index represents the total accepted failure duration covering all possible failure rates, or the total accepted failure rate covering all possible failure durations. This index concept is associated with the plots presented in the magnitude-duration curve. First, by computing the area under the magnitude-duration curve, the vulnerability at the assessed instant of time, named VIT, is computed, using the following equation 259
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Fig. 1. Flowchart of steps for quantifying the dynamic vulnerability.
VITt =
100% 1%
ft (x ) dx
computed. The vulnerability level at the specific instant of time is expressed in comparison with the normal condition without any failures in the context of vulnerability rate, named VR, as follows.
(1)
where ft (x ) is the function from the magnitude-duration curve at the assessed time, VITt is the vulnerability at the assessed time, t is the assessed instant of time, and x is the failure rate. VITmax , which is based upon the condition in which all power source components are fully capable at the assessed instant of time, is
VRt =
VITmax VITt × 100(%) VITmax
(2)
A greater VRt corresponds to a greater vulnerability at the assessed 260
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instant of time. Finally, the computed vulnerability at the assessed time is synthesized into an overall vulnerability index, named OVI, for each of the power source components in the simulated condition of a specific capacity size. The vulnerability of the hybrid system is dynamically altered with time in a specific pattern. Given the sequential shift of the load and generation pattern throughout the day, it is assumed, in this study, that the vulnerability plots at the time between 0:00–24:00 could be linearly connected. On the basis of this assumption, OVI is obtained using the following equation
OVI =
24:00 00:00
g (t ) dt
flow [56]. Due to the non-linear nature of power flow, the author has used SD to express the electricity demand and supply system (e.g., [57]). Since this study utilizes a fictitious house with an imaginary hybrid system, and any observation of actual behavior is non-existent, simulated results using SD cannot be compared with real data. Meanwhile, studies by the author [52,57] have assessed the same power configuration in an identical fictitious ZEH, in which the accuracy and adequacy of the model developed on the basis of SD was validated. Given the identical subject in modeling with a previously validated system, it is conceivable that SD would be employed for the current hybrid renewable energy and battery system. The model structure is presented in Fig. 2. As mentioned above, in this study, solar PV represents the renewable energy while the battery acts as storage technology. The summation of power generated by the solar PV and discharged from the battery is named power delivery. The demanded amount of power delivery is consumed in the ZEH. The surplus power over the demand is automatically channeled to the battery to be stored as energy. The energy stored in the battery is used when the demand exceeds the power generated from the solar PV. It is assumed that, when the battery is fully charged, the power output from the solar PV is controlled so that the power delivery is matched with the demand. The power from the solar PV is basically computed based on the radiation and PV efficiency. The measured total radiation depends on the area of the solar panel. In this study, the solar panel rate, or rate of power from the solar panel area delivered to the roof-top area of the house, is integrated in the calculation as a parameter of solar PV capacity. The detailed system model equations are listed in Appendix B. All variables are summarized in Appendix C.
(3)
where g (t ) is the function generated by connecting the VITt at each instant of time. OVImax , which is based upon the condition in which all power source components are fully capable throughout a day, is computed. The overall vulnerability level in the hybrid renewable energy and battery system is expressed in the comparison with the normal condition without any failures throughout the day, in the context of the overall vulnerability rate, named OVR, as follows.
OVR =
OVImax OVI × 100(%) OVImax
(4)
A greater OVR corresponds to a more vulnerable hybrid system. For either VR or OVR , a vulnerability rate of 100% corresponds to the state of not meeting the demand, while a vulnerability rate of 0% corresponds to the condition of no risk of disruption, an ideal case under the assessed condition.
3.3. Data collection and simulation input
3. Case study
Among all variables, the failure-specific and capacity-specific variables are parametric components for the assessment of vulnerability. On the other hand, a constant value is used as input for the rest of the variables. The maximum demand load curve in Japan [58] is utilized as the input for the demand. The irradiation data on the date of the maximum load demand in Japan taken from New Energy and Industrial Technology Development Organization (NEDO) [59] is used as the input for the radiation. The average house area in Japan [60], 140 m2, is used as the input for the roof-top area. The efficiency of crystalline silicon solar cells [61], 19%, is used as the input for the PV efficiency. The roundtrip efficiency of an Li-ion battery [62], 92%, is used as the input for the battery efficiency. To compare the vulnerability under a different capacity size in the hybrid renewable energy and battery system, the condition in the model simulation needs to be identical for each of the capacity size options. This study manually controls the minimum required energy stored in the battery at 00:00 h, such that no energy is left in the battery
3.1. Assessed hybrid renewable energy and battery system There are various scales of hybrid renewable energy and battery systems. As a starting point in analyzing vulnerability, this study focuses on the hybrid renewable energy and battery system in a standalone house. Power demand and supply flow in a house requires the simplest and smallest renewable energy (solar PV) and battery system. Assessment of vulnerability inherent in an imaginary off-grid ZEH could be applied to a hybrid renewable energy and battery system of any scale. In addition, this study selects Japan for the assessment of the off-grid ZEH, where the government sets a high target for ZEH installation [55]. 3.2. System modeling This study employs System Dynamics (SD) to model the hybrid renewable energy and battery system. SD is a simulation tool used to examine the non-linear behavior and evaluate complex and uncertain
Fig. 2. Hybrid renewable and battery model in the standalone ZEH. 261
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Fig. 3. Demand and supply balance in the fictitious assessed house.
Fig. 6. Dynamic change in the solar PV vulnerability rate with time for nine capacity sizes.
the daytime, solar PV operates not only to cover the demand but also to generate the excess energy. To meet the representative demand patterns of the house in Japan, the power is supplied accordingly from the battery in the nighttime. In the typical demand pattern, the greatest amount of electricity is consumed before midnight due to the increase in the use of TV and light. 4. Results 4.1. Relationship between magnitude and failure duration Fig. 4. Relationship between solar PV failure rate and duration at different times.
This section demonstrates the features of the relationship between magnitude and duration of power source component failures, using the case of 18% for the solar panel and a battery capacity of 13,000 Wh (20% of capacity margin), as an example. The magnitude-duration curve related to the use of solar PV (Fig. 4) and battery (Fig. 5), or the relationship between failure rate and failure duration analyzed at different times, shows that a greater maximum accepted failure rate is associated with decreased failure duration. Lower hybrid system vulnerability will be found obeying such a relationship. For any instant of time, a similar trend in the magnitude-duration curve, related to the use of solar PV and battery, could also be seen in Figs. 4 and 5. In this trend, repeated with increasing failure rate, the failure duration drastically decreases at a certain failure rate, then gradually declines from a certain duration. The cut-off for failure duration is called the magnitude boundary in this article. The magnitude boundary denotes a significant change in the vulnerability of battery use in the hybrid system. As for the use of solar PV in Fig. 4, only one magnitude boundary at the various solar PV failure rates is obtained in almost all assessed instants of time. Particularly, at 0:00 and 4:00, the magnitude-duration curve appears like a step function. In addition, a drastic drop-off in failure duration at the magnitude boundary is evident at 0:00, 4:00, 8:00, and 24:00, while its drop at 12:00 and 20:00 is insignificant; furthermore, at 16:00, a definite magnitude boundary is not observed. As for the use of battery in Fig. 5, the major magnitude boundary is 19%, which is the minimum margin of failure. In the cases of 0:00, 4:00, 20:00, and 24:00, two magnitude boundaries are obtained at battery failure rates other than 19%, while in the cases of 8:00, 12:00, and 16:00 only one magnitude boundary at a battery failure rate of 19% is obtained.
