Coordination of Wind Power and Hydro Power

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IN

DEGREE PROJECT ELECTRICAL ENGINEERING, FIRST CYCLE, 15 CREDITS

STOCKHOLM SWEDEN 2017,

Coordination of Wind Power and Hydro Power

Koordinering av vind- och vattenkraft

AXEL SOLHALL EDVIN GUÉRY

KTH ROYAL INSTITUTE OF TECHNOLOGY

SCHOOL OF ARCHITECTURE AND THE BUILT ENVIRONMENT

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TRITA -IM-KAND 2017:27

www.kth.se

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M2. COORDINATION OF HYDRO POWER

Coordination of Wind Power and Hydro Power

Axel Solhall and Edvin Guéry

Abstract- The goal of this project was to calculate how much wind power could be balanced with hydro power in our designated area consisting of five hydro power stations, four villages which consume power, possible locations for wind power and one connection to the national grid. To achieve this a simulation model was constructed in the GAMS software with the goal of achieving the maximum profit from the hydro power plants by considering electricity prices, inflow of water, the physical construction of the power plants and the time of year.

When this was achieved, restriction for the maximum transmission load on the power grid was added as well as local wind power production as to simulate the implementation of new power sources on an old system and power grid. This would result in a maximum income in SEK as well as the most wind power which could be maintained and balanced by the designated system. This project shows how to find the optimal way to use hydro power and wind power as well as how the integration between different sources of electricity production could work, which is vital for a future powered by renewable energy and will help towards lowering emissions.

I. INTRODUCTION

he purpose of this assignment is to make an optimized schedule of power generation from hydro power plants considering the local wind power production as well as the price of electricity on the market, concerns of water flow and limitations of the electric grid. Thanks to this optimization the society can save resources and utilize the wind power to its fullest and efficiently use the water in the hydro power plants when needed. As this project looks on value in money this is most important for companies owning these hydro power plants as they want the highest return on investment.

The goal is to maximize income from the hydro power plants and to determine how much wind power production can be implemented locally and still be balanced by the hydro power plants. The water should be used as efficiently as possible to make the most from a given resource in the strive for a sustainable future. The first step is to gather the data required to be able to run the simulations. Examples of such data is

installed effect on the power plants in question as well as water flow that fills the different reservoirs. This data will then be processed in a program called GAMS (General Algebraic Modelling System) which via a written program will take out the optimal times to release water through the turbines to maximize overall profit.

Figure 1. An image of the system and it’s five hydro power plants.[1]

Today, the demands on the current power system are changing as there are coming increasingly more new energy sources like wind power and solar power. These sources are the two mayor ones which are expanding in installed power, but they are also unreliable. Why these sources of energy are wanted is because they do not contribute to the climate change which is a hot topic now.[2] But the problem is their uncertainty, they do not work fulltime and we are dependent on the weather which is one of the few things we as a society can’t control.[3] Therefore, these new types of energy sources brings good but unreliable energy to our systems.

The balance between consumption and production in energy on the grid has to be maintained at all times, these uncertainties make it hard to do so.[4] That is why there must be changes in how the old power plants act and they must adapt to the new era where they have to compensate for the lack of wind power at times when the wind alone is not sufficient.[3]

T

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II. MODEL

• The hydro power turbines efficiency is assumed to lie between 92% and 96% [3].

• The earth's gravitation is assumed to be 9.82 m/s².

• The density of water is assumed to be constant 1000 kg/m³.

• The flow of water is assumed to take one hour to go from one hydro power plants to the next, meaning four hours to go through the entire system.

• The Gross heights of the reservoirs are assumed to be constant, even though the water levels are changing.

• The grid is assumed to be able to transmit 110% of the maximum power of the hydro power plants.

The optimization of hydro power will be made with the software GAMS. This data is gathered through phone calls to the owners of the power plants as well as information on their websites, articles and from other sources. The data is then handled by a written program that decides the best times to release water through the turbines to maximize the profit for the owners through linear Optimization. There are five different power plants used in this simulation that all lie after one another on a part of Indalsälven in Jämtland, Sweden.

Three of these plants are called Hissmofors, Kattstrupeforsen and Granboforsen and are all owned by a company called Jämtlandskraft AB, the last two power plants, Midskog and Näverede, are owned by Vattenfall AB. Hissmofors borders the big lake Stor sjön as seen in fig.1 which in this model is represented as a very big reservoir.

