ANETO: A System for the Automatic Generation of Theoretical Network Models J. A. García Conejo
A. Gómez Expósito, Fellow IEEE
D. Electrical Regulation Endesa, S.A. Seville, Spain
[email protected]
Dept of Electrical Engineering University of Seville Seville, Spain
[email protected]
G. Tévar Bartolomé
M. Rodríguez Montañés
D. Electrical Regulation Endesa, S.A. Madrid, Spain
[email protected]
Energy and Environment Isotrol, S.A. Seville, Spain
[email protected]
Abstract— This paper presents the main features characterizing ANETO, a tool intended to automatically generate a theoretical distribution network connecting available transmission sources with customers at all levels (high, medium and low voltages). In addition to the main modules, design criteria and algorithms behind ANETO, illustrative results arising from its application to the Spanish system will be shown. Keywords-component; distribution remuneration; reference network; network planning
I.
INTRODUCTION
Within the context of liberalized electricity markets, the distribution activity remains as a separate and regulated monopoly, for which appropriate and fair remuneration procedures, aimed at promoting efficiency and improvement of the quality of service, should be developed. However, putting into practice any of the available remuneration schemes, already implemented more or less successfully in other monopolistic sectors, is far from being trivial. The aim is to properly quantify the true costs incurred by a distribution utility when serving its market according to technical and reliability standards established by the regulator, assuming efficient planning criteria are adopted. This involves the commissioning, operation and maintenance, throughout their lifetime, of a large volume of interconnected installations
across a diversity of areas, each one characterized by different constraints (technical, administrative, environmental, etc.). Perhaps the biggest challenge in this regard lies in the socalled “information asymmetry”. This arises from the fact, that in order to properly assess the adequacy, fairness and efficiency of the economic incentives associated to each remuneration scheme, the regulator needs an exhaustive amount of information which can only be provided by the utilities. Obviously, there is always a risk for this crucial information to be manipulated, biased or incomplete, which explains the reluctance of regulators towards inventory-based approaches. Mainly for this reason, among the several possibilities available to remunerate the distribution activity, the Spanish regulatory system considers the option of comparing existing distribution networks with pseudo-optimal theoretical models developed from scratch. Such models try to minimize the total investment cost plus ohmic losses, keeping in mind all relevant constraints, including maximum number and duration of service interruptions [4]. This paper presents the first prototype of the theoretical network model promoted by Endesa, that constitutes the starting point for assessing the applicability of this remuneration scheme within the premises of the Spanish regulator. In a forthcoming paper, several features added more recently, related with the development of incremental network models, will be presented.
II.
GENERAL OVERVIEW OF ANETO
A. Objectives ANETO is a complex software tool intended to build from scratch a suitable subtransmission and distribution network interconnecting the transmission sources with all electricity customers located within a given geographical area. Following standard planning practices, the resulting network tries to minimize the investment cost plus ohmic losses while at the same time satisfying both electrical and interruption-related operating constraints.
- Miscelanea (customer density thresholds to identify urban areas, obstacles to network layout such as lakes or protected areas, etc.). D. Major blocks Figure 1 shows the major blocks composing ANETO along with their associated data flows.
B. Main Underlying hypotheses Given the complexity of the problem and the huge size of the data base, it has been necessary to adopt a series of simplifying assumptions, some of them similar to those on which standard planning practices are based, namely: - The electrical demand (peak and average power) is determined from customers billing information at a given time instant, without any consideration to past or future evolution. - The existing network is ignored (the entire distribution network is built from scratch). That is, a static suboptimal problem is considered, according to Spanish regulations.