Fig. 5. Relationship between battery failure rate and duration at different times.
when the full power from the solar PV meets the demand in the morning. Then, by setting the minimum required energy stored in the battery at 00:00 h, the minimum required capacity size in the solar panel rate and battery capacity is identified. This is identified through the analysis of the energy deficit in the power system. Referring to the result in the author’s earlier study [52], the minimum required solar panel rate is set to 15%, while the minimum required battery capacity is set to 11000 Wh. On the basis of identified minimum required capacity size, this study assesses nine options with 20% and 40% capacity margin, including (15%_11000 Wh), (15%_13000 Wh), (15%_15000 Wh), (18% _11000 Wh), (18%_13000 Wh), (18%_15000 Wh), (21%_11000 Wh), (21%_13000 Wh), and (21%_15000 Wh), combining the solar panel rate and battery capacity. The time in this study increases from 00:00 up to 24:00 in 4-h steps. This time step covers the different features of the battery, solar PV, and demand throughout the day, considering Fig. 3, which shows the assessed balance between supply and demand in the fictitious house. In
4.2. Dynamic vulnerability throughout a day The dynamic change in the vulnerability rate of the solar PV at the assessed instant of time is obtained for nine different capacity sizes. The result, shown in Fig. 6, presents different trends of dynamic vulnerability of solar PV with time among the nine options. 262
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vulnerability rate is in the range of 35–62%. Even with a capacity margin of 40%, compared with the ideal capacity size, the vulnerability rate of the battery in the hybrid system reaches greater than 60% at 16:00, which would hardly be considered secure. To generalize, at almost all instants of time, the differences in battery vulnerability rate in the hybrid system among the assessed nine options are in the range of 21–34%. This may indicate that the expectation of the battery vulnerability rate for a different capacity size is not as affected by uncertainties as the solar PV vulnerability. Although the vulnerability of the hybrid renewable energy and battery system is mitigated by increasing the capacity size, the dynamic battery vulnerability rate depends on the battery capacity rather than the solar PV capacity. Under the same solar panel rate with a different battery capacity, a capacity margin of 20% mitigates the battery vulnerability rate by up to 23%, and a capacity margin of 40% mitigates it by up to 37%. On the other hand, under the same battery capacity with a different solar panel rate, a 20% capacity margin mitigates it by up to 18%, and a 40% capacity margin mitigates it by up to 22%. Note that the range and value of the battery vulnerability rate at 0:00 and 24:00 are almost identical. This may indicate that the battery vulnerability in the hybrid system is not significantly affected by the energy stored in the battery. A comparative analysis of the dynamic vulnerability between the solar PV and battery with time under the nine capacity sizes is conducted. Considering that the vulnerability rates of 0% and 100% for both the solar PV and battery occur in the same condition, these rates could be compared under the same platform. The difference is obtained by subtracting the vulnerability rate of the battery from the vulnerability rate of solar PV. A positive outcome indicates greater vulnerability for the solar PV in the hybrid system, while a negative outcome indicates greater vulnerability for the battery. The result is shown in Fig. 8. The difference increases from 0:00 to 4:00, and after 4:00 it decreases and then increases again until 24:00. Whether it crosses zero depends on the capacity size. For a solar panel rate of 15%, other than at 20:00, the solar panel is more vulnerable in the hybrid system throughout the day. On the other hand, as long as the hybrid system has a certain amount of margin for the solar PV, the use of battery is more vulnerable, almost all day, even when the solar PV is actively operating after the morning.
Fig. 7. Dynamic change in the battery vulnerability rate with time under the nine capacity sizes.
Under a solar panel rate of 15% (the minimum required solar PV capacity), the same solar PV dynamic vulnerability is obtained regardless of battery capacity. In this case, it increases from 0:00 to 8:00 and then remains almost the same until 16:00. After 16:00, it declines up to 20:00 and then increases again up to 24:00. On the other hand, with a solar PV capacity of 18% and 21%, the battery capacity affects the trend of the solar PV dynamic vulnerability. In the case of 11000-Wh battery capacity, it increases from 0:00 to 4:00 and then declines until 12:00. After 12:00, it remains the same (for a solar panel rate of 18%) or even increases again (for a solar panel rate of 21%) until 16:00. It declines again until to 20:00 when it reaches the least vulnerable solar PV rate. Meanwhile, in the case of 13000-Wh and 15000-Wh battery capacity, it increases from 0:00 to 4:00, then declines constantly until 16:00, when it reaches the least vulnerable time in the solar PV supply. Finally, it increases again until 24:00. Particularly, at 8:00 and 12:00, the impact of the battery capacity on the dynamic vulnerability is not evident, while at 16:00, it is affected by the change in battery capacity in the case of the 18% solar panel rate. Consequently, among the nine options of capacity size, the most vulnerable time associated with the use of solar PV is in the range between 4:00–16:00, while the least vulnerable time is around 16:00–20:00, completely dependent on capacity size. Note that the range in solar PV vulnerability at 00:00 and 24:00 is markedly different. At these instants of time, the demand and solar supply are the same, while the energy stored in the battery is different among the nine capacity size options. This may indicate that the energy stored in the battery has a significant impact on solar PV vulnerability in the hybrid system. In general, the range of solar PV vulnerability rates at the various times is broad. Especially at 16:00, it is in a broad range between 7% and 95%, depending on the capacity size. Its expectation at a specific time and different capacity size would be difficult to determine, considering the high level of uncertainties. Next, the dynamic change in the battery vulnerability rate with time is obtained for the nine capacity size options. The result, shown in Fig. 7, indicates that the dynamic change in vulnerability arising from the use of a battery exhibits the same trend throughout the day. The battery vulnerability rate gradually deteriorates with time from 0:00 until 16:00. At 16:00, the operation of the solar panel reaches a stop, and the battery starts supplying power after storing the excess power from the solar PV. Then, the vulnerability level moderates with time from 16:00 until 24:00. When the power is supplied from the battery, the system is less vulnerable by up to around 40% compared with when the power is stored. For the minimum required capacity size, 15%_11000 Wh, the battery vulnerability rate is in the range of 60–97%. In this case, a small amount of trouble with the battery occurring at 16:00 could easily lead to insufficient supply, which would be highly critical. Meanwhile, under the most reliable capacity size, that is, 21%_15000 Wh, the
4.3. Overall vulnerability in the hybrid renewable energy and battery system By using Eq. (4), the overall vulnerability rate for the different capacity size is presented in Fig. 9. The trend in the differences in dynamic vulnerability at the assessed instant of time between the solar PV and battery, presented in Fig. 8, mainly reflects the result in Fig. 9. This indicates that, regardless of battery capacity, for a solar panel rate of 15%, the solar PV vulnerability in the hybrid system is greater by up to 34% compared with that of the battery, while, for solar panel rates of
Fig. 8. Comparison of dynamic vulnerability between solar PV and battery with time. 263
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increase in battery capacity reduces only the overall vulnerability of the battery, and its effect is hardly seen in the overall vulnerability of the solar PV. 5. Discussion The greater overall vulnerability associated with power source components in the hybrid system under the various capacity sizes is more likely to cause a disruption in power supply. Vulnerability is based on the magnitude and duration of failure in this study. In particular, the change in the failure rate for the specific power source component means a sudden change in component capacity. The parametric change in the failure rate and duration implicitly describes how much the other components can contribute to the supply and potentially evaluates the overall supply capability in the hybrid system. The greater overall vulnerability of an assessed power source component indicates the low contribution of the other components to meeting the demand, which leads to the low supply capability. In other words, this situation describes a heavy reliance on the assessed component. Therefore, the state of the overall vulnerability developed in this study represents the extent of the reliance on the power source in a continuous power supply. While various factors are considered as vulnerabilities to the security of energy supply [63,64], heavy reliance on a specific power source is one of the major concerns. To evaluate the extent of the reliance on the power source, diversification of energy generation by power source type has been assessed as a particular attribute [65–68]. Diversification and reliance is based on the concept where, even if one of the power sources is disrupted, power is continuously supplied as long as the other power sources could compensate for its loss. This concept is highly associated with the theory of vulnerability developed in this study. As such, it is of interest to the author to investigate the differences in reliance measurement factors between the vulnerability developed in this paper and the energy generation amount widely utilized. It must be mentioned that assessing the diversification in the national energy mix has evolved due to the geopolitical instability in the countries that supply fossil fuels, heavily relied on in the demand country [69]. Given only the renewable energy utilized in this study, a higher reliance
Fig. 9. Overall vulnerability rate under the nine capacity sizes.
