Energy Engineering - Energy Conversion A

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PROJECT 1 ECONOMICS OF POWER PLANT S 2 Index of Contents Abstract ................................ ................................ ................................ ................................ ............................. 3 Fixed Costs Evaluation ................................ ................................ ................................ ................................ ....... 4 Wind farms investment costs (IC) evaluation: ................................ ................................ .............................. 5 Evaluation of the yearly allocated investment cost ................................ ................................ ...................... 5 Integral efficiency evaluation ................................ ................................ ................................ ........................ 6 Variable costs e valuation ................................ ................................ ................................ ............................... 7 Incentive costs evaluation ................................ ................................ ................................ ............................. 7 Evaluation of the externalities ................................ ................................ ................................ ...................... 9 Carbon tax ................................ ................................ ................................ ................................ ................... 11 Fuel cost evaluation ................................ ................................ ................................ ................................ ..... 11 Case A ................................ ................................ ................................ ................................ .............................. 13 Comments ................................ ................................ ................................ ................................ ............... 14 Case B ................................ ................................ ................................ ................................ .............................. 15 Comments ................................ ................................ ................................ ................................ ............... 15 Case C ................................ ................................ ................................ ................................ .............................. 16 Comments ................................ ................................ ................................ ................................ ............... 16 Case D ................................ ................................ ................................ ................................ .............................. 17 Abstract This analysis aims to evaluate the yearly cost of the energy production referred to the kWh as unit of energy [ € �� ∗���� ] for power plants adopting different technologies. Eventually, through the exploitation of a summarizing char t, the reader will be able to easily compare the results for the given technologies. Hereunder, the list of the technologies of interest: • Hydroelect ric : hydroelectric pumped storage power plant ; • PWR : nuclear power plant with Pressurized Water Reactor ; • NGCC : Natural Gas -fired Combined Cycle ; • HDGT : natural gas -fired Heavy -Duty Gas Turbine in simple cycle ; • ADGT : natural gas -fired Aero -Derivative Gas Tu rbine in simple cycle ; • NGSC : Natural Gas -fired Steam Cycle ; • CHP : Combined Heat and Power (CHP) natural -gas fired Combined Cycle ; • PCSC : Pulverized Coal Steam Cycle + FGD (Flue Gas Desulphurization) ; • USC : pulverised coal Ultra -Super Critical Steam Cycle + FGD ; • CSP : Concentrated Solar power Plant ( parabolic trough, diathermic oil, steam cycle) ; • Wind : onshore wind farm 1. For each power plant , a similar general approach will be followed: • The overall investment costs will be calculated, being slightly different in type and magnitude according to the considered technology, and a fraction will be allocated to each year through the carrying charge factor (CCF); • Fixed costs allocated to each year will be identified : they take into account the alloc ated fraction of the investment costs and fixed costs of operation and maintenance (O&M) ; • Variable costs will be evaluated , referred to the electric kWh : they consider the variable fraction of the O&M costs, cost of fuel, incentives, externalities, and carbon tax. Even for the variable costs, not all the power plants account all the hereabove mentioned class es of cost; • The “Levelized Cost Of Energy” (LCOE ) will be quantified , and so the cost per kWh of energy generated ; • The plant total specific cost specific to nominal power will be plotted as a function of the plant equivalent working hours. 