The electric power system is being modernized to enable a sustainable energy system. New developments include the possibilities and challenges with generation, delivery, and usage of electricity as an integrated part of the energy system. This involves new forms of electricity usage, for example, for transportation and demand response and the updating of existing electricity infrastructure. For electricity generation, the trend is toward new large-scale developments, such as offshore wind farms, as well as small-scale developments such as rooftop solar energy. At the same time, the digitalization of society is creating new opportunities for control and automation as well as new business models and energy-related services. The overall trend for technology development is new possibilities for measurement and control. An example is phasor measurements units (PMUs), generally located in the transmission network, which provide measurements of voltage and current up to 30–20 times per second. Another example is smart meters placed with the end consumer, which enables the integration of private small-scale electricity production from solar cells or energy storage from electric vehicles and general distributed control of energy use. Europe has been at the forefront of several of these deployments, especially in the areas of managing large penetrations of renewable sources of energy, advanced metering infrastructure (AMI), and advanced information technology [1].

The main challenges for the current development of the European power system can be summarized as follows (resulting from the EU project ERA-Net):

• • Enabling an increased flexibility of the power system to cope with the growing share of intermittent, variable, and decentralized renewable generation as well as managing the complex interactions.
• • Increase network capacity to support increased generation and transmission resulting from renewables and in support of the internal energy market.
• • Provide information, services, market architecture, and privacy guarantees to support open markets for energy products and services while facilitating the active participation of customers.

Solutions for this modernized power system are rapidly evolving and have been analyzed from a number of perspectives [2,3], often from a data communication, monitoring, and control perspective such as [4]. In addition, studies of capacity-increasing benefits [5] and different solutions to facilitate the integration of intermittent distributed generation [6] have been conducted, such as demand response [7,8], energy storage [9], and dynamic rating (DR) [10,11] or looking at reliability aspects of this [12]. Comprehensive studies have been performed on the relationship between weather parameters and power system properties [13].

This chapter presents an approach in analyzing various solutions for a future sustainable energy system using the case system of the Swedish demonstration project of Smart Grid Gotland.

1.2 Smart grid demonstration project at the Swedish island Gotland

The island Gotland in Sweden has been used for exploring the new technologies for a sustainable energy system. Recently, the Swedish government expressed visions to further investigate the expansion of generation supply from renewable energy resources instead of an extension with an additional capacity connection with mainland Sweden.

Gotland is an isolated power system by geography. It is small enough to get a good overview but still large enough to illustrate and analyze comprehensive challenges and synergies [14]. There are already major challenges and opportunities of renewable distributed generation as electricity from wind power has approached the ceiling of what the system can handle with traditional technology and existing infrastructure. Gotland's subtransmission system can partly be described as a transmission system in miniature because Gotland is isolated from the rest of the Nordic power system transmission system.

Gotland is connected to the mainland with a high voltage direct current (HVDC) link [8]. There are both export and import situations for the HVDC link. At the island, there is a double onshore VSC link (HVDC Light) to connect large amounts of electricity, today typically from wind power from the south parts of Gotland, with the area around Visby. Visby is the largest city on Gotland having the highest electricity consumption. The mainland HVDC link connection outgoes from Ygne (just south of Visby). This 96 km long HVDC Link was awarded an IEEE Milestone in 2017 for being the worlds' first commercial HVDC transmission link using the first submarine HCDC cable [15]. Fig. 1 illustrates the case system of Smart Grid Gotland.

In 2011 the total installed wind turbine capacity was 170 MW. From a smart grid analysis perspective, it is of interest that the power system with current technology and infrastructure is expected to handle 195 MW, that is that installed wind power today is close to its upper calculated limit. The electricity production in 2011 was 340 GWh, representing 38% of Gotland's electricity consumption. However, both electricity consumption and electricity generation from wind turbines are unevenly spread over the year, which means that it can have both high import and export peaks. In the long run, there will be capacity problems in both ways of the HVDC link to the mainland; there are plans to increase its capacity. Furthermore, Gotland has a relatively high amount of electricity consumption by industrial customers [8]. Another difference with an average Swedish area is a relatively large amount of summer visitors, which could possibly partly compensate for the industry's low season from a power consumption perspective.

