Electricity economics
An adaptation of the Norwegian hydropower model to the Mexican mixed energy market
Edwin Castellanos Bordon
Thesis for the Master of Philosophy in Economics University of Oslo
November 2016
I Acknowledgments
This study is an acknowledgment to Norway, a country that has provided me with an outstanding education at the University of Oslo, by contributing to the further development of the knowledge gathered by its top-class researchers. Also, it is also a contribution to the development of my home country, Mexico, which is a country that has provided everything that constitutes me as a person and has given me countless opportunities to grow. This study is a depiction of my interests in the energy development of the country and the accomplishment of environmental goals to achieve sustainable growth in one of the most relevant sectors in Mexico in the present.
I am grateful to my supervisor Finn R. Førsund who provided the guidance I needed and motivated me with his supporting spirit and interest in my work. Also, I recognize the importance of his work to provide us economists the tools to understand the energy market, a sector that was mostly reserved for the engineering field. It is because of his contributions and feedback that I was able to successfully perform this study.
I am also very grateful to my family’s unconditional and consistent support during all my life. It is because of the values that they transmitted to me that I have been able to pursue my goals. They have given me invaluable advice and I am most proud of having them as my parents. I am very thankful to my brother who has been by my side since I am able to remember as a family member and as my friend.
I would also like to thank my friends for the hours that we worked together at the University and for the fun moments during my studies.
Finally, I would like to thank Karen for believing in me and her encouragement during my whole Master’s degree. It is because of you that I always hold a high spirit and that I keep on moving forward. Thank you for the immeasurable love and support you always provide me and for making me happy. I am honored to love you and most fortunate to say that you are my girlfriend and my best friend at the same time.
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Summary
This thesis studies the Mexican electricity market by adapting and applying the Norwegian electricity model to the specific characteristics of the country. Mexico and Norway operate their electricity system using a completely different mix of fuels to run their power plants and, as a result, the economic interpretations may vary. Mexico is divided in eight different electrical regions, with different prices and different technologies for power generation. The aim of this study is to understand how the six regions that are interconnected interact with each other according to their power generation and the prices in specific periods.
Geographic and climate conditions of the country play an important role on the interaction of the electrical regions in Mexico. The northern regions are mostly dominated by dry ecosystems while the south and center regions have prominent rainfall, forests and jungle. In turn, these conditions determine the type of technologies used for power generation and create specific region to region interactions. When comparing this scenario to Norway, a country that generates most of its power through hydroelectric plants we find quite different patterns. The models rely on the basic economic assumption of finding an equilibrium price at the intersection of the demand and supply curves.
In order to study this interaction, the electricity models proposed by Finn Førsund are applied to the specific characteristics of each region and interpreted in their own perspective. In order to find qualitative information about the electrical regions in the country non-linear programming methods are used in order to build realistic social planning problems and finding the corresponding optimal solutions. The decision for optimal power generation in each region will depend on the restrictions imposed in the system and the differences in prices. In essence, it will be optimal for a region to generate and export electricity in high price periods while the opposite will happen during low-price periods. The models may include thermal, hydro and intermittent energy according to their participation in generation activities in each region.
However, when reservoir, trade and capacity constraints become binding prices are affected and they influence the optimal generation of power in order to maximize the consumer and producer surplus. Despite of the fact that the six relevant regions are interconnected, the size and shape of the country make trade between some of them unfeasible as it is too expensive to transport
III electricity through extended lengths due to the lack of high voltage direct current transmission lines in Mexico. This thesis proposes bilateral trade models between the regions that engage in trading activities taking into account the respective constraints that apply to their specific circumstances. These models provide insight on when it is optimal to generate with each technology, the effects of trade in prices and consumption and the correct management of water reservoirs.
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Table of Contents
1. Introduction--- 1
Electricity demand in Mexico--- 8
Hydropower in Mexico--- 12
2. Background for the Energy Model--- --- 14
Thermal Energy in Mexico--- 15
Renewable Energy in Mexico--- 17
3. The Energy Model--- 18
4. The Mexican Hydropower Model--- 22
Constraints in the Mexican Hydropower Model--- 24
Optimal management of a hydropower system--- 24
The output constraint--- 25
Flow-of-the-river and wind power generation--- 28
5. Multiple Producers in Hydropower--- 32
Coupled Hydropower--- 35
6. Mix of Thermal and Hydropower Generation--- 37
The Complete Mexican Energy Mix--- 40
Multiple Producers in a Mixed Energy Model--- 43
7. Regional models with trade--- 47
Transmission General Model--- 51
8. Region-Specific Models for the Mexican System--- 53
Northwest-North Model--- 54
North-Northwest Model--- 56
Northwest-South Model--- 56
North-South Model--- 58
Northeast-South Model--- 68
North-Northeast Model--- 59
South-Northwest Model--- 61
South-North Model--- 63
South-Northeast Model--- 64
South-Center Model--- 64
Center-South Model--- 67
South-Peninsular and Peninsular-South Models--- 67
9. Qualitative Conclusions about the Mexican Region-Specific Models--- 69
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Northwest Region--- 69
North Region--- 70
Northeast Region--- 70
South Region--- 71
Center Region--- 72
Peninsular Region--- 72
Environmental Policies in Mexico and their Impact on Prices--- 73
Pricing Policies and the Effects of Subsidies on Consumption--- 73
Management of the Mexican System--- 74
10. Conclusions--- 75
References--- 78
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© Edwin Castellanos Bordon 2016
Electricity Economics: An adaptation of the Norwegian hydropower model to the Mexican Mixed Energy Market
Edwin Castellanos Bordon http://www.duo.uio.no/
Printed at Reprosentralen, University of Oslo
1 1. Introduction
For many years, the Mexican energy sector was solely operated and managed by the State and its authorities. In order to understand the current state of the electricity industry in Mexico, some general information will be provided.
Energy generation started in Mexico in the late 19th century with the first generating plant built in 1879 in a city called Leon in Guanajuato. It was used by a textile company and this scheme was also used by the mining industry, marginally providing electricity to the public sector and some citizens. The hydroelectric history of Mexico starts in 1889 with the first plant built in Chihuahua under the name Batopilas powering urban and commercial areas.
