EMK:Multi Dimensional Water Values - Revision history

Sisep: /* Marginal Benefit of Storage - Buffers */

2012-11-26T20:47:30Z

Marginal Benefit of Storage - Buffers

Sisep: /* Appendix 1: Relationship between Water Value and Benefit */

2012-11-26T20:45:44Z

Appendix 1: Relationship between Water Value and Benefit

Sisep: /* Marginal Benefit from Unconstrained Convergence */

2012-11-26T20:44:36Z

Marginal Benefit from Unconstrained Convergence

Sisep: /* Marginal Benefit from Unconstrained Convergence */

2012-11-26T20:39:18Z

Marginal Benefit from Unconstrained Convergence

Sisep: /* Appendix 2: Alterations and Corrections to the Projection Method */

2012-11-26T20:38:39Z

Appendix 2: Alterations and Corrections to the Projection Method

Sisep: /* Marginal Benefit Adjustment at Storage Constrained Convergence */

2012-11-26T20:33:26Z

Marginal Benefit Adjustment at Storage Constrained Convergence

Sisep: /* Appendix 2: Alterations and Corrections to the Projection Method */

2012-11-26T20:29:58Z

Appendix 2: Alterations and Corrections to the Projection Method

Sisep: /* Appendix 1: Relationship between Water Value and Benefit */

2012-11-26T20:28:38Z

Appendix 1: Relationship between Water Value and Benefit

Sisep: /* Appendix 1: Relationship between Water Value and Benefit */

2012-11-26T20:27:16Z

Appendix 1: Relationship between Water Value and Benefit

Sisep: /* Appendix 1: Relationship between Water Value and Benefit */

2012-11-26T20:27:03Z

Appendix 1: Relationship between Water Value and Benefit

← Older revision		Revision as of 20:47, 26 November 2012
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	In the trajectory shown the total cost associated with the incursion into undesirable storage levels will be proportional to the shaded areas. The rate at which this cost is measured would be in $/(time x Storage Units).		In the trajectory shown the total cost associated with the incursion into undesirable storage levels will be proportional to the shaded areas. The rate at which this cost is measured would be in $/(time x Storage Units).
		+
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		+	[[EMK:Water Values Bulletins \| Back to Water Values Technical Bulletins]]

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 This optimisation can also be expressed as a function of total release from the reservoir.  Here the total release (denoted here by the variable y) is treated as the sole decision variable
-Eq. 8.  [[File:Eq 8.jpg|250px|centre]]
+Eq. 8.  [[File:Eq 8.jpg|290px|centre]]
 Optimisation of v then implies that where the release decision variable is not constrained then
-Eq. 9.  [[File:Eq 9.jpg|300px|centre]]
+Eq. 9.  [[File:Eq 9.jpg|340px|centre]]
 When storage is unconstrained the resulting storage ''s''' will be directly and inversely dependent on release, so:
-Eq. 10. [[File:Eq 10.jpg|150px|centre]]
+Eq. 10. [[File:Eq 10.jpg|180px|centre]]
 Replacing this relationship in Eq. 9 gives:
-Eq. 11. [[File:Eq 11.jpg|190px|centre]]
+Eq. 11. [[File:Eq 11.jpg|220px|centre]]
 The expression on the right of the equation can be summed up as ‘the marginal benefit of release’ and will be expressed as B’(y) here.  In fact Eq. 11 summarises the intuitively rather obvious relationship otherwise stated as ‘given optimal, unconstrained, release, water value will be equal to the benefit of additional release’.

← Older revision		Revision as of 20:44, 26 November 2012
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	where α is the estimated rate of convergence.		where α is the estimated rate of convergence.
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		+	====Marginal Benefit of Storage - Buffers====
		+	This consideration takes into account any other factor that may make marginal storage desirable or undesirable. For example, flood protection may demand that areas of storage are avoided, or conversely the unpleasant environmental effects of a low lake at certain times of year may force the operator to try and avoid letting the lake get too low.
		+
		+	A method for modelling these ‘undesirable’ storage areas is to assume a cost associated with the time spent in these areas and the amount of intrusion into the area. Figure 10 illustrates this cost:
		+	[[File:MDWV Figure 10.jpg\|400px\|thumb\|centre\|Figure 10 - Cost of Incursion into Undesirable Storage Levels]]
		+
		+	In the trajectory shown the total cost associated with the incursion into undesirable storage levels will be proportional to the shaded areas. The rate at which this cost is measured would be in $/(time x Storage Units).