As new technologies and solutions involve unknown risks and opportunities, it is valuable to complement theoretical research and commercial development with large-scale smart grid demonstration sites. Ref. [16] provides examples for such projects in Europe. There have been three large national smart grid demonstration projects in Sweden, involving different actors and testing different aspects of a smart grid: the Royal Seaport, Hyllie, and Smart Grid Gotland. Smart Grid Gotland is a development and demonstration project to illustrate and investigate possibilities of modernizing an existing power system to handle more renewable energy while maintaining or improving power quality [17,18]. The project started in 2011 and is currently being evaluated. Smart Grid Gotland consists of nine subprojects: (1) Market tests, (2) Integration of wind power, (3) Power quality with distributed generation, (4) Market installations, (5) Smart meters, (6) Smart secondary substations and rural networks, (7) Communication technology, (8) Energy storage, and (9) Smart SCADA. For more detailed information about Smart Grid Gotland, see, for example, Refs. [8,17,18].

1.3 Initial data analyses used as input when developing the method

Based on the initial studies presented in this section, different models for calculating the average, maximum, and minimum values of electricity consumption and production as a function of weather parameters have been developed, presented, and used in later sections of this chapter.

The hourly data of electric consumption and wind power generation were obtained for the period October 2011 to September 2012 from the DSO of Gotland [8]. The Swedish Meteorological and Hydrological Institute (SMHI) is a governmental body that has made both historical and real-time data freely available online [19]. Hourly weather data from 1970 to 2003 at Visby Airport has been retrieved from SMHI. In addition, weather data have been gathered for a shorter time period from Huborg, another weather station at Gotland. Long data series are important to capture improbable risks and to achieve high statistical validation when different scenarios are studied. Visby Airport was chosen because it has a long data series, a high consumer density, and it's close to the mainland link. However, Huborg is located on the southern tip where a considerable part of Gotland's wind power capacity is located.

Some smart grid solutions are directly affected by weather parameters [11]. At the same time, the capacity requirements of components often indirectly depend on the weather in different ways. Hence it is valuable to investigate the weather dependency of power system utilization. Heating and air conditioning are examples of human behavior that depend on outdoor temperature and that affect electricity consumption; this provides strong correlation between temperature and consumption [20]. The tendency of an increased amount of intermittent distributed generation gives situations where the power line congestion depends on the weather [21]. An example is the dependency between wind power production and wind speed, a weather parameter that also affects the dynamic capacity of overhead lines [22].

Table 1 provides correlations between wind power generation, electricity consumption, wind speed, and outdoor temperature. Note that electric generation and consumption refer to the entirety of Gotland while the weather parameters are only from the Visby Airport. When handling transfer limits to areas with both electricity generation and consumption, these can partly cancel each other out in some cases [21]. Fig. 2 shows the average value of electricity consumption, wind power generation, and net imports as a function of temperature. The wind power generation dependency can be explained by high pressure and low wind speed when it is hot or cold. Higher wind speeds in average occur during spring and fall.

The electricity consumption's temperature dependency is low when the temperature is low or high, but in midrange it is almost linear. That could be explained by maximal heating at about − 10°C and that most households do not heat above 15°C. These tendencies have also been observed in other studies; see, for example, Fig. 3 [23]. When it comes to electricity consumption, it is unlikely that it will reach > 80% of the peak value if the temperature is > 0°C and in the summer it rarely reaches > 60%. The import needs are highest when it is cold.

Because Gotland has a high share of industrial customers, a hypothesis is that the correlation between temperature and electricity consumption is lower compared with an average Swedish power distribution system. The correlation in a study of another Swedish power system [23] was “− 0.90” compared to “− 0.71” for Gotland. Fig. 3 shows all hourly measurements of temperature vs. electricity consumption, including the average trend in the other power distribution system. Compared to Gotland, there are many similarities. The conclusion is that the general model developed based on Gotland data provides a statistical relationship whose shape is similar to other power systems. This means that results using these dependences give results that are generally applicable.

Fig. 4 depicts the average electricity consumption and wind power generation as a function of the wind speed. Wind power generation strongly depends on the wind speed. The generation at 0 m/s is explained by the fact that the wind measurement is situated at one place and the height difference while wind power generation is an average for the whole island. Another interesting observation is that wind power generation increases with wind speed up to ~ 10 m/s and after ~ 13 m/s decreases. Note that it can be significantly much harder winds that hit the rotor blades than at the weather station, which explains that tendency already after 13 m/s.

Table 2 exemplifies the average, maximum, and minimum electricity consumption and wind power generation if the year is divided into four seasons. The minimum vale of wind power generation is 0% despite the season and is omitted in the table.

