In a power system, the basic physical law states that the total production is always exactly the same as total consumption. This physical law is always fulfilled no matter the type of power plants in the power system. In a power system with large shares of solar and wind power, this means that the other power plants have to fill the gap between actual solar plus wind power and the demand during each second/minute/hour. However, if there are large amounts of solar and wind power, then sometimes the available power from solar and wind exceeds the demand. In a future system based on large shares of solar and wind power, all these different situations have to be handled, and the question is how to analyze this. Three different methods concerning how to analyze systems with large shares of solar and wind power will be presented. The methods are applied to a Swedish case with close to 100% renewable power based on hydro, solar, wind and biofueled combined heat and power (CHP). This chapter shows that there are limited balancing costs for this case. The costs for curtailment of surplus as well as to keep enough capacity to cover a high load combined with low solar and low wind is comparatively small, below 0.3 Eurocent/kWh. However, more detailed studies are needed to quantify the exact cost under different conditions, but this chapter indicates the size of the challenges.

INTRODUCTION

In principal, electricity cannot be directly stored. There are storage technologies, such as batteries, but these formally mean a transfer from electrical energy to chemical energy. This means that as soon as electricity is consumed, it has to be generated and vice versa, that is, as soon as electricity is generated, it has to be consumed. This always applies and is a physical law that we cannot change. In practice, this means that as soon as we switch on a lamp, the corresponding electricity has to be produced somewhere else. The other way around it is that when a wind or hydropower station (or any other power station) generates power at exactly the same time, the electricity has to be consumed somewhere else. This means electricity cannot “disappear.”

From a physical perspective, there is no “excess power” or “power shortage.” There are, of course, always losses in the power system if we look at the entire chain from the generation in power stations via power lines all the way to the consumer. Losses are caused by power lines and transformers that get warmer when electricity flows through them. In practice, this means that total production (what generators feed into the power system) is always larger than what consumers take out of the power system. Sometime, the words power shortage or excess power are used in this context. These terms, however, refer to economic issues. Power shortage means that somebody would like to consume electricity but that there is no electricity available at the consumer's location or at the price the consumer is willing to pay. As opposed to this, excess power refers to a situation where there are power stations that could produce power if consumers were willing to consume more and to pay the price for this power.

It is naturally a challenge for the power system to maintain an exact balance between production and total consumption, including power system losses. The largest challenge for many modern power systems is a situation of a sudden stop in a large power plant, e.g. a nuclear power station. In that case (which occurs once a year in every nuclear power station, approximately), about 1000 MW of power generation could be lost. In the exact moment when such an incident occurs, all consumers need to be supplied with power as usual, that is, as the nuclear power station cannot supply them any longer, the electricity has to come from another power source. A power source that is always available as “reserve” power are all the spinning generators (in hydropower stations, nuclear power stations, and others) of the entire power system. At the very moment a nuclear power station comes to a sudden stop, the power is supplied from the mechanical energy stored in all these spinning generators. This will also change the power flows on many transmission lines.

The extra challenges that are introduced to the needed balancing caused by variable wind and solar power will be discussed in this chapter. There have been many studies performed concerning the integration of large amounts of variable renewable (VR) energy in systems of different sizes. A summary of several studies is found in Ref.^[1]. There is a report on recommended practices concerning integration studies^[2]. However, a full study is very time consuming and requires large amounts of date, while this chapter shows what kind of results it is possible to obtain from three different levels of simplified studies and which types of challenges that are the most important for a hydro‐dominating system.

KEEPING THE CONTINUOUS SHORT‐TERM POWER BALANCE

As stated in the introduction, there will be a continuous balance between production and consumption.