It was during the government of Porfirio Diaz that the electricity sector was deemed as a public service and public lighting was placed in several main roads in Mexico City. International companies such as The Mexican Light and Power Company of Canadian origin and The American and Foreign Power Company started operating in the country along with The Electric Company of Chapala in the west. By the start of the 20th century Mexico had an installed capacity of 31MW and it was owned by private companies. Ten years later the sector grew to 50MW of installed capacity and 80% of the electricity was generated by The Mexican Light and Power Company through the first big hydroelectric project which was the Necaxa plant in Puebla.
It was not until December 2nd 1933 that generation and distribution were established as public utility services. However, by 1937 Mexico’s population was of 18.3 million habitants but only 7 million had access to electricity and the three companies could barely cope with the demand.
Tariffs were high and blackouts were very frequent since these companies were focused on the most profitable urban markets while rural areas were completely abandoned despite of the fact that 62% of the population lived in them. By then the total installed capacity in the country was of 629MW. In order to face this challenge, the federal government created the Federal Electricity Commission (which will be named CFE), which is the public electricity company that is in charge of most of the generation and all the distribution and transmission activities to date. The main purpose of its creation was to organize and run a national system of generation, transmission and distribution of electricity, based on technical and economic principles as a non-profit company to
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obtain a minimum cost and the highest performance possible in order to address the general interests (law published in the Diario Oficial de la Federacion on August 24th 1937).
It was then when the CFE started building generating plants and expand the transmission and distribution lines. The first hydroelectric plant that was in charge of the CFE started its construction 1938 by building the canals, roads and highways to what eventually would become the Ixtapantongo Hydroelectric System in the State of Mexico, later to be called the Miguel Aleman Hydroelectric System. In only eight years CFE’s capacity increased from 64kW to over 45MW. It was then when the foreign companies ceased to invest and CFE was forced to increase the installed capacity and distribute power through these private companies. By 1960 the CFE owned about 54% of the available 2308MW of installed capacity, Mexican Light and Power Company 25%, American and Foreign Power Company 12%, and the rest of the companies 9%.
Despite of the efforts to bring electricity to the Mexican population only 44% had access to it, which is why President Adolfo Lopez Mateos decided to nationalize the electric industry in 1960.
It was then when the National Electric System was created expanding the supply reach and accelerated industrialization. The State acquired the foreign goods and infrastructure which had serious operational and labor deficiencies due to the lack of investment. From here on, installed capacity increased considerably to almost 8GW in 1970 and 17GW by 1980 through important public investment in those years. It is also important to note that during the first years of history of the Mexican electric industry over 30 voltages for distribution, 7 for high tension and 50 and 60 hertz frequencies coexisted. It was because of that that distribution was an important challenge for CFE and the national company managed to unify the economic and technical criteria to standardize equipment and reduce costs.
As demand continued to grow, in 1991 the installed capacity grew to 26.8GW but more importantly it was during the beginning of the 21st century that the coverage reached 94.7% with 36.4GW of installed capacity and 614,653 kilometers of transmission and distribution lines. Until 2005, CFE generated 99% of the total electricity in the country.
The company that was in charge of the electricity services in Mexico’s central area was Luz y Fuerza del Centro (another company owned by the State), but since 2009 CFE has been in charge to provide the service to the whole country when Luz y Fuerza del Centro was closed down by
3 President Felipe Calderon Hinojosa. By 2015 the total installed capacity for CFE was 41.9GW, however, the independent producer sector has grown during the last decade importantly, reaching an installed capacity of 12.9GW for a total of 54.8GW. Independent producers generate electricity to sell it exclusively to CFE under a contract following the Law of the Public Service of Electric Energy. If we add to this the recently built plants by privates, the total installed capacity in Mexico is 68GW.
It is also important to consider the Energy Reform that passed through the congress in 2014. Before the energy reform, there were limited opportunities for privates to generate electricity, being the self-supply scheme the only viable possibility to make this projects happen. While electricity generation was considered as a matter that was only to be addressed by the state, self-supply was not considered under the scope of the Mexican constitution. However, paperwork and the operating framework represented important challenges reducing the attractiveness of the market. Under the self-supply scheme, it was necessary to find off-takers to sign long-term Power Purchase Agreements, lasting usually over 20 years. Naturally, financial institutions required that these off- takers were low risk companies, with AA or AAA credit grades, so the off-taker pool of companies was rapidly depleted. Smaller companies had to deal with important struggles in order to participate in these projects.
The Energy Reform’s objective is to create incentives to bring a higher quality service, with lower costs and more environmentally friendly. For the first time in Mexico the generation and distribution markets are open to free competition. Reporting of the electricity market has been made official through the National Center of Energy Control (CENACE) since 2016. This was done in order to avoid conflicts of interest since they could arise if CFE remained as the generator and coordinator of the system. This will allow the development of renewable energy projects as they need higher investments in transmission. However, transmission and distribution will remain as natural monopolies and these activities are still reserved for the government. However, the expansion plans of the transmission system will be responsibility of CENACE. The main purpose of the Energy Reform for the electricity market is to allow private investors to invest in new capacity. As a comparison to the Norwegian electricity market, demand in Mexico has grown consistently and there are no signs of overinvestment. The case is, in fact, the opposite. The fast grow in demand had become a challenge too difficult to overcome by the public sector.
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On the other hand, the Law for the Exploitation of Renewable Energies and the Financing of the Energy Transition (LAERFTE) has established ambitious plans for Mexico’s climate change strategy. Published in 2008, the law states that Mexico has the goal having a limit on the use of fossil fuels for electricity generation of 64% by 2024, 60% by 2035 and 50% by 2050. This represents an important challenge because today, more than 75% of the electricity is generated through fossil fuels and by 2027 the more pollutant fuels used for generation will be replaced with natural gas. On the other hand, Mexico is committed to reduce greenhouse gas emissions by 30%
for 2020 and 50% by 2050 through the General Law of Climate Change (LGCC). This implies that the renewable energy investments will depend entirely on the private sector. This is where the importance of hydro comes into place and it is one of the main motivations of this project. While the law is supporting the development of renewable energy projects, the hydroelectric sector has not received a lot of attention during the last years. While CFE’s current hydro participation represents around 16%, the private sector has focused mainly on developing wind and solar energy projects. While the investment has been considerable, it is important to notice that solar and wind power are intermittent energies, and to cover the increasing demand more base load supply will be needed. It is safe to assume that there are two technologies that can contribute to the reduction of greenhouse emissions and base load supply: hydro and nuclear power.