18% and 21%, the battery vulnerability is greater by up to 45% than that of the solar PV. Among the assessed capacity size options, the maximum overall vulnerability rate for both solar PV and battery reaches 80%, while the minimum overall vulnerability rate for the solar PV reaches 40% and, for the battery, 50%. This means that the increasing the capacity margin by 40% decreases the vulnerability level in the hybrid system by 50% and 38% for the solar PV and battery, respectively. Based on Fig. 9, the relation between the overall vulnerability rate and the change in solar PV and battery capacity is identified by setting the OVR to zero for the minimum required capacity size. The result is presented in Fig. 10. The relationship between the normalized OVR and the battery capacity, shown in Fig. 10(a), indicates that the difference in OVR between the solar PV and battery is not evident for a battery capacity margin of 20%, while it is less than 0.1 for a capacity margin of 40%, except for the case of solar PV with a solar panel rate of 15%. On the other hand, the relationship between the normalized OVR and solar panel rate, shown in Fig. 10(b), indicates that the difference in OVR between the solar PV and battery ranges from 0.16 to 0.3 for a capacity margin of 20% and 0.27–0.4 for a capacity margin of 40%. Consequently, an increase in the solar PV capacity significantly contributes to the mitigation of the overall vulnerability rate of both the solar PV and battery in the hybrid system. On the other hand, an
Fig. 10. Relation between the normalized overall vulnerability and the change in solar PV and battery capacity.
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availability of such a prediction of supply capability would assist the service operator in determining an appropriate strategy (e.g., setting the limit time for recovery based on the information of time and failure duration). The main goal of the hybrid renewable energy system is to determine the optimal capacity size on the basis of multiple dimensions [72,73]. Together with economic indicators (e.g., [74,75]) and environmental indicators (e.g., [76,77]), the static reliability is often evaluated as one of the dimensions for indicating the degree of confidence in a continuous power supply. Meanwhile, little attention has been paid to the dynamic condition of a power system. Therefore, the inclusion of dynamic vulnerability assessments developed in this study would assist in the comprehensive optimization of capacity size. Meanwhile, the limitations of this research need to be mentioned. Differences between the static and dynamic evaluation of the power system may be the degree of generalization. In the static assessment, one year is often used as the evaluated time span to cover the various patterns of loads and solar irradiation as much as possible. This would lead to a high generality in the specifically assessed area. On the other hand, in the dynamic assessment, among the infinite patterns of loads and irradiation with time, a certain short term (one day in this paper) needs to be selected for the simulation. This may lead to a low generality. Although this study selects representative one-day patterns of loads and irradiation provided by Japanese government as a common trend, the obtained outcomes may not be applicable in general. Since this study develops the method for quantifying the concept of vulnerability in the power system as a starting point, a second-step time-span extension from one day to one year is required to improve the generality of outcomes. This is the subject of a future study. In addition, the developed approach can be further improved with inclusions of additional factors. Since the current model is highly dedicated to the standalone power system, the power exchange with external infrastructure is not accounted for. The decrease in performance with duration would affect the outcome of supply capability even under the same specifications in the power source components. In addition, although this simulation model fixes the demand, it is highly expected that the demand will be controlled by a demand response tool in the future under the emerging situation, including the failure of power source components. The decrease in demand as a response to emergencies would moderate the vulnerability level in the hybrid system. Furthermore, the methodology developed in this study could be considered a “soft” assessment at this stage, and “hard” perspectives are left out such as technical limitations and control management including interactions between the solar PV and battery and intermittent uncertainties in solar radiation. The integration of technical assessment in the developed methodology would assist in presenting a more comprehensive framework for estimating the vulnerability.
Table 1 Comparison of reliance measurement factors for a solar panel rate of 21% and a battery capacity of 15000 Wh. Reliance measurement factor
Solar PV
Battery
Energy generation amounts Overall vulnerability rate
2.68 1
1 1.20
merely corresponds to a greater contribution to the continuous power supply. Features of reliance measurement factors are demonstrated, using a solar panel rate of 21% and a battery capacity of 15000 Wh as the example. Energy generated throughout the day by solar PV and battery is computed, and then, the ratio of solar PV to battery for both the energy generation amount and vulnerability is computed to compare the reliance measurement factors. A greater value corresponds to a more reliant power source component. As presented in Table 1, the reliance measurement factors indicate the inverse trend in which the solar PV is more reliant in the context of energy generation, while the battery is more reliant in the context of vulnerability. In the conventional approach, the reliance on battery appears to be insignificant. However, as this assessment considers a sunny day when the solar PV fully operates, it is surprising that the approach developed in this study reveals an unexpectedly greater contribution of the battery to the continuous power supply than the solar PV in the hybrid system, with capacity margins to some extent. In addition to the important role of the battery in improving power system resilience [4,70] due to its dynamic and quick response [71], the higher contribution of the battery to the continuous power supply would raise its status and encourage its installation. Considering this result, only using the energy generation as a reliance measurement factor potentially risks reaching a short-sighted conclusion in terms of power reliance. In view of the significant interaction of reliance with the diversification of energy mix in the context of energy security, it would be highly expected that the vulnerability assessment developed in this study could be applied to the national energy supply and demand system and assist in revealing the hidden elements associated with energy diversification. As energy security is a driving force of energy policy, this approach may be of use in designing well-grounded energy policy narratives. The proposed method helps to understand the dynamic vulnerability throughout the day in the hybrid renewable energy and battery system in the following ways. The attractive point of the methodology developed in this study is the ease of adapting it into any other scale of power demand and supply system. Its application could be completed by just changing the energy source components in the assessed power system and the precondition of simulation input. While this study selects a fictitious home for the analysis of power system vulnerability, the algorithm is readily employed in any electricity flow system including ZEB, microgrids in urban and rural areas, and even in the national grid. The simulation in the developed model runs with time steps of one minute. Meanwhile, the most of the earlier studies conducted hourly simulations in the static reliability assessment (e.g., [17]). The higher time resolution of the simulation would improve the accuracy of outcomes. Additionally, the vulnerability assessment conducted in this study is not affected by any type of failure causes or any technological innovation of the hybrid system. The developed magnitude-duration curve represents the prediction of supply capability in the hybrid system in the near future. The
6. Conclusion This research has developed the methodology of quantifying the dynamic vulnerability of power source components throughout the course of a day in the hybrid renewable energy and battery system. The concept of vulnerability is developed based on the magnitude and duration of component failures. Then, by following the established methodology, the dynamic vulnerability with time and overall vulnerability of the system has been presented in the case of power demand and supply system in a fictitious house. Finally, as the reliance measurement factor, the developed vulnerability is compared with the amount of energy generation to identify the extent to which power components contribute to the continuous power supply.
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Findings in the case of representative load and irradiation in Japan are as follows.
the solar PV actively operates after the morning.
• The increase in solar PV capacity significantly contributes to the
• The dynamic mitigation of vulnerability associated with the use of
•
solar PV and battery with capacity size could be quantified using the developed methodology. The trend of dynamic vulnerability of solar PV throughout the day varies depending on the capacity size and amount of energy stored in the battery. The dynamic change in vulnerability arising from the use of battery has the same trend regardless of the capacity size, in which the system is less vulnerable by up to around 40% when the power is supplied from the battery, compared with when the power is stored. This trend is not significantly affected by the energy stored in the battery. As long as the hybrid system has a certain amount of margin of solar PV, the use of battery is more vulnerable almost all day, even when
•
mitigation of the overall vulnerability rate of both solar PV and battery in the hybrid system, while the increase in battery capacity reduces only the overall vulnerability of the battery, and its effect is hardly evident in the overall vulnerability of solar PV. The approach developed in this study would potentially reveal the greater contribution of the battery to the continuous power supply compared with the solar PV in the hybrid system.
Acknowledgement This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.
