Critical evaluation of the currently discussed approach and the PFD method

Transcription

1 Critical evaluation of the currently discussed aroach and the PFD method Prof. Dr.-Ing. habil. B. R. Oswald Dil.-Wirtsch.-Ing. B. Merkt Dil.-Ing. J. Runge Institute of Electric Power Systems Division of Power Suly niversity of Hanover Hanover, 8. May 2006

2 Contents 1 Requirements on an ITC mechanism 2 2 Technical evaluation of the currently discussed aroach 2 3 PFD (Power Flow Decomosition) method 3 4 Derivation of the PFD method 4 5 Conclusions 6 References 6 1

3 1 Requirements on an ITC mechanism Article 3 of E Regulation 1228/2003 secifies the requirements on an Inter-TSO Comensation (ITC) Mechanism with regard to grid costs accruing from cross-border ower flows. In detail, according to E Regulation 1228/2003, this mechanism must be comliant with the following requirements: The utilisation of every single network element in the interconnected transmission system caused by cross-border ower flows has to be identified. The mechanism shall take into account benefits that a network incurs as a consequence of hosting cross-border ower flows, with the result that comensations received may be reduced accordingly. Cross-border ower flows have to be determined based on hysical flows of electricity actually measured in a given eriod of time. To meet these rovisions, a model has to be based on technically correct engineering rinciles (ower flow equations) for the comutation of cross-border ower flows. Such a technically correct aroach taking into consideration the resonsibilities for all ower flows in the interconnected network is necessary to meet all the other requirements on a longer term ITC mechanism: A technically sound method fulfils the criterion of cost reflectiveness because only if the utilisation of a network is determined in a technically correct manner associated costs are reflected correctly by the resective model. Every TSO is charged or comensated on the basis of the actual utilisation of network equiment due to cross-border flows. A method based on technically correct engineering rinciles of network calculation is valid for every ower system and therefore suitable for the Euroean network. Aroved engineering rinciles are comliant with the criteria of imlementation and transarency as they can be understood and interreted on the basis of common technical knowledge and hysical rinciles. 2 Technical evaluation of the currently discussed aroach The currently discussed aroach, described in the ERGEG Draft Proosal on Guidelines on Inter TSO Comensations, as well as all formerly roosed methods 1 suffer from their technical incorrectness and thus are not comliant with the rovisions of Regulation (EC) o 1228/2003, Article 3. The main drawbacks of the aroach within the ERGEG Draft Proosal are: - The hysics of electrical ower flows are ignored by disregarding that every generator 1 Average Particiations Method, With and Without Method, With and Without Method alied to Transits, Marginal Particiations Method 2

4 in a network articiates in the suly of every load. - The calculation of transit ower flows in an interconnected network with the alied method of minimizing the total use of transited networks is neither based on the aroved engineering rinciles (ower flow equations) nor technically justified. Furthermore, the aroach could lead to a discrimination of transited TSOs. - The definition of transit ower flows as the minimum of imort- and exort ower flows in the context of the calculation of losses is arbitrary. The general tenor that it is only ossible to identify transit ower flows with simlifications and arbitrary assumtions is wrong. Based on the ower flow equations and the rincile of suerosition it is ossible to decomose ower flows in the interconnected transmission system into imort, exort, transit, loo and internal ower flows. These ower flows can be assigned to agents located at the different nodes of the network. A technically correct method for the comutation of transit ower flows as well as imort, exort, loo and internal ower flows, which comlies with Article 3 of Regulation (EC) o 1228/2003, is introduced in the next section. 3 PFD (Power Flow Decomosition) method There are widely acceted and aroved engineering rinciles for the comutation of ower flows in electrical ower systems, namely the ower flow equations based on Kirchhoff s laws /1,2/. Additionally, in the context of an ITC mechanism the rincile of suerosition has to be alied for the decomosition of a total ower flow into individual resonsibilities of agents in a network. This section introduces the PFD method, which is based on technically correct engineering rinciles. It allows for the decomosition of ower flows in interconnected transmission systems into imort, exort, transit, loo and internal ower flows. Based on the ower flow equations these ower flows are assigned to agents located at the different nodes of the network. It is ossible to determine the benefits that a network incurs as a result of hosting cross-border ower flows. Additionally, the PFD method is indeendent of olitical borders and consequently comlies with the single system aradigm. The PFD method is solely based on the well established algorithms of ower flow comutation and the rincile of suerosition and does not rely on any arbitrary assumtions. Hence, the method is straightforward and cost effective to imlement. Furthermore it follows, that it can be easily understood and verified. It can be alied to an entire interconnected transmission system or a single transmission system. 2 For the imlementation of the PFD method the same ower system data as for the usual ower flow comutation is needed: - network toology, 2 In the latter case, it is generally imossible to determine the resonsibilities of external agents for cross-border ower flows. 3