While nuclear power has received intense criticism around the world after the historical disasters such as Chernobyl and Fukushima, hydropower is a viable option for Mexico due to the availability of resources. However, the growth of the hydropower sector in Mexico has stagnated for some years, despite being an industry with a mature technology that offers one of the lowest costs per kWh produced in the sector in a competition with natural gas. The enormous natural gas reservoirs found in the United States of America in the recent years and the construction of pipelines transporting this fossil fuel to Mexico has significantly decreased the price from $10USD in 2008 to approximately $2.5USD per million BTUs. On the other hand, the current devaluation of the Mexican peso that has impacted the exchange rate from $12.30 to $19.60 MXN per USD from 2013 to 2016 has definitely affected the demand for natural gas, giving new grounds for hydroelectric and renewable energy competition.
To date, there is no formal economic analysis on the Mexican energy model and the political pricing policy in Mexico allows different prices both regionally and between different user groups.
5 In Mexico’s electricity market there are seven different domestic tariffs and 36 industrial tariffs.
However, these tariffs are determined by the amount of subsidy that is given by the government, rather than by the actual price of generation. In addition, the country’s electric system is divided in ten different transmission regions but three of them are completely isolated from mainland Mexico’s system and from each other: the Baja California (connected to the California system in the United States), Baja California Sur and Mulege systems. However, tariffs differ in eight regions and only six of them are part of the mainland system. Also, the environmental and climate change policy has been implemented and was seriously enforced recently, which may not allow the construction of profitable but environmentally hazardous projects anymore. Figure 1.1 shows the transmission regions in Mexico:
Figure 1.1. Regions of the National Electric System (Transmission) Source: CENACE, official operator of the transmission network as of 2015
The lack of a formal economic analysis of the Mexican electricity sector is the main motivation of this study. As opposed to Norway, who restructured its electricity market in the 1991, the Mexican Energy Reform was approved until 2014 and it is still too soon to determine the quantitative effects of this new policy. However, the establishment of an open market will allow us to consider new
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economic assumptions for qualitative analysis. However, the remarkable achievements of the Norwegian market reform could be used as a baseline for the optimal development of the newly restructured Mexican energy sector.
Electricity has come to play an increasingly important role in the development of modern economies. Quoting from the book Hydropower Economics written by Finn Førsund:
“The nature of electricity is such that supply and demand must be in a continuous physical equilibrium. The system breaks down into a relatively short time if demand exceeds supply and vice versa. A system failure may lead to grave economic consequences if the blackout lasts too long.” (Førsund, 2011, p. 6)
It is there where the importance of the analysis comes into play. The country used as a baseline to develop the theory behind Hydropower Economics was Norway. This study will aim to give qualitative analysis on the Mexican electricity market based on the main findings in these fields, testing the adaptability of the model at the same time.
This thesis will be based on the finding published by Finn Førsund in his book Hydropower Economics, in which he provides a qualitative economic analysis of how to use the stored water in hydropower systems with fixed generating capacities. While the problem exists as a dynamic problem, new energy projects take time to develop, even more than the time necessary to empty multiyear reservoirs.
Thus, the dynamic problem can be solved through fixed generating capacities for a given set of periods. These concepts and the theory involved will be adapted to the Mexican scenario, in which there are several types of generating technologies, and five interconnected regions with different prices. This scenario can be addressed by using the trade theory included in the previously mentioned book. Instead of considering scenarios of trade between countries, they will be referred to as regions but the methodology will be adapted as necessary. An important assumption that will be needed for simplicity is that regions will trade only with bordering entities due to elevated costs of transmission across large distances. This can be observed by comparing the territorial division of the regional tariffs and the Interconnected National System in the following figures.
7 Figure 1.2. Regional tariff division map in Mexico.
Source: Comision Federal de Electricidad, official government electricity agency
The transmission system for electricity is what links the consumers to the generating plants. In Mexico, the electricity delivered to customers has 110-120 volts and 60 Hertz. However, transmission lines have different voltages according to the distances traveled by electricity. The extension of the Mexican territory and its geographic composition cause significant energy losses when electricity travels through long distances. In addition, Mexico does not have any direct current high voltage transmission lines that allow the transmission of electricity at a lower cost and with less energy losses. However, the infrastructure expansion program of the electricity sector does consider using this technology in the future.
The Mexican Energy Reform established that CENACE is in charge of monitoring and operating the electricity market as it was published in the Nation’s Official Journal (DOF). In the short run CENACE will operate a Day Before Market which closes on day before to the Operation Day and a Real-Time Market which closes before every Hour of Operation. It is planned to introduce an Hour Before Market in the coming years to complement these two markets.
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Figure 1.3. Interconnected National System
Source: CENACE and Comision Federal de Electricidad, official government electricity agency It is because of the reform that the equilibrium of the market can now be found in power, with an operator that is independent of suppliers and consumers and controls the transmission network. As the theory suggests, these conditions are sufficient for the assumptions of the economic model to be valid. As a comparison, CENACE acts in the same way as Nord Pool in Scandinavia.
Electricity Demand in Mexico
Electricity demand data in Mexico has been publicly available since 2015 and it is usually measured in weekly periods. Daily data per hour is available but as a new entity data series are not yet officially published, though it is definitely possible to acquire and organize it. In Figure 1.4 and Figure 1.5 we can see the differences in hourly use of electricity in the North and South regions, during summer and winter and during a weekday and a weekend.