Figure 1. Major blocks composing ANETO and relevant data flows
- Three-phase balanced situation is assumed. - The overall design problem is decomposed into three weakly coupled subproblems, each one focused on a particular type of network (subtransmission, primary distribution and secondary distribution). - Transmission sources are ideal (infinite power capability). - Operating and maintenance costs are ignored, as they are remunerated through a different mechanism. C. Input data The most relevant information for the model is the one associated with transmission sources and customers. Existing 400 kV and 220 kV substations feeding the subtransmission and/or distribution networks constitute ideal power sources located at their actual geographical coordinates. Individual customers, or sets of customers fed at the same voltage and location, constitute the sink points (about eight million aggregated points result from some twenty million customers in Spain). Such points are characterized by their geographical coordinates, voltage level, aggregated power demand and municipal entity to which they belong. Other input data can be summarized as follows: - Technical parameters (permissible rated voltages, catalog of standard equipment such as cables or switching devices, maximum voltage drops, ampacities, etc.). - Unitary cost associated to each piece of equipment or investment decision. - Parameters related to standard planning practices (simultaneity coefficients, power and load factors, percentage of underground networks in urban areas, maximum number of cables allowed to share a trench, etc.).
The lowest block in the figure, electrification of low voltage customers (secondary distribution level), comprises four blocks: identification of urban entities and classification of customers, location and sizing of MV/LV transformers, electrification of rural areas and electrification of urban areas. Based on the location and size of both medium voltage customers and MV/LV transformers, the intermediate block determines the size and location of distribution substations and builds a pseudo-optimal MV network (primary distribution level). Different electrification algorithms and switching strategies are used for rural and urban feeders so that satisfactory interruption indices are obtained. Finally, the subtransmission high voltage level, linking distribution substations to transmission sources is defined in such a way that the N-1 contingency criterion is satisfied. The thin feedback arrows in the figure represent situations in which a feasible solution can not be found and the previous module has to be reconsidered (for instance, an extra transformer may be needed if the low voltage network cannot satisfactorily reach all customers). The objective and outcome of each of those blocks will be explained in more detail in Section III below. E. Hardware and software platforms The system runs on a Linux-based distributed platform, as shown in Figure 2. Object-oriented C++ programming environment, along with auxiliary tools (oracle data bases, graph-related libraries, web-based interface execution control, etc.) have been adopted. The hardware is based on twenty Pentium machines linked via a 100 Mbps LAN. Nine of the computers are used for the distributed execution of the algorithms, while the remaining ones are devoted to code development, web interface, control, DNS, oracle server, etc.
typically the case of a city crossed by a river, containing a park, etc.
Figure 3. Market classification and identification of urban nuclei.
- Convex contour building. The perimeter of most urban areas is rather irregular and non-convex. At this step, the smallest convex contour containing each urban entity is determined (see Figure 3, right), which will be useful when designing the HV and MV overhead networks surrounding the nucleus.
Figure 2. Hardware architecture of ANETO
III.
FUNDAMENTAL COMPONENTS OF ANETO
A. Market classification At this preliminary stage ANETO detects clusters of customers and classify them as being urban (medium and large cities), rural (small urban nuclei) or disseminated (scattered loads). This is needed because of the different reliability requirements, network configurations, switching schemes, etc. adopted in each market niche. For each demand point the following information is used: coordinates, power consumption and number of aggregated customers. This stage comprises five major steps: - Market grid creation. The Spanish peninsular territory (about 490,000 km2) is divided into a uniform grid of regular size and each demand point is then assigned to the cell where it lies. The size of the cell is critical for the success of the next steps, 200x200 meters being a good compromise obtained after several trials. - Classification of market cells. For each municipal entity, each cell is labelled as urban or disseminated, depending on whether or not the number of customers within the cell exceeds 10. Again, this threshold, which has a significant influence on the results of subsequent steps, is the result of several trial-and-error processes. - Market identification. Sets of two or more urban adjacent cells are identified and considered as a potential urban entity (see Figure 3). For each candidate nucleus its perimeter is determined, which is composed of the outer bound plus eventually the border of inner areas composed of non urban cells. Each nucleus is classified as urban or rural according to the total power demand being or not larger than 10 MW. - Aggregation of neighboring nuclei. In addition to actual urban entities, the former step leads usually to a large number of small adjacent nuclei, which are aggregated at this step according to a distance threshold (see Figure 3). This is
