英国曼彻斯特大学金融数学专业留学生毕业dissertation范文下载-introduction

英国曼彻斯特大学金融数学专业留学生毕业dissertation范文下载-introduction

 

background

Progress of UK electricity

Since the Great British push its electricity industry to the market in 1990s, tariff liberalization has experienced more than 10 years’ construction process. Until the agreement BETTA officially implemented in April 2005, Scottish network and Northern Ireland network merged with England - Wales network, which was operated by the National Grid Gas PLC, in order to establish the unified balance trade and Clearing system. It leads to the formation of uniform transmission pricing method and grid usage contract system based on the England - Wales mode. To ensure the pricing market running smoothly, National Grid was established as GBSO to transmit the electricity power, which is independent from electricity generations and supply agencies. And, OFGEM regulated the agencies in the electricity industry which is independent from government. All the great changes were benefited from the serious of acts, such as Electricity Act in 1989, Basic Implementation Act in 2000 and Energy Act in 2004. 

背景

英国电力进度

由于大不列颠推动其电力行业市场的20世纪90年代，关税自由化经历了超过10年的建设过程。直至协议BETTA于2005年4月正式实施，网络苏格兰和北爱尔兰的网络合并，英格兰 - 威尔士的网络，这是由国家电网天然气PLC的操作，以建立统一平衡的贸易和结算系统。这导致了统一的输电定价方法，并根据英国电网使用合同制度的形成 - 威尔士模式。为确保市场价格平稳运行，国家电网成立为GBSO传输电力，这是独立于电力世代和供应机构。而且， OFGEM监管机构在电力行业里面是独立于政府。所有发生的巨大变化是受惠于1989年在2004年严重的行为，如电力法，基本实现法于2000年与能源法案。

 

From the considerable application of natural gas generation in the 1990s，British have replaced coal-fired stations. At the same time, wind power, nuclear power and other clean and renewable energy were vigorously developed in recent years. By all these efforts, the carbon emissions of the British electricity power industry fell by nearly one quarter from 1990 to 2010. The data show that wind and other renewable energy sources account for about 10 percent of England generating capacity. In addition, nuclear power accounted for 16percent, with the total renewable energy power generation accounts for one quarter in the Great British generating sources. According to ‘energy dynamics’ issued by the Ministry of Energy and Climate Change on June 30, 2011, in the first quarter of 2011, the British coal-fired and nuclear power increased 7.1 percent and 6.9 percent, natural gas power reduced 19.9percent, and wind energy, hydro as well as other renewable energy electricity supply increased by 27.4C. Meanwhile, market-oriented electricity prices and TOU power price are made the peaks and valleys to be effectively regulated. Thus, the total power supply amount had a decrease of 2.0 percent over the same period in last year. #p#分页标题#e#

 

However, in the next 10 years, Because Britain will close old coal-fired power stations and nuclear power plants in succession, the whole generating capacity will be reduced by one quarter, while facing with the possible continuing rise in electricity consumption. Under this situation, the government will invest over 110 billion pounds to build new power plants to meet the electricity demand with reducing dependence on fossil fuels, including offshore wind power stations system, solar power stations and nuclear power stations. Besides, government will upgrade the network and construct smart grid to reduce energy loss. And also the country will regulate the electricity supply and demand by price incentives, differences contracts, derivates and carbon rights.

 

These changes on the electrical energy supply will lead to large fluctuations of the electricity price in the market. Besides, the participation proportion of new energy will make changes in the electricity prediction method. Faced with these changes, the establishment of effective estimation model will reduce the impact of tariff changes on the market.

 

Smart Grid

The smart grid can collect information of consumption behaviors and make relevant adaptive adjustments on the suppliers. Due to the combined effects of smart meters, transmission sensors and control elements, the smart grid can be achieved ‘flexible, accessible, reliable and economic’ characteristics. [Reference: 2006 EU <Green paper_ A European Strategy for Sustainable, Competitive and the Secure Energy>]. The particular concern was paid upon the application of low-voltage grid power control, flow balance control, distributed adaptable energy control and intelligent protection control. 

