Optimization based method to consolidate European Transmission Data

Transcription

1 Optimization based method to consolidate European Transmission Data Manuel Ruiz Michael Gabay Artelys Paris, France Jean Maeght Mireille Lefevre Patrick Panciatici RTE Versailles, France Abstract In this paper we present a merging procedure which is used to build a consistent description of the European network based on the data provided by the different Transmission System Operators (TSOs). In order to deal with inconsistencies in the data, we introduce a modified Optimal Power Flow (OPF) minimizing the deviation from TSOs data. Results on the European network demonstrate the interest of this approach on real-life cases and illustrate the impact of the deviation measure in the optimization process. Index Terms Power Systems Network Merging; Optimal Power Flow; Non Linear Programming; State Estimation I. INTRODUCTION This study is part of the itesla project which aims at improving European network operations with a new security assessment tool. This tool aims at improving security on the European high voltage transmission network by assessing the risks in the system and providing preventive and curative actions to keep the system in a secure state. In order to perform the security assessment it is essential to have a reliable description of the underlying network. However, there is no such data at the European scale. In this paper, we present a merging procedure, based on an Optimal Power Flow (OPF), to build a consistent and reliable description of the European network based on the data provided independently by European TSOs. We introduce several variants and provide an analysis of their results and a sensitivity analysis The security assessment is performed ex post and requires a description of the network at an earlier time t. In an ideal case, each TSO would provide accurate data, representing the network state at the exact time t. A simple power flow computation would then be sufficient to establish the state of the whole network. Unfortunately, available data are not synchronized between TSOs and may be erroneous since some parts of the network cannot be observed. In real-life, each TSO collects measurements on its own network at a slightly different time than t and estimates values of the data in the missing parts of the power system. In the scope of the itesla project, these non-synchronized and erroneous data, have to be collected in real-time and merged in order to build a consistent state of the European network for security assessment. This problem of state estimation enhancement [1] leads to the resolution of an Optimal Power Flow whose objective is to find a feasible solution minimizing the deviations from the well-estimated parts of the network. This problem has already been considered by RTE, the French TSO, who introduced an objective of minimizing a weighted least squares distance and implemented the OPF in an optimizer for merging European networks. This merging tool is used at CORESO (COoRdination of Electricity System Operators) on a day-to-day basis since More details on power system optimization and OPF formulations can be found in [2]. The itesla project is introduced in the following Section II. In Section III, the problem is formally introduced and the contribution is detailed. The optimal power flow which is solved and three available deviation measures which are experimented are introduced Section IV. Finally, computational experiments illustrating the results and the differences between deviations measures are presented Section V. II. THE ITESLA PROJECT The Innovative Tools for Electrical System Security within Large Areas (itesla) project is a European research and development project co-funded by the European Commission [3] and involving 6 European TSOs, 13 other R&D providers and several academic partners. The aim of this project is to develop a flexible inter-operable toolbox which is able to support future operations of the pan-european electricity transmission network. This toolbox shall enable to perform: Accurate security assessments taking system dynamics into account using time-domain simulations Risk assessments taking into account: uncertainties (especially intermittent power generation uncertainties), probabilities of contingencies and possible failures of corrective actions. The itesla toolbox includes two main components: an off-line platform, running every week, in charge of exploring the network state space to draw the separation between stable and unstable states (using data mining techniques and high-fidelity dynamic simulations). This platform is especially in charge of identifying security rules to apply.

2 with TSOs data, the objective function is used to penalize modifications of the data. The data provided by each TSO become targets and the aim of the optimization problem is to find a feasible merged network state minimizing the deviation between targets and actual values in a feasible network state, as illustrated Figure 3. Fig. 1. The itesla work flow an on-line platform, running every day, dedicated to security assessment. This second platform evaluates the off-line platform security rules on the current network and issues curative or preventive actions, when necessary. The high-level itesla work flow is described Figure 1. The on-line platform is also in charge of acquiring and merging data provided by the European TSOs. III. MAIN CONTRIBUTION This paper describes the OPF implemented in the itesla toolbox to consolidate TSOs networks into a single, consistent, European network. The input of this OPF is a topological merge of European TSO s network data performed with the most reliable data available for time t. The output is a feasible European network state for the time t, minimizing the deviation from these data. Figure 2 illustrates the network state after the topological merge: the network state in each country is consistent but the whole network is not. One of the reasons is the power flow on interconnections: when a European AC load flow is solved, the active power flow on interconnections is computed using the characteristics of the interconnections quadripoles and the voltage of the buses. The computed and the telemetered values are usually incompatible since data from the different TSOs are not synchronized. Fig. 3. Merged network Additionally, there are different types of data and different levels of confidence on the data: Time differences: the aim is to compute a network state at time t but the data provided by the TSOs can be up to one hour older There are different reliability levels: 1) Snapshots (SN): data based on real-time observations and measurements on the network. If they are recent, these data are very reliable. 2) Day Ahead Congestion Forecasts (DACF): these are forecasts data for a given time. If a TSO is not able to provide its snapshot data in time, the DACF data (which have been provided the day before) are used as a replacement. Obviously these data are less reliable than SN data. The different confidence levels are accounted for by penalizing the deviation from the original data differently depending on the type of data. In the subsequent Section IV, we present the OPF (decision variables, constraints and objective). Advantages and drawbacks of the different deviation measures are also considered. Experimental results are provided Section V. IV. MATHEMATICAL FORMULATION Fig. 2. Network to merge In order to build a consistent merged network, we introduce and solve a modified ACOPF. For the sake of consistency The power flow is modeled using an AC formulation. The model is similar to the polar PQV ACOPF presented in [2]. Additionally, the loads are decomposed into two parts: a constant part given by TSOs plus a slack variable for the deviation. The deviations model the gap between the values provided by the TSOs and the values in a feasible solution. The collected data describe the buses of the network. Two types of buses are distinguished: PV and PQ. For PV buses, active production, voltage and load are given. For PQ buses, active and reactive production and load are specified.

