Power Market Economics and Security
Problem 1: The generator data are given in Table 1 and the load and reserve data are given in
Table 2. The fuel consumption functions of the generating units are quadratic H(P) = af + bf * P
- cf * P2
(MBtu). The fuel prices are all 1 $/MBtu. The unit shutdown costs and the system
losses are assumed to be zero. Unit 3 has a fuel contract of 2000 MBtu. The initial Lagrangian
multipliers for power balance and reserve requirements are given in Table 3. The initial
multiplier for Unit 3’s fuel constraint is zero. The adjustment steps of multipliers are given in
Table 4. Set Γ=10,000 if the ED is infeasible based on a given commitment. Use the LR method
to solve the UC problem. Obtain two different feasible solutions and show the corresponding
relative duality gaps.
Table 1: Generator data
Unit af
(MBtu)
bf
(MBtu/MW)
cf
(MBtu/MW2
)
Pmin
(MW)
Pmax
(MW)
Min
ON
(h)
Min
OFF
(h)
Startup
Cost ($)
Initial
Status
(h)/(MW)
1 2000 62.3 0.06 100 400 2 2 2000 ON 4 /300
2 2100 64 0.07 80 400 2 1 1500 ON 4 /200
3 1900 59 0.05 40 200 1 2 0 OFF 4 /0
Table 2: Load and reserve data
Hour Load (MW) Reserve (MW)
1 500 50
2 700 70
3 800 80
4 400 40
Table 3: Initial and
Hour (Power balance) (Reserve requirements)
1 75 0
2 100 0
3 110 0
4 70 0
Table 4: Adjustment steps of Lagrangian multipliers
Lagrangian Multiplier k1 k2
(Power balance) 0.02 0.01
(Reserve requirements) 0.02 0.005
(Fuel constraint for unit 3) 0.005 0.001
Sample Solution
Those people held under mental health legislation the principle of consent continue to apply for condition not related to the mental disorder. Nurses who are involved in the care or treatment of patients detained under the relevant mental health legislation, must ensure that they are aware of the circumstances and safeguards needed for providing treatment and care without consent (NMC, 2011) The similarity between Adult and Child branch In both Adult and Mental Health settings seeking consent is part of a respectful relationship, regardless of the patient’s age, gender, culture, background and race. Therefore, consent may be withdrawn at any time, even after signing a consent form.. Another similarity is that when asking consent the healthcare professional has to identify whether the person is able to understand what is being said and the person’s state of mind. This is where patients are competent and free from mental illness. Communication difficulties may arise if a patient’s first language is not English, or with those who are deaf. In a case where a patient is deaf, the healthcare professional would have to communicate with them in sign language. Gaining consent is a way to promote the health of patients. In term of life and death the healthcare professional must act kindly and considerately for the child’s health if they are unable to get in touch with child’s parents. (Department of Health 2003) CONCLUSION Seeking consent is something that is important in the healthcare sector. It is important that all healthcare professionals realise the importance of following the procedure at all times as otherwise there can be legal implications. Respect on behalf of both patient and professional should lie at the heart of every decision taken. Clarity of explanation is important in order to allow the patient or someone acting on their behalf, to make an informed choice. Those involved in healthcare have a serious responsibility in ensuring that the information they offer patients is factually accurate and takes into account any differences in opinion, race, religion age or other factors. Consent increases patients’ power to make an informed choice about their situation and treatment and puts safeguards in place for both the professionals and the patient involved which should lead to the best course of action.>
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