智能电网

智能电网可以收集消费行为信息，并就供应商相关适应性的调整。由于智能电表，传感器，传动和控制元件的综合影响，智能电网可以实现“灵活，方便，可靠，经济的特点。 [参考价格：2006欧盟<Green paper_一个欧洲战略Sustainable,竞争和安全Energy>]。在低压电网功率控制，流量平衡控制，分布式能源适应性控制和智能保护控制应用的特别关注支付。

 

For Britain, the lack of fossil fuels like oil, coals, natural gas caused the supplies of energy rely heavily on imports. With the sustained rise of natural gas prices and international crude oil prices, electricity price increases and the energy crisis intensifies. Although fossil fuels can guarantee the stable supply of electricity, the rich supply of wind power and solar power can provide clean energy in the future. However, the supplies of these energies mainly depend on weather, which will have instability characteristic. And because of technical limitations, we cannot capture enough energy to meet electricity demand. To solve these difficulties, we will consider the intervention of the smart grid. It can change the original centralized generation of fossil fuel power to the distributed generation of wind energy, which will take advantage of the distributed generation systems in smart grid. Through the regulation and control, each plant can access and exit the grid timely. Also it can ensure the different suppliers access to national grid and even European grid system.#p#分页标题#e#

 

In addition, real-time control of smart grid can increase the power supply efficiency and reduce excessive electricity production. When the low point of electricity usage occurs, it can control the storage of excess power trough power plants or batteries, which can increase the mean load rate and utilization efficiency of the network. The storage can complement the electricity supply in the peak period and alleviate the supply pressure. Then, we can achieve the relatively flat tariff and price spikes of the electricity price can be partly avoided. 

 

In the end, smart meters can carry out real-time statistics of consumption information, which will be transmitted to the central transmission sector (the agent). Afterwards the smart grid can replace the equipment and network quickly and efficiently to meet the demand based on real-time statistics. According to the accounting of the different electricity sector cost and electricity operating loss, the agent can realize real-time pricing by considering the supply and demand equilibrium. Meanwhile, due to the dynamic interactive control, smart grid can monitor the operation situations of the suppliers. Once the event of a local power failure or huge power outage happens, it can automatically shift from this line to another normal line in order to reduce the possibility of a disruption and to avoid the repeated occurrence of similar blackouts in London.

 

Smart grid is energy-saving and efficient. It not only allows the spread application of clean energy, but also moderates the contradiction between demand and supply. All these features can achieve lower electricity price and carbon emission while the demand is growth in the future. Moreover, the smart grid will realize the storage of electricity power, which will bring the change of power supply mode and the reform of the electricity price calculation model. These new changes will be the focus of the simulation in our analysis.

 

literature review 

With the development of the power industry, almost all of the electricity sectors in the whole world are increasingly concerned about the management of the power load, which is to manage the load by the economic and technical means. These means encourage users in the system employ more electricity when power capacity is wealthy, and save electricity when the capacity is tension. This will lead to the load shifting behavior for the users in order to ease energy pressures. To achieve this purpose, the electricity price can not be a simple value; it should be a tariff structure to reflect the cost of electricity production mode. Although the different types are divided to sub-high-voltage users, industrial users and commercial users, the pricing formula of the electricity tariff structure patterns are the same.

 

Before the writing of the article, we must first consider the current tariff system in the UK and possible defects. By reading the ‘Tariff History’ complied by BM RAMOKGOPA, and the related policy files, we can conclude the following conclusions.#p#分页标题#e#

 

There are four mainly tariff mode.

First model is the price ladder. This pricing mode changed with the amount of the used power. When power consumption is more than a certain number, the electricity price is cheaper. In this way, one can enhance competitiveness with other forms of energy such as natural gas, and improve the users’ electricity load rate. Considering the relatively stable power capacity, the higher the electricity load rate, the better for the company and the users. 

 

The second mode is two-part tariff system, which is proposed by J. Dr. Hopkinson in 1892. This system is still used by many countries in the world and also in GB. The billing of such tariff is composed of two parts. The first part is called standing change, which will not consider the amount but the different voltage level and the different consumption types. The second part is the amount tariff, which will calculate the size of the electricity consumption. In fact, such a two-price structure is widely used for telephone and gas billing.

 

The third model is TOU tariff which is generally used by British. It divided the day into two sections. During period from 7:00 pm to 7:00 in next morning, the price will be 70 percent of the day. And another uses have low hours from 0:00 to 7:00, the electricity is cheaper with 35 percent to the day. Currently, some person are still is used in combination with the two kinds.

 

Fourth mode is real-time pricing, which actually belongs to the TOU mode. Britain executed this mode on some large industrial users with pricing every half hour. The pricing is based on real-time changes in the production costs of the power system, which is not only related with the abundance and dry of reservoir inflow, but also related with system operation conditions, like load level of the turbine, combination of different boilers, and maintenance cost of the line. More time period, more accuracy.