Appendix A Detailed steps for obtaining the magnitude-duration curve are described as follow: (1) Select one of the n types of power source components. (2) Initial setting of parameters: failure rate = 1%, failure duration = 1 min, instant of time = 00:00 h. (3) Start of simulation and energy deficit verification. In this assessment, the energy deficit is defined as the total lack of power supply to the meet the demand in 24 h. (4) For NO energy deficit observed, failure rate is increased in steps of 1%. Model simulation is repeated until energy deficit appears. (5) For energy deficit observed, the previous failure rate is recorded in the simulated condition of failure duration and instant of failure. (6) Step (3), (4) and (5) are repeated increasing the failure duration from 1 min until 24 h by 1 min. (7) Step (3), (4), (5) and (6) are repeated increasing the instant of time until 24:00 h by its corresponding step. (8) Obtained results are plotted on a 2-axis graph of failure rate versus failure duration in curves representing instant of time under the selected power source component. (9) Step (2), (3), (4), (5), (6), (7) and (8) are repeated changing the assessed power source component.
Equation
Number
Solar PV = Roof top area × PV efficiency × Radiation × Solar panel rate
Eq. (A-1)
× (1
Solar PV failure)
Instant of Solar PV failure)
Eq. (A-2)
*1
Solar PV failure = STEP (Solar PV failure rate , STEP (Solar PV failure rate ,
Instant of Solar PV failure + Solar PV failure duration)
Surplus Power = IF THEN ELSE (Power delivery = 0, 0, Power delivery
Eq. (A-3)
Demand <*2
Demand )
Eq. (A-4)
Energy Stored in battery =
IF THEN ELSE (Energy stored in battery > battery capacity × (1
Battery failure ),
Battery /Battery efficiency,
Surplus Power
Battery /Battery efficiency ) Battery failure = STEP (Battery failure rate, STEP (Battery failure rate,
Eq. (A-5)
Instant of battery failure) Instant of battery failure
+ Battery failure duration)
Eq. (A-6)
Battery = IF THEN ELSE (Energy stored in battery < = 0, 0, IF THEN ELSE (Demand
Solar PV < 0, 0, Demand
Solar PV )) Eq. (A-7) Power delivery = Battery + Solar PV Eq. (A-8) Electric Power = Power delivery Demand Surplus Power *1 STEP (a , b) , where the equation a is summed when the time reaches the instant b *2 IF THEN ELSE (p, q, r ) , where it is switched to the equation p when the condition p is true, or to the equation r when the condition p is false.
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Appendix B Each component of Hybrid renewable and battery model in the standalone ZEH can be computed as follows: Appendix C All variables used in the model are summarized in Table C1. Table C1 Summary of variables. Variable
Unit
Definition
Power delivery
W
Electric Energy
Wh
Demand Surplus power Solar PV PV efficiency
W W W %
Radiation Roof-top area Solar panel rate Solar PV failure rate Solar PV failure duration Battery Energy stored in battery Battery efficiency Battery capacity Battery failure rate Battery failure duration
W/m2 m2 % % h
Summation of power from both solar PV and battery Imaginary energy stock of discrepancies between the sum of both demand and surplus power and power delivery Home electricity demand Exceeding power over the demand Power generated by the solar PV Conversion efficiency from the solar radiation to electricity Solar irradiation per area Horizontal area of home roof-top Rate of solar panel area to roof-top area Magnitude of solar PV failure Duration of solar PV failure
W Wh
Power discharged from the battery Energy stored in battery
% Wh % h
Buttery round-trip efficiency Maximum energy fully stored in the battery Magnitude of battery failure Duration of battery failure
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Contents lists available at ScienceDirect
Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman
Dynamic vulnerability in standalone hybrid renewable energy system Shoki Kosai
T
Department of Mechanical Engineering, College of Science and Engineering, Ritsumeikan University, Shiga, Japan
ARTICLE INFO
ABSTRACT
Keywords: Redundancy Battery performance Energy security Reliance Diversification Zero energy building
Ensuring continuous power supply in the hybrid renewable energy and battery system is important because power utilization is fundamental to economy and human well-being. Earlier studies have been concerned with the ability to supply a desired amount of power in a long-term static condition in the context of system reliability. Meanwhile, short-term dynamic behavior and its relevant vulnerability in a hybrid system associated with a continuous power supply has been given less attention due to the modeling complexity of the problem. This study uses a parametric approach to assess the dynamic transition of vulnerabilities potentially leading to disruptions in electricity supply throughout a given day to identify a specific vulnerable time. The methodology of quantifying the dynamic vulnerability of power source components during a given day in a hybrid system is developed. Then, the temporal dynamic vulnerability and overall vulnerability in the system are presented by changing the capacity size in the case of a fictitious standalone house. Through the analysis, the approach developed in this study would potentially highlight the greater contribution of the battery to continuous power supply, compared with the solar PV in the hybrid system.
1. Introduction
In these applications of hybrid renewable energy and battery systems, ensuring a continuous power supply without disruption is significant because power utilization is crucial for stable economy and human well-being. A sustainable hybrid renewable energy and battery system can be achieved via thorough evaluation of vulnerabilities to disruptions of electricity supply. Particularly, vulnerability is highly related to facilities of power generation, including renewable energy sources and storage technology. Many studies have been concerned with the ability of hybrid renewables and batteries to supply a desired amount of power in a long-term static condition. The common vulnerability associated with power generation is insufficient capacity size [11]. Development of an adequate infrastructure containing redundant capacity would assist in the uninterrupted access of power products [12]. Reflecting the intermittent and stochastic characteristics of renewables, the probability of power disruption over a long period (e.g., one year) is, in many cases, assessed to quantify system reliability. Various reliability indices have been developed so far, including loss of power supply probability (LPSP) [13–20], loss of load expectation (LOLE) [21], and loss of load probability (LOLP) [22–27], and each index is computed under various options of capacity size. Additionally, earlier studies have also focused on the uncertainties potentially affecting long-term reliability. Uncertainties in intermittent renewable energy, such as wind speed and site [22,28] were analyzed using a design-space approach [21,29–32] and chance-constrained approach [33–36]. Uncertainties in consumption patterns were also
In last few decades, heavy reliance on fossil fuels has raised an alarming number of various energy-related issues, such as economic and environmental concerns, and energy security. To decrease the reliance on fossil fuels, renewable energy has been increasingly considered a panacea. Meanwhile, the use of renewable energy (e.g., solar PV) brings uncertainties of constant power supply due to the high dependency on weather conditions. The stochastic and intermittent nature of renewables require the installation of storage technology. Despite high capital costs and energy losses in the process of conversion [1,2], storage technology can contribute to power and load leveling, and the retention of power stability [3]. In addition, storage technology also operates as an energy source when the demand exceeds the power generated by renewables [4]. Because of its community-based nature, renewable energy is highly matched with the concept of local production for local consumption. It can be applied as a microgrid of a medium-sized power flow system in both rural and urban communities. Rural communities are often isolated communities in which the electrical support of a centralized power grid is not provided [5]. Urban communities are under the shift from a centralized to a distributed power system to establish a society more resilient to climate change and natural disasters [6–8]. Besides its application as a microgrid, the hybrid system can be used as a smallersized system for an individual building and house, named zero energy building (ZEB) and zero energy house (ZEH) (e.g., [9,10]).
E-mail address: [email protected]. https://doi.org/10.1016/j.enconman.2018.10.087 Received 30 August 2018; Received in revised form 26 October 2018; Accepted 27 October 2018 0196-8904/ © 2018 Elsevier Ltd. All rights reserved.
