Unit commitment problem - Revision history

Mlhegeman: /* Applications */

2021-12-16T05:46:22Z

Applications

← Older revision		Revision as of 01:46, 16 December 2021
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	Costs are then calculated for each combination and the optimum combination that minimizes cost for each period may be selected, as seen below.		Costs are then calculated for each combination and the optimum combination that minimizes cost for each period may be selected, as seen below.
	[[File:Optimized unit combinations.png~~\|left~~\|thumb\|501x501px\|'''Fig. 4''' Optimized unit combinations]]		[[File:Optimized unit combinations.png\|thumb\|501x501px\|'''Fig. 4''' Optimized unit combinations\|alt=\|none]]










	==Applications==		==Applications==
	Unit commitment problems can be further adjusted for components that reflect the real-world problem. A simple categorization can be divided into two major groups. One is related to the commitment of power generation/production/manufacturing process, and the other group involves output allocation to the committed units, often known as unit commitment and economic dispatch <ref>A.J. Conejo, L. Baringo, “Power System Operations,” Power Electronics and Power		Unit commitment problems can be further adjusted for components that reflect the real-world problem. A simple categorization can be divided into two major groups. One is related to the commitment of power generation/production/manufacturing process, and the other group involves output allocation to the committed units, often known as unit commitment and economic dispatch <ref>A.J. Conejo, L. Baringo, “Power System Operations,” Power Electronics and Power

Kk733: /* Flowchart for the UC problem by Dynamic programming */

2021-12-16T05:41:34Z

Flowchart for the UC problem by Dynamic programming

← Older revision		Revision as of 01:41, 16 December 2021
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	<math>R = \text{Stage of DP execution}</math></small>		<math>R = \text{Stage of DP execution}</math></small>
	===== Flowchart for the UC problem by Dynamic programming =====		===== Flowchart for the UC problem by Dynamic programming =====
	<gallery class="center" mode="packed" heights="~~460~~">		<gallery class="center" mode="packed" heights="430">
	~~File:Index.php?title=File:~~DP.png\|'''Fig. 1''' Flowchart provided on <ref name = "Krsn">Krishna Mohan, R., Gopichand Naik, M., & Rajendra Prasad, S. (2021). A comparative study of unit commitment problem by dynamic programming and genetic algorithm. Lecture Notes in Electrical Engineering, 61–77. https://doi.org/10.1007/978-981-15-8439-8_6 </ref>		<gallery>
			<gallery>
			DP.png\|'''Fig. 1''' Flowchart provided on <ref name = "Krsn">Krishna Mohan, R., Gopichand Naik, M., & Rajendra Prasad, S. (2021). A comparative study of unit commitment problem by dynamic programming and genetic algorithm. Lecture Notes in Electrical Engineering, 61–77. https://doi.org/10.1007/978-981-15-8439-8_6 </ref>
	</gallery>		</gallery>

Mlhegeman: /* Flowchart for the UC problem by Dynamic programming */

2021-12-16T05:33:10Z

Flowchart for the UC problem by Dynamic programming

← Older revision		Revision as of 01:33, 16 December 2021
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	Costs are then calculated for each combination and the optimum combination that minimizes cost for each period may be selected, as seen below.		Costs are then calculated for each combination and the optimum combination that minimizes cost for each period may be selected, as seen below.
	[[File:Optimized unit combinations.png\|left\|thumb\|501x501px\|'''Fig. 4''' Optimized unit combinations]]		[[File:Optimized unit combinations.png\|left\|thumb\|501x501px\|'''Fig. 4''' Optimized unit combinations]]

Mlhegeman: /* Single Period Unit Commitment */

2021-12-16T05:28:11Z

Single Period Unit Commitment

← Older revision		Revision as of 01:28, 16 December 2021
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	The three generators have the following characteristics:		The three generators have the following characteristics:


	'''Table 1''' Generator power and unit cost		'''Table 1''' Generator power and unit cost
	{\| class="wikitable"		{\| class="wikitable"
	\|+
	\|		\|
	\|'''G1'''		\|'''G1'''
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	The feasible unit combinations (states) of the generators are determined by calculating the power output for each generator combination and denoting which combination is able to satisfy the energy demand at each interval.		The feasible unit combinations (states) of the generators are determined by calculating the power output for each generator combination and denoting which combination is able to satisfy the energy demand at each interval.
	[[File:Feasible unit combinations.png\|alt=\|none\|thumb\|501x501px\|'''Fig. 3''' Energy load profile over 6-hour period]]		[[File:Feasible unit combinations.png\|alt=\|none\|thumb\|501x501px\|'''Fig. 3''' Energy load profile over 6-hour period]]


	Costs are then calculated for each combination and the optimum combination that minimizes cost for each period may be selected, as seen below.		Costs are then calculated for each combination and the optimum combination that minimizes cost for each period may be selected, as seen below.