1 *for the onshore wind farm, we will consider two different arrangements. The first (marked as “Onshore wind”) with a wind velocity of 8 [� �] and the last one (marked as “Onshore wind 2”) with a wind velocity of 16 [� �] Politecnico di Milano 1863 - Energy Engineering page 4 An opening set of data has been provided and reported below: The investment costs (IC) have been reported in the first column. For almost every kin d of power plant the IC has been provided initially. However, for the CSP and the wind farms, they have been suitably computed according to the plant peculiarities and already reported in the hereabove summarizing table . Fixed Costs Evaluation They must be computed as the sum between the yearly allocated fraction of the investment cost and the fixed part of the O&M costs. �������������� = �������������� + �������&�,�������� [ € �� ∙���� ] CSP investment cost (IC) evaluation For the CSP power plant IC we need to account: • Power island cost of 600 [ € �� ��� ]; • Expenses related to the troughs section (including the balance of plant ), equal to 400 [€ �2]; • Expenses related to the field of 5 [€ �2]; • A shadow coefficient (�������ℎ���� ) of 5 when determining the field area ; • Direct irradiation of 0,8 [�� �2]; ��� ���� = �������ℎ���� ���������� ������ ∙������� [ € �� ��� ] ��� ����� = ����������� ������ ∙������� [ € �� ��� ] ��� ����� = 600 [ € �� ��� ] ������� = ��� ����� + ��� ���� + ��� ����� Fixed (€/kWy) Variable (€/MWhe) Hydroelectric 700 0,0905 3000 11 1 0,71 PWR 4000 0,0989 7600 53 1,5 0,35 NGCC 600 0,1053 8000 12,3 1,2 0,61 HDGT 250 0,1009 8000 6 9 0,35 ADGT 300 0,1009 8000 8 9 0,4 NGSC 800 0,1076 7500 13 2 0,41 PCSC+FGD 1300 0,1124 7500 17,5 2,5 0,39 USC+FGD 1450 0,1124 7500 17,5 3 0,44 CSP 2725 0,0977 2100 11 3 0,25 Onshore Wind 6654,2257 0,1053 2000 8 0,2 0,42 Onshore Wind 2 831,77821 0,1053 2000 8 0,2 0,42 0,43 Nominal Electric Efficiency 5500 0,1175 700 CHP Power Plant Technology Investment Cost (€/kWnom) Carring Charge Factor (1/y) Typical Equivalent Hours (h/y) 1,5 16 Operation & Mainteinance (€/kWy) Politecnico di Milano 1863 - Energy Engineering page 5 The efficiency used is the nominal e fficiency of the power plant, and not the integral one . Wind farm s investment cost s (IC) evaluation : The wind farm investment cost is a function of the spanned area of the turbines . The evaluation could be done by inverting the net power formula here below: ��= 1 2�������������� ������������� ��������������3 �������� [�� ] Where the value of 1kW has been given to �� and the density of air has been computed using the ideal gas equation, assumin g the ambient air in standard conditions (T=288.15 [K] and P=101325 [Pa]). The relation for ��� ����� is the following: ��� ����� = ������������������ ������������� �� [€ �� ] ������������������ = 850 [€ �2] Here it is possible to appreciate the eff ect of wind speed: doubling it will result in an eight times smaller spanned area and, therefore, in the same reduction for ��� ����� . Finally, it is important to note that we must add to the investment cost a field purchase cost, which is approximately 2% of the overnight interment, and insurance and general expenses, amounting to 1%. Evaluation of the yearly allocated investment cost After havi ng computed the IC of each plan, we have to evaluate the total investment cost ( ��� ��� ) accounting the field purchase and the insurance costs, weighted respectively as the 2% and the 1% of the IC. Attention must be given to the CSP plant, whose field purchase costs are null. Finally, by multiplying the total investment by the carrying charge factor (CCF), the yearly allocate d cost referred the kWh is found . ��� ��� = ��� ����� + ��� ���������� + ��� �������������� + ⋯ [€ �� ] ��������������= ������������������ ∙��� ��� [ € �� ∗���� ] Finally, the overall yearly allocated fixed costs have been evaluated. Hydro PWR NGCC HDGT ADGT NGSC CHP PCSC+FGD USC+FGD CSP O.W OW 2 721 4120 618 257,5 309 824 721 1339 1493,5 2752,25 6853,852 856,7316 IC (field + insurance) [€/kWnom] Hydro PWR NGCC HDGT ADGT NGSC CHP PCSC+FGD USC+FGD CSP O.W OW 2 65,251 407,47 65,0754 25,9818 31,2 88,662 84,72 150,5036 167,8694 268,8948 721,7107 90,21383 Yearly allocated cost of the investment (C_inv) [ €/(kWh*year)] Hydro PWR NGCC HDGT ADGT NGSC CHP PCSC+FGD USC+FGD CSP OW OW 2 76,251 460,47 77,3754 31,9818 39,2 101,66 100,7 168,0036 185,3694 279,8948 729,7107 98,21383 Fixed costs (C_fix) [ €/(kWh*year)] Politecnico di Milano 1863 - Energy Engineering page 6 Integral efficiency evaluation The nominal efficiency of the power plant is affected by different penalizations due to aging, partial load operation, wearing, fouling and other phenomena. It is required to evaluate the integral efficiency of the plant over the entire year, accounting the average efficiency penalties. For gas turbine -based power plants, the average efficiency penalty is of the 5%. For steam turbine -based powers cycles and the other technologies, it is of the 3%. For combined cycles, the total efficiency penalty is attributable to both the turbines, according to the formula reported below: ∆�������� ������������� = 0.05 ∆��������� �������������� = 0.03 ∆������������������� _����� = 2 3∙∆�������� ������������� + 1 3∙∆���������� ������������� Hydro PWR NGCC HDGT ADGT NGSC CHP PCSC+FGD USC+FGD CSP OW OW 2 0,6887 0,3395 0,58357 0,3325 0,38 0,3977 0,411 0,3783 0,4268 0,2425 0,4074 0,4074 η electric average Politecnico di Milano 1863 - Energy Engineering page 7 Variable costs evaluation Variable costs comp rise any c ost item related to power generation once the power plant has been started, from those being strictly related to the energy output (such as the fuel cost, or the variable O&M cost ) up to taxes, externalities and incentives . Each of the last three items can have