9 Figure 1.4. Daily load curve for the Northern Regions
Source: SENER (Energy Secretariat) with data of CFE
Figure 1.5. Daily load curve for the Northern Regions Source: SENER with data from CFE
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The data is available for the year 2014 and it is compared to the maximum demand in the operation area. In the Northern regions there is a noticeable difference between summer and winter, while in the southern regions the demands overlap in several hours of the day. The use of air conditioning increases demand in the north, while in the southern region the differences between summer and winter are not so clear. The peak comes at night when all the lights in households are turned on as well as TV sets in the southern region. On the other hand, in the north electricity consumption remains high during the whole night and decreases during the morning, reflecting decreasing temperatures at night. In warmer regions consumption in the summer remains high throughout the day and it is somewhat stable during winter months. In the southern regions the differences between lows and highs is more noticeable, having sharp peaks between 19 and 22 hours.
Despite of not having hard data on household demand of electricity by use, it can be easily categorized. Due to Mexico’s climate, there is mostly no need for space heating. On the other hand, air conditioning plays an important part of the country’s electricity consumption, especially in the northern regions. In fact, the average temperature acts as an indicator to determine the proportion of subsidies given by the government to consumers, i.e., the warmer the region, the higher the subsidy for air conditioning activities. This is not the case in the central and southern regions. Also, in general stoves and hot water appliances use liquefied or natural gas to operate, washing machines are much more common than dryers and dishwashers. Thus, electricity is mostly used for lighting, refrigerating, deep freezing, washing, TVs and PCs. Air conditioning increases demand during the day in the Northern regions. The impact of air conditioning can be seen comparing the central and southern regions to the northern ones; the increases on electricity consumption in the former are much sharper compared to the stable demand of the latter regions.
As opposed to the Norwegian case, in Mexico electricity demand is higher in summer than in winter. Also, demand increases in the summer due to water pumping for agricultural purposes.
This illustrates an opposite scenario as the one depicted by Førsund. Using weekly periods, which are officially available, Figure 1.6 illustrates the demand evolution throughout the year.
11 Figure 1.6. Weekly demand evolution in Mexico’s interconnected system
Source: CENACE
The lowest demand of the year has been recorded coincidentally on the first week of the year for the last three consecutive years. The highest recorded demand was recorded during week 24 in 2014 (39,000MWh), during week 33 in 2015 and week 28 in 2016 as shown in Figure 1.6 by the solid green, black and red lines. The area between the dotted green vertical lines show the period of highest consumption during the year, while the red and blue dotted lines (not the horizontal red dotted line) show the Reserve Operational Margin (ROM). The ROM shows the difference between the total demand and the available capacity for power generation. With increases in demand, we can see that during the 22nd week of 2016 this margin came at an all-time low of 6%.
For economists, it is natural to assume that as capacity becomes scarce, also electricity prices naturally increase, thus demand is affected by price. We can see important differences between summer and winter days and it may be attributable to the use of air conditioning during warm weather seasons since this type of appliances are intensive users of electricity. Electricity
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consumption increases by 80-90% in the northern regions in summer, while in the other regions the increase is close to 20-30% compared to the first week of the year.
We know that the ROM was in quite a low level during the peak demand week of 2016. While demand is growing, also increasing participation from the private sector due to the Energy Reform will play an important role to satisfy the demand and increase the generating capacity, while CENACE will have to work accordingly to increase transmission availability.
Hydropower in Mexico
Mexico has important potential in hydropower resources. However, the country is divided in half with tropical weather and deserts; thus, most of the water is located in the center-southern region.
Mexico had over 12GW of hydropower installed capacity by 2014 and approximately 90% of the reservoirs and plants are located in the center and southern regions. Despite of the advantages of hydropower generation, in Mexico’s long term energy plans hydro will lose importance gradually, unless interest is awoken in the private sector. Natural gas combined cycle plants will drive the growth of the Mexican electricity sector as years go by.
Figure 1.7. Development of accumulated energy in reservoirs 2014-2015.
Source: SENER, Expansion of the National Transmission Grid Program 2016-2030.
13 Storage capacity in Mexico is significant but it depends strongly on the type of pluvial years: dry, medium and humid years. Figure 1.7 shows the development of accumulated energy of reservoirs in Mexico. The year 2014 started with 22,503 GWh of stored water and it declined until June, it then increased due to the rainy season and grew since September (when the period to fill up reservoirs starts) to 21,054GWh at the end of the year. However, 2015 was a dry year, reaching minimum values of 10,960GWh in June and lowering the stored capacity to 18,091GWh, a 4,412 GWh reduction in comparison to the previous year. The total energy generation in 2014 was 31,222GWh and due to the lower inflows in 2015, production was reduced to 23,240GWh. It is expected that hydropower generation will be lower in 2016 in comparison with the two previous years due to low inflows. This behavior will be consistent with the economic theory that will be used in this study. Figure 1.8 shows the behavior of stored energy in the Mexican reservoirs.
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2. Background for the energy model
“The key economic question in hydropower production is the time pattern of use of water in the reservoir given each time period. With enough storage capacity the water used today can alternatively be used tomorrow. The analysis of hydropower is therefore essentially a dynamic one.” (Førsund, 2011, p.14)
The behavior of hydropower generation appeals to this assumption, taking into account the opportunity cost of using water in different periods. Also, the costs of operating hydropower plants are very low since there is no cost on inflows and labor costs are quite small when measured against production. Investment costs are high, but they play no role in the optimal operation of plants according to the water resources available. In order to address the problem of not including investment in the model it is required to solve for the optimal management of stored water given production capacity. In order to find qualitative information about the social planning problem while optimizing power generation we will use nonlinear programming models using Kuhn- Tucker conditions. The quantitative analysis and the use of stochastic dynamic programming tools used in engineering for variables and methodology will not be addressed. Details on the variables and methodology will be covered in the next sections.
Environmental concerns regarding hydropower in Mexico are important to consider. Hydropower does not contribute to the generation of harmful regional greenhouse emissions such as sulfur dioxide (SO2), nitrous oxide (NOx) or the global pollutant carbon dioxide (CO2). Nevertheless, this type of energy does not only include environmental hazards but also political issues.
