Formulas of HFO Power Plant Efficiency Calculation

Heat Rate (Energy Efficiency)

Overall thermal performance or energy efficiency for a power plant for a period can be defined as

φhr = H / E         (1)

where

φhr = heat rate (Btu/kWh, kJ/kWh)

H = heat supplied to the power plant for a period (Btu, kJ)

E = energy output from the power plant in the period (kWh)

Thermal Efficiency

Thermal efficiency of a power plant can be expressed as

μte = (100) (3412.75) / φ          (2)

where

μte = thermal efficiency (%)

Capacity Factor

The capacity factor for a power plant is the ratio between average load and rated load for a period of time and can be expressed as

μcf = (100) Pal / Prl               (3)

where

μcf = capacity factor (%)

Pal = average load for the power plant for a period (kW) Prl = rated capacity for the power plant (kW)

Load Factor

Load factor for a power plant is the ratio between average load and peak load and can be expressed as

μlf = (100) Pal / Ppl                (4)

where

μlf = load factor (%)

Ppl = peak load for the power plant in the period (kW)

Economic Efficiency

Economic efficiency is the ratio between production costs, including fuel, labor, materials and services, and energy output from the power plant for a period of time. Economic efficiency can be expressed as

φee = C / E         (5)

where

φee = economic efficiency (cents/kW, euro/kW, ...) C = production costs for a period (cents, euro, ..)

E = energy output from the power plant in the period (kWh)

Operational Efficiency

Operational efficiency is the ratio of the total electricity produced by the plant during a period of time compared to the total potential electricity that could have been produced if the plant operated at 100 percent in the period.

Operational efficiency can be expressed as

μoe = (100) E / E100%               (6)

where

μeo = operational efficiency (%)

E = energy output from the power plant in the period (kWh)

E100% = potential energy output from the power plant operated at 100% in the period (kWh)

Physical characteristics of water at the atmospheric pressure

At atmospheric pressure, water exhibits several physical characteristics that are commonly observed under normal conditions:

1. State of Matter: Water exists predominantly in the liquid state at atmospheric pressure and temperatures typically encountered on Earth's surface (0°C to 100°C). However, it can also exist as a solid (ice) below 0°C and as a gas (water vapor) above 100°C.

2. Boiling Point: At sea level, where atmospheric pressure is approximately 101.3 kilopascals (kPa) or 1 atmosphere (atm), water boils at 100°C (212°F). This is the temperature at which the vapor pressure of water equals the atmospheric pressure, causing it to change from liquid to gas.

3. Freezing Point: Water freezes into ice at 0°C (32°F) at atmospheric pressure. At this temperature, the molecules in the liquid phase lose enough thermal energy to form a solid lattice structure, resulting in the solidification of water molecules into ice.

4. Density: The density of liquid water is approximately 1 gram per cubic centimeter (g/cm³) at 4°C, making it denser than ice. However, water's density decreases as it approaches its freezing point, causing ice to float on liquid water.

5. Surface Tension: Water molecules exhibit cohesive forces, resulting in surface tension, which causes the surface of water to behave like an elastic membrane. This property allows water droplets to form spherical shapes and enables certain insects to walk on the water's surface.

6. Specific Heat Capacity: Water has a relatively high specific heat capacity, meaning it can absorb and store a large amount of heat energy compared to many other substances. This property helps regulate temperature variations in the environment and contributes to the moderating effect of large bodies of water on climate.

7. Viscosity: Water has a relatively low viscosity compared to other liquids, meaning it flows relatively easily. However, its viscosity can increase with temperature and pressure changes.

8. Refractive Index: The refractive index of water is approximately 1.333 at room temperature, causing light to bend when passing from one medium (e.g., air) into water. This property is responsible for phenomena such as the apparent bending of objects viewed through water and the formation of rainbows.

These physical characteristics of water at atmospheric pressure play crucial roles in various natural processes, industrial applications, and everyday activities.

Pressure:	Atmospheric pressure at 1,01325 bar, i.e. normal atmospheric pressure on the sea level at 0°C.
Density:	Ratio of the mass of water (kg) occupied in a volume of 1 m3.
Specific enthalpy:	Sensible Heat, it is the quantity of heat contained in 1 kg of water according to the selected temperature.
Specific heat:	Quantity of heat necessary to increase the temperature of a 1° Celsius per unit of mass of 1 kg of water.
Volume heat capacity:	Quantity of heat necessary to increase the temperature of a 1° Celsius on a unit of volume of 1 m3 of water.
Dynamic viscosity:	The viscosity of a fluid characterizes the resistance to the movement of the fluid.

NB: Energy values in kcal/kg are given on a basis of 4.1868 J .Values not normally used.