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 This effect can be approximated by assuming discretionary offers are made at water value and estimating the probability of item above 2 multiplied by the value in item 1.  This value will give the rate of convergence between the trajectories.  When convergence occurs it implies the difference in offers between the two marginally different cases has resulted in a difference in dispatch between them.  This in turn implies that the offer prices are on the price margin. There is a loose implication that marginal offers are made with a price that reflects water value (at least on average), so when convergence occurs we could assume that energy price will on the whole be the same as the current water value.  Using this assumption the expected marginal benefit of this convergence will be estimated as the current water value.  This implies a combination of the current water value with the marginal benefit being projected, at the rate of the expected convergence, altering Eq. 4 to:
-Eq. 15. [[File:Eq 15.jpg|400px|centre]]
+Eq. 15. [[File:Eq 15.jpg|600px|centre]]
 where α is the estimated rate of convergence.

@@ Line 276: / Line 276: @@
 ===Appendix 2: Alterations and Corrections to the Projection Method===
-As mentioned in section 4.4 the method of projecting marginal benefit back from the point of convergence needs to be done with some extra considerations in mind.  Currently EMarket implements the spill penalty (4 10.1) and storage buffers (4 10.4), with the other considerations left as possible future enhancements.
+As mentioned in section 4.4 the method of projecting marginal benefit back from the point of convergence needs to be done with some extra considerations in mind.  Currently ''EMarket'' implements the spill penalty (4 10.1) and storage buffers (4 10.4), with the other considerations left as possible future enhancements.
 ====Marginal Benefit Adjustment at Storage Constrained Convergence====
@@ Line 285: / Line 285: @@
 ====Gradated Storage Constrained Convergence====
 While reservoirs are modelled here as being forced to spill beyond a certain level, in reality this constraint is rarely as sudden as this implies.  Usually there is a gradual ramping up of forced release over a given level of high storage.  This can be modelled by combining a zero marginal benefit with the projected marginal benefit in progressive amounts as the storage exceeds this level.

← Older revision		Revision as of 20:33, 26 November 2012
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	====Marginal Benefit Adjustment at Storage Constrained Convergence====		====Marginal Benefit Adjustment at Storage Constrained Convergence====
		+	Where storage is full it can be assumed that marginal extra storage would not affect generation, so the marginal benefit derived from generation and energy prices will be zero. However, there may be a cost associated with the spillage of water, and it is straight-forward to incorporate this cost by adding a penalty to the marginal benefit, resulting in a negative marginal benefit: this is referred to here as a Spill Penalty.
		+
		+	Where storage is empty, marginal extra storage directly affects generation, indicating a marginal benefit equal to the energy price. Additional generation will also affect nodal price, the marginal benefit of which is zero if generation and retail load and hedge cover are perfectly balanced. Calculating the marginal benefit to the total portfolio of the operator is a complicated business involving assessment of the price impact of generation and the portfolio balance. Some approximations can be made such as assuming a portfolio size that is commensurate with average expected generation and using a rule of thumb for estimating the relationship between marginal price and generation (which is normally far from simple).
		+
		+	====Gradated Storage Constrained Convergence====
		+	While reservoirs are modelled here as being forced to spill beyond a certain level, in reality this constraint is rarely as sudden as this implies. Usually there is a gradual ramping up of forced release over a given level of high storage. This can be modelled by combining a zero marginal benefit with the projected marginal benefit in progressive amounts as the storage exceeds this level.

← Older revision		Revision as of 20:29, 26 November 2012
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	===Appendix 2: Alterations and Corrections to the Projection Method===		===Appendix 2: Alterations and Corrections to the Projection Method===
		+	As mentioned in section 4.4 the method of projecting marginal benefit back from the point of convergence needs to be done with some extra considerations in mind. Currently EMarket implements the spill penalty (4 10.1) and storage buffers (4 10.4), with the other considerations left as possible future enhancements.
		+
		+	====Marginal Benefit Adjustment at Storage Constrained Convergence====

← Older revision		Revision as of 20:28, 26 November 2012
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	Eq. 14. [[File:Eq 14.jpg\|180px\|centre]]		Eq. 14. [[File:Eq 14.jpg\|180px\|centre]]
		+
		+	Which summarises the relationship: '''''water value is equal to the marginal change in expected benefit over change in storage.'''''
		+
		+	===Appendix 2: Alterations and Corrections to the Projection Method===

← Older revision		Revision as of 20:27, 26 November 2012
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	Combining Eq. 13 with Eq. 12 gives:		Combining Eq. 13 with Eq. 12 gives:

−	Eq. 14. [[File:Eq 14.jpg\|~~160px~~\|centre]]	+	Eq. 14. [[File:Eq 14.jpg\|180px\|centre]]