Mlhegeman: /* Single Period Unit Commitment */

2021-12-16T05:24:41Z

Single Period Unit Commitment

← Older revision		Revision as of 01:24, 16 December 2021
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	<math>R = \text{Stage of DP execution}</math></small>		<math>R = \text{Stage of DP execution}</math></small>
	===== Flowchart for the UC problem by Dynamic programming =====		===== Flowchart for the UC problem by Dynamic programming =====
	<gallery class="center" mode="packed" heights="460" >		<gallery class="center" mode="packed" heights="460">
	DP.png\|Fig 1, Flowchart provided on <ref name = "Krsn">Krishna Mohan, R., Gopichand Naik, M., & Rajendra Prasad, S. (2021). A comparative study of unit commitment problem by dynamic programming and genetic algorithm. Lecture Notes in Electrical Engineering, 61–77. https://doi.org/10.1007/978-981-15-8439-8_6 </ref>		File:Index.php?title=File:DP.png\|'''Fig. 1''' Flowchart provided on <ref name = "Krsn">Krishna Mohan, R., Gopichand Naik, M., & Rajendra Prasad, S. (2021). A comparative study of unit commitment problem by dynamic programming and genetic algorithm. Lecture Notes in Electrical Engineering, 61–77. https://doi.org/10.1007/978-981-15-8439-8_6 </ref>
	</gallery>		</gallery>

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	=== Single Period Unit Commitment ===		=== Single Period Unit Commitment ===
	Consider an electricity market with a particular load profile, as seen below. This demand varies throughout the course of a 6-hour period and must be satisfied by the electrical energy output from a set of three generators. Each generator has a set energy output limit, as well as unit production cost associated with energy generation. Each generator may be in an on or off state and may be started or stopped throughout the 6-hour period. The utility may wish to operate the system so that the load demand is met while minimizing cost.		Consider an electricity market with a particular load profile, as seen below. This demand varies throughout the course of a 6-hour period and must be satisfied by the electrical energy output from a set of three generators. Each generator has a set energy output limit, as well as unit production cost associated with energy generation. Each generator may be in an on or off state and may be started or stopped throughout the 6-hour period. The utility may wish to operate the system so that the load demand is met while minimizing cost.
	[[File:Energy load profile over 6-hour period.png\|alt=\|none\|thumb\|500x500px\|Energy load profile over 6-hour period]]		[[File:Energy load profile over 6-hour period.png\|alt=\|none\|thumb\|500x500px\|'''Fig. 2''' Energy load profile over 6-hour period]]

	==== Solution ====		==== Solution ====
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	The three generators have the following characteristics:		The three generators have the following characteristics:

			'''Table 1''' Generator power and unit cost
	{\| class="wikitable"		{\| class="wikitable"
			\|+
	\|		\|
	\|'''G1'''		\|'''G1'''
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	\|'''G3'''		\|'''G3'''
	\|-		\|-
	\|Power (MW)		\|Power (MW)
	\|800		\|800
	\|700		\|700
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	\|125		\|125
	\|}		\|}



	To determine the generator schedule, we carry out the following optimization problem to meet demand over the 6-hour period, while minimize operating cost, using a dynamic programming approach.		To determine the generator schedule, we carry out the following optimization problem to meet demand over the 6-hour period, while minimize operating cost, using a dynamic programming approach.
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	The feasible unit combinations (states) of the generators are determined by calculating the power output for each generator combination and denoting which combination is able to satisfy the energy demand at each interval.		The feasible unit combinations (states) of the generators are determined by calculating the power output for each generator combination and denoting which combination is able to satisfy the energy demand at each interval.
	[[File:Feasible unit combinations.png\|alt=\|none\|thumb\|501x501px\|~~Feasible unit combinations~~]]		[[File:Feasible unit combinations.png\|alt=\|none\|thumb\|501x501px\|'''Fig. 3''' Energy load profile over 6-hour period]]


	Costs are then calculated for each combination and the optimum combination that minimizes cost for each period may be selected, as seen below.		Costs are then calculated for each combination and the optimum combination that minimizes cost for each period may be selected, as seen below.
	[[File:Optimized unit combinations.png\|left\|thumb\|501x501px\|Optimized unit combinations]]		[[File:Optimized unit combinations.png\|left\|thumb\|501x501px\|'''Fig. 4''' Optimized unit combinations]]

Mlhegeman: /* Numerical example */

2021-12-16T05:18:48Z

Numerical example

← Older revision		Revision as of 01:18, 16 December 2021
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	To determine the generator schedule, we carry out the following optimization problem to meet demand over the 24-hour period, while minimize operating cost.
			To determine the generator schedule, we carry out the following optimization problem to meet demand over the 6-hour period, while minimize operating cost, using a dynamic programming approach.