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Nomenclature
PV SD VIT VR ZEB ZEH
List of abbreviations LOLE LOLP LPSP NEDO OVI OVR
loss of load expectation loss of load probability loss of power supply probability New Energy and Industrial Technology Development Organization overall vulnerability index overall vulnerability rate
photovoltaic System Dynamics vulnerability at the assessed instant of time vulnerability rate zero energy building zero energy house
List of subscripts t x
assessed to evaluate the impact of demand side management [15,37]. The combination of both aforementioned uncertainties was also addressed to cover various characteristics of system uncertainties [18,26]. However, the existing approach used for long-term assessment cannot simply be used to reveal the vulnerability inherent in power supply generation in the short term. As the basic pattern of both power demand and generation changes with time, the state of vulnerabilities in the power system is dynamically altered. Assessing the dynamic change in vulnerabilities in the short term (e.g., one day) is of the utmost importance to identify the specific time when the hybrid renewable energy and battery system is most vulnerable to interruptions in continuous power supply. As for the short-term dynamic behavior of general power systems, many studies have assessed the ability of power grids to address sudden disturbances in the context of system security [38–41] and resilience [42–45]. Meanwhile, these existing approaches have shortcomings, including complications in computational modeling, high simulation cost, theoretical constraints, and insufficient data [46–48]. To overcome these issues, the author has proposed a simplified concept of dynamic behavior for the short term, using a parametric approach on the national scale [49,50], microgrid scale [51], and individual building scale [52]. However, the vulnerability associated with short-term behavior for the dynamic condition in the hybrid system has been scarcely analyzed. As such, the objective of this study is to assess the dynamic change in the vulnerability of a hybrid renewable energy and battery system in the short term. This paper is structured as follows. Section 2 develops the methodology of quantifying the vulnerability dynamically altered during a day. Section 3 explains the case study. Section 4 presents the dynamic vulnerability in the case study. Section 5 compares the dynamic vulnerability developed in this study with the existing approach for evaluating the reliance of the energy mix. Section 6 concludes this paper.
the assessed instant of time failure rate
The supply capability reflects a fundamental aspect of the ability of the hybrid system to withstand failures of power source components and to remain self-sufficient. The state of self-sufficiency depends on the magnitude and duration of failures. The hybrid power system remains self-sufficient within the maximum accepted magnitude and duration of failures. In other words, the combination of the greatest accepted magnitude of failure and the longest accepted duration of failure at a given instant leads to a hybrid system with the most resilient supply capability at an arbitrary time. The magnitude of failure represents the percentage of component trouble, named the failure rate in this paper. The failure rate is 0% when the power source components operate perfectly under normal conditions, and it rises to 100% when all components fail. The failure duration refers to the span in which the component failure lasts, measured on a time scale, named the failure duration. The failure duration is set to less than 24 h in this study, so the time scale of the assessment is limited to one day as the short term. It is assumed that the failure rate instantly increases, remains at the same level until recovery to measure the failure duration, and then instantly decreases at the recovery time. The relationship between the maximum accepted failure rate and the maximum accepted failure duration is evaluated at any instant of time to quantify the potential vulnerability inherent in each of the power source components of the hybrid system. In this case, the highlight is on the maximum accepted trouble duration corresponding to a particular trouble rate. A reverse interpretation of this graph is also possible, where the reading would be the maximum accepted failure rate corresponding to a certain failure duration at which the standalone system remains self-sufficient. This relationship graphically is known as the magnitude-duration curve. Flowchart of steps for quantifying the dynamic vulnerability is presented in Fig. 1. Power source component failures could be considered sudden disturbances, occurring in the flow of time. Addressing sudden disturbances leads to the evaluation of power systems under dynamic conditions [54]. In this study, sudden disturbances are parametrically induced in the system model, so the obtained outcomes indicate the dynamic behavior of the power system. In addition, this assessment is considered an uncertainty assessment since the concept of sudden disturbances in the form of failures is matched with uncertainties in the continuous supply.
2. Methodology 2.1. Concept of vulnerability in hybrid renewable energy and battery system The core analysis of this study corresponds to assessing the vulnerability of the hybrid renewable energy and battery system, which can lead to potential disruptions in power supply. This study focuses on vulnerabilities arising from the failures in facilities of renewable energy and storage technology in the hybrid system. The cause of failure might be human error; such as damage on the terminal base due to construction failure or screw loosening; technical error, such as burning due to the heat generation from the module, dirt and damage on the panel, or accidental connection; or environmental phenomena such as lightning, fallen trees, or weeds [53]. The potential risk of supply disruption depends on the physical supply capability determined under the dynamic condition of balance between demand and supply at a certain time. Therefore, vulnerability is based upon supply capability while avoiding supply disruptions and analyzing the supply capability at a given time highlights the dynamic change in potential vulnerability inherent in hybrid renewables and battery systems.
2.2. Quantification of vulnerability To quantitatively assess the vulnerability of the hybrid renewable energy and battery system, this study develops an index dedicated to the vulnerability based on the proposed relationship between magnitude and failure duration. The index represents the total accepted failure duration covering all possible failure rates, or the total accepted failure rate covering all possible failure durations. This index concept is associated with the plots presented in the magnitude-duration curve. First, by computing the area under the magnitude-duration curve, the vulnerability at the assessed instant of time, named VIT, is computed, using the following equation 259
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Fig. 1. Flowchart of steps for quantifying the dynamic vulnerability.
VITt =
100% 1%
ft (x ) dx
computed. The vulnerability level at the specific instant of time is expressed in comparison with the normal condition without any failures in the context of vulnerability rate, named VR, as follows.
(1)
where ft (x ) is the function from the magnitude-duration curve at the assessed time, VITt is the vulnerability at the assessed time, t is the assessed instant of time, and x is the failure rate. VITmax , which is based upon the condition in which all power source components are fully capable at the assessed instant of time, is
VRt =
VITmax VITt × 100(%) VITmax
(2)
A greater VRt corresponds to a greater vulnerability at the assessed 260
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instant of time. Finally, the computed vulnerability at the assessed time is synthesized into an overall vulnerability index, named OVI, for each of the power source components in the simulated condition of a specific capacity size. The vulnerability of the hybrid system is dynamically altered with time in a specific pattern. Given the sequential shift of the load and generation pattern throughout the day, it is assumed, in this study, that the vulnerability plots at the time between 0:00–24:00 could be linearly connected. On the basis of this assumption, OVI is obtained using the following equation
OVI =
24:00 00:00
g (t ) dt
flow [56]. Due to the non-linear nature of power flow, the author has used SD to express the electricity demand and supply system (e.g., [57]). Since this study utilizes a fictitious house with an imaginary hybrid system, and any observation of actual behavior is non-existent, simulated results using SD cannot be compared with real data. Meanwhile, studies by the author [52,57] have assessed the same power configuration in an identical fictitious ZEH, in which the accuracy and adequacy of the model developed on the basis of SD was validated. Given the identical subject in modeling with a previously validated system, it is conceivable that SD would be employed for the current hybrid renewable energy and battery system. The model structure is presented in Fig. 2. As mentioned above, in this study, solar PV represents the renewable energy while the battery acts as storage technology. The summation of power generated by the solar PV and discharged from the battery is named power delivery. The demanded amount of power delivery is consumed in the ZEH. The surplus power over the demand is automatically channeled to the battery to be stored as energy. The energy stored in the battery is used when the demand exceeds the power generated from the solar PV. It is assumed that, when the battery is fully charged, the power output from the solar PV is controlled so that the power delivery is matched with the demand. The power from the solar PV is basically computed based on the radiation and PV efficiency. The measured total radiation depends on the area of the solar panel. In this study, the solar panel rate, or rate of power from the solar panel area delivered to the roof-top area of the house, is integrated in the calculation as a parameter of solar PV capacity. The detailed system model equations are listed in Appendix B. All variables are summarized in Appendix C.
(3)
where g (t ) is the function generated by connecting the VITt at each instant of time. OVImax , which is based upon the condition in which all power source components are fully capable throughout a day, is computed. The overall vulnerability level in the hybrid renewable energy and battery system is expressed in the comparison with the normal condition without any failures throughout the day, in the context of the overall vulnerability rate, named OVR, as follows.
OVR =
OVImax OVI × 100(%) OVImax
(4)
A greater OVR corresponds to a more vulnerable hybrid system. For either VR or OVR , a vulnerability rate of 100% corresponds to the state of not meeting the demand, while a vulnerability rate of 0% corresponds to the condition of no risk of disruption, an ideal case under the assessed condition.