The prices of electricity are taken from Nordpool which handle the entire Nordic market of electricity.[5] Wind data was gathered from Svenska Kraftnät on their website Mimer where energy production numbers can be gathered.[6] Wind production data for our area will be scaled appropriately to simulate different levels of installed wind power so the impact on the power grid and the production of hydro power can be analysed. To gather the numerical data of the natural flow of water, we used the “Vattenwebb” at SMHI that shows the natural way that the water flows and watershed.[7]

The problem is a linear optimization problem which is rather simple but with too many variables for a human to handle so a computer is needed to get the calculations done in a reasonable time. GAMS give us raw data that is hard to read and the result data is therefore sent into excel to make cleaner sheets and readable plots and diagrams.

The total energy (E) that is converted into electricity is equal to the potential energy recovered in the fall times the efficiency (e) of the turbine meaning the gross height (h) times the gravity (g) and the mass of water (m) passing through. As we are working with quantities of water we can get the mass by multiplying the cubic meter of water (q) times the density (d) which have been assumed to be constant. This is shown in equation (1) below.

𝐸 = 𝑒×𝑚𝑔ℎ = 𝑒×(𝑞𝑑)𝑔ℎ = 𝑒𝑞𝑑𝑔ℎ (1)

𝐼 = 𝐸×𝑐𝑝 (2)

The energy produced is then converted into income (I) by the simple multiplication with the current price (cp) of the electricity produced as show in equation (2). The total income is then the sum of the income gained for each power plant for every hour over these four days and the total of 96 hours. The water balance is calculated through a balance of flow through the turbines (q), spillage (s), incoming water from rain and other sources (inflow) and the water kept in the reservoir (r) as shown in (3). The balance is calculated with an hourly timeframe (t) and having the hydro power plants numbered from one to five (p), one being Hissmofors at the top and five being Näverede at the bottom.

𝑟_(𝑡,𝑝)= 𝑟_{(𝑡−1,𝑝)}+ 𝑖𝑛𝑓𝑙𝑜𝑤_(𝑡,𝑝)… + (𝑞_{(𝑡−1,𝑝−1)}+ 𝑠_{(𝑡−1,𝑝−1)})

−(𝑞_(𝑡,𝑝)+ 𝑠_(𝑡,𝑝)) (3)

As seen in equation (3) the reservoir for each hour is calculated as the water that was there the hour before added with the water coming from the power plant higher up in the chain that was released the hour before as well as the natural inflow from the surrounding nature, for example rain. The water going out of the reservoir, the flow through the turbines and spillage of the hydro power plant that hold the water, is then subtracted. The water flow is restricted by the maximum flow capacity of the power plants and the reservoirs are of different sizes.

The water left in the reservoir at the end of the day is calculated to go through the all the hydro power plants used in this simulation on its way down to the final output. This means that the water in the highest reservoir is worth more than water in lower reservoirs as it has more potential energy while the water that has already passed hydro power plants have lost some of its potential energy and therefore value.

But the same calculations have been done for the start of the

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day, meaning that only the difference in water from start to finish counts. This makes so if the reservoir has more water at the end of the day then when it started, you will be able to use that for later and so it is a gain. If on the other hand you have used more water then has come in, you have used up some of your resources and it’s then counted as a loss. If this is the case though, the income made from using this water outweighs the loss in the reservoir if it was used correctly when the current electricity price was high.

Hydro power plants are always connected to a grid, either a small local grid or the big national grid, and these grids have limitations. Normally you build the local grids at the same time you build a power plant and make the grids capacity match that of the power plants, and possibly some more. The grid is not built with a massive overcapacity as it would be too expensive for the same result. This means that when wind power plants are now being built, the grid can’t always handle all the power that is getting pushed through the cables.

There is a limit to how much power the grid can sustain at any given time and this model is based on bottleneck that the cables pose. The cables maximum amount of power that can be transmitted cannot be exceeded.

III. CASE STUDY

In the fig. 2 below, a clear picture of the system, with the big lake at the top of Hissmofors that then directly links into Kattstrupeforsen and Granboforsen, then into a smaller lake.

