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June 2003 | 1.0 | Baseline version for P82 | CVA Programme |

12 May 2017 | 2.0 | Modification P350 | |

29 March 2019 | 3.0 | 29 March 2019 Standalone Release for P369 | |

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1 Introduction

This __Load Flow Model__ (LFM) Specification has been established by the __Panel__ in accordance with Balancing and __Settlement__ __Code__ (BSC) Section T Annex T-2 paragraphs 2 and 3, with support from __BSCCo__ and the __National Electricity Transmission System Operator__ (NETSO). This __LFM Specification__ is a __Code Subsidiary Document__, which forms part of the Service Description of the __Transmission Loss Factor Agent__ (__TLFA__) (reference 1).

The __LFM Specification__ contains the requirements, obligations, assumptions and approximations required to be supported by the LFM. The exact mechanism for the derivation of Nodal __Transmission Loss Factor__s (TLFs) by the __TLFA__ is the required function of the LFM. For the avoidance of doubt, the LFM produces Nodal TLFs and any further data manipulation is carried out by the __Transmission Loss Factor Agent__. For example, converting the Nodal TLFs into Zonal TLFs and then into __BM Unit__ specific TLFs.

In the event of any discrepancy between the __LFM Specification__ and the __TLFA__ Service Description, Section H 1.5.2 (b) of the __Code__ places the obligation on the __Panel__, with support from __BSCCo__, to determine the precedence and resolve any discrepancy by raising the relevant amendment in accordance with Section F.3. of the __Code__. Furthermore, in the event of any discrepancy between the __LFM Specification__ and the __Code__ Section H 1.5.2 (b) places the obligation on the __Panel__, with support from __BSCCo__, to determine precedence, and to resolve the discrepancy by raising the relevant amendment, in accordance with the __Code__, Section F 3.

1.1 Model Reviewer

The BSC __Panel__ will appoint a Model Reviewer who will verify that the LFM produced by the __TLFA__ produces Nodal TLFs in accordance with this __LFM Specification__, in accordance with Section T, Annex T-2 of the __Code__. __Load Flow Model__

1.2 Background

The intent of __Load Flow Model__ is to derive a set of annual average __Transmission Loss Factor__s (TLFs) to recover heating losses on a zonal basis and fixed losses on a uniform basis, using a scaling factor of 0.5. The TLFs are to be derived annually on an ex ante basis using historical metered and network data. Nodal TLFs will be derived for a set of __Sample Settlement Period__s.

A __Load Flow Model__ to be used for evaluation of TLFs is to be based on a DC load flow, i.e. a modelling approach for an interconnected network utilising data reflective of alternating current (AC) electrical flows on that network, but with a set of simplifying assumptions that render the equations for the AC flows similar in form to those for a direct current (DC) flow. The __Load Flow Model__ Produces Nodal TLFs for each __Sample Settlement Period__.

1.3 Objectives

A LFM is a mathematical model of an electrical network which represents power flows between pairs of adjacent nodes on the network, and from which Nodal TLFs can be determined for each __Node__ for given power flows. TLFs are representative of the changes in transmission losses arising from marginal changes in demand or generation at __Node__s on the Transmission Network.

The key objectives of the LFM are to:

1. Accurately represent the physical characteristics of the England and Wales Transmission Network via a direct current (DC) load flow model;

2. Use Network Data that reflects, as far as is reasonably possible, the conditions prevailing on the network at any time, representative of an ‘intact network’, i.e. a complete England and Wales Transmission Network assuming no circuits de-energised or disconnected with all lines in operation;

3. Capture the delivery, injections onto the network, and offtake, withdrawals from the network, for a large number of __Node__s for __Sample Settlement Period__s throughout each __Reference Year__; and

4. Generate TLFs that are representative of the changes in transmission losses arising from marginal changes in demand or generation at nodes on the Transmission Network.

1.4 Assumptions and Approximations

The __Load Flow Model Specification__ shall provide for the following assumptions and approximations to be made in the __Load Flow Model__:

1. Only electrical losses associated with power flows on circuits (forming part of the network) will be used in determining Nodal TLFs (fixed losses will be set in line with those in the NETSO Seven Year Statement)

2. In respect of the power flow between adjacent nodes, it is assumed that:

There is no

__Reactive Power__component;The ratio of the change of power flow over a circuit to the injection at a given node is not dependent on overall electrical load on the network;

The sine of the voltage phase angle is equal to the phase angle (as measured in radians); and

The power flow in a circuit is equal to the difference in the voltage phase angles across the circuit multiplied by the circuit susceptance.

2 __Load Flow Model__ Requirements

On the basis of the required assumptions listed above, the specification of an appropriate DC load flow model is presented in the following sections (3.1 to 3.3). A conventional DC __Load Flow Model__ relates real power flows (i.e. generation or demand MW) to voltage phase angle (voltage magnitude being assumed constant and equal to 1 pu) using only branch reactances, all resistance being ignored.