B. Siting and sizing of MV/LV transformers This module determines the theoretical number of service transformers, as well as their location and size, necessary to cover the LV demand within the area of interest (in this case a municipality), keeping in mind the electrical constraints (power balance considering simultaneity coefficients and maximum voltage drop). This task is obviously coupled to that of determining the layout of both MV and LV feeders (a larger number of transformers decreases the length of LV feeders and tends to increase that of MV lines), turning the overall problem into a very complex one. For this reason, an off-line theoretical analysis was previously performed in order to determine the economic reach of a service transformer as a function of the load density (W/m2) and number of LV customers served (demand points/m2). Such a study is based on regular geometric patterns of customer locations and feeder layouts (both at the MV and LV levels), from which the optimal reach of LV feeders, and hence the area served by the associate transformer, is found. As a result, a transformer reach table for each environment (rural and urban) and typical load density scenarios is obtained. A greedy-like algorithm is applied to all the cells of a municipality, starting with the area of highest load density. When the economic reach of the transformer in hand is attained (according to the respective reach table and catalog of standard equipment), a new transformer is considered, and so on until all of the cells are included within the area of influence of a unique transformer. Each transformer is finally located at the barycenter of the load it feeds (Figure 4). If needed, urban transformers at the periphery can feed nearby disseminated customers. C. LV electrification This module builds the LV network, from each transformer to its associated loads, that minimizes the investment cost plus losses, keeping in mind the electrical constraints (ampacity and voltage drop) as well as simultaneity coefficients. A heuristic minimum-distance iterative algorithm, whose details are omitted here for the lack of space, has been developed to determine the radial topology of the pseudo-
optimal network, as well as the conductor size. For this purpose, an extensive list of standard conductor sizes, electrical parameters, costs, etc. is employed. Note that, in rural areas, extra nodes, known as Steiner nodes, may appear in addition to demand points, in order to decrease the total length (see Figure 5). This is not the case of urban areas, where feeders are forced to track streets (real or synthetic), as shown in Figure 6. Conductors are selected on the basis of linear cost approximations, as explained in [1], chapter 7.
simultaneity coefficients and maximum voltage drop) as well as continuity of supply reliability indices.
Figure 6. Details of a LV network in an urban area.
Figure 4. Service areas of MV/LV transformers for a sample case
Two relevant features of the adopted solution are: the size of each feeder section is not constant but economically adapted to the respective load; the number of feeders is not fixed a priori, but determined on the fly by the algorithm.
A province is divided into smaller areas by means of a heuristic divide-and-conquer algorithm. At every step, the surface in hand is divided into two components by means of a maximum-distance regression line, in such a way that approximately one half of the total load lies at each side of the line. The maximum-distance regression line is the one that maximizes the weighted sum of distances from all demand points (each demand point, transformer or MV customer, is weighted according to its peak power). The process is recursively repeated until the resulting areas comprise a total load that can be fed from substations of standard capacity (at least two transformers are sited at each substation so that the N-1 security criterion is satisfied). Once suitable service areas are identified, a substation of appropriate size is located at the barycenter of the load. In case the barycenter lies within a populated area, an attempt is made to locate the substation as close as possible to the convex contour of the urban zone, in order to minimize the length of underground HV feeders. Furthermore, based on average failure rates of MV feeders, a maximum feeder length is computed a priori for each load density so that the resulting SAIFI index is lower than the legal limit. This maximum length is imposed as an upper bound to the distance of any MV load or transformer to the substation, assuring in virtually all cases that MV feeders designed at the next step are not too long.
Figure 5. Details of a LV network in a rural area.