a significa nt effect on the economic competitiveness of the plant , making the variable costs vary greatly . ��������� = �������&�,��� + ����� ��������,������� + �������������� + �������� 2+ ��������� + ⋯ [ € �� ℎ��] • pfuel : takes into account the cost of the fuel adopted by the plant; • ηel,average : it is the integral of the electric efficiency over a certain time period of reference (typically one year, as in this case); • Cinc: cost of incentives , which in the analysis is actually a profit for the power plant ; • CCO2 : an annual tax , based on the carbon dioxide emission, aiming to compensate the impact of CO 2 emissions in terms of social costs; • Cext: cost of the externalities . In our case, it is price paid by the power plant to a third defenceless and unprotected part for the disadvantages caused to it by the emission of pollutants (NO X, SO X, PM); Incentive costs evaluation The state provides incentives to encourage the penetr ation of renewable power generation technologies, so only hydroelectric, CSP and the two Wind technologies are considered in this analysis. The incentives are considered constant (so they already incorporate the inflation rate) among a time span of 15 year s and equal to 100€/MWh per year. Knowing the inflation rate (2%) and the discount rate (9%) over the lifetime, it is possible to evaluate the lifetime revenue from incentives. In order to obtain an equivalent annual rate of the revenue ( �������������� ) it is ne cessary to rearrange every annual income due to the incentives in a wider lifespan specific to each technology. It is assumed that this value is constant along the years. The Net Present Value (NPV) method to calculate lifetime revenue from incentives come s in handy, as in the following formula: ∑ ��������� 15 �=1 (1+ ������)� (1+ ������)�= ∑ �������������� (1+ ������)� (1+ ������)� �� �=1 Where: • ��������� is the nominal value of incentives; • ������ is the inflation rate; • ������ is the discount rate; • �� ( ��������� T�������� ) varies depending on the technology, notabl e is 60 years for hydroelectric, 30 for CSP and 25 for Wind. The following image shows the logic behind the NPV calculation reported above: the goal is to spread the effect of the incentives, which last only fifteen years , on the whole lifetime of the power plants, thus following the yearly -approach of the analysis performed in this report. Politecnico di Milano 1863 - Energy Engineering page 8 The revenue is a negative cost in the cost analysis, because the incentives are an amount of money that the owner of the power plan t receives. In order to obtain the updated ��������� , it’s therefore necessary to subtract the �������������� term from ��������� . Politecnico di Milano 1863 - Energy Engineering page 9 Evaluation of the externalities For any power plant the following procedure has been followed: CASE 1: pollutant with unknown concentration in the exhaust • Evaluation of the fuel mass flow rate referred to the energy unit , expressed in [ �� �� ℎ��]; • Evaluation of the mass flow rate referred to the energy unit of the pollutant in the fuel through the knowledge of the fuel composition on mass basis; • Evaluation of the moles flow rate of pollutant in the fuel; • Evaluation of the molar flow rate of pollutan t in the combustion exhaust through a chemical balance under stoichiometric conditions , before the FDG; • Evaluation of the molar flow rate of pollutant at the stack, accounting the FDG efficiency; • Evaluation of the cost due to the pollutant pouring in the e nvironment. CASE 2: pollutant with known concentration in the exhaust • Evaluation of the fuel mass flow rate referred to the energy unit, expressed in [ �� �� ℎ��]; • Evaluation of the molar flow rate referred to the energy unit of each compound comprising the fuel through the knowledge of fuel composition; • Evaluation of the molar flow rate referred to the energy unit of each compound of the exhausts through chemical balances under stoichiometric conditions , taking into account the inert N 2; • Evaluation of the volumetric flow rate referred to the energy unit of each component in the exhaust and of the overall volumetric flow rate, in nominal condition s; • Evaluation of the dry, ash free exhaust volumetric flow rate re ferred to the energy unit, with a X% percentage of O 2; • Evaluation of the cost due to the pollutant pouring in the environment. All the evaluations will be carried out under the assumption of complete and stoichiometric combustion, treating air and exhaust gases as ideal gases , and air composed by 79% of N 2 and 21% of O 2 on molar basis . Politecnico di Milano 1863 - Energy Engineering page 10 CASE 1 ����� = 3.6 ��� ∙��������,������� [�� ���� �� ℎ��] ���������� = ����� ∙����� . �� ��������� [���� ��������� �� ℎ�� ] ���������� + �2→ �� 2 ⟹ ��� 2= �� ���2= ���2∙� ���2 �������= ��∙(1− ������������� )∙��������� ,� [ € �� ℎ��] CASE 2 ����� = 3.6 ��� ∙��������,������� [�� ���� �� ℎ��] � ������−�ℎ ���� ��������� ← = ����� ∙�������−�ℎ �� ������−�ℎ [���� ������−�ℎ �� ℎ�� ] (Natural gas -fired power plants) ������� 4+ 2�2→ ������� 2+ 2�2� ������2�6+ 7 2�2→ 2������� 2+ 3�2� ��2→ = 79 21 ��2← + ��2,���� ← [���� �� ℎ��] ��2� → = 2��� 4 ← + 3��2�6 ← [���� �� ℎ��] ��� 2 → = ��� 4 ← + 2��2�6 ← [���� �� ℎ��] ∗∗ (Coal -based power plants) ������ + �2→ ������� 2 �2+ 0.5∙�2→ �2� �+ �2→ �� 2 ��� 2 → = ��← ∗∗ ��2,�������� ← = ��← + 0.5∙��2← + ��← − ��2,���� ← ��2→ = ��2← + 79 21 ��2,�������� ← ��� 2→ = ��← ��2� → = ��2← ��2→ = 0 [���� �� ℎ��] ������������−�ℎ → = �������−�ℎ → ∙�� � [�� 3 �� ℎ��] ��������������→ = ( ∑ ������������→ �° ������������ ������=1 )− ��������ℎ�� → − �����������→ = = �������2→ + �������� 2→ + (1− ������������� )∙��������2→ [�� 3 �� ℎ��] �������������� ,�% → = ��������������→ ∙21 − ��2,������ 21 − �% [�� 3 �� ℎ��] �������= �������������� ,�% ∙[�]∙��������� ,� [ € �� ℎ��] Politecnico di Milano 1863 - Energy Engineering page 11 Carbon tax Given ��� 2→ the conversion of the tax is calculated through: �������� 2= ������������ ��� ∙10 −3∙��� ������ → ∙�� �� 2 Fuel cost evaluation The subsequent data have been provided for the reach of our purpose. Different approaches have been followed as a function of the considered fluid . Refined considerations have been considered when required by specific power plants. Other facts which to pay attention are: • Dollar/Euro exchange rate is equal to 1.20 [$ €]; • Standa rd conditions are set at T=288.15 [K] and P=101325 [Pa]; • For combined cycle (C HP) an additional term in the evaluation of the fuel price must be considered, accounting the savings of natural gas that would have been burned using a boiler instead of a combi ned arrangement. Politecnico di Milano 1863 - Energy Engineering page 12 Natural gas • Evaluation of the mixture mean molar mass [�� ���� ] and LHV [������� �� ]; • Evaluation of the specific volume under standard conditions; • Evaluation of the fuel price [ € �� ℎ��]. �� �������� = (∑ ������� �� ������ # ������������ ������=1 ) −1 [ �� ���� ] ��� �������� = ∑ ������� # ������������ ������=1 ∗��� ������ [�� �� ] �������������� = �� �� �������� � [������� 3 �� ] ����� = ���� ∗�������������� ��� �������� ∗3.6 Coal Since we already have the prices for both the raw material and the naval transport and also we know coal LHV, we only need a conversion up to the desired measurement units and a ration between them ����� = ���� �������� + ���� ��������� �� ����� ∗10 −3 1.2 Nuclear fuel ����� = ���� ∗3600 10 6 CHP We have to highlight the savings due to the adoption of a combined arrangement. Furthermore, the amount of the savings has to be evaluate using the “Thermal -use Natural Gas” price, for clear r easons. Hence, from the natural gas price given by the procedure hereabove listed, we have to subtract the savings term. Taking into account a boiler efficiency of ����������������� = 0.9 and a n annual thermal efficiency of �������ℎ����� = 0.33 , the savings term is computed as ������������ = ��� ,�ℎ �������ℎ ����������������� ����� ,��� = ����� − ������������ To compute the actual variable co st related to fuel expenses, the efficiency of the cycle must be considered , since only considering the LHV would mean that the plant has unitary efficiency: ��������� ,���� = ����� ��������,������� Hydro PWR NGCC HDGT ADGT NGSC CHP PCSC+FGD USC+FGD CSP OW OW2 0,03 0,0036 0,03167 0,03167 0,03167 0,042 0,01619 0,01130 0,01130 0 0 0 Fuel price [€/kWhe] Hydro PWR NGCC HDGT ADGT NGSC CHP PCSC+FGD USC+FGD CSP OW OW2 0,04356 0,01060 0,05427 0,09525 0,08335 0,10561 0,03935 0,02986 0,02647 0 0 0 Fuel price/ η_el,average [€/kWhe] Politecnico di Milano 1863 - Energy Engineering page 13 After having described how to manage every issue related to both the fixed and the variable costs and how to evaluate each of their components, tables reporting the final results of the economic evaluation will be turned up. Subsequently, sequential plots will be shown, considering different sets of cost items, and highlighting the variation of the “Total specific annual cost – Annual equivalent operating hours” bond with the considered set of cost items. The aim is to focus on how each element comprising f ixed and variable costs can affect the LCOE and consequently the choice of pursuing the investment on a certain technology. Case A The first case will report what the “Cost -Equivalent hours” bond would be without any kind of incentives, externalities, of c arbon tax. In this first “base case” only the costs related to the fixed initial required investment, and those linked to the plant operation will be considered. More specifically, we are considering the yearly allocated investment costs, the fuel price (a lready evaluated and reported a few pages hereabove) and the O&M costs. Attention must be paid in the conversion of the variable fraction of the O&M costs from [MWhe] to [KWhe]. -200 0 200 400 600 800 1000 0 1000 2000 3000 4000 5000 6000 7000 8000 Total Costs Typical equivalent hours Hydroelectric PWR NGCC HDGT ADGT NGSC CHP PCSC+FGD USC+FGD CSP Onshore Wind Onshore Wind 2Hydroelectric 721 65,2505 0 76,2505 0,03 0,0445603 133,68099 209,93149 0,0699772 PWR 4120 407,468 0 460,468 0,0036 0,0121038 91,989102 552,4571 0,0726917 NGCC 618 65,0754 0 77,3754 0,0316717 0,0554726 443,78107 521,15647 0,0651446 HDGT 257,5 25,98175 0 31,98175 0,0316717 0,1042532 834,02587 866,00762 0,108251 ADGT 309 31,1781 0 39,1781 0,0316717 0,0923466 738,77263 777,95073 0,0972438 NGSC 824 88,6624 0 101,6624 0,042 0,1076072 807,05431 908,71671 0,1211622 PCSC+FGD 1339 150,5036 0 168,0036 0,0112971 0,0323627 242,72048 410,72408 0,0547632 USC+FGD 1493,5 167,8694 0 185,3694 0,0112971 0,0294692 221,01929 406,38869 0,0541852 CSP 2752,25 268,894825 0 279,89483 0 0,003 6,3 286,19483 0,1362833 Onshore