	min <math>\sum_{i\in I} g_i * c_i </math>		min <math>\sum_{i\in I} g_i * c_i </math>
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	<math>u_{i,t} \in \{0,1\}, \forall i \in I, \forall t \in T</math>		<math>u_{i,t} \in \{0,1\}, \forall i \in I, \forall t \in T</math>

			The feasible unit combinations (states) of the generators are determined by calculating the power output for each generator combination and denoting which combination is able to satisfy the energy demand at each interval.
	~~To determine the generator schedule, we carry out the following optimization problem to meet demand over the 6-hour period, while minimize operating cost, using a dynamic programming approach.~~ The feasible unit combinations (states) of the generators are determined by calculating the power output for each generator combination and denoting which combination is able to satisfy the energy demand at each interval.
	[[File:Feasible unit combinations.png\|alt=\|none\|thumb\|501x501px\|Feasible unit combinations]]		[[File:Feasible unit combinations.png\|alt=\|none\|thumb\|501x501px\|Feasible unit combinations]]
	Costs are then calculated for each combination and the optimum combination that minimizes cost for each period may be selected, as seen below.		Costs are then calculated for each combination and the optimum combination that minimizes cost for each period may be selected, as seen below.

Mlhegeman: /* Single Period Unit Commitment */

2021-12-16T05:13:36Z

Single Period Unit Commitment

← Older revision		Revision as of 01:13, 16 December 2021
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	=== Single Period Unit Commitment ===		=== Single Period Unit Commitment ===
	Consider an electricity market with a particular load profile, as seen below. This demand varies throughout the course of a 24-hour period and must be satisfied by the electrical energy output from a set of three generators. Each generator has a ~~minimum and maximum~~ energy output limit, as well as unit production cost associated with energy generation. Each generator may be in an on or off state and may be started or stopped throughout the 24-hour period. The utility may wish to operate the system so that the load demand is met while minimizing cost.		Consider an electricity market with a particular load profile, as seen below. This demand varies throughout the course of a 6-hour period and must be satisfied by the electrical energy output from a set of three generators. Each generator has a set energy output limit, as well as unit production cost associated with energy generation. Each generator may be in an on or off state and may be started or stopped throughout the 6-hour period. The utility may wish to operate the system so that the load demand is met while minimizing cost.
	[[File:Energy load profile over 24-hour period.png\|thumb\|500x500px\|Energy load profile over 24-hour period~~\|alt=\|none~~]]		[[File:Energy load profile over 6-hour period.png\|alt=\|none\|thumb\|500x500px\|Energy load profile over 6-hour period]]

	==== Solution ====		==== Solution ====
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	The three generators have the following characteristics:		The three generators have the following characteristics:
			{\| class="wikitable"
			\|
			\|'''G1'''
			\|'''G2'''
			\|'''G3'''
			\|-
			\|Power (MW)
			\|800
			\|700
			\|1200
			\|-
			\|$ / MWh
			\|88
			\|110
			\|125
			\|}

	~~''Generator 1''~~

	~~<math>G_{1~~,~~min} </math>= 300 MW~~, ~~<math>G_{1,max} </math>= 800 MW~~		To determine the generator schedule, we carry out the following optimization problem to meet demand over the 24-hour period, while minimize operating cost.

	<math>~~c_1~~ </math>~~= $88 / MWh~~		min <math>\sum_{i\in I} g_i * c_i </math>

	~~''Generator 2''~~		such that

	<math>G_{2,min} ~~</math>= 250 MW~~, ~~<math>~~G_{2,max} </math>~~= 700 MW~~		<math>G_{i,min} * u_{i,t} \leq g_i \leq G_{i,max} * u_{i,t}, \forall i \in I</math>

	<math>~~c_2~~ </math>~~= $110 / MWh~~		`<math>\sum_{i \in I} g_i * u_{i,t} \geq d_{i,t}, \forall t \in T</math>

	~~''Generator 3''~~		<math>u_{i,t} \in \{0,1\}, \forall i \in I, \forall t \in T</math>

	<math>G_{3,~~min~~} ~~</math>= 400 MW, <math>G_~~{3,~~max~~} </math>~~= 1200 MW~~

	~~<math>c_3 </math>= $125 / MWh~~


	To determine the generator schedule, we carry out the following optimization problem to meet demand over the 24-hour period, while minimize operating cost.		To determine the generator schedule, we carry out the following optimization problem to meet demand over the 6-hour period, while minimize operating cost, using a dynamic programming approach. The feasible unit combinations (states) of the generators are determined by calculating the power output for each generator combination and denoting which combination is able to satisfy the energy demand at each interval.
			[[File:Feasible unit combinations.png\|alt=\|none\|thumb\|501x501px\|Feasible unit combinations]]
			Costs are then calculated for each combination and the optimum combination that minimizes cost for each period may be selected, as seen below.
			[[File:Optimized unit combinations.png\|left\|thumb\|501x501px\|Optimized unit combinations]]