 

The TOU tariffs are calculated with the marginal cost, recommended by World Bank. According to the method, the adequate or tension situation has relation with the production cost. And the spot price can balance the consumption. However, considering the calculation cost, the appropriate period will be half an hour. 

The calculation of the tariff is complex, which is also depended on the reaction of the users. Because the difficulty to accurately estimate the response of the users, we should consider the possible behaviors of them. For family users, they will optimize their consumption behavior to pay fewer bills. For enterprises, they will contrast the electricity cost and the reorganized labor cost. And these user characteristics are called the elasticity price elasticity. 

 

And we can simulate the calculation process. We obtained a real-time pricing by the calculation of the marginal cost and then adding a margin profit. Besides, we should consider the penalty factor which reflects the tense situation or accident state. So, all of this can formulate a shadow price. And the shadow price of every company will be collected. Then the regulatory will predict the total amount of the next day's load, and determine operation mode of the system. According to the margin cost and shadow price of different company, there will be different price list. #p#分页标题#e#

 

However, if accurate load forecasting is not allowed or major accidents happen, the RTP will be ineffective. And the related study is needed, which conclude the market research, the hardware developed, the marginal cost and related tariff, the user billing and the results analysis. And the thinking pattern will be reference of this article.

 

Except for the mentioned method to balance the peak and valley, we also need consider the storage of valley electricity. The final choice is to boil hot water for bath with valley power. The boiler control method can definite time in the period from midnight to 7:00. And the time-sharing watt-hour meter can flexibly calculate the bill. 

 

With the progress of the tariff system, the power stochastic model has also undergone a corresponding change. The tariff is a core evaluation with the efficiency of electric power market competition, which is related to the direct interest of the power suppliers and electricity purchasers. To maximize profits and consumer utilities, we must forecast the electricity price accurately.

Compared with general merchandise, power has its own characteristics, the low demand elasticity, difficult to store, vulnerable to the effects of the power system-specific constraints like power generation capacity, transmission congestion. All of this has brought the uncertainty to the forecasting. 

The scholars generally believed that the price forecasting needs to use mathematical tools by considering the relationship of supply and demand in the market, the market power of the market participants, the cost of electricity, and the electricity market institutional structures, social and economic situation and other important factors conditions. However, due to the complex of the electricity system, we cannot directly apply with the traditional financial model, which require us to make step-by-step innovation. 

 

Structural model

Structural model consider the balance of supply and demand and the related impact like fuel prices, hydrology, temperature as well as local economic environment external factors. It focuses on the internal relations law by describing the relationship between the electricity price, the demand and the system load.

Pindyck (1998) pointed out that the structural equation model is usually composed of three parts, the demand equation, the supply equation and the balance equation, which can be able to fully consider the various factors that impact on the tariff. Skantze et al (2004) assume that the processes of load and supply obey mean reverting stochastic process. They described the price as an exponential function of the demand, and re-build the model. Thompson et al (2004) predicted optimal strategy of hydropower by the structural model and improved jump-diffusion model, which can provide a more realistic optimal strategy in a simple way. Kanamura (2007) build a more simple and practical tariff structure model through a combination of improved supply function and a clear seasonal demand on the basis of supply and demand balance.#p#分页标题#e#

 

Johnsen (2001) established a supply and demand equilibrium model for the Norwegian electricity market whose mainstay is hydropower. The relationship between electricity supply and demand and the formation of market electricity price is explained with the water, snow, and temperature conditions. James (2004) introduced in the model with the flow magnitude of the four seasons, and used it for solving the determined ingredients of price. Baldick (2005) constructed temperature model and the demand load model considering the temperature influence and the market balance behavior. And then built the price model on the basis of that two models.

 

The structural model also introduced the idea of dynamic regression models, It use the transfer function modeling to predict the relationship between the variables and the explanatory variables, considering the characteristics of the behavior of electricity spot prices as well as external factors that impact on the tariff. The results are considered more credible by emphasizing the chain reaction of the independent variable on the dependent variable. F. J Nogales (2006) build a transfer function model to forecast prices based on the history data and demand, which mainly focus on   the market demand information and data.

 

Structural model concentrates on the study of comprehensive exogenous variables, which can be carried out in various electricity markets without too many restrictions on the specific market. But the introduction of hydrology, temperature external factors need the fully support of data, which often bring some difficulties to the study.

 

Econometric model

Econometric model is to build electricity price model by using regression analysis methods from the variables endogenous variable angle through statistical analysis of the observation data variables and the relationship of the price series.