Wind 6853,852472 721,7106653 0 729,71067 0 0,0002 0,4 730,11067 0,3650553 Onshore Wind 2 856,731559 90,21383316 0 98,213833 0 0,0002 0,4 98,613833 0,0493069 Power Plant Technology CHP Fuel (€/kWhe) Fixed Cost (€/kWy) Investment Cost (€/kWy) Other Fixed Cost (€/kWy) Variable Cost (per hour) (€/kWhe) Variable Cost (per year) (€/kWy) Total Cost (€/kWy) LCOE Investment Cost (field+ins.) (€/kWnom) 100,7175 0 84,7175 721 0,0591634 325,39891 224,68141 0,0408512 0,0161878 Politecnico di Milano 1863 - Energy Engineering page 14 Comments Using the LCOE as a measure of comparison, it can be highlighte d that: • A wind farm is convenient only when there is a certain guaranteed wind speed, as can be surmised from the fact that the LCOE of a wind farm with wind speed of 8 m/s is the highest among our analysis; • Of the conventional power plants, the coal based ones have the lowest LCOE, due to the low cost of the fuel and the high equivalent working hours; • While the nuclear power plant has by far the highest investment costs (excluding the improbable wind farm), its LCOE is lower than most natural gas fueled po wer plants, due to the fact that nuclear fuel is the cheapest among all conventional fuels; Politecnico di Milano 1863 - Energy Engineering page 15 Case B In this case the effect of the incentives will be reckoned. Of particular importance is how the wind farms are affected by their more than appreciable presence, which makes this investment more temping. The fixed costs will obviously remain unchanged, so they will not be further reported for sake of redundancy Comments • The CSP plant , thanks to the incentives, now becomes competitive with the other technologies; • The wind farm now has a negative LCOE, which means that producers will be paid to generate electricity through a wind turbine; • A detail to remember is that while renewables ca n be promoted through incentives , their application is still dependant on the right location and atmospheric condition, while most of the time a fossil fuel power plant has no need of that, since fuel supply lines (like gas ducts) are well developed; -200 0 200 400 600 800 1000 0 1000 2000 3000 4000 5000 6000 7000 8000 Total Costs Typical equivalent hours Hydroelectric PWR NGCC HDGT ADGT NGSC CHP PCSC+FGD USC+FGD CSP Onshore Wind Onshore Wind 2Hydroelectric 0,064248313 -0,019688 -59,063944 17,186556 0,0057289 PWR 0 0,0121038 91,989102 552,4571 0,0726917 NGCC 0 0,0554726 443,78107 521,15647 0,0651446 HDGT 0 0,1042532 834,02587 866,00762 0,108251 ADGT 0 0,0923466 738,77263 777,95073 0,0972438 NGSC 0 0,1076072 807,05431 908,71671 0,1211622 PCSC+FGD 0 0,0323627 242,72048 410,72408 0,0547632 USC+FGD 0 0,0294692 221,01929 406,38869 0,0541852 CSP 0,073 -0,07 -147 132,89483 0,0632833 Onshore Wind 0,077865243 -0,0776652 -155,33049 574,38018 0,2871901 Onshore Wind 2 0,077865243 -0,0776652 -155,33049 -57,116652 -0,0285583 Power Plant Technology Total Cost (€/kWy) Variable Cost (incentives) (€/kWhe) LCOE Variable Cost (per hour) (€/kWhe) Variable Cost (per year) (€/kWy) 0,0591634 325,39891 224,68141 0,0408512 0 CHP Politecnico di Milano 1863 - Energy Engineering page 16 Case C Hereunder both the externalities and the carbon tax will be accounted, highlighting their effect Comments • Due to their high emissions, coal based power plants are now less convenient than both a combined cycle and a CHP plant ; -200 0 200 400 600 800 1000 0 1000 2000 3000 4000 5000 6000 7000 8000 Total Costs Typical equivalent hours Hydroelectric PWR NGCC HDGT ADGT NGSC CHP PCSC+FGD USC+FGD CSP Onshore Wind Onshore Wind 2Carbon Tax (€/kWHe) Hydroelectric 0 0 -0,019688 -59,063944 17,186556 0,0057289 PWR 0,003000 0 0,015104 114,7891 575,2571 0,0756917 NGCC 0,000309 0,010202 0,065984 527,86851 605,24391 0,0756555 HDGT 0,000572 0,017909 0,122735 981,87751 1013,8593 0,1267324 ADGT 0,000501 0,015671 0,1085179 868,14282 907,32092 0,1134151 NGSC 0,000416 0,016500 0,1245235 933,92656 1035,589 0,1380785 PCSC+FGD 0,002714 0,027137 0,0622133 466,60004 634,60364 0,0846138 USC+FGD 0,002405 0,024053 0,0559277 419,45799 604,82739 0,0806437 CSP 0 0 -0,07 -147 132,89483 0,0632833 Onshore Wind 0 0 -0,0776652 -155,33049 574,38018 0,2871901 Onshore Wind 2 0 0 -0,0776652 -155,33049 -57,116652 -0,0285583 Variable Cost (externalities) (€/kWhe) Variable Cost (per hour) (€/kWhe) Variable Cost (per year) (€/kWy) Total Cost (€/kWy) LCOE Power Plant Technology 0,000438 0,0740743 407,40861 306,69111 0,055762 0,014472 CHP Politecnico di Milano 1863 - Energy Engineering page 17 Case D As a final step, it’s further highlighted the effect of the carbon tax on different technologies, specifically comparing the LCOE of the natural gas combined cycle (N GCC) with the coal based power plant, with the objective of showing how different approaches to the same policies can have a substantial effect on the choice of technologies, focusing on the adopted fuel and emissions; also, this analysis is a way to highl ight how power plants exploiting cleaner fuels have a lower impact on climate change. A first evaluation between two different power plants (PCSC and NGCC) has been carried out with the aim to evaluate the NGCC carbon tax value required to equalize the LCOE of these different technologies. The PSCS plant carbon tax has been considered constant, aiming to put in evidence how much the taxes on carbon emission for plants exploiting cleaner fuels and adopting newer technologies must be higher to match the co st of energy of dirtier fuels. Carbon Tax NGCC 56.33 €/t €/kg 0.08461 0.34015 523.62852 8000 0.05633 LCOE PCSC+FGD CO 2 m. flow NGCC other costs NGCC equivalent hours NGCC he €/kWy kg/kWhe ANALYSIS OF ONE -PRESSURE LEVEL HEAT RECOVERY STEAM CYCLE Index of contents Abstract ................................ ................................ ................................ ................................ ............................. 3 Counterpressure effect; gas turbine power loss; flue gases temperature. ................................ .......................... 5 Vaporization pressure optimization ................................ ................................ ................................ ................... 7 Enthalpy in the expansion process (referred to mass unit) ................................ ................................ ............ 7 Water mass flow rate ................................ ................................ ................................ ................................ ..... 8 Thermodynamic points evaluation ................................ ................................ ................................ ................ 8 Point 9’s - 9’ ................................ ................................ ................................ ................................ .............. 8 Point 9s – 9 ................................ ................................ ................................ ................................ ................ 9 Evaluation of the properties of interest ................................ ................................ ................................ .......... 9 Steam mass flow rate evaluation ................................ ................................ ................................ ............. 10 Net electric energy referred to mass unit ................................ ................................ ................................ . 11 Net electric power output ................................ ................................ ................................ ........................ 11 Recovered heat in the HRSG ................................ ................................ ................................ ................... 11 First law efficiency ................................ ................................ ................................ ................................ .. 11 Heat recovery efficiency ................................ ................................ ................................ .......................... 11 Recovery efficiency ................................ ................................ ................................ ................................ . 11 Trend depiction of the variables of interest ................................ ................................ ................................ . 12 Optimal pressure and related cycle values ................................ ................................ ................................ .. 16 T-Q Diagram ................................ ................................ ................................ ................................ ................... 17 Second law analysis ................................ ................................ ................................ ................................ ......... 18 NOMENCLATU RE ................................ ................................ ................................ ................................ ........ 23 3 Abstract The aim of the report is to display the results of the analysis and optimization process carried out on a one - pressure level heat recovery steam cycle queued to an open -loop Brayton cycle . Thanks to this technological improvement, a dditional power is produced by exploiting the residual energy content of the exhausts downstream the gas turbine. The optimization analysis is performed b y varying the steam cycle evaporation pressure and investigating the dependency and the variation of the other quantities of interest against it. Results will be depicted through charts, highlighting how different evaporation pressures can be chosen in ord er to optimize different cycle parameters. Particularly , it will be investigate d the evaporation pressure leading to the utmost energy content exploitable by the steam cycle working fluid. Previous data have been provided regarding exhaust gases, environme nt, arrangement of the steam cycle and relative to the performances of different components which the combined cycle is comprised by : • Flue gases ��0= ������0+ ������1�1+ ������2�2+ ������3�3+ ������4�4 [ � �������� ] • Gas turbine parameters • Steam cycle arrangement The adiabatic efficiency of the steam turbine if affected by the vapor quality, once it reaches values below 0.98 thought the relation : �������,�� = min [0.93 ;0.93 − (0.98 − �9)] • Environmental parameters a0 [J/kgK] a1 [J/kgK 2] a2 [J/kgK 3] a3 [J/kgK 4] a4 [J/kgK 5] 1081,680 -0,376266 0,0010736 -7,28176E-07 1,58086E-10 ηe l _GT ηme ch_GT ηs _GT 0,99 0,995 0,925 Ts te a m_ma x [K] Pcond [bar] Pde a e ra tor [bar] Ps te a m_ma x [bar] ∆T PP [K] ∆T ap [K] ∆T SC [K] ∆P HRSG [Pa] ∆P/P e co [-] 811,15 0,05 2 200 10 25 10 3000 0,1 Ta mb [K] Pa mb [Pa] 288,15 101325 mex [kg/s] TOT GC [K] ηe l _ge n [-] We l _ge n [MW] MM [kg/kmol] 659,8 847,650 0,3800 241,90 28,40 ηs ,ST [-] ηa ux [-] ηs ,PMP [-] ηe l ,ST [-] ηme ch,ST [-] ηth, ST ge n [-] ηe ,m,PMP [-] See under 0,96 0,8 0,985 0,995 0,99 0,93 4 The reference plant layout is shown below: Due to the adoption of a HRST , a counterpressure of 3000 [Pa] arises at the outlet of the gas turbine. The pressure enhancement causes a reduction in the useful power exploitable by the gas cycle, a negative effect which is however hugely overrode by the additional power generated by the bottoming steam cycle. 