Optimal coordination of wind and hydro power generation

Ovaj rad istražuje postojanje prirodne komplementarnosti združene proizvodnje električne energije iz vjetra i vode, a koja rezultira operativnom sinergijom. Ovim se radom također nastoji kreirati univerzalan matematički model koordinacije stohastičkog i determinističkog izvora s ograničenim zalihama primijenjen na vodno-vjetrenu koordinaciju. Koordinacija podrazumijeva angažiranje hidroelektrane kada ostvarena proizvodnja vjetrene elektrane odstupa od ugovorene. Jasno je da će u koordinaciji vrijednost vode biti različita nego u inicijalnom slućaju, a te izmijenjene vrijednosti ključne su za kreiranje zajedničke krivulje kratkoročnog marginalnog troška i optimalne krivulje ponude, a koje su pak važne za dugoročnu opstojnost ovakve koordinacije. Rad ne razmatra tehničke uvjete integriranja vodno-vjetrene koordinacije u elektroenergetski sustav kao ni utjecaj na rad elektroenergetskog sustava odnosno utjecaj na termalno opterećenje, stabilnost napona, prijelaznu stabilnost, stabilnost frekvencije i ostalih kriterija za siguran i pouzdan rad sustava. Kako bi se osigurala univerzalnost rada, spoznaje do kojih se došlo tijekom istraživanja su iskazane koristeći metode i rezultate odnosno simbole i definicije područja suvremene matematike nazvano funkcijska analiza. U pravilu se izbjegava kratko spominjanje činjenica bez dokaza kada nisu bitne za raspravu, a kada su one bitne, čitatelj se upućuje na relevantnu literaturu. Svjesna je namjera da se ostavi čitatelju izbor hoće li ili ne dublje razmatrati ostala područja znanosti koja ovaj doktorski rad dodiruje, stoga su sve činjenice, spoznaje, teoremi i pripadajući dokazi drugih autora, koji su bitni za ovo istraživanje, navedeni ili u poglavljima rada ili u prilozima, te je jasno naznačeno autorstvo. Prilozi su detaljno numerirani po poglavljima i definicijama bitnim za ta poglavlja. Pregled specijalnih simbola i skraćenica koje se upotrebljavaju u doktorskom radu dan je odmah iza popisa literature. Istraživanje je podijeljeno u pet poglavlja. U prvom je poglavlju napravljen kratak uvod u problematiku, a u drugom se poglavlju predlaže pristup za kvantificiranje utjecaja vjetra na cijenu u sjeni vode. U trečem je poglavlju predstavljen model za kreiranje zajedničke krivulje kratkoročnog marginalnog troška vodno-vjetrene koordinacije. U četvrtom poglavlju predstavljen je pristup za kreiranje optimalnih krivulja nadmetanja vodno-vjetrene koordinacije u oligopolu. I konačno, u petom poglavlju nalaze se sveobuhvatni zaključci.The aim of this study is to investigate the existence of natural complementarity of coordinated wind and hydro power generation and the resulting operational synergies and also to create a universal mathematical model of coordinated wind and hydro generation. By coordination it is assumed the situation of engaging hydroelectric power generation for wind power deviation from the forecasted (scheduled) power generation. It is clear that in the wind and hydro coordination the financial value of water (price of water) is changed compared to the initial case (with no coordination with wind generation). These revised values are a key to successful construction of the short-run marginal cost curve and the strongly optimal supply curve of a wind and hydro coordinated generation, which in turn are important for long-term financial feasibility of such coordination. The work does not consider the technical requirements of integrating coordinated wind and hydro power generation in the power system or on the operation of the power system and the impact of the thermal load, voltage stability, transient stability, frequency stability and other criteria for safe and reliable operation of the system. In order to ensure the universality of the proposed mathematical formulation it is presented using the findings of functional analysis, a branch of mathematical analysis. As a rule, short mentioning of facts without respective proofs which are not relevant to the discussion is avoided and when it is relevant, the reader is referred to the appropriate literature. All the facts, insights, theorems and respective proofs of the other authors, which are essential for this study, are listed in the text or in the appendixes with clearly stated authorship. The overview of the used symbols and abbreviations is provided at the end of the work. In general, over the past decade there was a significant transformation of energy systems, ranging from deregulation to a significant increase in power generation from renewable energy sources. A certain characteristics of renewable energy sources require appropriate management of the power system and the appropriate organization of the electricity market. Currently, in some countries (Germany, Spain, United Kingdom) renewable energy bare the risk of financial losses due to the deviation of actual production from the forecasted schedule. In these circumstances, wind power plants should have mechanisms to avoid these risks. Generally, hydropower plant generates electricity from the potential energy of water that can be stored for a longer period. Wind power plant exploits the kinetic energy of the wind and can’t store energy by itself. The high flexibility and a high ramp rate (MW / min) hydropower plants are good choice for addressing wind power deviations. In the wind and hydro coordinated generation the optimal production dispatch of a hydropower system is altered and consequently the price of water i.e. the water shadow price is also altered. Generally speaking, the shadow price of a concerning constraint equals to the change of the optimum value of the objective function per unit change of the right hand side (r.h.s.) of the concerning constraint. Simply put, it is the marginal benefit of relaxing the constraint and the marginal cost of strengthening the constraint. Here, the water shadow price, ?, in particular hour, t, ?