There are several challenges regarding the handling of large amounts of wind and solar power in power systems. The overall general challenge is to maintain a continuous balance in an economical and reliable way with minimum environmental effects. Within this context, there are two important special cases that are often discussed. The main challenge C1 and the two important special cases C2–C3 are:^[3]

• C1. Handling the continuous balancing. The challenge for the continuous balancing process is that controllable production and consumption have to maintain the balance on all time scales. With larger amounts of wind and solar power, there is a larger uncertainty, e.g. wind power forecasts are not as accurate as the corresponding power consumption forecasts. An important issue of an economic operation is the efficiency of a power station if it remains on standby in order to compensate changes in production levels. The continuous balancing process applies to the technical capacity available for both increasing other generation when wind power decreases (i.e. enough ramp rates), and for decreasing other generation in an economically feasible way when wind power increases.
• C2. Low wind and solar power production and high power consumption. Such situations are the basis for dimensioning the capacity that has to be installed. This issue is called “capacity adequacy issue.” This challenging situation may occur comparatively, seldom depending on the size of the peak demand, amount of solar and wind power, transmission capacity to neighbors, etc. Power consumption may also be high in the neighboring countries, which reduces the possibilities of importing power. In many systems in Europe and USA, the common set up is to have a rather good adequacy in each area and then in extreme situations, rely on the neighbors. This means that outages that depend on a lack of capacity is extremely rare in these systems. With large‐scale solar and wind power, this situation will persist, not only on a consumption level but also regarding variable wind and solar power production. When dimensioning the power system, in order to handle such situations in a rational way, wind and solar power production both in the studied area and in its neighboring areas have to be taken into account regarding high power consumption levels. If the risk is too high, then additional capacity has to be provided using, e.g. new production units to be used during few yours per year such as Open Cycle Gas Turbines, more trading capacity to areas with capacity and/or flexible demand.
• C3. High wind and solar power production and low power consumption. Such situations can be handled in many different ways, but it has very high importance for the dimensioning of the system. If one adds large amounts of wind and solar power to a certain area without changing anything else, this may result in very low prices and/or that water has to be spilled past the turbines and/or that not all wind or solar power can be used. In addition to this, one has to consider the needs of other units that can act as reserves for different situations. Therefore, one has to analyze how frequently this kind of situation can be expected to occur and adjust the operation and investment plans according to this evaluation. Challenges for these situations are that there has to be enough inertia, frequency control reserves, and enough voltage support equipment, as all these three issues mainly come from controllable synchronous machines, which is not the case for solar and wind power.

In the following sections, we will describe these challenges in more detail. The most complex challenge (to explain) is C1, the continuous balancing of production and consumption. C2 is mainly important for system security reasons (i.e. How is it possible to maintain a reliable balance even if the solar radiation is low and the wind does not blow?). Three levels of analysis will be performed where more details are considered.

LEVEL 1 ANALYSIS: MAXIMAL SHARE OF VARIABLE RENEWABLE

This level is based on a rather few samples of statistics and experience from countries with different levels of variable renewable (VR). It mainly studies challenge C3. The basic method is to calculate the following index:^[4]

(26.1)

The important content of this formula is that one compares the maximal possible variable renewable with the lowest demand and possible export. This corresponds to challenge C3 above. The main challenge is at high levels of VR and low load, but one has to consider the exchange possibilities as these limit the challenges concerning both the balancing challenges and inertia challenges.

Actual figures are shown in Table 26.1.

With this simplified analysis, it is possible to see that:

• Denmark has the highest energy share from wind power (29.7%), but the integration challenges are lower than for Spain and Portugal (lower maximal share of variable renewable [MSVR]). This depends on Denmark being comparatively well interconnected to its neighbors.
• Sweden has significantly lower share concerning both energy share and MSVR. Sweden could have around four to five times more wind power in order to come up to the same integration challenges as in the other countries. This corresponds to around 30 TWh of wind power per year.

However, this is a fast but simplified analysis. Issues that are not considered include:

1. There may be a high correlation between neighboring regions, e.g. Spain and Portugal, which means that one may not be able to export to this country in high wind situation.
2. Correlation between demand and wind power is not considered. The question is how often one gets the highest wind at the same time as the lowest load. At least in Sweden and Denmark, the low load is in the summer and the high wind in the winter.
3. Only challenge C3 is considered, not C2 or C1.
4. Internal bottlenecks in each country are not considered.
5. In the table, only wind power is considered, not solar power.

Data needed for first‐level analysis is limited to maximal VR power (one MW level), lowest consumption (one MW level), and possible export (one MW level). The method provides a fast estimation, and if the MSVR for the studied area is around 60–70%, then one will probably get almost the same challenges as in the corresponding countries.