3.3. Data collection and simulation input
3. Case study
Among all variables, the failure-specific and capacity-specific variables are parametric components for the assessment of vulnerability. On the other hand, a constant value is used as input for the rest of the variables. The maximum demand load curve in Japan [58] is utilized as the input for the demand. The irradiation data on the date of the maximum load demand in Japan taken from New Energy and Industrial Technology Development Organization (NEDO) [59] is used as the input for the radiation. The average house area in Japan [60], 140 m2, is used as the input for the roof-top area. The efficiency of crystalline silicon solar cells [61], 19%, is used as the input for the PV efficiency. The roundtrip efficiency of an Li-ion battery [62], 92%, is used as the input for the battery efficiency. To compare the vulnerability under a different capacity size in the hybrid renewable energy and battery system, the condition in the model simulation needs to be identical for each of the capacity size options. This study manually controls the minimum required energy stored in the battery at 00:00 h, such that no energy is left in the battery
3.1. Assessed hybrid renewable energy and battery system There are various scales of hybrid renewable energy and battery systems. As a starting point in analyzing vulnerability, this study focuses on the hybrid renewable energy and battery system in a standalone house. Power demand and supply flow in a house requires the simplest and smallest renewable energy (solar PV) and battery system. Assessment of vulnerability inherent in an imaginary off-grid ZEH could be applied to a hybrid renewable energy and battery system of any scale. In addition, this study selects Japan for the assessment of the off-grid ZEH, where the government sets a high target for ZEH installation [55]. 3.2. System modeling This study employs System Dynamics (SD) to model the hybrid renewable energy and battery system. SD is a simulation tool used to examine the non-linear behavior and evaluate complex and uncertain
Fig. 2. Hybrid renewable and battery model in the standalone ZEH. 261
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Fig. 3. Demand and supply balance in the fictitious assessed house.
Fig. 6. Dynamic change in the solar PV vulnerability rate with time for nine capacity sizes.
the daytime, solar PV operates not only to cover the demand but also to generate the excess energy. To meet the representative demand patterns of the house in Japan, the power is supplied accordingly from the battery in the nighttime. In the typical demand pattern, the greatest amount of electricity is consumed before midnight due to the increase in the use of TV and light. 4. Results 4.1. Relationship between magnitude and failure duration Fig. 4. Relationship between solar PV failure rate and duration at different times.
This section demonstrates the features of the relationship between magnitude and duration of power source component failures, using the case of 18% for the solar panel and a battery capacity of 13,000 Wh (20% of capacity margin), as an example. The magnitude-duration curve related to the use of solar PV (Fig. 4) and battery (Fig. 5), or the relationship between failure rate and failure duration analyzed at different times, shows that a greater maximum accepted failure rate is associated with decreased failure duration. Lower hybrid system vulnerability will be found obeying such a relationship. For any instant of time, a similar trend in the magnitude-duration curve, related to the use of solar PV and battery, could also be seen in Figs. 4 and 5. In this trend, repeated with increasing failure rate, the failure duration drastically decreases at a certain failure rate, then gradually declines from a certain duration. The cut-off for failure duration is called the magnitude boundary in this article. The magnitude boundary denotes a significant change in the vulnerability of battery use in the hybrid system. As for the use of solar PV in Fig. 4, only one magnitude boundary at the various solar PV failure rates is obtained in almost all assessed instants of time. Particularly, at 0:00 and 4:00, the magnitude-duration curve appears like a step function. In addition, a drastic drop-off in failure duration at the magnitude boundary is evident at 0:00, 4:00, 8:00, and 24:00, while its drop at 12:00 and 20:00 is insignificant; furthermore, at 16:00, a definite magnitude boundary is not observed. As for the use of battery in Fig. 5, the major magnitude boundary is 19%, which is the minimum margin of failure. In the cases of 0:00, 4:00, 20:00, and 24:00, two magnitude boundaries are obtained at battery failure rates other than 19%, while in the cases of 8:00, 12:00, and 16:00 only one magnitude boundary at a battery failure rate of 19% is obtained.
Fig. 5. Relationship between battery failure rate and duration at different times.
when the full power from the solar PV meets the demand in the morning. Then, by setting the minimum required energy stored in the battery at 00:00 h, the minimum required capacity size in the solar panel rate and battery capacity is identified. This is identified through the analysis of the energy deficit in the power system. Referring to the result in the author’s earlier study [52], the minimum required solar panel rate is set to 15%, while the minimum required battery capacity is set to 11000 Wh. On the basis of identified minimum required capacity size, this study assesses nine options with 20% and 40% capacity margin, including (15%_11000 Wh), (15%_13000 Wh), (15%_15000 Wh), (18% _11000 Wh), (18%_13000 Wh), (18%_15000 Wh), (21%_11000 Wh), (21%_13000 Wh), and (21%_15000 Wh), combining the solar panel rate and battery capacity. The time in this study increases from 00:00 up to 24:00 in 4-h steps. This time step covers the different features of the battery, solar PV, and demand throughout the day, considering Fig. 3, which shows the assessed balance between supply and demand in the fictitious house. In
4.2. Dynamic vulnerability throughout a day The dynamic change in the vulnerability rate of the solar PV at the assessed instant of time is obtained for nine different capacity sizes. The result, shown in Fig. 6, presents different trends of dynamic vulnerability of solar PV with time among the nine options. 262
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vulnerability rate is in the range of 35–62%. Even with a capacity margin of 40%, compared with the ideal capacity size, the vulnerability rate of the battery in the hybrid system reaches greater than 60% at 16:00, which would hardly be considered secure. To generalize, at almost all instants of time, the differences in battery vulnerability rate in the hybrid system among the assessed nine options are in the range of 21–34%. This may indicate that the expectation of the battery vulnerability rate for a different capacity size is not as affected by uncertainties as the solar PV vulnerability. Although the vulnerability of the hybrid renewable energy and battery system is mitigated by increasing the capacity size, the dynamic battery vulnerability rate depends on the battery capacity rather than the solar PV capacity. Under the same solar panel rate with a different battery capacity, a capacity margin of 20% mitigates the battery vulnerability rate by up to 23%, and a capacity margin of 40% mitigates it by up to 37%. On the other hand, under the same battery capacity with a different solar panel rate, a 20% capacity margin mitigates it by up to 18%, and a 40% capacity margin mitigates it by up to 22%. Note that the range and value of the battery vulnerability rate at 0:00 and 24:00 are almost identical. This may indicate that the battery vulnerability in the hybrid system is not significantly affected by the energy stored in the battery. A comparative analysis of the dynamic vulnerability between the solar PV and battery with time under the nine capacity sizes is conducted. Considering that the vulnerability rates of 0% and 100% for both the solar PV and battery occur in the same condition, these rates could be compared under the same platform. The difference is obtained by subtracting the vulnerability rate of the battery from the vulnerability rate of solar PV. A positive outcome indicates greater vulnerability for the solar PV in the hybrid system, while a negative outcome indicates greater vulnerability for the battery. The result is shown in Fig. 8. The difference increases from 0:00 to 4:00, and after 4:00 it decreases and then increases again until 24:00. Whether it crosses zero depends on the capacity size. For a solar panel rate of 15%, other than at 20:00, the solar panel is more vulnerable in the hybrid system throughout the day. On the other hand, as long as the hybrid system has a certain amount of margin for the solar PV, the use of battery is more vulnerable, almost all day, even when the solar PV is actively operating after the morning.
Fig. 7. Dynamic change in the battery vulnerability rate with time under the nine capacity sizes.