(t), equals to the change of the optimum value of the objective function (profit maximization) when 1 m3 of water is withdrawn from the other hours {1,...,24}\{t} and used in the hour t. The withdrawal of water from the other hours results in an opportunity cost, and since the withdrawal of water actually means strengthening of constraints in the other hours, then the opportunity cost is actually and by definition marginal cost of water usage. Therefore, in this work, the opportunity cost of water, the marginal cost of water, the water shadow price and the price of water are to be synonymous. Defining the water shadow prices as the opportunity cost of water is important because issue arises from the direct cost of electricity generation from water which is almost equal to zero. Therefore, obtaining the short-run marginal cost curve in this case is more complicated in comparison with the case of fossil fuels where the short-run marginal cost curve is obtained as a first derivative per production of a function for the total short-run cost of production. If this standard approach is used then the short-run marginal cost of electricity generation for hydro generation is equal to zero which in fact misrepresents short-run marginal costs of production that owner actually suffers. The actual costs are the opportunity costs of water usage which is the consequences of the fact that water is a limited resource in the short-term. This is not the case with fossil fuels which are considered available in the short-term because since there is no intrinsic variability such as for precipitation on a particular basin. There is a broad consensus that the electricity and the frequency regulation ancillary services should be simultaneously traded in order to minimize the overall cost of electricity supply. Such co-optimization is necessary because of the strong interactions between electricity supply and reserves. Therefore, the simultaneous day-ahead electricity and frequency regulation ancillary services market with uniform pricing is assumed. In order for wind and hydro coordinated generation to bid successfully, the short-run marginal cost curve of coordinated electricity generation is needed. If coordination also participates in the frequency regulation ancillary services market, then the short-run marginal costs curves for regulation and 10 minutes spinning reserve services are needed. The ancillary services, particularly regulation and 10 minutes spinning reserve are specifically addressed in the proposed approach. Those services are engaged using automatic generation control. For these reasons, the state of automatic generation control (probability of engagement) is considered as a random variable. The used short-run stochastic optimization model enabled the implementation of a risk measures. The convenient risk measure to use is the conditional-value-at-risk. This relatively new measure is a coherent measure of risk which accurately represents the financial risks that occur in reality, also it is important for the implementation in the convex optimization problems since it does not undermine their convexity. After the short-run marginal cost curves are constructed, the wind and hydro coordinated generation competes by offering a schedule of quantities and prices into a market – the so called supply curve, rather than using a single strategic pair of quantity or price. Therefore, the supply function equilibria which occurs in environment of simultaneous day-ahead electricity and frequency regulation ancillary services market is analysed. The state of the competition on this market is the imperfect competition and a non-cooperative game modelled with the supply function equilibrium. Therefore, this work proposes a unique and novel approach based on a supply function equilibrium modelled as a non-linear programming problem for addressing the issues of a market power and optimal bidding strategies of the company with the zero direct costs of electricity generation such as hydro and wind generation. The supply function equilibria has been used extensively in the analysis of wholesale electricity markets as well as in other environments. The equilibrium behaviour when companies differ, both with regard to their costs and their capacities is studied, and this is so called the asymmetric case. A single-stage competition process is assumed which means auctions following the observed auction will not be considered. The study in this paper studies wind and hydro coordinated generation as a company which competes with other companies with non-decreasing supply function. After all supply curves are provided then stochastic demand realizes and the market is executed at a single price that is paid to all competitors (uniform price). The used numerical approximation of the supply function equilibrium is presented and the main mathematical objects of oligopolistic market with asymmetric firms are defined. The case study analyses the oligopolistic electricity market in Croatia. It consists of hydro-wind coordination of Vrataruša wind farm and Vinodol hydropower system; the dominant company in the Republic of Croatia; imports from Hungary; imports from Slovenia and demand in Croatia. The transmission capacity of cross-border transmission lines is taken into account, while the internal transmission is not taken into account. In this environment the optimal strategy of competition in the form of the supply curve is analysed. It will be examined if the observed hydro-wind coordination has a market power and at what amount of installed capacity. It will be shown that there are certain operational synergies due to coordinated wind and hydro generation that result in lower short-run marginal costs and also it will be examined if the observed coordinated wind and hydro generation has an operational synergies which follow from its market position. The work contributes with: the approach for quantifying the impact of wind variable generation on the water shadow price; the approach that innovatively combines the hourly conditional-value-at-risk, automatic generation control state as a random variable and the water shadow price in order to determine the short-run marginal cost curve for electricity production and the curves for regulation and 10 minutes of spinning reserve services; the novel approach based on the supply function equilibria for addressing the issues of a market power and optimal bidding strategies for companies with zero direct costs of electricity generation such as hydro and wind generation. Therefore, the thesis is divided into five chapters. In the first chapter, a brief introduction to the problem is given where the review of the current state of research of the analysed subjects is presented. In the second chapter, the approach for quantifying the impact of wind variable generation on the water shadow price is proposed. The third chapter presents an approach for the creation of a short-run marginal cost curve for the wind and hydro coordinated generation. In the fourth chapter, the approach for constructing a strongly optimal supply curve for wind and hydro coordinated generation in the market oligopolistic electricity market is given. Finally, in the fifth chapter, the overall conclusions are given. The sixth chapter gives extensive literature list used during this research. The comprehensive list of symbols and abbreviations is given just after the literature list. The abbreviations and symbols are given in the alphabetical order with the list of symbols divided into Latin and Greek symbols. The appendices are extensive in definitions, theorems and respective proofs which are essential for this study with clearly stated authorship. Also, the appendices contain all the extensive data and graphs not suitable for presentation in the main text in order not to reduce readability