The figure clearly shows the smaller lake before Midskog power plant has additional inflow from a river. This causes the flow at Midskog and Näverede to be higher than in the previous three power plants. The red inclosures is to show which power plants are affected by the same grid bottleneck.

The three upper hydro power plants and wind power plants are limited by the inner bottleneck. The outer bottleneck encloses the entire system of five hydro power plants and

separate wind power production inside of both the two bottlenecks. Where the connection to the national grid is located is irrelevant.

The main inflow of water comes from the lake that Hissmofors holds and from a connecting river that joins up just before Midskog which can be seen in the fig. 2 that shows total flow of water through the different plants. The graph in fig. 3 shows that there is almost no extra inflow at Kattstrupeforsen, Granboforsen and Näverede as the total amount of water flow stays around the same as the hydro power plant higher up in the river. The chart is showing the different flows the different dates added together, but they all follow the same pattern that is shown in the total result.

Figure 3. Total water flow at the five hydro power plants in cubic meters per second.[7]

These five power plants do not have any side flows for letting fish go upstream meaning all the water that goes though these power plants are either going through the turbines or just getting spilled in case of the reservoirs getting full. This is not a problem since salmon and other fish does not go this far upstream in Indalsälven.[8]

In the fig. 4, you can see the water level in the reservoirs throughout Sweden during an entire year. The red labels show the different selected dates and how full the average Figure 4. Water storage in Swedish reservoirs during the year 2015-2016.

Figure 2. The system with its grid limitations in form of bottlenecks surrounding the upper part and the whole system.

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Swedish reservoir is throughout the year. These degrees of filling in percent of all Swedish hydro power reservoirs are set as the degree of how full the reservoirs in the system at the start of each day to mirror real worlds time of year.[9]

The plot of fig. 5 shows the different prices during the day on these four chosen dates. Nordpool has divided Sweden into four different segments and all these power plants lay in the segment of SE2 and that is the data used as well.[5] The price of electricity goes up during the day and falls to its lowest during the night, this follows the natural cycle of the day, as most people and factories are active during the day and resting or unused during the night.

Figure 6. Wind power production as % of installed wind power on an hourly basis for area SE2.[6]

In the graph of fig.6 the percentage of wind power production over the four selected dates can be seen. The percentage was gathered by taking the wind power production in section SE2 on an hourly basis from Svenska Kraftnät [6] and dividing it by the installed capacity in the same area SE2 [10]. This

percentage is then easy to apply to chosen amounts of installed local wind power production, which then is used in the optimization to simulate the same conditions as the rest of SE2 where the system model is located.

The grid is assumed to be able to transmit 110% of the maximum power of the hydro power plants as the grid was built at the same time as the power plants and calculated for the hydro power plants production. The upper part of the grid which supports the three smaller power plants Hissmofors (60 MW), Kattstrupeforsen (60 MW) and Granboforsen (24 MW), can support up to 158 MW. The lower part that connects both the upper part and the other two hydro power plants, Midskog (145 MW) and Näverede (68 MW), to the national grid can transmit up to 393 MW. These limitations are the bottlenecks of fig.2

The maximum power the grid can handle is also the maximum amount of wind power which can be installed safely, meaning at the upper part of the grid there is a total of up to 158 MW of installed wind power and at the lower end a total of up to 235 MW.

Figure 7. Effect in MW from different power plants during the day of January, the balance between wind and hydro power can easily be seen in this graph.

The installed wind power then together meets the criteria of never overloading the cables even when working at peak efficiency. Any higher level of installed wind power may cause the grid to overload. The level of installed wind power has then been evaluated to see how different levels of wind power would affect the spillage of the hydro power plants.

Figure 5. Market prices for group SE2 on the Nordic market for electricity in SEK/MWh for these four different dates.

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With the wind data from fig. 6, installed maximum capacity of 393MW and the market prices of electricity from fig. 5, the net gain is 2.2 million SEK over these four days from the wind power. As can be seen in fig. 6 that was shown earlier, the day of January was particularly windy. On the other hand, this means that to keep the grid stable, the hydro power plants had to slow down their production to not go over the grid limitations. This can be seen in fig. 7. If fig. 6 and fig. 7 is compared it can be seen how the high wind production did force the hydro power production to decrease. This means that less water is being used and is then stored in the reservoirs for later use.