The proposed method is general and can study a power system part of any size and voltage level as well as with flexible composition of generation and electricity consumption. The algorithm is illustrated in Fig. 6. The model contains of calculation modules, which are flexible to separately develop and improve:

• • Electricity consumption, see Section 2.2.
• • Wind power generation, see Section 2.3.
• • Solar power generation, see Section 2.4.
• • Dynamic rating, see Section 2.5.
• • Energy storage, see Section 2.6

The basic idea is illustrated in Fig. 5: a local system area (C) is connected with the rest of the power system (A) by a set of components with limited transmission capacity (B).

• • Block A represents the rest of the power system. From this area it is assumed that desired electrical energy either can be exported to or imported from.
• • Block B symbolizes a link between A and C where the transmission capacity is limited and may correspond to a set of several components. The transmission capacity can both be modeled as equal or different in both directions. This can in reality correspond to limited transfer by various factors. For example, if generation from solar power gives voltage problems, it may cause different transfer restrictions on imports versus exports as opposed to thermal restriction.
• • Block C symbolizes a system area flexibility to define. One or several of the following categories is connected: (a) electricity consumption, (b) wind power, (c) solar power, and/or (d) energy storage. The sizes of these in relation to each other are free to define.

The method focuses on the worst case, for example, high electricity consumption and low generation given the weather if import transfer limitations are evaluated and the opposite for export limitations. The calculations are deterministic, apart from the energy storage module that has a mix of deterministic and stochastic parts; the latter is explained and justified in Section 2.5. The approach is to go through a huge database of hourly weather conditions. This will give a good statistical basis with real measured historical data and consequently decrease the need for using hypothetical assumptions.

Fig. 6 shows the algorithm of the developed method:

1. I. Matlab receives input data from an Excel file. No upper limit for the number of records; the more input, the more reliable results. For each hour: month (1 − 12), time (1–24), temperature (°C), and wind speed (m/s).
2. II. Hourly calculations: Calculate various properties for each hour by sending inputs to modules and getting back results. The modules are described in Sections 2.2–2.6.
3. III. Analyses are performed by using the large amounts of raw results that were produced during step B. By defining system characteristics and analysis questions, different analysis results are produced. These are defined before running the entire algorithm.
4. IV. Energy storage calculations: Just as in step C, system properties and analyses questions are defined and results from step B are used. In addition, a module for energy storage is contacted.
5. V. Write results to an Excel document: Examples of possible results are given in Section 3.

Each module described in Sections 2.2–2.6 can be separately modified or refined from the main algorithm, for example, to consider more properties or base these on other input data than used here.

2.2 Electric energy consumption model

Input data consists of the outdoor temperature and the calculation model returns maximum, minimum, and mean values of electricity consumption. Estimated averages for different temperature ranges are based on the initial analysis in Section 1.3. The unit is procent of its peak value while maximum and minimum values are two standard deviations from the mean (normal distribution is assumed) and validated against real input data. The model is presented in Table 3. Extreme values are important because worst-case scenarios are analyzed.

2.3 Wind power generation model

Input data consists of the wind speed and the calculation model returns maximum, minimum, and average values of wind power generation. The model is based on analyses presented in Section 1.3 and is presented in Table 4. Wind power generation is in general significantly less predictable compared to electric consumption, which is reflected by a larger range between extreme values. Note, low wind speeds can give generation. That is explained in Section 1.3.

2.4 Solar power generation model

Input data consists of month (1–12) and hour (1–24) and the model returns the maximum value of solar power generation in % of annual maximum production. The model is illustrated by Table 5 and calculates the peak production at perfect conditions, based on how high the sun is over the horizon in Visby [24]. This is justified because the model focuses on the worst case and that the minimum value is assumed to be zero.

Table 5

Electric energy production model from solar power

2.5 Dynamic rating introduction, assumptions, and model used

Overhead line DR is used. It is possible to replace this module with other DR models or to expand it with more power component models. Wind power generation has a correlation with the weather in a positive way [12], that is, high production correlates with high dynamic transfer capacity. Furthermore, in Sweden there are positive correlations between low temperature and high energy consumption [21]. A challenge is that the measured wind speed often is optimistic to use because the wind speed is neither the same through the entire line nor perpendicular. One way to handle this is to introduce a scale parameter that scales down the available wind speed input data to have a margin.

IEEE standard 738 [22] provides a formula for calculating the maximum current allowed [A] of bare OH conductors. Based on this, a DR model has been developed and is proposed in Ref. [11]. The method is simplified to be implemented in the daily operation and is also evaluated by comparing it with the more detailed standard [11]. Evaluations performed conclude that its results only differ minimally from more complex models. The proposed calculation model calculates the dynamic line rating capacity (DLR_x) as a function of static line capacity, wind speed, and ambient temperature. DLR_x has no unit and indicates how many times the transfer capacity is compared to static line rating. If, for example, the static line rating is 3 MW and DLR_x is 2, the new DR is equal to 6 MW.

