BỘ GIÁO DỤC VÀ ĐÀO TẠO TRƯỜNG ĐẠI HỌC SƯ PHẠM KỸ THUẬT THÀNH PHỐ HỒ CHÍ MINH LUẬN VĂN THẠC SĨ HOÀNG QUÁCH KHOA XÁC ĐỊNH GIÁ BÁN ĐIỆN CỦA NHÀ MÁY ĐIỆN GIÓ TRONG THỊ TRƯỜNG ĐIỆN CÓ XÉT ĐẾN HỖ TRỢ CỦA NHÀ MÁY THỦY ĐIỆN NGÀNH: KỸ THUẬT ĐIỆN - 8520201 SKC008014 Tp Hồ Chí Minh, tháng 3/2023 BỘ GIÁO DỤC VÀ ĐÀO TẠO TRƯỜNG ĐẠI HỌC SƯ PHẠM KỸ THUẬT THÀNH PHỐ HỒ CHÍ MINH LUẬN VĂN THẠC SĨ HOÀNG QUÁCH KHOA XÁC ĐỊNH GIÁ BÁN ĐIỆN CỦA NHÀ MÁY ĐIỆN GIÓ TRONG THỊ TRƯỜNG ĐIỆN CÓ XÉT ĐẾN HỖ TRỢ CỦA NHÀ MÁY THỦY ĐIỆN NGÀNH: KỸ THUẬT ĐIỆN - 8520201 Hướng dẫn khoa học: PGS.TS TRƯƠNG VIỆT ANH Tp Hồ Chí Minh, tháng 03/2023 Determination of Profitable Wind Farm Generating Capacity Based on Weibull Distribution of Wind Speed in the Competitive Electricity Market Pham Quoc Khanh1(B) , Thanh Long Duong1 , Hoang Quach Khoa2 , and Viet-Anh Truong3 Faculty of Electrical Engineering Technology, Industrial University of Ho Chi Minh City (IUH), Ho Chi Minh City, Vietnam phamquockhanh@iuh.edu.vn Ho Ho Chi Minh City High Voltage Power Network Company, Ho Chi Minh City, Vietnam Faculty of Electrical and Electronics Engineering, University of Technology and Education, Ho Chi Minh City, Vietnam Abstract Wind power is developing rapidly because of the need to develop renewable energy to replace fossil energy gradually However, the electricity supplied by wind power plants varies continuously with the outside wind speed, which makes energy insecure Therefore, when participating in the deregulated electricity market, wind power plants will suffer significant losses when they not guarantee the capacity according to the signed power generation contracts Many methods have been proposed, such as forecasting wind capacity, energy storage, and combining other power generation sources to solve this disadvantage The paper proposes a method to determine the optimal wind capacity for profit based on the Weibull distribution The proposed method allows determining which wind capacity is most profitable considering the probability of not guaranteeing the contract capacity The effectiveness of the proposed method is tested through simulation using Matlab/Matpower software Simulation results allow using local weather forecasts to determine the amount of electricity sold to get the most revenue for wind farms Keywords: Wind power · Deregulated electricity markets · Probabilistic forecasting · Weibull distribution Introduction Fossil energy faces significant problems such as environmental pollution, rising fuel prices, and increasingly difficult to exploit Renewable energy development policies have been issued by governments to encourage the participation of renewable energy plants in the power system Among renewable energy sources, wind energy has been promoted in recent years, with many factories being built and put into commercial operation © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 Y.-P Huang et al (Eds.): GTSD 2022, LNNS 567, pp 389–400, 2023 https://doi.org/10.1007/978-3-031-19694-2_35 390 P Q Khanh et al With the disadvantage of not being able to store fuel and being utterly dependent on external natural conditions, wind power plants always face the problem of not ensuring the power supply as committed to customers As the penetration rate of wind power increases, so does this shortfall The instantaneous capacity shortage of the power system is the leading cause of power system insecurity; the risk of power supply interruption also increases In order to reduce the negative impact on the security of the power system, electricity buyers always offer higher compensation than the purchase price for the shortfall in generating capacity committed in the power purchase agreement The amount of compensation is much more significant than the selling price of electricity, which has reduced the profit of wind power plants This significant drawback reduces investor interest in wind power development in competitive power markets In order to improve the profitability of wind power plants when there is no guarantee of the required generating capacity, several solutions are proposed, such as forecasting wind speed in the short term using energy storage systems Volume, and coordinate with other power plants Studies [1, 2] have presented short-term wind speed forecasting results, an essential premise in wind power capacity forecasting Botterud [3] proposed the application of short-term wind speed forecasts to the electricity market Nielsen [4] recommends using quantile