The production of the hydro power plants for the four days of the simulation is dependent on the level of local wind power production. Different levels of the maximum capacity of installed wind power were tested and the results are shows in table I.

Table I. Here are the results from different levels of wind power implementations and the effects on the hydro power plants gain in income.

Installed wind power

0%

0M W

25%

98M W

50%

197M W

75%

295M W

100%

393M W Hydro income 7,28 7,27 7,12 6,86 6,50 Resevoir value -0,47 -0,46 -0,316 -0,06 0,27

Total gain 6,81 6,81 6,80 6,79 6,78

As can be seen in the table above, the income from the hydro power plants is only affected ever so slightly even with maximum variation of the local wind power production. This is mostly because with higher wind power production, more water can be saved in the reservoirs for a later date and the loss in income is therefore saved in water resources. Since the hydro power plants produce electricity when the price is a variable higher than the reservoir price, saving water in the reservoirs will always reduce the profit compared to running on full production. Why the hydro income is not much deeper is likely because there were not that much wind except for the day of January shown in fig.7.

IV. DISSCUSSION

The point with this optimization is to determine how much wind power can be balanced and to maximize the income for the two companies owning these five hydro power plants, the income is calculated as a sum of all five individual incomes.

This might seem weird because they are owned by competing companies and their incomes does not accumulate together

but since the water flow through the power plants are controlled by Vattenregleringsföretagen AB and the power plants are located on the same river it makes sense. This is because the power plants up the river will determine the flow of water for power plants further down the river and since several of the plants have very limited reservoirs they would be forced to either run the water through the power plant or spill it by the side when the water arrives if the electric grid is already working at full capacity in a realistic scenario.

Through the central control of Vattenregleringsföretagen AB the entire system of power plants can be run in a way which is most efficient for the system as a whole, which allows for the sum of their incomes to be a valid assumption.

The entire computer simulated optimization and its results are mainly controlled by the assumed price on the active reservoir of water. This information could not be sourced from any power company so an assumption was made that the price would be an average of the Nordpool price data each day. This price has a huge impact on the production since it decides if the hydro power plants should run on installed effect or save the water for a later time with higher prices on an hour by hour basis. If the current price is higher than the assumed price for the reservoir the hydro power plants will run on full power and if the current price is lower than no power will be produced. The price of the reservoir is assumed to be a mean value of the hourly prices.

The hydro power plants will maximize their income if they produce energy when the current electricity price’s is higher than that of the water reservoirs and only limit their production by the limitations of the power grid. This means the hydro power plants should run at their maximum power when the wind power production is low which leaves the grid available. But when the production of wind power increases, the hydro power production will be forced to decrease to not overload the grid.

To make sure that water already released into the river and heading towards another power plant is not wasted if the wind power is high when the water arrive it is beneficial to never have the water reservoirs completely full. If the reservoir is full and the grid is working at full capacity due to high wind production the water must be spilled and this is of course a waste of resources and therefore lost income.

Though big reservoirs often aren’t full and this becomes more of a problem for hydro power plants with small or no reservoirs. Therefore, planning is very important and only releasing water from a higher reservoir when knowing that

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the water can reach all the way down to the next big reservoir without any spillage having to be done is very important to waste neither resources or money.

The problem with spilling water due to an increase in wind power in combination with full water reservoirs is however not very relevant for this project. This is because GAMS do not calculate in chronological order, you could say it “knows the future”. Spillage only happens when things don’t go as planned, so if we are taking fourth a plan, the spillage should be planned to zero. The future wind data and reservoir data is already available for the software and available before the simulation starts. This allows the program to compensate for future events and never spills any water as it can compensate for changes in advance. In reality, future values are not known to 100% but can often be estimated to a good enough margin. This is what is called stochastic programming, a framework for modelling optimization where the variables are only known to be within certain values. This may be non- negative, or as in this case, the estimated energy price, and the estimated wind production. These values do not vary far from estimates and therefore low amount of spillage in the hydro power plants can be achieved.

The value of the reservoirs has a huge impact on the income of the hydro power plants. And since the whole optimization boils down to the question, “do we run the turbines now, or can we get more money for the same work later?”, and that question is answered by setting a value on the saved water in the reservoir. The value was set to the mean value of the current day meaning it produced electricity at the day’s high peaks and saved it as active storage during the day’s lowest priced hours. But as no real answer to the question of how the value was set in real life could be obtained, the most logical solution was to set the value to a mean of the day.