5 Counterpressure effect; gas turbine power loss; flue gases temperature . The adoption of the HRSG determines a slight change in the outlet condition of the gas turbine. At the GT discharge pressure is slightly increased, due to the pressure drop (3000 Pa) happening through out the steam generator. The gas turbine TOT will rais e, leading to a reduction of the work extracted by the gas cycle . The very first part of the project deals with finding the new TOT, a fundamental parameter in t he analysis of the Recovery Steam Cycle. Exhausts derived by a combustion process involving air have different composition according to the exploited fuel. However, the chemical species which the exhausts are comprised by have critical values of temperatur e and pressure thanks to which they can be considered ideal gases at the temperature range of interest (190°C to 600°C). Ideal gas la w will therefore be applied , so the enthalpy is considered to be a sole function of temperature. In the evaluation of ��� �� , the Excel solver is exploited to solv e a two -equations -in-two -unknowns system. The unknowns are ��� �� and ��� ���. The enthalpy and entropy variation s must be evaluated according to the ideal gas model adopted ∆ℎ��−��� = ∫ ���� ��� �� ∆ℎ��−��� = ������0(���� − ���)+ ������1 2 (����2 − ���2)+ ������2 3 (����3 − ���3)+ ������3 4 (����4 − ���4)+ ������4 5 (����5 − ���5) ∆��������−��� = ∫ �� � �� ��� �� − � �� ∫ ������� ������ ��� �� ∆��������−��� = ������0ln(���� ��� )+������1(���� −���)+������2 2(����2 −���2)+������3 3(����3 −���3)+������4 4(����4 −���4)− � �� ln (��������� �������� ) • Attention must be paid to the fact that the isentropic efficiency can be evaluated only if adiabatic conditions are verified. In this case study this condition holds, as it generally happens in the last stages of gas turbines. This procedure would not have been correct if the case study had been carried out in the first stages, which are cooled exploiting fresh, compressed air coming from the compressor. 6 Since these integrals will be recalled multiple times, a VBA module has been implemented, in order to be run when needed. Once the ��� �� has been evaluated , the gas turbine wasted work due to the counterpressure effect is evaluable in turn . ∆������̇��������� = ������̇��ℎ[ℎ(��� �� )− ℎ(��� �� )]��������,����������� ℎ,�� The results are reported : As already discussed , although 4 MW is not a small loss, it’s overshadowed by the gain in power produced by the recovery steam cycle. TOT GC [K] TOT CC [K] TOT GCs [K] Wasted Power [MW] 820,65 826,23 820,20 4,228 7 Vaporization pressure optimization The aim of this section is to investigate the evaporation pressure , maximizing the net power out obtainable by the steam cycle. The net power output is computed as follo ws : ������̇��������� = (������̇���� − ������̇��������������������� )��������� = ������̇�(∆ℎ�� ������������������� ℎ�� − ∆ℎ���� �������,������������������� )��������� A variation in the evaporation pressure leads to a variation in all the t hermodynamic properties in each point of the cycle but those provided by the initial data. Some constrain ts must be identified before the evaluation: • The highest temperature of the steam cycle is chosen considering the strictest requirement between the subsequent ones: o Maximum allowable temperature set by materials; o Minimum ∆��� , with �8= ��� �� − ∆��� . • ∆��� = 10 • ∆��� = 10 After the evaluation of ��� ��, complying with the first of the listed points, the maximum temperature of the steam cycle is set at �8= 528 ,08 [������].° . The other constrain ts come from previously given data . Taking into account these constrain ts, it is useful to forecast the general trend of the enthalpy gap across the turbine and the mass flow rate of the steam cycle as functions of the evaporation pressure : Enthalpy in the expansion process (referred to mass unit) The reduced temperat ure at the end of the superheating process is about �8�= 1.238 . Since the fluid is in subcritical condition , �8� will be lower than one ; even if the ideal gas condition is not strictly met for saturated vapor due to the reduced pressure higher than 5%, the super -heating process narrows the vapor to the ideal gas condition . As a result , starting from pressure reasonably low, we can neglect the enthalpy dependency on pressure for ℎ8 intro ducing a slight approximation , consider ing ℎ8 being almost constant with �8 when varying the evaporation pressure. To increase the evaporation pressure and so the pressure at the turbine inlet (preserving both �8 and ����� ) means to lower the vapor quality at the end of the expansion and so to reduce the enthalpy content downstream the expander. The decreasing trend of the 8 turbine efficiency with the vapor quality reduction should be accounted for a more precise evaluation. Nevertheless, at least