3 In the model, the active and reactive production of the PQ buses and the active production of the PV nodes are fixed. For feasibility reasons, the voltage of PV nodes is allowed to be modified with a very strong penalty applied to the deviation. The voltage of PQ buses and the reactive power of PV buses are within their bounds but not penalized. The aim is to find a consistent network state which is as close as possible to the collected data. This means that the deviations on the loads have to be minimized. The deviation variables on the loads and voltage levels ensure that a feasible network state exists. They also model the deviations from the targets (TSOs data). As a result, the objective is to minimize a weighted sum of these deviation variables. In order to account for different phenomena the minimization different penalty functions has been considered: Manhattan norm (L 1 ) Sum of squares (L 2 ) Huber function The parameters of these functions are the normalized deviations and the results are multiplied by a factor representing the confidence in the data. The advantages and drawbacks of these functions are presented in the sequel. 1) Manhattan norm: The Manhattan norm sums the values of the normalized deviations. It helps focusing on minimizing the total sum of the deviations. Since the results are weighted, using this norm, helps focusing on modifying data in which there is small confidence. Additionally, since the impact is linear there is no advantage at modifying several variables preferably to a single variable. As a result it may help localizing incorrect data and correct them. However it can fail to spread corrections when many small deviations are necessary, because of small measure errors or a small time difference. 2) Sum of squares: This is the mean squared error: the weighted sum of squares of the normalized deviations is minimized.this favors very small modifications over many variables preferably to significant modification on few variables. This prevents the deviations from being too significant. It helps finding a feasible solution within a limited range of the original one which is especially interesting if TSOs data is reliable but can fail to correct a localized error. 3) Huber function: The Huber function is quadratic for small differences and linear for wide variations. This favors spreading deviations provided they remain small and does not strongly penalize strongly a significant change of a variable. The Huber function is equal to: { r 2 if r c ρ(r) = c 2 + 2c( r c) if r c where c is the threshold between the quadratic and linear part of the function. Theoretically, with a good value of c, it combines both the advantages of L 1 and L 2 norms. This approach has already been successfully applied in [4]. Additionally, the value of the sum of two Huber functions is constant and minimum over a confidence interval. This is especially interesting if there are different targets T 1 and T 2 for the same data, as illustrated Figure 4. In this study, each country provides a telemetered active power flow for interconnections. There are therefore two telemetered values for each interconnection. These two targets can then be used as a sum of Huber function. cost value Fig. 4. Sum of to Huber functions centered in 250 and 260, with c = 2 V. COMPUTATIONAL EXPERIMENT The itesla toolbox will operate at a Pan-European level. The European very high voltage grid is composed of around 6000 buses. This underlines how challenging this project is. The three different penalty methods are therefore tested at the European scale to understand their impact on the optimization. The OPF is implemented using AMPL [5] and solved with KNITRO [6], [7] non-linear optimization solver. Experiments The model used in CORESO, which we call L2-OPF, uses L 2 (actually sum of squares) for deviations on loads and voltage of PV buses and Huber functions for deviations on interconnections. In this paper, we design an alternative OPF model using L 2 norm for deviations on voltage level of PV buses and L 1 norm for deviations on loads and interconnections. This OPF is called L1-OPF. In the experiments, we compare the results obtained with L2-OPF and L1-OPF. Starting from a consistent network state, a is introduced and both OPF are used to consolidate the network data. Then we compare the results obtained with both OPF. Unfortunately, there exists no real-life consistent dataset for the whole European network (recall this is why this OPF is made for). Instead, we compute a consistent solution using the L2-OPF and then disturb it and apply the L1 or L2-OPF. This approach makes sense because for both variants of the