Concerning the environment, the use of water and the creation of reservoirs can alter the microclimate and the ecosystems’ cycles in general. Artificially creating reservoirs involves flooding entire areas that can importantly alter the ecosystem, potentially endangering species and their habitats. The change in water flows may affect aquatic wildlife. As opposed to Norway, the value of the use of natural waterfalls, lakes and rivers is not considered to be a major deterrence for the creation of hydropower projects, but population displacement and relocation plays a key role in their success.
Hydropower projects use large plots of land in order to build the reservoirs and the infrastructure needed. Naturally, the amount of land required depends on the scale of the project. In Mexico,
15 large hydropower projects are developed and operated by CFE, and the state is fully responsible for acquiring the land and mitigating the environmental hazards created. The private sector usually participates with smaller projects which are, under Mexican standards, considered to be renewable energy projects up to 50MW. Larger projects are not considered “renewable energy” projects under the Mexican operating framework since they involve flooding considerable areas of an ecosystem, alter the microclimate of a region and change water levels in water bodies that may affect aquatic life. Also, large projects require aggressive capital investments, with examples like the Chicoasen I that required an investment of over 800 million USD. The private sector in Mexico has focused on developing hydropower projects with less than 50MW of capacity, and despite being a sector that is not growing nearly as fast as the wind or solar industries, the potential to build small hydro and mini hydro is 56GW. (Castellanos, et. al., Mexico Energy Review, 2014).
Thermal Energy in Mexico
The choice of technology used for power generation in Mexico is closely related to the price evolution of different types of fuels. Mexico has promoted the construction of infrastructure to satisfy the demand for natural gas in the coming years. Also, the discovery of large natural gas reservoirs in the United States has pushed the price of natural gas to the lowest levels in the last 20 years due to the construction of pipelines across the border that has made imports easier.
However, the low prices of oil are not related to the regional behavior of natural gas in North America. The future planning of the electric sector in Mexico has directed its efforts towards a lower use of oil and its sub products in the next years while plans to increase the participation of natural gas in order to reduce greenhouse emission. Coal, fuel oil and diesel use will be reduced drastically by 2029 while, in addition to natural gas, geothermal steam and uranium’s participation will increase.
Wind and solar power plants are expected to be developed by the private sector. CFE has also to substitute older power plants for more efficient ones in order to take proper advantage of the available resources, maintain a reliable MRO and reduce power failures. Thermal power capacity accounted for over 72% of Mexico’s energy mix and for 75% of total power generation in 2014.
Compared to hydroelectric power generation the participation of thermal technologies is importantly dominant, however, the participation of hydropower is not negligible. Figure 1.8 shows the participation of each energy source in Mexico’s electricity generation. The graph uses
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data from CFE and the Energy Regulation Commission (CRE). The CRE is in charge of creating and enforcing the optimal operating framework in the energy sector. This commission is responsible for managing and issuing resource exploitation permits in every activity related to energy. Also, it is responsible for planning long term strategy and design laws to promote the efficient operation of the energy market, being also the enforcer of such laws.
Figure 1.8. Generation by source in Mexico
Source: National Energy Strategy, SENER with information from CFE and CRE
As opposed to hydropower, thermal power does have important operation costs, which mostly depends on the amount and the price of the fuel used to operate the plants. This implies that the production function will include costs that negatively affect energy generation. These variables will be considered in the model in order to obtain precise first order conditions. However, often thermal plants have lower investment costs but higher operating costs which affect the optimal decision of generation technology. In the Mexican case not only this comes into play but also the geographical availability of resources. While natural gas has been considered as the “cleanest”
fossil fuel, important greenhouse emissions originate from these technologies. On the other hand, Mexico is still producing roughly 20% of its electricity through highly polluting technologies (coal and fuel oil) raising environmental concerns.
17 Renewable energy in Mexico
Environmental concerns have become increasingly important on a global scale, promoting investment in renewable energy sources as an effort to reduce greenhouse emissions and mitigate climate change. Europe’s investment in renewables grew through the combined efforts of the private sector and public policies, offering tax exemptions and the famous feed-in tariff schemes.
However, due to the economic recession in the European Union in 2009 public expenditure on these schemes was drastically reduced. As a result, renewable power generation companies started expanding to new and promising markets for growth. Mexico has been one of the countries that started developing renewable energy projects benefiting of the European expertise. As a result, investments in the renewable energy sector in Mexico started growing after 2008 through self- supply schemes despite of the strong limitations of private participation in power generation, especially in wind energy.
The Energy Reform allows more direct private participation in the Mexican energy market and investments have intensified. Although the current participation of renewable energy in Mexico is low, it is important to include this type of generation in the model as wind energy as it is the technology that is expected to have a higher impact on Mexico’s future energy mix. It is expected that wind power’s participation on total installed capacity will become approximately 13%.
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3. The energy model
In order to analyze de economics behind energy generation we need to establish baselines on the methodology. As mentioned before, it is possible to use discrete time since capacity growth and project development takes more than one year to start operating from any given year. The new projects that contribute to capacity and production growth are negligible from one year to another when taking into account the proportion they represent compared to the country’s total. The use of discrete time makes it possible to use the previously mentioned non-linear programming tools.
Also, technical change of hydropower can be dismissed since it is an embodied technology.
The variables that will be considered in this study will be the amount in the reservoir, 𝑅𝑡, net inflow of water, 𝑤𝑡, electricity production from regulated hydro, 𝑒𝑡𝐻, unregulated river, 𝑒𝑡𝑅, wind power, 𝑒𝑡𝑊 and thermal capacities, 𝑒𝑡𝑇ℎ, and release of water, 𝑟𝑡, respectively just as described by Førsund.
Capitalized variables represent stock variables and lowercase variables stand for flow variables, indexed t to refer to the time period. More variables will be introduced as the model is developed and will be explained accordingly.
Starting with hydropower, the transformation of water into electricity depends on the release of water and the gross head, which is the vertical height from the upper level of the dam to the outlet of water from the turbines. However, in order to successfully measure the output of the plant it is necessary to convert the cubic meters of water into power generation. For this, the fabrication coefficient, (𝑎), will allow us to identify how many cubic meters of water are needed to generate 1KWh. The production function will have standard assumptions implying that production is increasing in input and height. Assuming that the latter equation holds with equality the water measured in cubic meters would exactly correspond to water measured in kWh.