LEVEL 2 ANALYSIS: TRANSITION DIAGRAMS

The next level of analysis refers to the drawing of transition diagrams. This method refers to challenge C1 above, i.e. that there must be enough resources in order to follow the continuous variations in the system. The method has three steps:

1. Draw the transition diagram for the current needed regulation for different time spans.
2. Draw the same for a future situation with more variable renewable power.
3. Compare and draw conclusions about possible needed changes.

Step 1:

We will, as an example, study the historical transitions for Sweden. Transitions mean the changes for a certain variable over time, and all these changes are plotted in a diagram. The transition diagram for one‐ and four‐hour changes of hourly energy values of the Swedish load is now shown in Figure 26.1.

Figure 26.1 shows the load transitions that have to be balanced with corresponding production transitions. From hour to hour, the demand can change up to around 2000 MWh h⁻¹, while changes over four hours can be up to around +6000 and −4000 MWh h⁻¹.

Step 2:

Now, assume that we integrate larger amounts of variable renewable power in the system. The controllable power stations have to balance the net load instead:

The net load can be calculated for each hour, and then the same type of transition diagrams can be plotted. For this example, we have integrated 46.8 TWh of wind power and 11.6 TWh of solar power corresponding to 40% of yearly energy production. The result is shown in Figure 26.2.

Figure 26.2 shows that the net load transitions from hour to hour are slightly higher than the load transitions, up to around 2500 MWh h⁻¹ while changes over four hours can be up to around +8000 and −7000 MWh h⁻¹. It can be noted that in this case, there is 15 633 MW of wind power and 9148 MW of solar power. However, solar power normally follows the load pattern that can decrease the transitions, and for wind power, the changes for Sweden are not so high as Sweden is a rather large country. This is the explanation to why the transitions do not increase so much in this case.

Step 3:

The final step is to see what kind of challenges arise for the controllable part of the power system to meet the required transitions. The first step is to study the historical controllability of the existing power system. For Sweden, most of the balancing control is performed in the hydropower station. Figure 26.3 shows the Swedish hydro‐transitions in 2008 and 2011.

As shown in these figures, the hydropower was used for faster regulation during 2008 (up to around +3500 MW between two hours), while the maximal change during 2011 was around 2500 MW between two hours. Corresponding figures for changes within four hours are shown in Figure 26.4.

The four‐hour transitions were also higher during 2008 (around +7000 MW), while changes during 2011 were up to around +6000 MW. The reason for the differences is that sometimes Sweden helps its neighbors to balance, and from Figures 26.3 and 26.4, it is obvious that during 2008, Sweden helped its neighbors as the changes were larger than the changes in the Swedish load, c.f. Figure 26.1.

Figures 26.3 and 26.4 also show that the hydropower transitions during 2008 were up to the same level as the requirement for a system with 40% wind + solar, c.f. Figure 26.2.

However, the method includes the following limitations:

1. The transition figures show the total amounts of transitions during a certain year. It may occur that the requirements are in one period of the year, while the historical large transitions have happened in another part of the year.
2. The required transition balancing (x‐axis in Figure 26.2) includes the whole power interval from 0 up to 22 000 MW, while the Swedish hydropower (x‐axis in Figures 26.3 and 26.4) can only act in an interval from around 1900 to 13 000. This means that all balancing cannot be performed by only Swedish hydropower.
3. The general conclusion is that more information is required if more details of the balancing possibilities are to be evaluated.

Data needed for second level analysis are hourly load and production for balancing and VR sources for different historic years. Concerning VR, an estimation of hourly production in future years is also needed. The method provides a fast estimation of the transitions from hour to hour or longer periods where one can compare the requested need with what has happened historically in a certain system.