1) The mean reversion model

 

Tariff is significant mean reversion. We can describe its intermittent gapped nature by jump-diffusion model. The Brownian motion can characterize "normal" fluctuations, and Poisson process can characterize the discontinuous process to reflect the occurring large fluctuations. The equation can be  .

dXt = adt + dWt ; St = e Xt.

 

However, W is a standard one-dimensional Brownian motion in this model without reflecting the behavior characteristics of mean reversion. Schwartz (1997) extended OU (λ, α, σ) process of mean reversion model, and constructed stochastic differential equations:  without using historical data. Johnson (1999) and Deng (2000) introduced the mean - recovery price model (BM) model to reflect the average recovery and bounded variance characteristics. But they only considered the historical changes and ignored the supply and demand relationship without seizing the price spikes in the summer and winter period. #p#分页标题#e#

 

Barlow (2002), extended the jump-diffusion model from a simple supply-demand model,  , where r is rate, μ represents the available area. However, the model is static, which is difficult to explain the spot price with the futures, and difficult to deal with multi-variable problems. Cao Yigang and Shen Gang (2006) proposed stochastic model with 2 and 3 jump components based on the diffusion process, which can use the historical pricing data to solve equation by the approximate parameter calibration method and reduce the errors.

 

2) The time series model

Time series models include autoregressive model, the moving average model, autoregressive moving average model, cumulative autoregressive moving average model and GARCH Models. These models have been widely used in the short-term load forecasting. Contreras (2003) commented ARMA model and GARCH model as usual ones.

ARMA (1,1) model:    , where θ1 is moving average coefficient, Pt is the tariff of time, and α is the expectation, φ1 is the regression coefficients of tariff sequence, εt is the random numbers with normal distribution (0, σ2). GARCH (1,1) model used the new distribution  function of εt , which is   . Knittel (2001) extended the GARCH model to EGARCH model for the asymmetry volatility of spot price.

 

Deng (2000) introduced Markov state transition model, and constructed the jump diffusion model with mean reverting and state transitions of spot prices. Considering the characteristics of the high volatility, mean reversion, and spikes jumping behavioral characteristics of spot prices, Lucia (2000) established single-factor model P = f (t) X and two-factor model P = f (t) X + ε. However, Lucia assume that Xt only obey mean-reversion process. And the following scholars assume Xt mean-reversion jump-diffusion process. Hadsell (2004) constructed TGARCH model by considering the cyclical fluctuations characteristics. 

 

Contreras (2003) is the first one who used the ARIMA model to forecast electricity price. Derk J (2006) combined the GARCH model, the Gauss matrix and system conversion method on the basis of the ARMA model, and he found that the model can be used for electricity Dynamic prediction by testing historical data in Germany. Zhang(2006) achieve a smooth price series by co-integration model and error correction model.

 

Econometric model is used to forecast short-term spot price throughout the trading day. It required less historical data, less work and can achieve higher calculation speed. But it was limited to the multi-variable problems, non-stationary process of time-series data, and inaccuracy of simple time series.

 

The neural network model

D.E.Rumelhart and J.L.Mcclelland (1986) proposed back-propagation algorithm of multilayer forward-feed network, referred as the BP network. The neural network has adaptive function with non-structural, non-precision rule, which can effectively deal with the multi-variable and nonlinear problems. Thus the scholars pay more attention with the method. Ram Say B (1997) extracted the fractal dimension of the attractor and the Lyapunov exponent on the reconstruction univariate time series space, and predicted SMP of British power pool for each period of the next trading day. He opened up a new path.#p#分页标题#e#

 

In recent years, the scholars adapted active exploration of the neural network prediction method. Hsiao Chuan-y (2002) used regression neural network methods; Guo Jau-ia (2003) used a radial basis function (RBF) neural network; Yamin HY ( 2004) established adaptive neural network model. The Chinese scholars Li Caihua (2002) proposed dynamic clustering and BP neural network to predict the short-term marginal price; Zhu Hongwei,, Lidong Chen et al (2006) proposed the BP neural network to establish the price spike recognition model. 

 

The neural network model is generally applied to short-term electricity price forecasting. It can be mapped to any function that is difficult to describe with mathematical models, and have good predictive results of the average electricity sequences. However, these methods require the support of a large number of historical data, which is difficult in practical application.

 

The dynamic simulation model

In order to achieve a multi-market environment electricity price forecast, the dynamic simulation model indirectly describe the quoted supply curve of the system through the establishment the exponential relationship between tariff and load, and adjust the shift factor according to the price difference. The study of the simulation model is currently focused on computational economics (ACE) and System Dynamics method. 