𝑒𝑡𝐻 = 𝑓𝑡(𝑟𝑡, ℎ𝑡), 𝑓′𝑟𝑡> 0, 𝑓′ℎ𝑡> 0 (3.1)
𝑒𝑡𝐻 ≤ 1
𝑎𝑟𝑡 (3.2)
The objective of using non-linear programming is to optimize the management of current capacity;
therefore, capital costs are not included in the production function. In the case of the unregulated river the water release should be replaced by the unregulated river flow in both equations. Another important assumption regarding hydropower is the lack of presence of operational costs. At present
19 time the capacity is given and water is a renewable resource provided by nature. As opposed to thermal power, water for power generation is not purchased as an input in any market. Maintenance does not act as a variable cost but rather as a part of the capital expenditures of the project. On the other hand, labor costs do not vary according to output; the same amount of employees is needed to operate the plant in any production scenario. The only relevant cost for this analysis will be the opportunity cost of water comparing between the costs and benefits of using water today or tomorrow. In any other sense, we will assume that there are zero variable costs in the present.
Just as in the Norwegian case, the number of run-of-the-river facilities in Mexico is quite small and the height of the waterfalls varies from dam to dam. Water management is a dynamic problem since water is used to generate electricity reducing the amount of water in the reservoirs, but there are also inflows that fill them up at the same time. Thus, the amount of water available has to be constrained according to its use and renewal. Nevertheless, as opposed to what happens in a northern country such as Norway, temperatures in Mexico are higher and the need to adapt the Norwegian hydropower model for water evaporation is necessary. CONAGUA estimates that 72%
of the total precipitation evaporates; however, precipitation and evaporation happen throughout all the year. The evaporation of water that is released for energy generation becomes irrelevant for the reservoir (except in coupled hydro plants which will be covered in Appendix 5), thus, it has to be calculated to find the total amount of losses that the reservoir incurs.
𝑅𝑡 ≤ 𝑅𝑡−1+ 𝑊𝑡− 𝑟𝑡− 𝑣𝑡, 𝑡 = 1, … , 𝑇 (3.3) 𝑅𝑡 ≤ 𝑅𝑡−1+ 𝑤𝑡− 𝑟𝑡, 𝑡 = 1, … , 𝑇 (3.4)
Equation (3.3) indicates that the amount of water at the end of period t is less or equal to the amount of water in the previous period (which is equal to the reservoir content at the beginning of period t) plus the water inflow minus the release of water minus the evaporation of water in period t and the variable W stands for gross inflow. Strict inequality means that there is overflow. Equation (3.4) shows that the variable 𝑤𝑡 stands for net inflow accounting for the losses generated by evaporation at the end of period. Evaporation varies according to climate conditions and specific conditions of the water reservoirs, such as depth, the amount of water in the reservoir, and the total area that is exposed to sunlight.
20
Figure 3.1. Groups of climates in Mexico
Source: INEGI (Instituto Nacional de Estadistica Geografia e Informatica) National Institute of Statistics Geography and Informatics
The equation goes in line with the fact that the more water there is in the reservoir the less proportional evaporation while it might be higher in absolute terms (Goor, et. al., 2010). Figure 3.1 shows a map of the temperature variations in the Mexican territory and we can see how temperatures vary according to the different regions. Hydropower is mostly present in the southern area of the country so an analysis of the average temperatures is relevant in order to show the importance of the role of evaporation in energy generating models.
In Mexico climate is determined by several factors such as altitude over sea level, geographic latitude, different ecosystems, and the existing distribution of water and land. Following the order of the numeration in Figure 3.1 the warm humid climate covers 4.7% of the country and has an average annual temperature between 22°C and 26°C with high precipitations between 2000 and 4000 millimeters per year. The warm sub-humid climate covers 23% of the Mexican territory and has the same average temperatures as the warm humid region, but in certain areas the average temperature goes well above 26°C. The yearly precipitation in these regions varies from 1000 and 2000 millimeters.
21 The dry regions in Mexico are mostly located in the center and northern areas of the country, corresponding to 28.3% of the territory. The average temperatures vary between 22°C and 26°C in some regions and in other regions it goes from 18°C and 22°C. The annual rainfall is between 300 and 600 millimeters. The regions with very dry climate have an average temperature between 18°C and 22°C and precipitation is extremely low, from 100 to 300 millimeters. These areas cover 20.8% of Mexico’s territory.
Finally, the mild weather is divided in humid and sub-humid. The humid mild climate registers average temperatures between 18°C and 22°C and has significant rainfall averaging 2000 to 4000 millimeters per year in 2.7% of the country. The mild sub-humid climate covers 20.5% of the country and temperature can vary significantly. Some regions register temperatures from 10°C to 18°C (center), others from 18°C to 22°C (south), and in certain regions it can drop below 10°C (north) with precipitation averaging from 600 to 1000 millimeters during the year.
This climate map of Mexico shows us that the southern region is mostly dominated by warm and mild humid and sub-humid climates with mostly high average temperatures. This goes in line with the proposed model taking into account the high average temperatures and the important precipitation levels where hydropower is present.
In a practical case for Mexico, as energy demand and generation is usually measured in weeks.
The model allows to find qualitative information using horizons of 2 years as an example, but it can be extended to all periods. This proposal is based on the fact that the reporting of Mexican energy authorities follows this format.
In order to convert water flows to energy units we need to use the annual profile of inflows and releases for the Mexican hydropower system as it is shown in Figure 1.7. In Norway inflows are low in the winter weeks due to the low temperatures and the freezing of water. In Mexico, the strong inflow season starts during the summer and finishing in December due to the rainy season.
In this period generation is slightly higher than during the winter and spring season. It follows to clarify that since hydropower is mostly present in the southern region, air conditioning follows a rather stable path during the year for intensive users such as hotels, restaurants and buildings. Most homes do not have air conditioning and the ones that do, use it sparingly.
22
4. The Mexican Hydropower Model
In order to make a more realistic model we have to introduce an upper reservoir constraint, deal with the treats of overflow, and no emptying of the reservoir until the terminal period. For simplicity, we will also assume that water is present in the first period. This is a quite realistic assumption as the hydropower infrastructure is already present in the Mexican market and reservoirs will have given amounts of water for the period chosen. The variations in the pattern of inflow can be of up to ±25% between dry and humid seasons.