The maximum voltage drop is checked a posteriori, once the feeder topology and size is obtained. In case of limit violations, a sensitivity-based analysis is performed in order to increase the feeder size at minimum extra cost so that the resulting voltages become acceptable. In case it is not feasible for a transformer to properly feed all the load within its service area, the system goes back to the former stage, where the number and size of transformers is reconsidered. D. Siting and sizing of substations This module determines, at the province level, the number, location and size of the distribution substations needed to feed all service transformers and MV customers, keeping in mind the electrical constraints (power balance considering
E. MV electrification This module builds a least-cost MV network between the substations and the demand points inside their service areas, in such a way that electrical constraints (ampacity and maximum voltage drop), as well as continuity of supply reliability indices, are satisfied. Both rural and urban feeders can be fed from the same substation. Sectionalizing centers are located at the urban periphery when external substations must feed urban areas. The urban network is composed of self-sufficient radially operated rings. An open ring is composed of two feeders, without laterals, departing from the same substation, each one with enough spare capacity to satisfy the demand of the other half in case of emergency. Urban feeders are assumed underground within the perimeter of the urban nucleus and aerial otherwise.
The service area of an urban substation is radially divided into sectors of similar load, each one fed by a ring. Then each sector is approximately divided in two halves, each one corresponding to the area served by a radial feeder. Finally, keeping in mind the actual or synthetic layout of streets, each feeder is designed by means of a minimum-length heuristic algorithm, in such a way that all transformers are sequentially reached. The last transformers of each half ring are connected through a normally-open feeder section.
The topology of both networks, eventually containing laterals, is obtained by applying least-cost electrification algorithms which are quite similar to that employed for the LV rural network. Conductors are selected from a MV catalog on the basis of linear cost approximations, as explained in [1], chapter 7. A major difference with respect to the LV network is that in this case due attention must be paid to the switching and protection equipment (reclosers and fuses) necessary to achieve an acceptable level of continuity of supply indices. Figure 8 shows the theoretical MV rural network of an entire province, comprising 2,401 transformers which are connected through 4,260 km of overhead lines. For comparison, the actual network is composed of 3,638 transformers and 4,748 km of lines. If the service area initially assigned to a substation is too large for the MV network to be electrically feasible, then it is split in two approximate halves and the process is repeated with two substations.
Figure 7. MV urban network of a nucleus demanding more than 30 MW
An example of urban network feeding over 30 MW is shown in Figure 7. The length of the theoretical MV network generated by ANETO is 298 km, feeding a total of 842 transformers, whereas the actual network comprises 279 km of underground cables interconnecting 821 transformers.
F. Area of influence of HV power sources Assuming ideal power sources, this module determines, in a purely geometric manner, the area of influence associated to each transmission substation. First, Thiessen polygons are determined for the set of sources in the entire national territory. The boundaries of such polygons, mathematically characterized by the perpendicular bisectors of the lines between a set of points, define the area that is closest to each point relative to all other points. Then, the resulting polygons are divided into the so-called Delaunay triangles. Each couple of adjacent Delaunay triangles sharing the edge opposite to the vertices where the power sources are located, defines a rhomboid that will be the basic unit for HV electrification, es explained below. G. HV electrification This module builds the HV rings necessary to connect subtransmission substations and HV loads to the HV sources, taking into account ampacity and voltage drop considerations. First, each rhomboid defined above is longitudinally divided into sectors of similar load when no conductor in the catalog has enough capacity to feed the total rhomboid load. Then, a minimum-length ring is determined interconnecting the set of loads within a sector, starting and ending at the rhomboid vertices where a power source is located. In case a single Delaunay triangle remains (this happens for instance in coastal or frontier provinces), the ring starts and ends at the same source.
Figure 8. MV rural network spanning a Spanish province
The MV overhead network, running outside the urban areas, is designed in two steps: - First, a trunk or primary network is built between the substations and sectionalizing centers, making it sure that the N-1 security criterion is satisfied. - Then, a capillary or secondary network is built linking disseminated transformers, and those of very small populated areas, to sectionalizing centers or substations.
Each ring is dimensioned keeping in mind the worst-case contingency, namely the situation in which it is open from one edge and all loads are fed from the other. Two voltage levels (50 and 132 kV) and several conductor sizes in the catalog are tested, and the one with lowest cost (investment plus losses) is chosen. Figure 9 shows the theoretical HV network obtained in this way for the Spanish peninsular territory. It feeds 1,172 distribution substations by means of 38,595 km of overhead lines (in the actual network, 45,679 km of lines feed 1,366 substations).