regression to extend an existing wind power forecasting system with probabilistic forecasts Studies on short-term wind speed forecasting help to recommend more accurate wind power generation capacity, minimizing the amount of compensation when there is a shortage of vital capacity However, the forecast does not show which wind speed obtains the greatest profit Research [5, 6] proposes a combination of wind and hydroelectric power plants Hydroelectric power plants have several advantages when they are the most flexible technologies in performing continuous start-ups and shutdowns without a significant detrimental effect on the equipment lifetime, and their load variation speed is high On the other hand, using auxiliary sources requires huge costs when constructing these energy sources This is only reasonable when ancillary energy sources are near wind power plants This is appropriate when diversifying power generation sources will help reduce electricity costs if it is on the side of electricity buyers When no auxiliary energy sources are available, the solution of using energy storage units for wind power plants is proposed as an alternative An Energy Storage System (ESS) can Exible charge and discharge Recent development and advances in the ESS and power electronic technologies have made the application of energy storage technologies a viable solution for modern power applications [7] Many studies have been carried out to determine the capacity and capacity of ESS in solving the shortage of electricity capacity for wind power plants [8, 9] The storage units have a significant advantage in fast construction, compact construction space However, energy storage costs are often very high, so this is the last resort when considering power capacity stabilization solutions for renewable energy sources To reduce initial construction costs and improve competitive advantage, we need to cut costs for energy storage units or ancillary power plants The first concern is how much generating capacity must be sold so that the total revenue (electricity sales minus contract violation penalties) is the largest Some studies on electricity prices have been proposed Determination of Profitable Wind Farm Generating Capacity 391 in recent years [10–12] and focus on electricity prices for different wind power capacity levels The article proposes a method to determine the generated wind power capacity based on the Weibull probability distribution of wind speed Then, the generated wind power capacity, considering the possibility of contractual compensation for the shortfall, is proposed to the customer The proposed profit point calculation method allows the wind power plant to be more proactive in determining the optimal profit point according to actual environmental conditions and accept power generation to supply customers at this capacity level In addition to the introduction mentioned in this part, the paper is organized into several main parts, including Part presents the problem of wind energy and wind power obtained by wind speed Part presents the method of determining the wind power selling capacity in the future based on the Weibull probability distribution Part is the calculation results for the proposed method of determining wind power prices, and the last part is the conclusion Power Capacity of Wind Power Plant The Mechanical output power of the turbine obtained from the wind turbine following equation Pmech = ρAR Cp (λ, β)ω3 (W ) (1) where: Cp ρ λ A β ω Performance coefficient of the turbine Air density (kg/m3 ) Tip speed ratio of the rotor blade tip speed to wind speed Turbine swept area Blade pitch angle (°) Wind speed (m/s) A generic equation is used to model Cp(λ, β) This equation, based on the modeling turbine characteristics of [13], is shown in (2) The results of the values of Cp(λ, β) at different values of λ and β are shown in Fig −21 116 − 0.4β − e λi + 0.0068λ (2) CP (λ, β) = 0.5176 λi 0.035 − = (3) λi λ + 0.08β + β3 The maximum value of cp (cpmax = 0.48) is achieved for β = degree and for λ = 8.1 This particular value of λ is defined as the nominal value (λ_nom) With a turbine at constant air density, the output power of the wind turbine depends only on the surface wind speed and the power factor Cp as in (4) with a constant m determined by (5) Pmech = ρAR CP (λ, β)ω3 = mCP ω3 (4) 392 P Q Khanh et al Fig Power Coefficient characteristic Cp(λ, β) m= ρπ R2b (5) The output power of a wind turbine significantly