Under a solar panel rate of 15% (the minimum required solar PV capacity), the same solar PV dynamic vulnerability is obtained regardless of battery capacity. In this case, it increases from 0:00 to 8:00 and then remains almost the same until 16:00. After 16:00, it declines up to 20:00 and then increases again up to 24:00. On the other hand, with a solar PV capacity of 18% and 21%, the battery capacity affects the trend of the solar PV dynamic vulnerability. In the case of 11000-Wh battery capacity, it increases from 0:00 to 4:00 and then declines until 12:00. After 12:00, it remains the same (for a solar panel rate of 18%) or even increases again (for a solar panel rate of 21%) until 16:00. It declines again until to 20:00 when it reaches the least vulnerable solar PV rate. Meanwhile, in the case of 13000-Wh and 15000-Wh battery capacity, it increases from 0:00 to 4:00, then declines constantly until 16:00, when it reaches the least vulnerable time in the solar PV supply. Finally, it increases again until 24:00. Particularly, at 8:00 and 12:00, the impact of the battery capacity on the dynamic vulnerability is not evident, while at 16:00, it is affected by the change in battery capacity in the case of the 18% solar panel rate. Consequently, among the nine options of capacity size, the most vulnerable time associated with the use of solar PV is in the range between 4:00–16:00, while the least vulnerable time is around 16:00–20:00, completely dependent on capacity size. Note that the range in solar PV vulnerability at 00:00 and 24:00 is markedly different. At these instants of time, the demand and solar supply are the same, while the energy stored in the battery is different among the nine capacity size options. This may indicate that the energy stored in the battery has a significant impact on solar PV vulnerability in the hybrid system. In general, the range of solar PV vulnerability rates at the various times is broad. Especially at 16:00, it is in a broad range between 7% and 95%, depending on the capacity size. Its expectation at a specific time and different capacity size would be difficult to determine, considering the high level of uncertainties. Next, the dynamic change in the battery vulnerability rate with time is obtained for the nine capacity size options. The result, shown in Fig. 7, indicates that the dynamic change in vulnerability arising from the use of a battery exhibits the same trend throughout the day. The battery vulnerability rate gradually deteriorates with time from 0:00 until 16:00. At 16:00, the operation of the solar panel reaches a stop, and the battery starts supplying power after storing the excess power from the solar PV. Then, the vulnerability level moderates with time from 16:00 until 24:00. When the power is supplied from the battery, the system is less vulnerable by up to around 40% compared with when the power is stored. For the minimum required capacity size, 15%_11000 Wh, the battery vulnerability rate is in the range of 60–97%. In this case, a small amount of trouble with the battery occurring at 16:00 could easily lead to insufficient supply, which would be highly critical. Meanwhile, under the most reliable capacity size, that is, 21%_15000 Wh, the
4.3. Overall vulnerability in the hybrid renewable energy and battery system By using Eq. (4), the overall vulnerability rate for the different capacity size is presented in Fig. 9. The trend in the differences in dynamic vulnerability at the assessed instant of time between the solar PV and battery, presented in Fig. 8, mainly reflects the result in Fig. 9. This indicates that, regardless of battery capacity, for a solar panel rate of 15%, the solar PV vulnerability in the hybrid system is greater by up to 34% compared with that of the battery, while, for solar panel rates of
Fig. 8. Comparison of dynamic vulnerability between solar PV and battery with time. 263
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increase in battery capacity reduces only the overall vulnerability of the battery, and its effect is hardly seen in the overall vulnerability of the solar PV. 5. Discussion The greater overall vulnerability associated with power source components in the hybrid system under the various capacity sizes is more likely to cause a disruption in power supply. Vulnerability is based on the magnitude and duration of failure in this study. In particular, the change in the failure rate for the specific power source component means a sudden change in component capacity. The parametric change in the failure rate and duration implicitly describes how much the other components can contribute to the supply and potentially evaluates the overall supply capability in the hybrid system. The greater overall vulnerability of an assessed power source component indicates the low contribution of the other components to meeting the demand, which leads to the low supply capability. In other words, this situation describes a heavy reliance on the assessed component. Therefore, the state of the overall vulnerability developed in this study represents the extent of the reliance on the power source in a continuous power supply. While various factors are considered as vulnerabilities to the security of energy supply [63,64], heavy reliance on a specific power source is one of the major concerns. To evaluate the extent of the reliance on the power source, diversification of energy generation by power source type has been assessed as a particular attribute [65–68]. Diversification and reliance is based on the concept where, even if one of the power sources is disrupted, power is continuously supplied as long as the other power sources could compensate for its loss. This concept is highly associated with the theory of vulnerability developed in this study. As such, it is of interest to the author to investigate the differences in reliance measurement factors between the vulnerability developed in this paper and the energy generation amount widely utilized. It must be mentioned that assessing the diversification in the national energy mix has evolved due to the geopolitical instability in the countries that supply fossil fuels, heavily relied on in the demand country [69]. Given only the renewable energy utilized in this study, a higher reliance
Fig. 9. Overall vulnerability rate under the nine capacity sizes.
18% and 21%, the battery vulnerability is greater by up to 45% than that of the solar PV. Among the assessed capacity size options, the maximum overall vulnerability rate for both solar PV and battery reaches 80%, while the minimum overall vulnerability rate for the solar PV reaches 40% and, for the battery, 50%. This means that the increasing the capacity margin by 40% decreases the vulnerability level in the hybrid system by 50% and 38% for the solar PV and battery, respectively. Based on Fig. 9, the relation between the overall vulnerability rate and the change in solar PV and battery capacity is identified by setting the OVR to zero for the minimum required capacity size. The result is presented in Fig. 10. The relationship between the normalized OVR and the battery capacity, shown in Fig. 10(a), indicates that the difference in OVR between the solar PV and battery is not evident for a battery capacity margin of 20%, while it is less than 0.1 for a capacity margin of 40%, except for the case of solar PV with a solar panel rate of 15%. On the other hand, the relationship between the normalized OVR and solar panel rate, shown in Fig. 10(b), indicates that the difference in OVR between the solar PV and battery ranges from 0.16 to 0.3 for a capacity margin of 20% and 0.27–0.4 for a capacity margin of 40%. Consequently, an increase in the solar PV capacity significantly contributes to the mitigation of the overall vulnerability rate of both the solar PV and battery in the hybrid system. On the other hand, an
Fig. 10. Relation between the normalized overall vulnerability and the change in solar PV and battery capacity.
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availability of such a prediction of supply capability would assist the service operator in determining an appropriate strategy (e.g., setting the limit time for recovery based on the information of time and failure duration). The main goal of the hybrid renewable energy system is to determine the optimal capacity size on the basis of multiple dimensions [72,73]. Together with economic indicators (e.g., [74,75]) and environmental indicators (e.g., [76,77]), the static reliability is often evaluated as one of the dimensions for indicating the degree of confidence in a continuous power supply. Meanwhile, little attention has been paid to the dynamic condition of a power system. Therefore, the inclusion of dynamic vulnerability assessments developed in this study would assist in the comprehensive optimization of capacity size. Meanwhile, the limitations of this research need to be mentioned. Differences between the static and dynamic evaluation of the power system may be the degree of generalization. In the static assessment, one year is often used as the evaluated time span to cover the various patterns of loads and solar irradiation as much as possible. This would lead to a high generality in the specifically assessed area. On the other hand, in the dynamic assessment, among the infinite patterns of loads and irradiation with time, a certain short term (one day in this paper) needs to be selected for the simulation. This may lead to a low generality. Although this study selects representative one-day patterns of loads and irradiation provided by Japanese government as a common trend, the obtained outcomes may not be applicable in general. Since this study develops the method for quantifying the concept of vulnerability in the power system as a starting point, a second-step time-span extension from one day to one year is required to improve the generality of outcomes. This is the subject of a future study. In addition, the developed approach can be further improved with inclusions of additional factors. Since the current model is highly dedicated to the standalone power system, the power exchange with external infrastructure is not accounted for. The decrease in performance with duration would affect the outcome of supply capability even under the same specifications in the power source components. In addition, although this simulation model fixes the demand, it is highly expected that the demand will be controlled by a demand response tool in the future under the emerging situation, including the failure of power source components. The decrease in demand as a response to emergencies would moderate the vulnerability level in the hybrid system. Furthermore, the methodology developed in this study could be considered a “soft” assessment at this stage, and “hard” perspectives are left out such as technical limitations and control management including interactions between the solar PV and battery and intermittent uncertainties in solar radiation. The integration of technical assessment in the developed methodology would assist in presenting a more comprehensive framework for estimating the vulnerability.