 

Using ACE, Derek Bunn transferred power system model into a commercial market network participated by regulatory agencies and strategic interaction markets. But ACE simulation model can not complete the complex system. Andrew Ford (1996) summarizes the application of system dynamics in the electric power industry. The practical application of the model concluded the national model developed by Naill, Energy 2020 developed by George Backus and Jeff Amlin, and CPAM and RPSM developed by Andrew Ford. Rafal Weron (2003) constructed a MRJD model concerning the instant tariff on the electricity market. 

 

The dynamic simulation model must take into account a number of matters. And the modeling approach needed to deal with a lot of issues, and also needed to collect a lot of data. Then it must express the complex interaction between generation and transmission systems using the formula expression. Therefore, it is difficult to use such a complex program for members of the general market.

 

Econometric model use straightforward model forecast electricity price trend throughout the trading day, and it is difficult to overcome the time-series and exogenous variables factors with inaccuracy results. Structural model established accurate and complex models which need to consider more variables. Due to the uncertainty, we can apply to long-term electricity market forecasting. For more complex electricity market, neural network model can improve the prediction accuracy of frequently changed prices. But the large amount of historical data brought a challenge to the practical application of the model. The dynamic simulation model using system dynamics thinking into the electricity price forecasting. It mainly focused on the impact of market supply and demand factors as well as the economic, environmental, and other multifactor details. And the complication is the limitation of the model. However, the combination of multi model will improve forecast accuracy, and become the focus of further research.#p#分页标题#e#

Considering the tariff system, the application of new energy and the combination of different models, we can make our research from the aspects of Brownian motion, simulation and differential analysis to predict the RTP based on the storage assume.

 

Methodology

All the production behaviors will be reflected by tariff In the Internet, and the bidding becomes open and transparent. How to ensure profits and lower costs will become most possible selection, which requires forecasting the next day's electricity consumption and supply situation accurately. And the real-time adjustments are also necessary. For users, lower electricity bills, will directly bring with a reduction in spending. Therefore, users will gradually choose to avoid the peak period by using modern means. Thus, the efficiency of valley period will be enhanced, which means the reduction of costs for suppliers. Spontaneous adjustment behavior is precisely the result of the price mechanism. And the most critical driver is the electricity tariff. 

 

The peak period can not be avoided because of the impact by temperature, weather and other special circumstance. Except that, the consumer behaviors of other time meet the Brownian motion. Brownian motion is molecular behavior of random diffusion motion proposed by scientists Brown in the 1820s. Einstein do a detailed research and make some extension in the 1900s, who put forward the famous formula of the diffusion length (1/2 formula). Based on the research of random walk, fluid mechanics, discrete stochastic differential process, the scholars obtain the Langevin equation and the fluctuation diffusion theorem. Then Ito Lemma and OU process give a more strict interpretation to the discrete stochastic differential process. The continuous integral introduction of infinite-dimensional by Nobert Wiener, founder of cybernetics, also extended statistical dimensions of the Brownian motion.

 

After the start of the real-time pricing (RTP) system, the Brownian motion is widely used in the study of price forecasting. Integrated with Brownian motion and Poisson distribution, Ito Lemma, Wiener process, we can solve the assumed diffusion equation, which is the tariff of electricity on demand side. For the supply side, we should also consider their generation costs, risks, and profit margins, etc.. There will be an upper limitation of the cost to the supply side from the supply-demand balance equation. The suppliers who are lower than the cost ceiling will receive the priority rights to sell the electricity. The client can also be free to select what they need on the demand side from the formed priority order. All of this will ensure basic profit based on the formation of healthy competition in the electricity market.

 

The introduction of new energy, for example the wind energy, will bring cheaper and cleaner energy into the power system. Due to the instability of this new energy, it is easier to form transmission pressures and supply risks. In order to ensure the stability of the users, we must consider the possible benefits and its threats of wind power generation, which has been unified in the system network. The energy storage will be the excellent method to solve this problem. Lack by the immaturity of the storage technology, large-scale use of storage control is still under the study.#p#分页标题#e#

 

Data validation is always the best means to verify the theory. After the inspection of the historical data, we can correct the defect in the model, and obtain more practical conclusions. After tested, we found that Brownian motion simulation will be a good description of the market random behavior, but the model ignores the descriptions of the peaks and the mean reversion characteristic. Neural network method can have a better statistical simulation result for a more complex system. After optimization of the cost-benefit for the storage model, storage solutions will bring obvious effect of shifting peak load, which can relief the supply pressure.