Figure 4.1. Annual Precipitation in Mexico
Source: CONAGUA (Consejo Nacional del Agua), National Water Council
23 Most of the hydropower plants are located in the southern region. As we can observe in Figure 4.1 the precipitation map is consistent with fact that reservoirs are located in the Center, South and Peninsular region.
“In the case of all water being present in the first period, utilization of water within a horizon can be regarded as a problem of managing a resource of finite amount, just like extraction of non- renewable resources like oil.” (Førsund, 2011, p.21).
In order to have equality in the production function (3.1) it is necessary to assume that production of electricity is efficient and that water is available in the first period. We also assume unlimited transferability of water to the other periods given the available water in the first period. Creating an example with water being available in the first period using the production function under these assumptions gives us:
∑ 𝑟𝑡 = 𝑤1 ⇒
𝑇 𝑡=1
∑ 𝑎𝑒𝑡𝐻= 𝑤1,
𝑇 𝑡=1
(4.1)
Where W represents water measured in KWh and w represents the net inflow accounting for evaporation. In this equation water is measured in cubic meters on the left hand sided, while dividing water by the fabrication coefficient lets us have units in KWh, as proposed before in equation (3.2).
In order to find the optimal energy generation standard economic assumptions, indicate that energy consumption will be measured by utility functions as a standard social planning problem with no discounting due to short cycles (T covers one seasonal cycle of one year). The horizon is somewhat lower when comparing Norway having three to five years of multi-year reservoirs to Mexico with multi-year reservoirs of two to three years. By standard assumptions and concavity properties of the utility functions the marginal utility will be measured in monetary units and represents the marginal willingness to pay and the social price of electricity as follows:
𝑈𝑡(𝑒𝑡𝐻), 𝑈′𝑡(𝑒𝑡𝐻) ≥ 0, 𝑈′𝑡(𝑒𝑡𝐻) < 0, 𝑡 = 1, … , 𝑇 (4.2) 𝑈′𝑡(𝑒𝑡𝐻) ≡ 𝑝𝑡(𝑒𝑡𝐻) (4.3)
24
Despite of the growth of the Mexican energy demand and capacity, the variations observed in one year cycles are quite low. In this analysis we will immediately introduce constraints into the social planning problem, but the basic model can be reviewed in Appendix 1.
Constraints in the Mexican hydropower model
In order to properly explain the behavior of a hydropower model it is necessary to include other restrictions in addition to the limit of water availability. The constraints vary according to the length of the periods chosen and if single or multiple plant models are considered. It is necessary to include storage, generation and emptying constraints. Storage constraints limit the maximal reservoir capacity for energy generation while the generation constraint is directly related to the maximum capacity in MW of power plants. In the basic model the result is that prices are equal in all periods. However, in reality electricity prices change in short periods of time. Also, excess emptying of the reservoirs may result in severe environmental damage damaging the flora and fauna along the water bodies. Environmental concerns in Mexico due to water release are rather constant since water flows are active during the year. Environmental concerns include the risk of flooding, impact in fishing activities and microclimate changes that impact agricultural activities.
In order to calculate the amount of energy that can be produced we use the maximal capacity in kW (or MW) in a period length of one hour to be measured in kWh (or MWh). In this analysis we will only use energy as the relevant variable for the power and production constraints. Ramping up and ramping down has also has to be considered in the model for shorter periods when release changes.
In the Mexican electricity model it will be important to establish trade constraints in order to be able to link the different regions and their interaction and will be addressed accordingly as the models are developed. The losses due to temperature variations will not be considered as the effects are negligible. Environmental constraints may reduce environmental problems; however, the most aggressive phase comes from building the hydropower plant rather than from operations.
Optimal management of a hydro system
In this section we will specify the objective function for power producers using standard economic assumptions to maximize producer and consumer surplus. The objective function will allow us to maximize the social surplus under the consumer demand function and using a partial equilibrium
25 approach we can simplify the methodology as the demand equals the supply in equilibrium where the consumer’s expenditures correspond to the producers’ profit. The demand function decreases in price. In the case of hydropower, we previously mentioned that operation costs are quite low so the objective function will be specified with zero operating costs as follows:
𝑂𝑏𝑗𝑒𝑐𝑡𝑖𝑣𝑒 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛: ∑ ∫ 𝑝𝑡(𝑧)𝑑𝑧
𝑥𝑡
𝑧=0 𝑇 𝑡=1
(4.4)
As we are using the consumer surplus approach it is necessary to include a choke price that yields zero demand. The reservoir constraint proposed for the reservoirs in this model can be specified as in (3.4) but divided by the fabrication coefficient in order to convert from cubic meters to energy units of kWh:
𝑅𝑡 ≤ 𝑅𝑡−1+ 𝑤𝑡− 𝑟𝑡 = 𝑅𝑡−1+ 𝑤𝑡− 𝑎𝑒𝑡𝐻 =>
𝑅𝑡
𝑎 ≤ 𝑅𝑡−1 𝑎 + 𝑤𝑡
𝑎 − 𝑒𝑡𝐻 𝑡 = 1, … , 𝑇 (4.5)
This way every variable is expressed in terms of energy units. However, for notational convenience we will not show the fabrication coefficient. We will introduce an upper reservoir constraint at the same time that an output constraint on hydropower generation. A more detailed explanation of the basic model, the optimal solutions, scarcity, and terminal periods can be found in Appendix 2. In this case we will directly cover the complex hydropower model that will be applied for the Mexican market.
The output constraints
As mentioned before Mexico has a total installed hydropower capacity of over 12GW but it represents around 18% of the total installed capacity, the rest is mostly generated by thermal power plants and a small participation of wind and nuclear energy. Also, the ROM hit a historic low this year at 6%, thus, constraining hydro, thermal and wind power’s output will be relevant in the final model. For now, the analysis will cover hydropower’s output constraint:
𝑒𝑡𝐻 ≤ 𝑒𝐻, 𝑡 = 1, … , 𝑇 (4.6)
26
Where 𝑒𝐻 stands for the upper limit for power generation. It has no time subscript since it is a technical constraint. If the highest power demand is lower than the power generation capacity, then we have sufficient power capacity. This highest peak in demand is the closest point to the left axis in the load-duration curve.