LEVEL 3 ANALYSIS: TIME SERIES ANALYSIS

With this method, one consider some more details concerning how a system is operated. The idea is to draw figures of the operation from hour to hour and consider some details about how to handle the balancing issues. This means a basic modeling of all the above challenges, C1–C3. The method is as follows:

1. 3a.  Study a certain system for a limited area with no transmission restrictions. It is assumed that all balancing has to be performed within this system.
2. 3b.  The units are divided into (i) variable power (VP), (ii) balancing power (BP), (iii) prescheduled power (PSP), and (iv) extra needs.
3. 3c.  (i) Variable power (VP) is modeled with time series. Surplus (more than system limits) has to be spilled.
4. 3d.  (ii) Balancing power (BP) only considers the maximum (BP_max) and minimum (BP_min) levels in this chapter. One can then study whether the ramps are too fast. Ramping issues are, however, already studied in second level analysis.
5. 3e.  (iii) PSP units, for example, combined heat and power (CHP and/or nuclear, are provided as time series in this chapter, but it is also assumed that they can be downregulated to a minimum level (PSP_min) in order to avoid wind or solar spillage.
6. 3f.  (iv) Extra needs' (EN) units are needed to cover the difference between available power from sources 1, 2, and 3 and the load.
7. 3g.  In addition to this, there is an additional requirement that there has to be a certain amount of conventional units (types 2 and 3) in all situations. The reason is that there has to be some inertia in the system to manage outages. If there is not enough inertia, there is a risk of blackouts as the frequency can drop too fast. There are possible solutions to this problem, but one has to have some kind of restrictions. Units of type 1 often do not provide inertia.
8. 3h.   The method is then to calculate the following for each hour:
   1. Calculate given production: GP = VP + PSP
   2. GP is then limited:
      • GP must be lower than a certain share of load (3 g), for example, 87%.
      • BP = Load − GP must be higher than BP_min
      • In order to avoid VP spillage, if GP decrease is needed (because of the earlier two points), then first decrease PSP. However, PSP can only be decreased down to PSP_min. If GP has to be decreased even more, then VP is decreased
   3. BP = Load − GP
   4. But if BP > BP_max, then BP = BP_max and EN = Load − BP_max

The method is rather close to the one presented in Ref.^[9]. Here, the challenges C1–C3 are handled in the following way:

• C1. Handling the continuous balancing. During each hour, the balance is kept within restrictions, so Load = VR + PSP + BP + EN. The changes from hour to hour are not considered a restriction but can be studied later.
• C2. Low wind and solar power production and high power consumption. In these situations, a check of enough power must be conducted. This means that one calculates how much extra EN is needed.
• C3. High wind and solar power production and low power consumption. There is a maximum share of VP assumed, and if there is more VP than this level, it is assumed that this power is spilled. Other types of use include export, extended possibilities to produce heat and gas or charging of electric vehicles, but then a more advanced model is needed. These other possibilities are neglected here.

Application of Level 3 Analysis

The Swedish power system is studied in this chapter, based on a future situation when nuclear power plants (oldest unit started in 1972 and last unit in 1986) are assumed to be replaced with solar and wind power. With third‐level analysis, one calculates the energy balance for each hour during the whole year. Some examples of weeks and type of results follow, as well as some general conclusions.

A week with high wind + solar is first shown in Figure 26.5,which graphs each source along with the lowest CHP, and photovoltaic (PV) production is the difference between the PV curve and the CHP curve, etc.

Figure 26.5 shows a situation that is not in balance, as there is a surplus during several hours. This is physically impossible, so in some way, the situation has to be managed. In addition to this, there have to be margins, as shown in Table 26.2. This chapter's approach is to decrease CHP to a minimum level, decrease hydro to minimum level, and finally, spill wind and solar to keep the requirements concerning minimum production levels. The result is shown in Figure 26.6.

