Multiple Criteria Decision Making Methodology Based on Probabilistic Evaluation of ATC

Real and reactive power allocation

in bilateral transaction markets

E. De Tuglie G. PATRONO F. Torelli

Dipartimento di Ingegneria dell’Ambiente Dipartimento di Elettrotecnica ed Elettronica

e per lo Sviluppo Sostenibile (DIASS) (DEE)

Politecnico di Bari Politecnico di Bari

Viale del Turismo, 8, 74100 Taranto Via E. Orabona, 4, 70125 Bari

Italy Italy

Abstract: - In deregulated power systems, transmission networks are available for third-party access to allow power wheeling. In such a deregulated environment, the ancillary services are no longer treated as integral to the electricity supply. They are unbundled and priced separately, and system operators have to purchase ancillary services from ancillary service providers.

Issues pertaining to costing of ancillary services, and hence appropriate pricing mechanisms for all market participants to recover the costs, become an important issue for proper functioning of the system. This paper presents a method able to allocate real power losses and reactive power support to each transaction in a multi-transaction environment. The approach utilizes a static power system representation in terms of nodal admittance matrix in conjunction with a classical power flow. With this formulation, it is possible to derive system losses as well as reactive supply expression as a sum of partial terms due to each transaction.

Key-Words: - Loss allocation, Reactive Allocation, Simultaneous bilateral contracts, Multiple wheeling transactions

1 Introduction

The last decade has seen a worldwide trend towards restructuring and deregulation of the power industry. The main objectives of these reforms are achieved through a clear separation between production and sale of electricity, and network operations. The energy can be sold by generation companies through long-term contracts or by bidding for short-term energy supply at the spot market [1,2]. Transmission is still a natural monopoly since the economics of scale are very high, even if transmission open access has proved to be an important requirement in deregulated systems. To guarantee a level playing field for generators and customers to access the transmission network, the transmission operator is required to be independent from other market participants.

The Independent System Operator (ISO) has acquired a central coordination role and carries out the important responsibility of providing for system reliability and security. It manages system operations, such as scheduling and operating the transmission-related services. The ISO also has to ensure a required degree of quality and safety, provide corrective measures when faced with incidents, and several other functions. In addition the ISO could also manage market administration, energy auction and unit commitment functions in the pool market structure.

To this effect, certain services, such as, scheduling and dispatch, frequency regulation, voltage control, generation reserves, etc. are required by power system, apart from the basic energy and power delivery services. Such services, which are now commonly referred to as Ancillary Services (ASs), had all along been part of the normal electricity supply and were not separated in the traditional vertically integrated power systems. However, in deregulated power systems, transmission networks are available for third-party access to allow power wheeling. In such a deregulated environment, the ancillary services are no longer treated as integral to the electricity supply. They are unbundled and priced separately, and system operators have to purchase ancillary services from ancillary service providers.

Issues pertaining to costing of ancillary services and hence appropriate pricing mechanisms for all market participants to recover the costs become an important issue for proper functioning of the system.

Among all ancillary services, electricity markets identify the supply of losses and reactive power as crucial factors in system support services. As markets develop in managing real power transactions, qualifying and compensating active and reactive power support service is becoming a more interesting research target, especially when an increasing number of transactions are utilizing the transmission system and losses and voltages become bottlenecked while transferring additional power.

Different methods are presented in technical literature in order to share transmission losses [3-10] or reactive power [11-20] among all participants.

Physical laws governing network flows can have anomalous and unexpected market implications [17] thus, real and reactive flows need to be considered in an integrated approach to perform a correct analysis of energy markets [21-27]. Following the same purpose, in this paper a method for allocating real and reactive power services to individual transactions is developed. The methodology considers all transactions acting simultaneously as characterizing the operating point in nodal voltage terms and evaluated by a usual load flow code. The system, represented by its nodal current equations, gives rise to an expression of complex powers evaluated at the slack bus and reactive generators as a sum of transaction terms plus a unique network term depending on transmission system parameters and nodal voltages. The method allocates real power losses and reactive power support to each transaction in a multi-transaction environment.

2 Bilateral Transaction Framework

Modern electricity markets give the possibility to exchange power in different ways from the past among market participants. In fact, if in the past all generated power was centrally dispatched from generators to loads, nowadays unbundling and open transmission access gives the possibility to have direct agreements between generators and loads. Moreover, this brisk and lucrative market enables others purely financial actors to participate in the games. Thus, individual generators can sell power directly to loads or to a pool or to trading entities, bringing transactions to assume a double aspect: both physical and financial.

Trading entities, responsible for financial transactions, play an important role in modifying power flows through the network, impacting the physical world. For such transactions, it is necessary to quantify their responsibilities in terms of costs associated to the transmission network usage and losses. Fortunately, in [2], it is demonstrated that all kind of transactions can have bilateral generator-to-load (or bus-to-bus) equivalents. Thus, without loss of generality, we refer only to physical bilateral transactions aimed to transfer active power from generators to loads.

For our purposes, as will be clear hereinafter, we need the following assumptions:

-  the market model is characterized by only bilateral transactions involving generators and loads and not third entities such as pools or marketers;

-  each agreement between generators and loads is assumed to be an active power exchange between one generator and one load, i.e., let with subscript k the generic k-th transaction, PGk and PLk the active powers sold by the generator and bought by the load, we have PGk=PLk.

On the basis of this model, assuming nT transactions settled in the market, we have 2nT transaction buses. Denoting with ST the 2nT-dimensional vector composed by the complex power injected by generators in the first nT rows and the complex powers of load demands in the remaining nT rows. The vector of injected powers ST, can be decomposed into a sum of nT terms of transactions acting simultaneously in the power system as follows:

(1)

where Wk is a 2nT-dimensional vector characterizing the complex powers of the generic k-th transaction in which only two elements are different from zero corresponding to the generator and load involved in the k-th transaction. The following example aims to clarify the ST vector structure:

As can be noted, each generator or load holds the position as it has been filled into the vector ST.