	~~min <math>\sum_{i\in I} g_i * c_i </math>~~



	~~such that~~

	~~<math>G_{i,min} * u_{i,t} \leq g_i \leq G_{i,max} * u_{i,t}, \forall i \in I</math>~~

	~~`<math>\sum_{i \in I} g_i * u_{i,t} \geq d_{i,t}</math>~~

	~~<math>u_{i,t} \in \{0,1\}, \forall i \in I, \forall t \in T</math>~~


	Modeling the system in the GAMS software package, we are able to obtain an optimized schedule for when each generator should be active or inactive throughout the course of the 24-hour period. Below are the optimized generator schedules superimposed on the load profile.
	~~[[File:Generator schedule on load profile.png\|none\|thumb\|501x501px\|Optimized generator schedule for load profile]]~~

	==Applications==		==Applications==

Kk733: /* Flowchart for the UC problem by Dynamic programming */

2021-12-16T04:26:58Z

Flowchart for the UC problem by Dynamic programming

← Older revision		Revision as of 00:26, 16 December 2021
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	<math>R = \text{Stage of DP execution}</math></small>		<math>R = \text{Stage of DP execution}</math></small>
	===== Flowchart for the UC problem by Dynamic programming =====		===== Flowchart for the UC problem by Dynamic programming =====
	<gallery class="center" mode="packed" heights="~~360~~" >		<gallery class="center" mode="packed" heights="460" >
	DP.png\|Fig 1, Flowchart provided on <ref name = "Krsn">Krishna Mohan, R., Gopichand Naik, M., & Rajendra Prasad, S. (2021). A comparative study of unit commitment problem by dynamic programming and genetic algorithm. Lecture Notes in Electrical Engineering, 61–77. https://doi.org/10.1007/978-981-15-8439-8_6 </ref>		DP.png\|Fig 1, Flowchart provided on <ref name = "Krsn">Krishna Mohan, R., Gopichand Naik, M., & Rajendra Prasad, S. (2021). A comparative study of unit commitment problem by dynamic programming and genetic algorithm. Lecture Notes in Electrical Engineering, 61–77. https://doi.org/10.1007/978-981-15-8439-8_6 </ref>
	</gallery>		</gallery>

Tk557: /* Dynamic Programming Based Approach */

2021-12-16T00:15:40Z

Dynamic Programming Based Approach

← Older revision		Revision as of 20:15, 15 December 2021
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	<math>P_{cost}(T,R)= \text{The production cost at state}(T,R)</math><br>		<math>P_{cost}(T,R)= \text{The production cost at state}(T,R)</math><br>
	<math>S_{cost}(T-1,P:T,R) = \text{The transition cost price from state}(T-1,P) \text{ to } (T,R)</math></small><br>		<math>S_{cost}(T-1,P:T,R) = \text{The transition cost price from state}(T-1,P) \text{ to } (T,R)</math></small><br>
	<small><math> T = \text{Number of hours}</math> <br>		<small><math>T = \text{Number of hours}</math> <br>

	<math>R = \text{Stage of DP execution}</math></small>		<math>R = \text{Stage of DP execution}</math></small>
	===== Flowchart for the UC problem by Dynamic programming =====		===== Flowchart for the UC problem by Dynamic programming =====

Tk557: /* Dynamic Programming Based Approach */

2021-12-16T00:14:32Z

Dynamic Programming Based Approach

← Older revision		Revision as of 20:14, 15 December 2021
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	where<br>		where<br>
	<small><math>F_{cost}(T,R)= \text{Minimum cost price at state}(T,R)</math>,<br>		<small><math>F_{cost}(T,R)= \text{Minimum cost price at state}(T,R)</math><br>
	<math>P_{cost}(T,R)= \text{The production cost at state}(T,R)</math><br>		<math>P_{cost}(T,R)= \text{The production cost at state}(T,R)</math><br>

	<math>S_{cost}(T-1,P:T,R) = \text{The transition cost price from state}(T-1,P) \text{ to } (T,R)</math></small><br>		<math>S_{cost}(T-1,P:T,R) = \text{The transition cost price from state}(T-1,P) \text{ to } (T,R)</math></small><br>
	<small><math> T = \text{Number of hours}</math>, <br>		<small><math> T = \text{Number of hours}</math> <br>

	<math>R = \text{Stage of DP execution}</math></small>		<math>R = \text{Stage of DP execution}</math></small>