Table 1 Comparison of reliance measurement factors for a solar panel rate of 21% and a battery capacity of 15000 Wh. Reliance measurement factor
Solar PV
Battery
Energy generation amounts Overall vulnerability rate
2.68 1
1 1.20
merely corresponds to a greater contribution to the continuous power supply. Features of reliance measurement factors are demonstrated, using a solar panel rate of 21% and a battery capacity of 15000 Wh as the example. Energy generated throughout the day by solar PV and battery is computed, and then, the ratio of solar PV to battery for both the energy generation amount and vulnerability is computed to compare the reliance measurement factors. A greater value corresponds to a more reliant power source component. As presented in Table 1, the reliance measurement factors indicate the inverse trend in which the solar PV is more reliant in the context of energy generation, while the battery is more reliant in the context of vulnerability. In the conventional approach, the reliance on battery appears to be insignificant. However, as this assessment considers a sunny day when the solar PV fully operates, it is surprising that the approach developed in this study reveals an unexpectedly greater contribution of the battery to the continuous power supply than the solar PV in the hybrid system, with capacity margins to some extent. In addition to the important role of the battery in improving power system resilience [4,70] due to its dynamic and quick response [71], the higher contribution of the battery to the continuous power supply would raise its status and encourage its installation. Considering this result, only using the energy generation as a reliance measurement factor potentially risks reaching a short-sighted conclusion in terms of power reliance. In view of the significant interaction of reliance with the diversification of energy mix in the context of energy security, it would be highly expected that the vulnerability assessment developed in this study could be applied to the national energy supply and demand system and assist in revealing the hidden elements associated with energy diversification. As energy security is a driving force of energy policy, this approach may be of use in designing well-grounded energy policy narratives. The proposed method helps to understand the dynamic vulnerability throughout the day in the hybrid renewable energy and battery system in the following ways. The attractive point of the methodology developed in this study is the ease of adapting it into any other scale of power demand and supply system. Its application could be completed by just changing the energy source components in the assessed power system and the precondition of simulation input. While this study selects a fictitious home for the analysis of power system vulnerability, the algorithm is readily employed in any electricity flow system including ZEB, microgrids in urban and rural areas, and even in the national grid. The simulation in the developed model runs with time steps of one minute. Meanwhile, the most of the earlier studies conducted hourly simulations in the static reliability assessment (e.g., [17]). The higher time resolution of the simulation would improve the accuracy of outcomes. Additionally, the vulnerability assessment conducted in this study is not affected by any type of failure causes or any technological innovation of the hybrid system. The developed magnitude-duration curve represents the prediction of supply capability in the hybrid system in the near future. The
6. Conclusion This research has developed the methodology of quantifying the dynamic vulnerability of power source components throughout the course of a day in the hybrid renewable energy and battery system. The concept of vulnerability is developed based on the magnitude and duration of component failures. Then, by following the established methodology, the dynamic vulnerability with time and overall vulnerability of the system has been presented in the case of power demand and supply system in a fictitious house. Finally, as the reliance measurement factor, the developed vulnerability is compared with the amount of energy generation to identify the extent to which power components contribute to the continuous power supply.
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Findings in the case of representative load and irradiation in Japan are as follows.
the solar PV actively operates after the morning.
• The increase in solar PV capacity significantly contributes to the
• The dynamic mitigation of vulnerability associated with the use of
•
solar PV and battery with capacity size could be quantified using the developed methodology. The trend of dynamic vulnerability of solar PV throughout the day varies depending on the capacity size and amount of energy stored in the battery. The dynamic change in vulnerability arising from the use of battery has the same trend regardless of the capacity size, in which the system is less vulnerable by up to around 40% when the power is supplied from the battery, compared with when the power is stored. This trend is not significantly affected by the energy stored in the battery. As long as the hybrid system has a certain amount of margin of solar PV, the use of battery is more vulnerable almost all day, even when
•
mitigation of the overall vulnerability rate of both solar PV and battery in the hybrid system, while the increase in battery capacity reduces only the overall vulnerability of the battery, and its effect is hardly evident in the overall vulnerability of solar PV. The approach developed in this study would potentially reveal the greater contribution of the battery to the continuous power supply compared with the solar PV in the hybrid system.
Acknowledgement This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.
Appendix A Detailed steps for obtaining the magnitude-duration curve are described as follow: (1) Select one of the n types of power source components. (2) Initial setting of parameters: failure rate = 1%, failure duration = 1 min, instant of time = 00:00 h. (3) Start of simulation and energy deficit verification. In this assessment, the energy deficit is defined as the total lack of power supply to the meet the demand in 24 h. (4) For NO energy deficit observed, failure rate is increased in steps of 1%. Model simulation is repeated until energy deficit appears. (5) For energy deficit observed, the previous failure rate is recorded in the simulated condition of failure duration and instant of failure. (6) Step (3), (4) and (5) are repeated increasing the failure duration from 1 min until 24 h by 1 min. (7) Step (3), (4), (5) and (6) are repeated increasing the instant of time until 24:00 h by its corresponding step. (8) Obtained results are plotted on a 2-axis graph of failure rate versus failure duration in curves representing instant of time under the selected power source component. (9) Step (2), (3), (4), (5), (6), (7) and (8) are repeated changing the assessed power source component.
Equation
Number
Solar PV = Roof top area × PV efficiency × Radiation × Solar panel rate
Eq. (A-1)
× (1
Solar PV failure)
Instant of Solar PV failure)
Eq. (A-2)
*1
Solar PV failure = STEP (Solar PV failure rate , STEP (Solar PV failure rate ,
Instant of Solar PV failure + Solar PV failure duration)
Surplus Power = IF THEN ELSE (Power delivery = 0, 0, Power delivery
Eq. (A-3)
Demand <*2
Demand )
Eq. (A-4)
Energy Stored in battery =
IF THEN ELSE (Energy stored in battery > battery capacity × (1
Battery failure ),
Battery /Battery efficiency,
Surplus Power
Battery /Battery efficiency ) Battery failure = STEP (Battery failure rate, STEP (Battery failure rate,
Eq. (A-5)
Instant of battery failure) Instant of battery failure
+ Battery failure duration)
Eq. (A-6)
Battery = IF THEN ELSE (Energy stored in battery < = 0, 0, IF THEN ELSE (Demand
Solar PV < 0, 0, Demand
Solar PV )) Eq. (A-7) Power delivery = Battery + Solar PV Eq. (A-8) Electric Power = Power delivery Demand Surplus Power *1 STEP (a , b) , where the equation a is summed when the time reaches the instant b *2 IF THEN ELSE (p, q, r ) , where it is switched to the equation p when the condition p is true, or to the equation r when the condition p is false.
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Appendix B Each component of Hybrid renewable and battery model in the standalone ZEH can be computed as follows: Appendix C All variables used in the model are summarized in Table C1. Table C1 Summary of variables. Variable
Unit
Definition
Power delivery
W
Electric Energy
Wh
Demand Surplus power Solar PV PV efficiency
W W W %
Radiation Roof-top area Solar panel rate Solar PV failure rate Solar PV failure duration Battery Energy stored in battery Battery efficiency Battery capacity Battery failure rate Battery failure duration
W/m2 m2 % % h
Summation of power from both solar PV and battery Imaginary energy stock of discrepancies between the sum of both demand and surplus power and power delivery Home electricity demand Exceeding power over the demand Power generated by the solar PV Conversion efficiency from the solar radiation to electricity Solar irradiation per area Horizontal area of home roof-top Rate of solar panel area to roof-top area Magnitude of solar PV failure Duration of solar PV failure
W Wh
Power discharged from the battery Energy stored in battery
% Wh % h
Buttery round-trip efficiency Maximum energy fully stored in the battery Magnitude of battery failure Duration of battery failure
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