3 Active and Reactive Power Injections

The aim of this section is to evaluate the active power for losses and the reactive power needed by the network and all market participants. For this purpose, we consider an n-nodes power system represented by its nodal equation having each line modeled with a p-equivalent:

(2)

where represents the complex current injection vector, is the complex nodal voltage vector and Y is the nodal admittance matrix.

Equation (2) can be rewritten for a system reduced to all nodes with a non-zero injected current. Moreover, in this representation, we split each generator with transactions into fictitious active and reactive generators.

Distinguishing electrical variables, associated to nG active power generators, nL load nodes, nC reactive synchronous or static compensators, nQ reactive power generators and the unique slack bus with subscript P, L, C, Q and S respectively, eqn. (2) can be reformulated in more detail as follows:

(3)

We perform a different partition of eqn. (3) as follows:

(4)

where:

The row and the column of the nodal admittance matrix corresponding to a reactive power generator are structured with only two elements that are different from zero. This characteristic is because such a generator is connected to the rest of the system through the unique line connecting it to its corresponding active power generator.

With the adopted system representation, the complex current vector IR will be:

(5)

Equation (5) represents the nR-dimensional vector (nR=nC+nQ+1) of complex currents injected by compensators, reactive generators and the slack bus. These currents are dependent on the transaction current vector, IT, and ER voltages at buses where reactive power is injected into the system.

The specified complex current vector IT can be expressed in terms of ET voltages and ST powers injected at same nodes as:

(6)

The (2nT=nG+nL)-dimensional vector, ST, representing transacted powers, is composed by active powers injected by generators in the first nG rows and complex powers of load demands in the remaining nL rows.

The vector of complex powers injected by the nR nodes, SR, will be composed by reactive powers injected by the nC compensators (QC), the nQ reactive power generators (QQ), and the complex power injected by the slack bus (PS+QS). With these assumptions, the SR vector will be synthetically described as follows:

(7)

Note that, the active power injected by the SR vector represents system losses.

The next step consists in evaluating the complex power injected by the R nodes, SR, depending on the active power transacted by market players. For this purpose, the following derivation is used:

(8)

where:

(9)

and

(10)

As can be noted, the complex power SR can be split into the terms SW and Snet The first term exhibits an explicit dependence on the transaction vector, ST, as well as on voltages at generator and load buses. The second term depends on network topology and voltages at nR nodes.

The right-hand side of eqn. (8) can be evaluated if ER, ET and ST are known, i.e., if the operating point is specified. This operating point can be determined considering all scheduled transactions acting simultaneously on the system. This hypothesis permits us to implement a load flow calculation where compensators are PV buses, where P=0, and transaction generators are split obtaining PQ buses, with Q=0 (active generators), and PV buses, with P=0 (reactive generators).

The obtained values of ER and ET enable eqns. (9) and (10) to be easily implemented and thus to obtain the transaction and the network components, SW and Snet.

4 Active and Reactive Power Contributions

The aim of this section is to evaluate the impact, due to each transaction, on reactive power injected by compensators, the slack bus and generators.

In the two following subsections we give a detailed knowledge of active and reactive contributions of the two terms SW and Snet leading to vector SR.

a) Transaction Power Contributions SW

The ST vector appearing in eqn. (9) can be replaced by expression (1) giving rise to power contribution SW depending on the sum of nT injection vectors as follows:

(11)

where represents the generic contribution to the complex power, SW, due to the k-th transaction.

b) Network Power Contributions Snet

The Snet complex power contribution, as can be noted by Eqn. (10), does not exhibit an explicit dependence on transactions. In order to share this term among injections, we propose a practical distribution rule. Derived network active and reactive factors are to be considered as fixed contributions due by market participants since they have the right to use the network. For this reason, we adopt a practical rule aimed to share the complex power network contribution, Snet, equally among all market participants as follows:

(12)

with

and representing the generic contribution to the complex power Snet due to the k-th transaction.

At this stage, eqn. (7) can be reformulated in terms of contributions due to each transaction as:

(13)

From the previous equation it is possible to evaluate the system loss component of each transaction as

(14)

where I0 is a (nR x 1) unit column vector used to sum losses induced on all nR nodes by the k-th transaction.

Reactive powers injected by compensators, generators and the slack bus can be obtained considering the imaginary part of (13):

(15)

Once the arbitrary sharing rule for the network term Snet has been applied, the overall power can be univocally broken down into terms depending on injections. We can observe that, for a fixed operating point, the unique term strictly dependent on injections is represented by SW. Thus, this term is the only one that can be rigorously shared among transactions.

The total amount of reactive power injected by all generating units, due to transactions and the network, will be:

(16)

The term represents the total reactive power needed to exchange the power involved in the market. Differently, the term is the total reactive power required by the network in order to support the specified voltage profile. This service could be considered as a common benefit of all market participants and, consequently, derived costs should be recovered by all of them as network fee.

5 Test Results

The loss allocation method presented in the paper was tested adopting a simple three bus system and the IEEE-14 Bus Test System.

We assumed all generators as PV bus whereas load buses as PQ bus. Reactive powers of loads were obtained fixing loads power factors equal to 0.9.

Results are provided in p.u. on 100 MVA base.

For this system, we assumed the node # 1 to be the slack bus.

Transaction data expressed in terms of active power agreed, voltage magnitude at sending buses and reactive power at receiving buses are reported in table 1.

Table 1

Transactions Data

The system operating point, evaluated through the load flow, is illustrated in Table 2.