4 OPF, if we start with a feasible solution, then the value of the objective is 0 and we have a global optimum. Different s are considered in order to assess the advantages and drawbacks of the different measures in various cases. A. No : Merging a consistent state First of all, we ensure that starting with a consistent network, the OPF is able to find a feasible solution with no deviation in short time. The merging procedure is applied to a consistent state (i.e. obtained by the merging procedure). This test might seem trivial but is actually not since there are many intermediate variables to estimate and additionally interior point algorithm are theoretically not good with restarts. In practice however, even if OPF are highly non-convex continuous optimization problems, the interior point algorithm implemented in KNITRO succeeds in reaching the global optimal value for both models. B. Pulse on snapshot In a pulse, the load on a snapshot node is increased by 100MW (the ratio reactive power / active power is kept constant). This corresponds to an error in a perfect data set. The focus here is not to correct this error but to ensure that the does not propagate to other countries.it is expected however that the propagates to a few nodes within the disrupted country. C. Multi-node on DACF The multi-node on DACF consists in applying a widespread and balanced on the loads over a total of 10 or 20 nodes. In order to generate this, 2 connected disjoint sets of 5 or 10 nodes are randomly selected in a DACF country. Then, the load of each node in the first set is increased by 20% and an opposite is applied to the nodes in the second set, proportionally to their initial loads. The aim of this is to ensure that a on a DACF country does not propagate to snapshot countries. Datasets We present an analysis of these s on an instance with 5542 nodes spread over 11 countries: Country Code Status Austria AT DACF Belgium BE SN Switzerland CH SN Czech republic CZ SN Germany DE SN and DACF France FR SN Croatia HR DACF Italy IT SN Netherlands NL SN Poland PL DACF Slovenia SI SN German network data are snapshot on some parts of the country and DACF on the other parts. Results One of the main objectives of the model is to keep power flow on interconnections within the targets. For all s, with both L1-OPF (using L1 norm on interconnections) and L2-OPF (using a Huber function on interconnections), the deviations on interconnections are all kept smaller than 1MW. Hence, in the following, we focus on the deviations on the loads. The performances of the different measures are assessed based on the active deviations on the loads. We analyze the total deviation, the maximum deviation and the number of non-zero deviations. We say that the deviation on a node is non-zero if its absolute value is smaller than 1MW. 14 experiments were conducted and are presented in Table I. The s detailed in the next subsection appear in bold in Table I. 1) Pulse on SN: In this example, 100MW are added to the active load of a single node located in France. The original load of the node was 110MW. The reactive power is modified to keep constant the reactive/active power ratio. The absolute values of the deviations are presented by decreasing order in Figures 5 to 8. Fig. 5. Deviations after merge with L1-OPF norm on a pulse Fig. 6. Deviations after merge with L2-OPF norm on a pulse In both cases, the total algebraic deviation has an opposite value to the pulse: its value is equal to -96MW for the L1- OPF and -102MW for the L2-OPF. Additionally, in both cases, the positive deviations are negligible: the sum of all positive deviations is smaller than 1MW.

5 Fig. 7. Log scale: Deviations after merge with L1-OPF norm on a pulse problem. 2) Multi-node on DACF: We now consider a balanced in a DACF country (Poland). The absolute values of the deviations are presented by decreasing order in Figures 5 to 8. With L1-OPF, the sum of absolute values of the deviations is equal to 6.9MW and only one node has a deviation larger than 1 (with value 6.74MW) so the overall deviation is balanced and a feasible solution is found within very close neighborhood of the disrupted instance. With L2-OPF, the sum of absolute values of the deviations is equal to 40.4MW while the sum of the signed deviations is equal to 9.5MW. No deviation is larger than 1MW and the sum of the absolute values of the deviations applied to the disrupted country is equal to 39.3MW: the deviation is spread over the nodes of the disrupted country. Using both OPF models, data are successfully consolidated and the is not spread to other snapshot countries. Distribution of the loads are very different between the two models but matches numerical property of the two norms. Fig. 8. Log scale: Deviations after merge with L2-OPF norm on a pulse Regarding locality of the perturbation, the deviations applied using the L1-OPF are very local: 7 deviations are larger than 1 and the sum all absolute values of the 5535 other deviations is equal to 1.3MW. These 7 deviations are located in the same country as the. However, the deviation on the disrupted node is null. The deviation is very local and the maximum value is equal to 42.9MW. With L2-OPF, some SN loads are modified in the disturbed country but most of the deviations comes from DACF countries. Only 13 loads are larger than 1MW, with the maximum deviation being equal to 2.9MW. The first 281 largest deviations are on DACF countries. All but 5 of the following 807 deviations are on the disturbed country (France). These deviations all have the same order of magnitude ( 0.02MW). The total deviation applied to DACF nodes is equal to 62.6MW while the total deviation applied to the disrupted country is equal to 16.6MW. The remaining 23MW are spread on 3156 nodes in other SN countries. While both OPF succeeds in finding feasible solutions. Only the L1-OPF does not spread the deviation to other countries, which is the expected behavior from a TSO point of view. We observe that with L1 norm, deviations are local and have a large magnitude while using an L2 norm favors spreading the deviations. These are known numerical properties of these norms but it was not obvious that they could be observed on a strongly constrained non-linear, non-convex, optimization Fig. 9. Deviations after merge with L1-OPF on a multi-node Fig. 10. Deviations after merge with L2-OPF on a multi-node 3) Overall: Disruptions are applied to the same instance. All tests are run using KNITRO 9.0 on a laptop computer. The optimization completes within 30 iterations performed in less then 2 seconds for L2-OPF and 4.5 seconds for L1-OPF. The results on the 12 other experiments are similar to the results presented in sections V-C1 and V-C2.