Source
Load	Same load as 2011. But the load is the net load where industrial back pressure is outside. Industrial back pressure is a local generation for a local load, so for these units, only the net load from the grid is considered. Maximum demand is 26 174 MW and minimum 8884 MW.
VR	The variable renewables are solar power (supply = 12 TWh yr−1, maximum 9365 MW, minimum 0 MW, spread over Sweden, year = 1999) and wind power (supply = 48 TWh yr−1, max. 15 808 MW, min. 27 MW, spread over Sweden, year = 1992). Historical time series are used, however, from different years depending on data availability. Synchronous data have not been available. Solar power is currently on a very low level, while wind power is increasing. Using historical metrological data means that one can simulate years with the same amount of installed capacity over the year and also test different spreading over the country. There is only a small amount of air condition in Sweden, so solar‐load correlation can be assumed to be low.
BP	As balancing power, hydropower is used: Maximum 12 951 MW (maximum during 2008) and minimum 1 875 MW (minimum during 2008).
PSP	Only biofueled combined heat and power; the capacity is assumed to increase with 50%[10] compared to 2012 data: yearly production 13.9 TWh, Max 4 127 MW, minimum 219 MW. Contacts with industry led to the assumption that production level can be decreased to 25% of the level from data in order to decrease wind/solar spillage.
EN	Assumption of gas turbines. Costs: 300 000 SEK/MW, year + 900 SEK/MWh. Availability: 95%.
System	An isolated Swedish system is assumed in order to not overestimate possibilities of import and export. Maximum share of solar + wind: 83% of demand as some synchronous generation is assumed. The level 83% was selected as an intermediate value of 75% assumed in Ireland[11] (synchronously isolated country) and 93% that has been experienced in Portugal[12], which is interconnected with Spain. In 2011, 45% of the demand was covered by hydropower and 4% by wind power. It is assumed that there are no internal bottlenecks within Sweden. For economic calculations, we use 8.8 SEK/euro.

BP, balancing power; EN, extra needs; PSP, prescheduled power.

In Figure 26.6, it is shown how the balance is kept per hour and that there is always a margin between solar + wind and the demand. The spillage in wind and solar is assumed to be proportional, so each source decreases its production with the same percentage. If one compares Figure 26.5 with Figure 26.6, there is a certain amount of spillage for each hour. For the whole year, a duration curve of the total spillage can be drawn, and this is shown in Figure 26.7.

As shown in Figure 26.7, there are 860 h yr⁻¹ with spillage, and the total energy spillage is 1.63 TWh. This means that 2.6% of all wind power and 3.6% of all solar power is spilled. Economically, this means that wind power becomes 2.6% more expensive and solar power 3.6% more expensive if one calculates costs/kWh, as all production is not used. There are other possibilities to use the power, e.g. export, charge electric vehicles, heat the water in district heating, power to gas, etc. but it is important to note that the spill level can be up to 9510 MW, and the utilization time for the technology is only 860 h yr⁻¹. Some of this surplus can probably be used, but it is probably not economically efficient to use all of it.

The next type of hours are the low wind – high load hours. An example is shown in Figure 26.8.

Figure 26.8 shows an example where there are high winds during the nights of 16–17 January, so one decreases the CHP to minimum level, 25%. However, later in the week, there is not enough capacity, so there is an EN, which is assumed to consist of gas turbines. The EN is only required during hours when hydropower is used to full capacity. If one then performs the same type of calculations for the whole year, a duration curve of the EN can be calculated, c.f. Figure 26.9.

As shown in Figure 26.9, there is a need for extra power during 765 hours with a maximum need of 5081 MW. The yearly energy need is 1.26 TWh, which corresponds to 0.9% of the total yearly energy production. We assume that all this need is covered by gas turbines. In reality, there are many different possibilities, such as import, demand‐side management (DSM), vehicle‐to‐grid, etc. but these competing technologies must have a lower cost. Both import and DSM are probably competitive technologies, but a much more detailed study must be performed.

To get an estimation of the extra costs caused by surplus and deficit, one can make the following assumptions: for surplus, the costs are the costs for wind power as wind power costs 60 ore/kWh = 6.8 Eurocent/kWh. The surplus amount is 1.63 TWh. For deficits, the cost is the extra cost compared to an assumed power price of 500 SEK/MWh as there is no extra cost if the cost of needed peak plants is the same as for other types of power. With this assumption, the extra cost is the difference between the operation cost of the gas turbines (900) and the assumed power price (500): 900–500 = 400 SEK/MWh = 4.54 Eurocent/kWh. The extra capacity costs 300 000/0.95 = 315 800 SEK/MW a year = 35 900 Euro/MW a year. The total cost is assumed to be divided among all consumers, that is, 145.6 TWh. Table 26.3 shows the result.