${\mathrm{DLR}}_t\approx \frac{\sqrt{\left(t_{\max }-t_i\right)}}{\sqrt{\left(t_{\max }-t_{\mathrm{SLR}}\right)}}=c1\ast {\left(t_{\max }-t_i\right)}^{0.5}$

Eq. (1) calculates the DLR_x, taking temperature into consideration (DLR_t). t_max is the maximal line temperature allowed, t_SLR is the worst-case outdoor temperature that static rating (SR) is based on, t_i is the outdoor temperature that is input to the calculation, and c1 is a constant defined in Ref. [11].

${\mathrm{DLR}}_v=max\left\{\begin{array}{l}1\\ c2\ast v_i^{0,26}\\ c3\ast v_i^{0,30}\end{array}\right.$

Eq. (2) calculates the DLR_x, taking the wind speed into consideration (DLR_v) where v_i is the wind speed. For information on how to calculate c2 and c3, see Ref. [11]. The contribution of wind speed and outdoor temperature can be approximately assumed to be independent of each other [11]. Therefore, taking both wind and temperature into consideration can be calculated by multiplying the respective contribution (Eqs. (2), (3)) to each other:

${\mathrm{DLR}}_{t+v}={\mathrm{DLR}}_v\ast {\mathrm{DLR}}_t$

2.6 Energy storage algorithm

The energy storage status regarding previous hour i − 1 (EStorage_i − 1), actual transfer limitation, electric generation, and consumption data is used as input data to this algorithm. The output data is the energy storage status of actual hour i (EStorage_i). The analyses are technique-neutral and produce specifications of requirements for energy storage. EStorage_i = 0 does not necessarily mean empty energy storage, but its “normal level” (is explained later). Required size and the normal level are determined after EStorage_i has been calculated for all hours.

Unlike other models proposed, this calculation model uses both deterministic and stochastic parts. The current status of the energy storage is based on both current hour and earlier hours. The probability of a worst-case situation during a specific hour is not negligible, but having that situation constantly during many hours or even several days is unlikely. Such an assumption would put unrealistic demands on the energy storage. However, it is important that here we note the precautionary principle and calculate pessimistically. A compromise is that a value between the mean and the worst-case extreme value is randomized (uniform distribution). Because the energy storage can be used to both handle import and export restrictions, two different pessimistic values are calculated see Eqs. (4)–(9).

${\mathit{EG}}_1=\left[max\mathit{solar}\mathit{gen}\right]\ast \text{Table}5+\left[max\mathit{wind}\mathit{gen}\right]\ast U\left(\mathit{averer}\text{Table}4,max\text{Table}4\right)$

${\mathit{EG}}_2=\left[max\mathit{wind}\mathit{gen}\right]\ast U\left(min\text{Table}4,\mathit{aver}\text{Table}4\right)$

${\mathit{EC}}_1=\left[maxe\mathit{cons}\right]\ast U\left(\mathit{aver}\text{Table}3,max\text{Table}3\right)$

${\mathit{EC}}_2=\left[maxe\mathit{cons}\right]\ast U\left(min\text{Table}3,\mathit{aver}\text{Table}3\right)$

where EG₁ and EG₂ are upper and lower estimates of electricity generation, respectively, and EC₁ and EC₂ are upper and lower estimates of electricity consumption, respectively.

$\mathit{High}\mathit{import}\mathit{level}\mathit{stochastic}\mathit{estimation}={\mathit{EC}}_1-{\mathit{EG}}_2$

$\mathit{High}\mathit{export}\mathit{level}\mathit{stochastic}\mathit{estimation}={\mathit{EG}}_1-{\mathit{EC}}_2$

If the import is higher than the import transfer capacity, the energy storage needs to deliver electrical energy to temporarily compensate for transfer limitation and hence be fully charged to be as prepared as possible. If, however, the export is higher than the export transfer capacity, the energy storage needs to store electrical energy to temporarily compensate for transfer limitation and hence be empty to be as prepared as possible. If no transfer limitations are reached, the energy storage is assumed to return to its normal level as quickly as possible with considered transfer constraints, trying to return to its normal level.

The algorithm is illustrated in Fig. 7. EStorage_i has the unit “hour.” When EStorage_i is multiplied by a transfer limit that has the unit power (e.g., MW), it gives the unit of energy (e.g., MWh) (see Eq. 10). Power requirements are calculated by taking the highest absolute value of the difference between EStorage_i and EStorage_i − 1 in both directions.