6 L1 Sum of squares Disruption type Abs. dis Country #Non-zeros Dev. max (MW) Total dev. #Non-zeros Dev. max (MW) Total dev. FR 7 42,9 96,5 13 2,9 102,4 FR 5 42,2 95,4 13 2,8 100,8 IT 8 39,6 99,9 23 3,3 117,8 DE 2 95,8 100,5 13 2,3 93,6 Pulse SN 100 FR 7 46,8 91,2 13 2,8 98,5 FR 3 50,1 97,5 13 3,0 107,4 FR 8 33,4 95,1 13 2,8 100,4 CH 7 54,9 100,0 12 3,3 102,4 FR 10 53,3 98,2 13 2,8 99,5 FR 6 40,8 89,4 12 2,7 96,2 DACF (10 nodes) 292 PL 3 3,8 7,1 22 1,7 106,6 259 PL 2 3,9 8,3 2 1,3 67,3 DACF (20 nodes) 511 PL 1 6,7 6,9 0 0,6 40,4 636 PL 3 15,2 30, ,3 236,1 The column Abs. dev gives the sum of the absolute values of the applied. The Non-zero column denotes the number of deviations which are larger than or equal to 1. Dev. max is the maximum absolute value of a deviation and Total dev. is the sum of all absolute values of the deviations. TABLE I RESULTS ON AN INSTANCE WITH 10 PULSE DISRUPTIONS AND 4 DISRUPTIONS ON DACF local but have a significantly larger magnitude. While OPF models are highly non-convex non-linear optimization problems, we observe that the numerical properties of the L1 and L2 norm still hold and can be observed on the results. Further work may focus on deviations on reactive power and voltage of PV nodes. As several criterion are to be taken into account, one may use a multi-stage optimization procedure and a hierarchical order of criterion (snapshot and then DACF, active power and then reactive power, etc. ). Fig. 11. Log scale: Deviations after merge with L1-OPF on a multi-node Fig. 12. Log scale: Deviations after merge with L2-OPF on a multi-node REFERENCES [1] M. Dancre, P. Tournebise, P. Panciatici, and F. Zaoui, Optimal power flow applied to state estimation enhancement, in Proc. 14th Power Systems Comput. Conf, [2] M. B. Cain, R. P. O Neill, and A. Castillo, History of optimal power flow and formulations, Federal Energy Regulatory Commission, Tech. Rep., [Online]. Available: opf-papers/acopf-1-history-formulation-testing.pdf [3] itesla project website. Project supported by the European Commission under the 7th Framework Programme. [Online]. Available: http: // [4] S. Fliscounakis, Influence of parameter accuracy on estimated resistive losses, IEEE PES France, Proceedings of the RTE-VT Workshop on State Estimation and Forecasting Techniques, [5] R. Fourer, D. M. Gay, and B. W. Kernighan, AMPL: A Modeling Language for Mathematical Programming. Duxbury Press, Nov [6] R. H. Byrd, M. E. Hribar, and J. Nocedal, An interior point algorithm for large scale nonlinear programming, SIAM Journal on Optimization, [7] R. H. Byrd, J. C. Gilbert, and J. Nocedal, A trust region method based on interior point techniques for nonlinear programming, Mathematical Programming, vol. 89, no. 1, pp , VI. CONCLUSION In this paper, an OPF for data consolidation is introduced and two variants are studied. Using the L2-OPF, one can find feasible solutions which are very close to the original data. However, deviations are spread over all nodes which may cause issues if there are errors, such as the presented s, in the data. Using L1-OPF deviations are more