𝑥𝑡𝑚𝑎𝑥 < 𝑒𝐻, 𝑡 = 1, … , 𝑇 (4.7)
We now insert the production constraint (4.6) into the social planning problem (4.4)
max ∑ ∫ 𝑝𝑡(𝑧)𝑑𝑧
𝑥𝑡
𝑧=0 𝑇
𝑡=1
𝑠𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜
𝑅𝑡 ≤ 𝑅𝑡−1+ 𝑤𝑡− 𝑒𝑡𝐻− 𝑣𝑡 (4.8) 𝑅𝑡 ≤ 𝑅
𝑒𝑡𝐻 ≤ 𝑒𝐻 𝑅𝑡, 𝑒𝑡𝐻 ≥ 0
𝑇, 𝑤𝑡, 𝑅0, 𝑅, 𝑒𝐻 𝑔𝑖𝑣𝑒𝑛, 𝑅𝑇 𝑓𝑟𝑒𝑒, 𝑡 = 1, … , 𝑇 Yielding the Lagrangian:
𝐿 = ∑ ∫ 𝑝𝑡(𝑧)𝑑𝑧
𝑒𝑡𝐻
𝑧=0 𝑇 𝑡=1
− ∑ 𝜆𝑡(𝑅𝑡− 𝑅𝑡−1− 𝑤𝑡+ 𝑒𝑡𝐻+ 𝑣𝑡) − ∑ 𝛾𝑡(𝑅𝑡− 𝑅)
𝑇 𝑡=1 𝑇
𝑡=1
− ∑ 𝜌𝑡(𝑒𝑡𝐻− 𝑒𝐻
𝑇 𝑡=1
) (4.9)
The endogenous variables are 𝜆𝑡, 𝛾𝑡, 𝜌𝑡 (𝑡 = 1, … , 𝑇) and the first order conditions are:
𝜕𝐿
𝜕𝑒𝑡𝐻 = 𝑝𝑡(𝑒𝑡𝐻) − 𝜆𝑡− 𝜌𝑡 ≤ 0 ( = 0 𝑓𝑜𝑟 𝑒𝑡𝐻 > 0)
𝜕𝐿
𝜕𝑅𝑡 = −𝜆𝑡+ 𝜆𝑡+1− 𝛾𝑡 ≤ 0 (= 0 𝑓𝑜𝑟 𝑅𝑡 > 0)
𝜆𝑡 ≥ (= 0 𝑓𝑜𝑟 𝑅𝑡 < 𝑅𝑡−1+ 𝑤𝑡− 𝑒𝑡𝐻) (4.10) 𝛾𝑡 ≥ (= 0 𝑓𝑜𝑟 𝑅𝑡 < 𝑅)
𝜌𝑡 ≥ 0 (= 0 𝑓𝑜𝑟 𝑒𝑡𝐻 < 𝑒𝐻 ), 𝑡 = 1, … , 𝑇
27 The production constraint reduces the maneuverability of the hydro system and if there is too much inflow and not enough water can be processed then the threat of overflow becomes an issue. Also, it makes the water value to be lower than the price according to the first condition since a lower amount of water is used. This situation may also arise in peak load periods in which electricity demand is very high and triggers the output constraint, using less water and raising prices. These are the two reasons that make the production constraint binding. Now maneuverability depends on a minimum number of periods 𝑡0 to empty the reservoir and, the higher it is, the more limited maneuverability. It can be described as follows:
𝑡0 = min 𝑡 𝑠𝑢𝑐ℎ 𝑡ℎ𝑎𝑡 𝑡𝑒𝐻 ≥ 𝑅 (4.11)
However, there are situations in which inflows are greater than the generation capacity with no maneuverability. The main objective is to avoid spilling water and maneuverability only happens when production is greater than the inflows. If the case is the opposite, then there will be a lock- in of water (meaning that water cannot be moved from the reservoir). The largest contribution for power generation comes from thermal energy using fossil fuels and inflows rarely exceed generation capacities. In this case, in periods with threats of overflow generation from thermal power plants can be decreased without turning off the plants to avoid start-up costs and increase hydropower’s participation. The constrained model can be explained by Figure 4.2 in which the production constraint binds in the second period.
If the output constraint is binding in the second period then the energy production for period 1 is covered at optimal prices, but not for period 2. To avoid water spilling then production has to be transferred to period 1, but this will lower the price of electricity in the first period and raise it in the second. The difference in prices will be the output constraint multiplier and the generation in period one will be AB’’. If the output constraint is not binding, then the transfer of water will be from B’. However, since the output constraint is binding the water transfer is lower, from B’’ to C. The price increase is caused by the binding constraint and the increase of water use AB’’ in period 1 leaving less water to be used in period 2.
28
Figure 4.2. Bathtub diagram of hydropower with capacity constraint binding in period 2.
Source: Hydropower Economics, Førsund, 2005, p.53.
In the case of a locking-in of water, spill would be necessary to avoid overflow making the reservoir constraint binding and implying a zero water value since the reservoir in the second period cannot exceed its capacity, in other words, the extra water accumulated ends up in overflow and cannot be used. Due to the production constraint and the changes in prices the social value of electricity generation is lowered. The illustration provides an example of how this happens and an explanation on why this price differences happen. In order to find the optimal solution, it is important to understand how these variations affect the equilibrium between supply and demand.
Flow-of-the-river generation and wind power generation
The flow-of-the-river generation has a very low participation in total yearly production of hydropower in Mexico. This type of energy uses water flows that cannot be stored and must be used continuously to produce electricity. The main feature of this type of resources is that generation cannot be controlled. Due to its minimal participation, generation through run-of-the- river power plants may not have any relevant effect in the social prices. However, wind power follows the same essence as it is an intermittent generation resource and power plants generate only in its presence. For the Mexican case we will only add wind power in the social planning