The value of the reservoirs is calculated by taking the value of water at the end of each day and subtraction the days starting value. This allows evaluation of the value of changed storage in the reservoirs as well as the production of electricity. Why the value of the reservoir is so important is because if the saved water is not valued then there would be no consequences to constantly producing full power in the hydro power plants. The energy of the saved water is valuable therefore it must be valued so it is not wasted. But this somewhat hides the value of produced electricity and the changes of the income from running the hydro power plants with different levels of wind power production.

The local wind power plants do not reduce the electricity prices since they are too small of a part of the Nordic electric market to affect the supply of power. What they do affect is the local grid capacity which has transmission limitations. If the grid does not have the capacity to handle full production of both the hydro power and the power coming for the wind power plants it will be overloaded and cables may take damage. This means that when the wind power is delivering a lot of effect to the grid some of the hydro power plants will have to reduce their production to not risk overloading the cables. The wind is an unreliable variable that must be considered since it can change from hour to hour and even though meteorologists try to predict the weather, it’s never truly accurate. This give arise to the risk of having to spill water due to full water reservoir and a grid working at full capacity. Spilling water would result in a loss of income and resources which is not beneficial for neither the owners of the power plants nor the environment as other sources of energy would be used in its stead, for example power plants using coal as fuel.

Something that can be done is spillage of wind. By turning the blades on the wind power plants and there how reduce the efficiency of the turbines. This would mean that higher amounts of wind power can be installed and a higher production value when the wind speed is considered low to medium. When reaching close to maximum capacity the grid would then not risk overloading as some spillage of wind could be made by lowering the efficiency. This allows for much higher capacity of wind power to be installed as the spillage loss only happens with exceptionally high wind speeds whereas the normal conditions allow for full efficiency and higher production and gain in income for the wind power companies. To take it in consideration in this case study the amount of wind power could theoretically be as high as possible and always run at grid capacity with any little wind, but it would not be practical in reality as it would cost immensely to build that many wind turbines and to never run them at full efficiency would be a waste of resources.

But installing high amounts of wind power where they cannot always run at their maximum efficiency is an obvious waste since wind power turbines are expensive. So, to maintain a cheap and efficient balance, the wind power production should be appropriately scaled to the limitations of the local grid and the other power plants connected to the same grid so the gain in production is larger than the loss that happens during the times when the wind has a high speed.

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Grid limitations is vital to consider in our system of hydro power plants and wind turbines which is connected in a way that causes two major bottlenecks to the transmission capabilities of the grid. The first bottleneck is around Hissmofors, Kattstrupeforsen and Granboforsen hydro power plant as well as wind power plants, this is the inner bottleneck of figure 2. The bottleneck will force the hydro power plants to reduce their production when wind power production is high. Why the hydro power plants must cut their productions is because the water in the reservoirs can be saved for future production but the wind cannot be controlled and saved. The second bottleneck includes all five hydro power plants and all wind turbines, this is the outer bottleneck of figure 2. This means the first bottleneck is inside of the second bottleneck.

When the data is inserted into GAMS, it becomes the all- knowing one and knows both past and future as it calculated the optimal way to run the entire system of hydro power plants. This means that when the software does its simulations and answers the question of how to manage the local power plants it does so without any mistakes, as in zero spillage. It knows when and how strong the wind will blow at all times and can optimize the water flow to avoid the time where the system could suddenly be forced to spill instead of produce electricity to not overload the grid because of a sudden change in wind and rise in wind power production.

This is the perfect world of GAMS where we would like to live, but when applied in reality, the future may have been foreseen incorrectly, and then the calculations are incorrect.

So, the wind might blow harder than expected and then the hydro power plants will be forced to spill as the reservoirs or grid will be at full capacity. But with good estimates in the stochastic programming as discussed earlier, no big losses or spillage should occur.

Possible future studies would be to run a double simulation, maybe in MATLAB alone or in combination with GAMS. To first make an optimization after how the future is believed to look and then run a simulation of how it really went and then run a “reality” that may run as foreseen at first but then diverse from the path and see how flexible the system is to changes it did not expect. Then spillage becomes an actual thing as this simulation we have done never had any reason to spill when it could work around it and had all the answers.