in this first part of process, we can assume the vapor quality to be higher than the threshold value for which the turbine efficiency starts to worsen, so an increase in pressure should lead to a higher enthalpy gap across the turbi ne. This trend must be considered only in a pressure range compatible with the almost -ideal -gas behaviour assumed at the end of the super heating process (point 8). As the evaporation pressure further increases beyond the ideal gas field , real fluid effect s turn appreciable and the behaviour of the super -heated vapor shows an increasingly heavier departure from that of the ideal gas. This makes the previously highlighted trend for the enthalpy gap vary hugely. Due to an enthalpy content of the fluid upstrea m of the turbine that starts to lower, coupled with an increasingly reduction of the turbine efficiency due to the vapor quality worsening that affect s the enthalpy of the fluid downstream the turbomachine, forecasting the trend of the enthalpy gap through the expander becomes more difficult. Water mass flow rate We must consider that the heat capacity and the initial temperature of the flue gases from the gas turbine are both defined and constant. The maximum temperature of the steam is also fixed , and so are the ∆��� and the ∆���. Increasing the evaporation pressure means to increa se the evaporation temperature and consequently to decrease the vaporizatio n enthalpy. The amount of heat transferred by the exhausts to water from the HRSG inlet the inlet of the evaporator decreases, and so also the am ount of steam produced. Thermodynamic points evaluation In compliance with all the constrain ts, an iterative process has been followed, consisting of: • Setting an evaporation pressure; • Evaluati on the thermodynamic properties of the fluid in each point of the cycle affected by the evaporation pressure value ; • Evaluati on the exploitable work specific to uni t mass ; • Evaluati on the water mass flow rate within the steam cycle; • Evaluati on the net electric power. The process will be implemented with the help of a provided VBA module for the evaluation of the thermodynamic properties of water . The thermodynamic properties evaluation of each steam cycle point will be pursued at different evaporation pressures . To fully character ize the thermodynamic state of each point from an intensive point of view, the previous knowledge of a certain number of independent state variables is required. According to the Gibbs phase rule, at the equilibrium that number is equal to the degrees of freedom of the system (variance, marked as “ �”) and can be evaluated as : �= � + 2− ������ When in single phase (liquid or vapor) we must know two independent intensive state variable s to be able to evaluate all the other s. Since in saturated, superheated and subcooled conditions we have no matter subdivision into different phases, this rule will be applied. When in two — phases condition (for instance during the wet expansion throughout the s team turbine), also the mole fractions are required to evaluate the thermodynamic properties of the fluid. For most of the points of interest, the couple of required thermodynamic properties can be easily found, so the evaluation can be performed easily . However, this does not occur for point s 9’s-9’ and 9s-9. The procedure to evaluate the properties at each point is slightly different. Point 9’s - 9’ At point 9’s the entropy is give n, being equal to the one in point 8 (evaluated through ”H2O.bas”). At point 9’ is given the quality vapor, equal to ������9′ = 0.98 . A further constrain t is given by the equality of pressure for both points , �9′�= �9′. Lastly, the adiabatic efficiency of the turbine is given, �������� = 0.93 . 9 The definition of adiabatic efficiency for a turbine must be accounted, defined as the ratio between the effective enthalpy gap across the turbine and the isentropic one : �������= ℎ8− ℎ9′ ℎ8− ℎ9′� Both ℎ9′� and ℎ9′ are unknowns , while ℎ8 is given by calculation on previous points. The objective function of the solver has been set to be the adiabatic efficiency of the turbine, and the value of the objective function has been set at 0.93. Both ℎ9′� and ℎ9′ have been expressed as a functio n of �9′�= �9′ and of entropy and vapor quality , respectively. The variable has been set to be �9′. �������= ℎ8− ℎ9′(������9′,������9′) ℎ8− ℎ9′�(������9′,������9′�) Both ℎ9′� and ℎ9′ are evaluated. Point 9s – 9 At both points the same pressure is found , being equal to the condensation one ������9= ������9�= ������1= ���������� At point 9’s also the entropy i s given, ������9�= ������9′. Since at point 9s two thermodynamic variables are known, the thermodynamic state can be fully described and also ℎ9� can be evaluated . The adiabatic efficiency �������, the vapor quality ������9 and the enthalpy ℎ9 are the unknowns of the system. { �������∗= 0.93 − (0.98 − ������9) �������∗∗= ℎ9′− ℎ9(������9,������9) ℎ9′− ℎ9� �������∗− �������∗∗= 0 For setting up the solver, it is necessary to express ℎ9 as a function of ������9 and ������9. The objective function is given by the last equation of the system . The variable cell is that of ������9. All the unknowns ( ℎ9, �������and ������9) are evaluated. A further VBA module has been implement ed , supplementary to the already provided one . Given an initial pressure, a final one, and a pressu