EMK:Dispatch, Pricing and Power Flows - Revision history

Sisep: /* Transformer and Fixed Loss Modelling in EMarket */

2012-12-02T20:57:03Z

Transformer and Fixed Loss Modelling in EMarket

Sisep: /* Aggregated Lines in EMarket */

2012-12-02T20:45:32Z

Aggregated Lines in EMarket

Sisep: /* Losses */

2012-12-02T20:36:47Z

Losses

Sisep: /* Losses */

2012-12-02T20:29:09Z

Losses

Sisep: /* Losses */

2012-12-02T20:26:14Z

Losses

Sisep: /* Transfer Admittance Matrix */

2012-12-02T20:24:23Z

Transfer Admittance Matrix

Sisep: /* Transfer Admittance Matrix */

2012-12-02T20:19:12Z

Transfer Admittance Matrix

Sisep: /* DC Power Flow */

2012-12-02T20:14:04Z

DC Power Flow

Sisep: /* DC Power Flow */

2012-12-02T20:11:52Z

DC Power Flow

Sisep: /* DC Power Flow */

2012-12-02T20:10:31Z

DC Power Flow

← Older revision		Revision as of 20:57, 2 December 2012
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	==== Transformer and Fixed Loss Modelling in EMarket ====		==== Transformer and Fixed Loss Modelling in EMarket ====
		+	As ''EMarket'' is typically run with an aggregated grid with 3-letter nodes representing all nodes at a location, transformer losses would go unaccounted for without explicit provision being made. ''EMarket’s'' grid configuration includes, for each node, an island for reserves purposes, and an associated resistance value. The resistance value is chosen by the user to represent the combined resistance of the transformers at each modelled node. ''EMarket'' models demand at the nodes as passing through a line with this resistance, and thus accounts for transformer losses on the grid with the associated direct or indirect impact on total losses, power flows, dispatch and nodal prices.
		+
		+	Fixed losses on the grid arising from transformers and the HVDC link amount to around 30 MW and are typically added to demand at strategically selected nodes, using functions in the ''EMarket'' Schedule.
		+
		+	=== DC Power Flow Accuracy ===
		+	In a theoretical sense, the DC power flows are constructed in the same way as the DC power flow in SPD and thus by construction the power flow modelling and agreement with SPD is excellent. SPD is, of course, a linear model, but the impact on the accuracy of its power flows, as compared to the full quadratic loss power flows implemented in IQP, is small in most lines on the grid.
		+
		+
		+	[[EMK:Technical Bulletins \| Back to Technical Bulletins]]

← Older revision		Revision as of 20:45, 2 December 2012
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	==== Aggregated Lines in EMarket ====		==== Aggregated Lines in EMarket ====
		+	SPD models hundreds of nodes and all individual lines and transformers. ''EMarket'' can model the full grid but to do so would slow ''EMarket'' down sufficiently to be counterproductive in most applications, with little or no gain in power flow accuracy.
		+
		+	Most users model the grid with about 180 nodes and 200 aggregated lines which gives high accuracy, excellent performance and has enough nodes that aggregating lines is straightforward – in most cases lines are either entered directly or aggregated with one or more lines in parallel. Using 180 nodes more or less eliminates the need to aggregate loops within the grid.
		+
		+	For n lines in series the per unit impedances (The use of Z to denote impedance should not be confused with its earlier use to denote power flow) of the lines are simply summed:
		+
		+	''Z = Z<sub>1</sub> + ... + Z<sub>n</sub>''
		+
		+	where ''Z = R + jX'' using complex notation.
		+
		+	For the more common case of lines in parallel the impedances of the aggregated line is the reciprocal of the sum of the reciprocals of the individual line impedances. For two lines parallel:
		+
		+	[[File:DP E32.jpg]]
		+
		+	The line limits also need to be adjusted. Lines in parallel typically have similar impedances and similar limits applied to them in SPD, in which case the limit of the aggregated line is the sum of the individual limits.
		+
		+	Where parallel lines have significantly different impedance then the lines with lower resistance will carry more power than the lines with higher per unit resistance. Most of the time in ''EMarket'' simulations are undertaken with a limited number of lines with limits enabled (The user would typically enable constraints on key lines and monitor all other lines to check if any are exceeding their limits to an extent that would warrant re-running with their constraints enabled), so the effort required to set limits on aggregated lines is typically minimal.
		+
		+	As the New Zealand grid is relatively static in its configuration, at least for the purposes for which ''EMarket'' is used, once a grid is aggregated it can be maintained with ease. Users will often liaise with Energy Link to obtain a grid suitable for immediate use.
		+
		+	==== Transformer and Fixed Loss Modelling in EMarket ====