Cost source	Amount	Cost	Total cost per year	Cost per consumed (kWh)
Surplus energy	1.63 TWh	6.8 Eurocent/kWh	111 MEuro	0.08 Eurocent/kWh
Deficit energy	1.26 TWh	4.5 Eurocent/kWh	57 MEuro	0.04 Eurocent/kWh
Deficit capacity	5080 MW	35 900 Euro/MW,year	182 MEuro	0.13 Eurocent/kWh
Total cost			351 MEuro	0.24 Eurocent/kWh

This means that the total cost with these assumptions (gas turbines for extra needs and no trading with neighbors) is 0.24 Eurocent/kWh.

An important assumption here is that the balancing resource, which is hydropower, can follow the net load variation. In order to study whether this is possible, one can start with an analysis based on Level 2 analysis, that is, study transitions. One can study the real changes for hydropower from hour to hour in Figures 26.6 and 26.8, and a summary for one‐hour transitions is shown in Figure 26.10 together with real changes during the year 2008.

The figure shows that the amplitude does not change so much, but the largest changes now happen in all intervals, while large changes during 2008 were more from mean hydropower production levels. An important issue is also that hydropower, with a large share of wind + solar, operates more often on the extreme levels, maximum and minimum. This is summarized in Figure 26.11 where the duration curve for hydropower is shown.

It can be noted that the transitions in Figure 26.10 show the ones for a full year, and it is not possible to directly compare high levels in the left and right figure as they might occur during different times of the year.

In order to make conduct more detailed studies, one can make a detailed simulation of the hydro system, consider all hydrological restrictions, efficiency levels, court decisions, etc. The two periods shown in Figures 26.6 and 26.8 have been tested in this way^[13], and from this point of view, the result was that it was not impossible to operate the hydropower plants, as suggested in these figures. This is a comparable advanced simulation, and details for this is found in Refs.^{[13, 14]}.

Data needed for Level 3 analysis is an hourly load and production for balancing and VR sources for some historical years. Concerning VR, an estimation of hourly production for future years is needed. In addition to this, one must have an estimation of upper and lower limits of balancing power, minimum level of PSP, costs of extra needs, and minimum level of conventional units in the system because of inertia requirement. The third‐level analysis presented here is still simplified in several ways. Issues that are not yet considered include transmission limits, reactive balance, different hydrological years, DSM in district heating and households.

CONCLUSIONS

This chapter discussed three simplified methods to perform analysis of power systems with high shares of variable renewables.

Level 1 analysis means that one compares a certain area, for example, wind power, with other areas with a large share of wind power. One can then obtain a general overview of the size of the challenges by comparing the MSVR. One limitation of this method is that one can only compare with other systems that contain the same amount of variable renewables; that is, one cannot draw any conclusions if there are no systems with the aimed share of the sources.

Level 2 analysis means that one compares the flexibility of the system, measured as obtained transitions in a certain system with and without larger shares of variable renewables. This is easier for systems with a high share of interconnections, as in these systems, there are often historical examples when the studied system helped their neighbors, i.e. it showed a higher flexibility than currently needed in the studied system.

Level 3 analysis is still comparatively simplified with a calculation of the estimated requirements of transitions, keeping of margins, curtailment of surplus, and extra needs. Based on the results from this analysis, one can go into more details in order to estimate whether the requirements can be fulfilled with the current system.

The overall aim of this chapter is to show that it is possible to make integration studies step‐wise, where one makes more and more analysis with more sophisticated tools. It is then important, in each step, to identify the challenges one sees in each step, which means that one can direct further studies into the right area. There are certainly different challenges in different systems.

For all three levels, a Swedish system with up to closely 100% renewables (hydro, bio, solar, and wind) has been studied, and the conclusion is that the costs for curtailment of surplus as well as to keep enough capacity to cover high load combined with low solar and low wind is comparatively small, below 0.3 Eurocent/kWh. As there is a comparatively large amount of hydropower and biofueled CHP, close to 100% renewables does not require specific storage compared to a country with small amounts of hydropower and biofuel resources.

Compared to the suggested methodology in Ref.^[2], several significant simplifications are proposed here, which include no details of flexibility in the CHP system, no treatment of possible international trading, no modeling of flexible demand, no details of the transmission system, and no details of reserves for imperfect forests. However, this chapter gives an indication about which areas require further studies.

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