The process of computing TLFs based on such a DC __Load Flow Model__ will involve the following three steps:

STEP 1: Calculate adjusted nodal power flows from Nodal metered generation and demand data, suitable for the application of the conventional DC

__Load Flow Model__;STEP 2: Calculate network power flows using the conventional DC

__Load Flow Model__;STEP 3: Determine flow-injections sensitivity factors and compute TLFs

These steps are detailed in the following section 3.1 to 3.3 and an example is contained in Appendix 2.

2.1 STEP 1: Calculation of adjusted nodal power flows from metered generation and demand data

The conventional DC __Load Flow Model__ excludes consideration of losses in the process of evaluating voltage phase angles and flows. It is proposed that a simple adjustment of metered volumes of generation (MWh) and demand (MWh) is performed and used to compute Nodal power flows as the input to the DC __Load Flow Model__:

where

This adjustment allows the conventional (loss-inclusive) DC __Load Flow Model__ to be applied for the evaluation of network power flows since:

Note that this process will produce consistent inputs for the DC Load Flow even if the metered data is inconsistent. For example, in case that the metered losses are inconsistent with metered generation and demand, as well as in the extreme case of the total metered generation being smaller than the total metered demand. The example presented in the Appendix 2 illustrates the adequacy of the proposed approach to computing Nodal power flows from the metered data.

2.2 STEP 2: Evaluation of network power flows using the conventional DC __Load Flow Model__

Active power balance at each of the __Node__s is given by the following expression:

Where

The conventional DC load flow is obtained by

neglecting losses in power flow calculations

_{$${G}_{\text{ab}}=0$$},assuming that the voltage magnitudes at all

__Node__s equal to 1 p.u (_{$$|{E}_{n}|=1$$}).assuming that the sine of the voltage phase angle is equal to the phase angle:

The corresponding load flow equations constitute a DC power flow:

given that

where, _{$${x}_{\text{an}}$$}is the reactance between __Node__s *a* and *n*, the corresponding conventional DC __Load Flow Model__ can be presented the standard matrix form:

where:

P_{1},..,P_{N }represents net power flow injections (given) at __Node__s 1 to *N*,

The net power flow is defined as the difference between generation and demand at the corresponding __Node__ (_{$${P}_{n}={G}_{n}-{D}_{n}$$}).

The matrix representing network characteristics (both the topology and electrical parameters of the circuits - reactances), belongs to the class of so-called *Y*_{bus} matrices, and is presented in (9). The diagonal elements of the matrix correspond to the sum of susceptances coincident with the corresponding __Node__, while off diagonal elements correspond to the negative values of susceptance linking the corresponding __Node__s.

In order to solve system of equations (8) a reference slack node needs to be chosen, since (9) is a singular matrix and hence equations (8) are linearly dependent. With no loss of generality but for the sake of simplicity of the presentation, __Node__ 1 is declared as the slack node. The system of equation (8) can be now solved and the corresponding voltage phase angles determined using matrix techniques routinely applied in load flow calculations:

where *Y*_{r} is obtained by removing the row and the column from the *Y*_{bus} that correspond to the slack node.

Once the voltage phase angles are calculated (10), circuit flows can be computed:

where *F*_{k} is the power flow in a circuit *k*, and circuit* k* is between __Node__s *a* and *b*.

2.3 STEP 3: Determine power injection sensitivity factors and compute TLFs

A Nodal TLF, associated with a particular __Node__ *n*, is defined as the incremental change in the network losses (*L*) due to an incremental increase in power injection (*P*_{n}) at __Node__ *n*:

(Symbol _{$$\Delta $$} indicates an incremental change)

As indicated above, network losses will be divided in “heating losses”, which depend on network loading conditions, and “fixed losses” that are independent from network loading. Therefore, the network model to be used for Nodal TLF evaluations will only include components that generate heating losses, which means that the network model will contain only series impedances and exclude all shunt impedances.

In a network with the total number of circuits (network branches) being *M*, the total “heating losses” are the sum of losses attributed to each individual transmission circuits *k* in the network:

The Nodal TLF associated with __Node__ n can now be expressed as follows:

Consistent with the conventional DC __Load Flow Model__, the heating losses in each of the individual circuits can be assessed as follows:

where:

Given that *F*_{k}_{ }is calculated through the conventional DC __Load Flow Model__, the Nodal TLF for a particular __Node__ *n* is now given by

This expression can be further expanded as follows:

The above expression is fundamental for the evaluation of the Nodal TLFs using the required DC Load Flow approach. The sensitivity factor _{$$\frac{{\mathit{\Delta F}}_{k}}{{\mathit{\Delta P}}_{n}}$$} in (17) measures the change in the power flow in circuit *k* due to an increase in power injection at __Node__ *n*. In the conventional DC __Load Flow Model__, these sensitivity factors do not depend on loading conditions but only on the network topology and reactances of the network circuits. Hence, for a network with a fixed topology the sensitivity factors are constant and are evaluated without considering generation and demand.