varies with wind speed Therefore, a power curve aids in wind energy prediction without the wind turbine generating system [14] The minimum speed at which the turbine delivers good power is known as the cut-in speed (VC ) Rated speed (VR ) is the wind speed at which the rated power, which is the maximum output power of the electrical generator, is obtained The cut-out speed (VF ) is usually limited by engineering design and safety constraints (Fig 2) Fig Typical wind turbine power curve of wind turbine [15] Most variable speed wind turbines are equipped with pitch angle controls The wind turbine controls the pitch angle to produce the most optimal power when the speed is less than rated When the wind speed is above the rated speed, it is necessary to control the pitch angle to reduce the mechanical power to the wind turbine Pitch angle control combined with speed control method to have a more comprehensive adjustment range Determination of Profitable Wind Farm Generating Capacity 393 Determination of the Maximum Profit Point of the Wind Farm 3.1 Calculating Electricity Economy for Wind Power Plants Wind speed characteristics are time-varying, not cyclical, can increase or decrease continuously depending on temperature and weather changes There are two distribution functions for wind speed, the Weibull distribution, and the Rayleigh distribution The Weibull distribution of wind speed [16] is often used in short-term wind speed forecasting studies The range of wind speeds throughout the work area is divided into n different levels and call these wind speeds vi (i = 1, 2,…, n) The probability of the wind speed vi is determined by (6) where k and c are the two coefficients in the Weibull distribution pv (vi ) = k vi k−1 − vi k e c c c (6) Let PWi be the largest wind power capacity obtained from wind energy with speed vi , PWi is determined by (7) All wind speeds greater than vi generate wind power PWi Thus, the probability of PWi power is equal to the sum of the probabilities of wind speeds greater than or equal to vi The probability of obtaining PWi capacity is determined (8), and the sales obtained under this condition are determined by (9) where Pprice is the selling price per MWh of electricity ⎧ vi ≤ VC ⎨ (7) PWi = ρπ Rb CP vi VC < vi < VR ⎩ Pe,rate VR ≤ vi ≤ VF pPWi = n pv (vk ) (8) k=i Ci = pPWi Pprice PWi = n pv (vk ).Pprice PWi (9) k=i When the wind speed vj is lower than the desired wind speed vi, the obtained wind power capacity PWj will be lower than the desired wind power capacity PWi At this time, the shortfall will have to compensate the customer for the loss Call the shortfall capacity compensation coefficient Kpt, the amount to be compensated to the customer will be calculated according to (10) (10) Fpt,PWj = Kpt Pprice PWi − PWj Considering the probability that the wind power plant works at wind speed vj , the amount to be compensated to the customer is determined according to (11) (11) Fpt,j = pv vj Fpt,PWj = pv vj Kpt Pprice PWi − PWj The amount of electricity sold at Pprice with wind power capacity PWj is: FPWj = pv vj Pprice PWj (12) 394 P Q Khanh et al Revenue of a wind power plant if operating at wind speed vj is determined by the amount of electricity sold minus the amount to be compensated to customers and shown in (13) (13) Cj = FPWj − Fpt,j = pv vj Pprice PWj − pv vj Kpt Pprice PWi − PWj In the case of wind power plants, compensation costs due to the shortage of power supply to customers only appear when the operating wind speed is lower than the desired wind speed Total sales in case of compensation costs are determined according to (14) Cj = i−1 pv vj Pprice PWj − pv vj Kpt Pprice PWi − PWj (14) j=1 Thus, the revenue of a wind power plant when generating electricity with a capacity of PWi is the sum of revenue when operating at different wind speeds and is expressed in (15) CPWi = Ci + Cj = + n k=i i−1 pv (vk ) · Pprice · PWi pv vj · Pprice · PWj − pv vj · Kpt · Pprice · PWi − PWj j=1 (15) The wind power plant will choose the generating capacity with the largest revenue value to sign a power sale contract based on the obtained results The profit based on the wind probability is maximum at the selected power level 3.2 Flow Chart of Determining the Maximum Profit Point of a Wind Farm The flow chart for the algorithm for determining the selling power based on the Weibull distribution is shown in Fig Step 1: Determine the actual wind speed levels This step selects the wind speed in the