D. MV network design The theoretical model considers different planning criteria for urban and rural environments. This includes reliability requirements, topology, protective schemes, etc. However, further efforts should be directed to better tune the theoretical network model to the constraints of the real world, such as: - Use of rated voltages at the MV level in accordance to the actual values existing in the area under consideration. - Actual location and size of service transformers should be resorted to whenever possible, especially in urban areas. - The degree of cable burying in urban areas should reflect as much as possible the one corresponding to each municipality.
Figure 9. Theoretical HV network for the Spanish peninsular territory
IV.
DISCUSSION
The following comments are in order regarding the results provided by ANETO and its potential limitations: A. Theoretical HV network The HV network historical evolution is significantly conditioned by a series of factors, in particular those related with the development of generating stations and national energy policies. This is in part a consequence of present subtransmission networks being initially conceived and designed to play the role of a transmission system. Such relevant factors cannot be taken into account by static algorithms, aimed at minimizing cost, which explains the large discrepancies between the reality and the theoretical results. B. Distribution substations and MV network In the same way, the location of distribution substations is strongly affected in practice by non technical factors, like the difficulties in finding appropriate locations, particularly in the surroundings of urban areas. Furthermore, the total cost of this subsystem is very sensitivity to the voltage level adopted, which is frequently the result of decisions taken decades ago. C. Service transformers The location and size of transformer centers, particularly in urban environments, is also conditioned to a large extent by municipal rules and other non technical factors. Therefore, it is expected that the theoretical model provides reduced figures in this regard. In view of the above considerations, since the volume of information necessary to perform a detailed account of assets at the transmission and subtransmission levels is rather modest and can be easily audited, it makes sense to conceive a remuneration system based on actual inventory of equipments whenever possible, leaving just the task of developing the MV and LV networks to the theoretical model.
E. Dynamic versus static network planning While any real network is the result of the cumulated dynamic evolution during the last decades, driven by load evolution, the theoretical model behind ANETO is of a static nature, that is, a network is built from scratch to satisfy all the present demand. Therefore, eventual discrepancies with respect to reality do not necessarily mean that the existing network is inefficient. In fact, the static model favors rural areas, where the load evolution tends to be much slower than in dense urban areas, particularly near touristic coastal regions. V.
CONCLUSIONS
This paper presents the main features and components of ANETO, an ambitious software tool intended to automatically build a theoretical but realistic model of the subtransmission and distribution systems spanning a huge territory, like the Spanish peninsula (490,000 km2, over 20 million customers). Sample results provided by the most relevant modules are shown, along with an analysis of where future efforts should be directed to. It can be argued that, owing mainly to the fact that the dynamic evolution of the market is ignored, significant discrepancies between the theoretical model and the actual network sometimes arise which cannot be attributed to inefficiencies of existing planning standards. An incremental model, intended to circumvent these limitations to a large extent, is currently under way that will be the subject of an upcoming paper. ACCKNOWLEDGMENT The authors are thankful to the many other people involved in this project. The third author acknowledges the support of Junta de Andalucía under grant TEP-1882. REFERENCES [1] [2] [3]
[4]
H. L. Willis, Power Distribution Planning Reference Book. Marcel Dekker, 1997. G. Strbac, R. Allan, “Performance Regulation of Distribution Systems using Reference Networks”, Power Eng. J., pp. 295–303, Dec. 2001. D. Giannakis et. al. “Benchmarking and Incentive Regulation of Quality of Service: An Application to the UK Electricity Distribution Utilities”, CMI Working Paper Series, The Cambridge-MIT Institute, 2003. J. Román, T. Gómez, A. Muñoz, J. Peco, “Regulation of distribution network business”, IEEE Trans. on Power Delivery, Vol. 14 (2), April 1999.