5 - imedances of the network elements (transformers and lines), - nodal owers (generation and demand). 4 Derivation of the PFD method inear ower flow equations are alied within the PFD method /1,2/. In transmission networks the active resistances of lines and transformers can be neglected. ines and transformers are modelled as quadruoles. Figure 1 shows a quadruole with the terminal voltages l and m and the terminal currents I l and I m. The terminals of the quadruoles are connected with the network nodes. I i i l I l I m m k I k i l m k Figure 1 equivalent-circuit diagram of a quadruole The correlation between the terminal values of all quadruoles of a network in terms of a matrix equation can be formulated with the admittance matrix Y as follows: Y u = i (1) T The incidence matrix K describes the correlation between the terminal voltages and the nodal voltages as follows: T K u = u (2) The nodal voltage equations can be formulated with the nodal admittance matrix follows: Y as Y u = i (3) Equations (1), (2) and (3) lead to a linear correlation between the terminal currents and the nodal currents: T 1 = Y K Y i i (4) Equation (4) is extended: * T 1* 1 = s Y K Y s with: = diag( u ), * = 3 s i = diag( u ), s * 3i = (5) The deendency of the active ower flows and the nodal active ower can be written as 4

6 follows: = D (6) with: * T 1* 1 D= Re{ Y K Y } (7) It is assumed that the integrated network consists of n transmission systems. In equation (8) the nodal and terminal owers are arrayed as follows: 1 D11 D12 D1n 1 2 D21 D22 D2n 2 = D D D n n1 n2 nn n (8) Equation (8) shows the imact of the nodal owers of every single transmission system on the ower flows in the network elements in all n transmission systems. By means of equation (8) and the rincile of suerosition, the ower flows on every network element can be decomosed into imort, exort, transit loo and internal ower flows. Furthermore, every ower flow (imort, exort, transit loo and internal ower flows) can be traced through the network, and resonsible injections and withdrawals for these ower flows can be identified. The decomosition of the ower flows by means of the rincile of suerosition leads to: 11 1n i1 ij in n1 nn n i1 ij i n n1 nn k = k k k k k k k 11 1n i1 ij in n1 nn n n n n n n n n (9) The suerscrits in the ower flow vectors in equation (9) reresent the resonsible transmission systems for this articular ower flow vector. For instance the ower flow vector reresents the transit ower flows through transmission system k originating in ij k transmission system i and ending in transmission system j. In equation (9) all imort, exort, transit loo and internal ower flows are included. Table 1 shows the notation for exort, transit loo and internal ower flows. Imort ower flows are not included because imort ower flows of a transmission system are equal to the negative exort ower flows of the transmission system where these ower flows originate. exort ower flow in k from k to i transit ower flow through k from i to j loo ower flow through k from i to i internal ower flow in k Table 1 notation of ower flows ki k ij k ii k kk k 5

7 5 Conclusions The aroach described in the ERGEG DRAFT Proosal on Guidelines on Inter TSO Comensations is not suitable to be imlemented within a longer-term ITC mechanism as it does not meet the requirements of Article 3 of Regulation (EC) o 1228/2003 shown in Section 1. Due to its technical inadequacies the currently discussed aroach would lead to an incorrect determination of transit ower flows. As a consequence the resulting comensation ayments are not cost reflective. Furthermore, the minimisation of the total utilisation of TSOs due to transit ower flows leads to a discrimination of transited networks. For the comutation of cross-border ower flows, as required in Article 3 of Regulation (EC) o 1228/2003, the PFD method should be alied within a longer-term ITC mechanism. The PFD method does solely rely on technically sound and established engineering rinciles without any arbitrary assumtions. Therefore, it is straightforward and cost effective to imlement and can be easily understood and verified. The PFD method needs the same data set as a ower flow calculation. References /1/ Stagg, G. W., El-Abiad, A. H.: Comuter Methods in Power system Analysis. Mc Graw- Hill Book Comany, ew York, Sydney, 1968 /2/ Oeding, D., Oswald, B. R.: Elektrische Kraftwerke und etze. 6. Auflage Sringer-Verlag