Temperature	Pressure	Saturation vapor pressure	Density	Specific enthalpy of liquid water		Specific heat		Volume heat capacity	Dynamic viscosity
°C	Pa	Pa	kg/m3	kj/kg	kcal/kg	kj/kg	kcal/kg	kj/m3	kg/m.s
0.00	101325	611	999.82	0.06	0.01	4.217	1.007	4216.10	0.001792
1.00	101325	657	999.89	4.28	1.02	4.213	1.006	4213.03	0.001731
2.00	101325	705	999.94	8.49	2.03	4.210	1.006	4210.12	0.001674
3.00	101325	757	999.98	12.70	3.03	4.207	1.005	4207.36	0.001620
4.00	101325	813	1000.00	16.90	4.04	4.205	1.004	4204.74	0.001569
5.00	101325	872	1000.00	21.11	5.04	4.202	1.004	4202.26	0.001520
6.00	101325	935	999.99	25.31	6.04	4.200	1.003	4199.89	0.001473
7.00	101325	1001	999.96	29.51	7.05	4.198	1.003	4197.63	0.001429
8.00	101325	1072	999.91	33.70	8.05	4.196	1.002	4195.47	0.001386
9.00	101325	1147	999.85	37.90	9.05	4.194	1.002	4193.40	0.001346
10.00	101325	1227	999.77	42.09	10.05	4.192	1.001	4191.42	0.001308
11.00	101325	1312	999.68	46.28	11.05	4.191	1.001	4189.51	0.001271
12.00	101325	1402	999.58	50.47	12.06	4.189	1.001	4187.67	0.001236
13.00	101325	1497	999.46	54.66	13.06	4.188	1.000	4185.89	0.001202
14.00	101325	1597	999.33	58.85	14.06	4.187	1.000	4184.16	0.001170
15.00	101325	1704	999.19	63.04	15.06	4.186	1.000	4182.49	0.001139
16.00	101325	1817	999.03	67.22	16.06	4.185	1.000	4180.86	0.001109
17.00	101325	1936	998.86	71.41	17.06	4.184	0.999	4179.27	0.001081
18.00	101325	2063	998.68	75.59	18.05	4.183	0.999	4177.72	0.001054
19.00	101325	2196	998.49	79.77	19.05	4.182	0.999	4176.20	0.001028
20.00	101325	2337	998.29	83.95	20.05	4.182	0.999	4174.70	0.001003
21.00	101325	2486	998.08	88.14	21.05	4.181	0.999	4173.23	0.000979
22.00	101325	2642	997.86	92.32	22.05	4.181	0.999	4171.78	0.000955
23.00	101325	2808	997.62	96.50	23.05	4.180	0.998	4170.34	0.000933
24.00	101325	2982	997.38	100.68	24.05	4.180	0.998	4168.92	0.000911
25.00	101325	3166	997.13	104.86	25.04	4.180	0.998	4167.51	0.000891
26.00	101325	3360	996.86	109.04	26.04	4.179	0.998	4166.11	0.000871
27.00	101325	3564	996.59	113.22	27.04	4.179	0.998	4164.71	0.000852
28.00	101325	3779	996.31	117.39	28.04	4.179	0.998	4163.31	0.000833
29.00	101325	4004	996.02	121.57	29.04	4.179	0.998	4161.92	0.000815
30.00	101325	4242	995.71	125.75	30.04	4.178	0.998	4160.53	0.000798
31.00	101325	4491	995.41	129.93	31.03	4.178	0.998	4159.13	0.000781
32.00	101325	4754	995.09	134.11	32.03	4.178	0.998	4157.73	0.000765
33.00	101325	5029	994.76	138.29	33.03	4.178	0.998	4156.33	0.000749
34.00	101325	5318	994.43	142.47	34.03	4.178	0.998	4154.92	0.000734
35.00	101325	5622	994.08	146.64	35.03	4.178	0.998	4153.51	0.000720
36.00	101325	5940	993.73	150.82	36.02	4.178	0.998	4152.08	0.000705
37.00	101325	6274	993.37	155.00	37.02	4.178	0.998	4150.65	0.000692
38.00	101325	6624	993.00	159.18	38.02	4.178	0.998	4149.20	0.000678
39.00	101325	6991	992.63	163.36	39.02	4.179	0.998	4147.74	0.000666
40.00	101325	7375	992.25	167.54	40.02	4.179	0.998	4146.28	0.000653
41.00	101325	7777	991.86	171.71	41.01	4.179	0.998	4144.80	0.000641
42.00	101325	8198	991.46	175.89	42.01	4.179	0.998	4143.30	0.000629
43.00	101325	8639	991.05	180.07	43.01	4.179	0.998	4141.80	0.000618
44.00	101325	9100	990.64	184.25	44.01	4.179	0.998	4140.28	0.000607
45.00	101325	9582	990.22	188.43	45.01	4.180	0.998	4138.75	0.000596
46.00	101325	10085	989.80	192.61	46.00	4.180	0.998	4137.20	0.000586
47.00	101325	10612	989.36	196.79	47.00	4.180	0.998	4135.64	0.000576
48.00	101325	11161	988.92	200.97	48.00	4.180	0.998	4134.06	0.000566
49.00	101325	11735	988.47	205.15	49.00	4.181	0.999	4132.47	0.000556