range [0–24] m/s Step 2: Calculate the wind probability according to the Weibull function Based on shortterm wind speed forecasts, the probability of wind at a particular speed is obtained This probability has a Weibull distribution and is estimated based on (6) Step 3: Calculate the revenue of the wind power plant for each different generating capacity Revenue is calculated according to the equations from (8) to (15) Step 4: update the result Revenue results for each desired wind speed for power generation are determined Necessary values such as generating capacity with the highest revenue are updated Determination of Profitable Wind Farm Generating Capacity 395 BEGIN Determine the actual wind speed levels vi (i=1,2, ,n) Determine the PWi values corresponding to vi (8) Calculate the wind probability p(v i) according to the Weibull function (6) Calculate revenue of wind power plant at generating capacity PWi (i=1,2, ,n) (9) ‒ (16) Update data END Fig Flow chart of profit calculation program of the wind farm Simulation Results 4.1 Simulation Modeling The paper applies the proposed strategies for wind power trading on the IEEE 9-bus test system [17] A Diagram of the IEEE 9-bus test system is shown in Fig IEEE 9-bus test system parameters are referred to reference [17] The wind farm is connected to bus of this transmission system In this simulation, the plant capacity is 150 MW with 100 turbines, with a rated capacity of 1.5 MW for each turbine Simulation results of wind farm output power for each different wind speed level are shown in Fig From the figure, it can be seen that the wind farm capacity reaches 150 MW as required at rated capacity Determining wind power generation capacity for maximum profit is applied to three different wind distribution cases and is detailed in the following sections 4.2 Weibull Distribution of Wind Speed with C = and k = 2.1 Figure shows the wind speed distribution when the average wind is m/s with c = and k = 2, The corresponding power per turbine for each desired output power level is determined based on this wind distribution, as shown in Fig When the average wind is m/s, the profit at various proposed capacity levels taking into account the power shortage compensation for customers, is shown in Fig The 396 P Q Khanh et al Fig Diagram of the IEEE 9-bus test system Fig Power capacity of 150 MW wind power plant at different wind speeds Fig Wind speed distribution at the average wind is m/s highest profit is obtained at a power level equivalent to a wind speed of m/s, and the maximum profit obtained is 176,1044 Determination of Profitable Wind Farm Generating Capacity 397 Fig Output power probability distribution when the average wind is m/s Fig Profit profit at various proposed capacities when the average wind is m/s 4.3 Weibull Distribution of Wind Speed with C = 11 and k = 2.1 Figure shows the wind speed distribution when the average wind is m/s with c = 11 and k = 2.1 The corresponding power per turbine for each desired output power level is determined based on this wind distribution, as shown in Fig 10 When the average wind is m/s, the profit at various proposed capacity levels taking into account the power shortage compensation for customers, is shown in Fig 11 The highest profit is obtained at a power level equivalent to a wind speed of m/s, and the maximum profit obtained is 586,71 4.4 Weibull Distribution of Wind Speed with C = 15 and k = 2.1 Figure 12 shows the wind speed distribution when the average wind is 12 m/s with c = 15 and k = 2, Based on this wind distribution, the corresponding power per turbine for each desired output power level is also determined in Fig 13 When the average wind is 12 m/s, the profit at various proposed capacity levels taking into account the power shortage compensation for customers, is shown in Fig 14 The highest profit is obtained at a power level equivalent to the wind speed of 10 m/s, and the maximum profit obtained is 1055,16 398 P Q Khanh et al Fig Distribution of wind speed when the average wind is m/s Fig 10 Output power probability distribution when the average wind is m/s Fig 11 Profit at various proposed capacities when the average wind is m/s Conclusions This paper proposes a method to determine the generating capacity of wind power plants based on the Weibull distribution for wind speed The results obtained allow wind power plants to determine the most profitable capacity 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