This is consistent with the requirement set in Section 2.3, point 2(ii). However, the Nodal TLFs (in expression 17) do depend on loading conditions since load flows in individual circuits (*F*_{k}) will be driven by loading conditions.

The sensitivity factors, the ratio of the change of power flow *F*_{k}, between __Node__s *a *and *b*, to the increase in power flow *P*_{n} at node *n* can be calculated from the following expression:

(18)

Given that (10) is expressed in the form of

the sensitivity factors are obtained by the following expression

where:

These factors can be readily computed using matrix techniques routinely employed in load flow calculations. The sensitivity factors only depend on values of network parameters but not on network loading.

The values of the sensitivity coefficients depend on the choice of slack node and therefore, the values of Nodal TLFs (17) will also depend on the choice of slack node. However, the differences in TLFs between any two nodes (TLF differentials) will remain constant irrespective of the choice of slack node, since the differences in sensitivity factors are also independent from the choice of slack node.

The above Nodal TLFs, as defined in (17), represent the incremental change in losses due to an incremental increase in power flow, i.e. incremental generation. Given that the formulas used to calculate TLMOs assume demand oriented definition, the polarity of these Nodal TLFs should be reversed for the subsequent application:

3 Compliance

The LFM should be compliant with the __LFM Specification__ (this document) at all times. The LFM should not be adopted, nor amendments implemented until the model reviewer has reported on the compliance of the LFM with the specification and the __Panel__ has agreed that the LFM is compliant with the LFM specification.

The __Panel__ is required to agree to any amendment to the __LFM Specification__, and therefore the LFM, and is required to instruct the __TLFA__ to amend the LFM to comply with the amendments to the specification.

4 Appendix 1 - Definitions and Terms

Adjusted nodal power flows | A form of nodal power flows used to calculate Nodal |

| each successive period of 12 months beginning on 1st April in each year. |

| Division of the |

Network Data | means the following data relating to the (i) the identity of each pair of adjacent (ii) for each such pair of Network data shall be established on the assumption of an 'intact network', that is disregarding any planned or other outage of any part of the |

| a node is a point on the electrical network at which: (i) a power flow on to or off the network can occur, or (ii) two or more circuit (forming part of the network) meet. A |

| 12 month period ending 30 September in the preceding |

| a representative |

slack node | is a node that acts: (i) in relation to adjacent nodes, as the reference node for calculating the phase angle of the power flow between nodes. |

| is the factor applied to a |

| the |

| a geographic area in which a |

5 Appendix 2 - Illustrative Example

Consider a simple three-__Node__ network with three circuits in Figure 1, with given metered generation and demand volumes.

Circuit per unit reactances and resistances, assuming 100MVA base, are given in Table 1:

| | |

1-2 | 0.1 | 0.02 |

1-3 | 0.2 | 0.03885 |

2-3 | 0.2 | 0.04 |

An advanced (non-standard), loss-inclusive DC __Load Flow Model__ was used to determine individual flows that approximately correspond to the given metered data. This load flow uses a piece wise linear representation of losses in individual circuits. Results of these calculations are shown in Figure 1, with sending and receiving powers in individual lines being presented.

Figure 1: Example system with metered volumes and load flows in individual circuits

Nodal TLFs can be calculated in the process composed of the following steps.

5.1 STEP 1: Adjust metered volumes

From given metered generation and demand data, metered heating losses are found to be 19MW (=233+78-292). Generation and demand are now adjusted to allow the application of the loss-inclusive DC __Load Flow Model__:

Clearly, the total adjusted generation equals the total adjusted demand.

5.2 STEP 2: Calculate network flows consistent using the conventional DC __Load Flow Model__

From given set of reactances and the network topology, the following *Y*_{bus} can be formed:

By removing the row and the column from the admittance matrix *Y*_{bus}* *that corresponds to the slack node, matrix *Y*_{r} is obtained. Assuming __Node__ 1 is selected to be a slack, *Y*_{r} is defined as:

Given the reduced matrix *Y*_{r} and power injections, voltage phase angles can be computed:

Finally, circuit load flows can be computed:

This is presented in Figure 2.

Figure 2: Nodal Power flows in the example system with adjusted generation and demand volumes (total adjusted generation equal total adjusted demand)

5.3 STEP 3: Determine flow-injections sensitivity factors and compute TLFs

Given the entries of the inverse *Y*_{r} matrix

flow-injection sensitivities can be computed:

5.3.1 Circuit 1-2

5.3.2 Circuit 1-3

5.3.3 Circuit 2-3

Applying equation (x), nodal TLFs can be calculated:

Table 2: Nodal TLFs for incremental increases in generation and demand

| | |

1 | 0.0 | 0.0 |

2 | -0.0232 | 0.0232 |

3 | –0.1303 | 0.1303 |

The TLFs that represent the incremental change in losses due to incremental change in demand (21) should be used for subsequent calculations of TLMOs.