50.00	101325	12335	988.02	209.33	50.00	4.181	0.999	4130.87	0.000547
51.00	101325	12960	987.56	213.51	51.00	4.181	0.999	4129.25	0.000538
52.00	101325	13612	987.09	217.69	52.00	4.182	0.999	4127.61	0.000529
53.00	101325	14292	986.62	221.88	52.99	4.182	0.999	4125.97	0.000521
54.00	101325	15001	986.14	226.06	53.99	4.182	0.999	4124.30	0.000512
55.00	101325	15740	985.65	230.24	54.99	4.183	0.999	4122.63	0.000504
56.00	101325	16510	985.16	234.42	55.99	4.183	0.999	4120.94	0.000496
57.00	101325	17312	984.66	238.61	56.99	4.183	0.999	4119.24	0.000489
58.00	101325	18146	984.16	242.79	57.99	4.184	0.999	4117.52	0.000481
59.00	101325	19015	983.64	246.97	58.99	4.184	0.999	4115.79	0.000474
60.00	101325	19919	983.13	251.16	59.99	4.185	0.999	4114.05	0.000467
61.00	101325	20859	982.60	255.34	60.99	4.185	1.000	4112.30	0.000460
62.00	101325	21837	982.07	259.53	61.99	4.186	1.000	4110.53	0.000453
63.00	101325	22854	981.54	263.72	62.99	4.186	1.000	4108.75	0.000447
64.00	101325	23910	981.00	267.90	63.99	4.187	1.000	4106.97	0.000440
65.00	101325	25008	980.45	272.09	64.99	4.187	1.000	4105.17	0.000434
66.00	101325	26148	979.90	276.28	65.99	4.188	1.000	4103.36	0.000428
67.00	101325	27332	979.34	280.46	66.99	4.188	1.000	4101.54	0.000422
68.00	101325	28561	978.78	284.65	67.99	4.189	1.000	4099.71	0.000416
69.00	101325	29837	978.21	288.84	68.99	4.189	1.001	4097.88	0.000410
70.00	101325	31161	977.63	293.03	69.99	4.190	1.001	4096.03	0.000404
71.00	101325	32533	977.05	297.22	70.99	4.190	1.001	4094.18	0.000399
72.00	101325	33957	976.47	301.41	71.99	4.191	1.001	4092.31	0.000394
73.00	101325	35433	975.88	305.60	72.99	4.192	1.001	4090.45	0.000388
74.00	101325	36963	975.28	309.79	73.99	4.192	1.001	4088.57	0.000383
75.00	101325	38548	974.68	313.99	74.99	4.193	1.001	4086.69	0.000378
76.00	101325	40190	974.08	318.18	76.00	4.194	1.002	4084.80	0.000373
77.00	101325	41890	973.46	322.37	77.00	4.194	1.002	4082.91	0.000369
78.00	101325	43650	972.85	326.57	78.00	4.195	1.002	4081.01	0.000364
79.00	101325	45473	972.23	330.76	79.00	4.196	1.002	4079.11	0.000359
80.00	101325	47359	971.60	334.96	80.00	4.196	1.002	4077.20	0.000355
81.00	101325	49310	970.97	339.16	81.01	4.197	1.002	4075.29	0.000351
82.00	101325	51328	970.33	343.35	82.01	4.198	1.003	4073.38	0.000346
83.00	101325	53415	969.69	347.55	83.01	4.199	1.003	4071.46	0.000342
84.00	101325	55572	969.04	351.75	84.01	4.200	1.003	4069.54	0.000338
85.00	101325	57803	968.39	355.95	85.02	4.200	1.003	4067.62	0.000334
86.00	101325	60107	967.73	360.15	86.02	4.201	1.003	4065.70	0.000330
87.00	101325	62488	967.07	364.35	87.02	4.202	1.004	4063.78	0.000326
88.00	101325	64947	966.41	368.56	88.03	4.203	1.004	4061.85	0.000322
89.00	101325	67486	965.74	372.76	89.03	4.204	1.004	4059.93	0.000319
90.00	101325	70108	965.06	376.96	90.04	4.205	1.004	4058.00	0.000315
91.00	101325	72814	964.38	381.17	91.04	4.206	1.005	4056.08	0.000311
92.00	101325	75607	963.70	385.38	92.05	4.207	1.005	4054.15	0.000308
93.00	101325	78488	963.01	389.58	93.05	4.208	1.005	4052.23	0.000304
94.00	101325	81460	962.31	393.79	94.06	4.209	1.005	4050.31	0.000301
95.00	101325	84525	961.62	398.00	95.06	4.210	1.006	4048.39	0.000298
96.00	101325	87685	960.91	402.21	96.07	4.211	1.006	4046.47	0.000295
97.00	101325	90943	960.20	406.42	97.07	4.212	1.006	4044.55	0.000291
98.00	101325	94301	959.49	410.64	98.08	4.213	1.006	4042.64	0.000288
99.00	101325	97760	958.78	414.85	99.09	4.214	1.007	4040.73	0.000285
100.00	101325	101325	958.05	419.06	100.09	4.216	1.007	4038.82	0.000282