$\left[\mathit{Energy},,\mathit{storage},,\mathit{size},,\mathit{needed}\right]=\left[\mathit{transfer},,\mathit{limit}\right]\ast \left(Max\left({\mathit{EStorage}}_i\right)-Min\left({\mathit{EStorage}}_i\right)\right)$

$\left[\mathit{Normal},,\mathit{level}\right]=\frac{-Min\left({\mathit{EStorage}}_i\right)}{\left[\mathit{Energy},,\mathit{storage},,\mathit{size},,\mathit{needed}\right]}$

Calculation example: Assume that EStorage_i varies between − 2.5 and + 10.0 during all hours analyzed and that the power transfer limitation is 1 MW (import). Then an energy storage of 12.5 MWh is needed (= 10 − (− 2.5)) and the normal level is 20% charged $\left(\frac{-\left(-2.5\right)}{10-\left(-2.5\right)}\right)$, i.e., 2.5 MWh.

Table 6 exemplifies results from DR analyses where the potential of taking advantage of identified weather correlations has been investigated. The figure of 100% corresponds to the maximum effect the overhead line can handle with a classic SR.

The potential benefits of using synergies between electricity consumption and generation have been analyzed, that is, how these factors cancel each other out in a mixed system part. Increased average electricity consumption provides the ability to handle more installed generation. Even when using pessimistic assumptions, each MW of peak power using traditional assumptions makes an additional 0.32 MW power possible. The opposite, that is, increasing electric consumption if intermittent generation increases is, however, not possible because the electricity generation sometimes is 0. With a variety of smart solutions where electricity consumption (e.g., demand response) and/or electricity generation can be controlled, the benefits of utilizing such synergies will probably increase more significantly. Table 7 shows results analyzing transfer limitation to mixed system parts. These analyses capture synergies of both the DR and taking advantage of cancellation at the same time. These two effects sometimes becomes stronger compared with just adding one of these two solutions.

3.2 Energy storage

Energy storage specifications as a function of a variable parameter to handle transfer limitations regarding different scenarios are presented in Table 8.

Fig. 8 illustrates a general comparison of how large energy storage is required for the three categories analyzed. Solar power generation is more advantageous compared with electricity consumption and wind power generation. The significant difference can be explained by the fact that the peak generation from solar power only lasts a few hours during summer days, making time to restore the energy storage to its normal level before the next peak. For the other two, there are longer periods with peak values with no time restoration. It would, however, probably be a more favorable outcome for using energy storage if the model considers electricity patterns between different times of the day.

Another aspect is that energy storage is unused for most of the year; analyses of possible usages for other purposes during these periods are addressed in Section 3.3. Fig. 9 compares the utilization levels. Energy storage has the lowest utilization while managing electricity consumption.

Analysis results of energy storage to manage a mixed system part that has periods of both import and export transfer limitations are provided in Table 9. Electricity consumption with solar power generation is exemplified. Note that energy storage size needed as a function of electricity consumption is low compared to the system part with only electricity consumption. That indicates the positive synergies of using both energy storage and taking advantage of cancellation effects.

Fig. 10 exemplifies how the energy storage level may vary over time regarding a node with 106.5% electricity consumption and 150% solar power generation, where the energy storage is about 42% charged in standby. The analysis extends over 40 years, 2 of these years are illustrated in the upper part of the figure. The energy storage during these two exemplified years never reaches its highest level. Clear seasonal variations can be discerned. Three days are showed in the lower part to get a detailed picture of how the energy storage may vary during a short period. These days are selected at the time when the energy storage was lowest.

3.3 Discussion and analyses of further energy storage utilization

Energy storage analysis results presented in Section 3.2 indicate that energy storage is unused most of the time. The possibility of using energy storage for another application, such as improved reliability, is best regarding scenarios where energy storage is used to manage electricity consumption as it is fully charged during normal operation. Furthermore, this scenario has the lowest utilization.

Table 10 shows the percentage of time the energy storage is unused, the size, and how long outages theoretically can be handled at low and high load. Energy storage to handle peak generation needs to be empty during normal operations. Thus, these are not available when there is a transfer limitation risk but can, however, be used during low risk periods. This risk can be predicted by weather forecasts, season, and time of day. Solar power generation can reach higher than 90% of its max generation only ~ 3% of the time and > 80% during ~ 6%. Another positive aspect is that the summer months have few outages compared to the rest of the year in Sweden [20].