GAMS is an optimization tool, and it is never optimal to waste a resource by spilling it and it will therefore successfully not be forced to do it, but like reality sometime do.

MATLAB could then possibly be used to make a loop that takes the hydro power plants through the day hour by hour without knowing what is next and trying to make the best out of a tough situation. GAMS and optimization tools can’t work with blind data, what may need to be done is to make a new optimization for each hour that passes that, depending on how the weather behaves, excepts a certain weather in the coming future. Then run it though the “real” weather and market price and see how much spill there is to then make a new optimization each hour that passes to recalibrate and change the weather and market price data accordingly. This requires more than just a way to optimize and to simulate the

“real” time. I would require a way to adjust these input data to, hopefully, fit in on reality better as sudden changes happen. This way has a dynamic system and not just an optimization a day and hope for the best, but have a system that adapts during the day.

What could be done in future studies is to make it a function of the water height. So, that when the reservoirs are almost full the reservoir value is low as it will then release water through the turbines even if the electricity price is low and therefore not risk the pons from overflow and spillage. While on the opposite side increase the reservoir value when the active storage is almost empty meaning it will not release the water at that stage to hinder the reservoir from going dry.

This would be good for maintaining the water level and may hinder spillage, but as there was no spillage already it would probably only decrease the maximum income as it forces the hydro power plants to produce electricity when the price is low and hinder it when it’s high, the opposite of what we want to maximize income.

Using this method of simulating the hydro power plants may result in seeing the amount of spillage that may occur during changes in the weather and inconsistencies with the unforeseen weather. This can then be compared to the gain in wind power and be used to see how much wind power plants would be okay to install in an area without causing too much spillage in the local hydro power plants. They would not calculate any exact numbers as there are too many assumed conditions but still give a good idea of the amount and can be used in decision-making when looking at areas to expand with wind power generation.

What we have done in GAMS does give an answer to these questions with a single optimization via GAMS. But it only shows us how to run the schedule perfectly with the coming

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conditions. This only applies to reality though if everything goes as the input data tells us, which often isn’t the case.

As can be seen with the data gathered, the losses in the hydro power plants income is not that large. This is because the loss in production is gained in reservoir funds, expected to be used at a later date. This is money though because as the prices of tomorrow will not change much from today, in such a short amount of time it will follow a predictable pattern.

The actual loss is not that big either as it goes from around 7.27 to 6.50 million SEK, so a little less than a million, but then if the income gained from the wind power (2.2 million SEK) is factored in, that gap is quickly filled and a loss is turned into a gain. Installing wind neglecting installment fees is a net gain that varies if calculating the water stored or not.

Even when spillage of wind is applied, meaning there can be as much wind power as there is space to build them, the grid will never be overloaded as they adapt their efficiency to the grids demands. It could in a perfect world, theoretically, have the grid at max capacity at all times with only wind power, meaning the hydro power would never get to use its turbines.

The hydro power plants would still have a gain in income, up until the point where the reservoirs are full and they are forced to spill the incoming water, as the water that is filling up the reservoirs are counted as a gain in income. During these four short days, the results would still give us a gain even if we did not produce any electricity. Therefore, it should be looked upon on a larger scale, take a week, or month with days that are connected to each other and some smaller reservoirs and the problem with spillage would become much bigger and harder to handle with enough wind power production in the system.

V. CONCLUSIONS

The question of how much wind power can be balanced by existing hydro power is a hard one as the grid is what sets the boundaries for the wind power production, and what is profitable. GAMS optimization does not simulate time in a chronological order which allows the software to compensate for information that should only be available in the future.

This eliminates the spillage of water but with realistic stochastic programming spillage is already minimized. This together with the ability to spill wind, an amount of wind power could then be calculated to not have too much spillage in the hydro power plants but still have a good amount of energy coming from wind power plants. There may not be an exact number to answer but this is a good way to get a

general idea of how much wind power there could be in a region to fit the local conditions.

VI. REFERENCES

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http://vattenweb.smhi.se/hydronu/.

[8] L. Mats, and S. Erik, Återskapande av vandringsmöjligheter för havsvandrande fisk - ekologiska effekter och

verksamhetspåverkan, 2009-08-18.

[9] "Hydro reservoir," (Mar, 2017); [Online], Available:

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