← Older revision		Revision as of 20:36, 2 December 2012
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	The per unit system used in electrical engineering requires a base power to which all parameters are referenced, including the line resistance, reactance and susceptance. In the case of IQP we use the same as in SPD, ie. 100 MW. Note that the equations above require scaling in some instances to get sensible units. For example, ''Z = 100Hy'' and [[File:DP E31.jpg]] give units of MW. The net injection y<sub>i</sub> also needs to be scaled down by 100.		The per unit system used in electrical engineering requires a base power to which all parameters are referenced, including the line resistance, reactance and susceptance. In the case of IQP we use the same as in SPD, ie. 100 MW. Note that the equations above require scaling in some instances to get sensible units. For example, ''Z = 100Hy'' and [[File:DP E31.jpg]] give units of MW. The net injection y<sub>i</sub> also needs to be scaled down by 100.
		+
		+	A DC power flow does not include losses in the line flows, even though the losses can be calculated. The typical approach to including losses is either to ignore losses (which is surprisingly accurate for pricing purposes) but creates the problem of a non-physical dispatch for the System Operator to deal with, or to add losses to the demand at the node at the downstream end of each line (this is also what happens in SPD). The latter requires iterations to get convergence but convergence is fast and stable in IQP.
		+
		+	Note that any imbalance between losses, generation and demand will always appear at the swing node. Since IQP performs a full market dispatch which balances losses, demand and generation, the swing node will always be in balance unless an infeasibility occurs.
		+
		+	=== Differences between EMarket and EMO ===
		+	Both ''EMarket'' and ''EMO'' include a wide range of inputs for the grid so both explicitly take account of line limits, equation constraints and losses.
		+
		+	''EMarket'' and ''EMO'' are designed for different purposes so there are some differences in the way the power flow works in the two models, as shown below:
		+
		+	{\|class="wikitable"
		+	! !! ''EMO'' !! ''EMarket''
		+	\|-
		+	\| Grid data and detail \|\| Grid data obtained from em6 or similar data source, hence every node, line and related constraint modelled, including equation constraints. \|\| Capable of solving the full grid but not generally done due to the reduction in performance – typically uses an aggregated grid with approx 180 nodes and 200 lines. <br/>Transformer losses between modelled nodes and lower voltage nodes are modelled at each node by entering transformer resistance values. <br/>Default line limits can be entered for summer and winter in line with Transpower time zones, or re-rated on the fly during simulations runs from the ''EMarket'' Schedule.
		+	\|-
		+	\| Line outages \|\| The power flow is re-solved at every period modelled so full or partial outages are catered for. This slows the power flow solve down considerably but techniques for solving large, sparse matrices are employed without loss of accuracy. \|\| The power flow equations are not re-solved each modelled period in ''EMarket'' so full outages during a simulation run can not be modelled. Partial outages (re-ratings) are modelled simply by scheduling the re-rating. Re-rating to zero is not allowed so 1 MW is the minimum line limit.
		+	\|}
		+
		+	==== Aggregated Lines in EMarket ====

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	''L = y<sup>T</sup> By''.		''L = y<sup>T</sup> By''.
		+
		+	The per unit system used in electrical engineering requires a base power to which all parameters are referenced, including the line resistance, reactance and susceptance. In the case of IQP we use the same as in SPD, ie. 100 MW. Note that the equations above require scaling in some instances to get sensible units. For example, ''Z = 100Hy'' and [[File:DP E31.jpg]] give units of MW. The net injection y<sub>i</sub> also needs to be scaled down by 100.

← Older revision		Revision as of 20:26, 2 December 2012
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	''L<sub>i</sub> = R<sub>i</sub> Z<sub>i</sub><sup>2</sup>'' and total losses are given by		''L<sub>i</sub> = R<sub>i</sub> Z<sub>i</sub><sup>2</sup>'' and total losses are given by

−	''L = y<sup>T/sup> By''.	+	''L = y<sup>T</sup> By''.

← Older revision		Revision as of 20:24, 2 December 2012
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	[[File:DP E30.jpg]]		[[File:DP E30.jpg]]
		+
		+	where G<sub>j</sub> is the total injection at node j.
		+
		+	The DC power flow matrix equation for the line flows is then
		+
		+	''Z = Hy''
		+
		+	where Z is the vector of all line flows and y the vector of net injections at all but the swing node. The swing node may be chosen arbitrarily but in ''EMarket'' and ''EMO'' it is chosen outside of IQP as a well connected node to maximise the speed at which the full power flow with losses converges.
		+
		+	=== Losses ===
		+	The assumption of X<sub>i</sub> > R<sub>i</sub> leads to losses in line ''i'' given by
		+
		+	''L<sub>i</sub> = R<sub>i</sub> Z<sub>i</sub><sup>2</sup>'' and total losses are given by
		+
		+	''L = y<sup>T/sup> By''.

← Older revision		Revision as of 20:19, 2 December 2012
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	[[File:DP E29.jpg]]		[[File:DP E29.jpg]]
		+
		+	where Z<sub>i</sub> is the flow in line ''i'' and y<sub>j</sub> the net injection at node j. The net injection is just generation less demand ''y<sub>i</sub> = G<sub>i</sub> - D<sub>i</sub>''. Where demand is not able to be dispatched on price, as occurs in the pricing runs of SPD, it is taken as fixed so that for the purpose of pricing
		+
		+	[[File:DP E30.jpg]]

← Older revision		Revision as of 20:14, 2 December 2012
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	[[File:DP E28.jpg]]		[[File:DP E28.jpg]]
		+
		+	=== Transfer Admittance Matrix ===
		+	Each element of the H (transfer admittance) matrix H<sub>ij</sub> is the rate that flow on line i varies with net injection at node j, i.e.
		+
		+	[[File:DP E29.jpg]]

← Older revision		Revision as of 20:11, 2 December 2012
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	[[File:DP E27.jpg]]		[[File:DP E27.jpg]]
		+
		+	which also leads to
		+
		+	[[File:DP E28.jpg]]

← Older revision		Revision as of 20:10, 2 December 2012
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	[[File:DP E26.jpg\|350px]]		[[File:DP E26.jpg\|350px]]
		+
		+	The transfer admittance matrix, H, is an m×n-1 matrix given by:
		+
		+	[[File:DP E27.jpg]]