--- title: "Expert System for topological remedial action discovery in smart grids" source_url: "https://hal.science/hal-01897931" source: "HAL MedPower PDF" --- # Expert System for topological remedial action discovery in smart grids Expert System for topological remedial action discovery in smart grids A Marot, B Donnot, S. Tazi, P Panciatici To cite this version: A Marot, B Donnot, S. Tazi, P Panciatici. Expert System for topological remedial action discovery in smart grids. MedPower, Nov 2018, Dubrovnik, Croatia. ⟨hal-01897931⟩ HAL Id: hal-01897931 https://hal.science/hal-01897931v1 Submitted on 18 Oct 2018 HAL is a multi-disciplinary open access archive L’archive ouverte pluridisciplinaire HAL, est des- for the deposit and dissemination of scientific re- tinée au dépôt et à la diffusion de documents scien- search documents, whether they are published or not. tifiques de niveau recherche, publiés ou non, émanant The documents may come from teaching and research des établissements d’enseignement et de recherche institutions in France or abroad, or from public or pri- français ou étrangers, des laboratoires publics ou vate research centers. privés. HAL Authorization Expert System for topological remedial action discovery in smart grids A. Marot, B. Donnot, S. Tazi, P. Panciatici (RTE R&D) Abstract— For power grid congestion management, lots of is sometimes flawed by habits. Our expert system should research have focused on using generation redispatching, load assist them in understanding their problem under study in a shedding or demand side management flexibilities. However, specific context, and ultimately help them discover and use a less costly option would be grid topology reconfiguration. Branch switching has been previously explored, since it could more strategical options. Indeed, it should : be formulated as a linear programming optimization problem - dynamically provide them on new situations a focused we can solve, and showed some benefits. This can further be representation of the grid, conditioned on their problem. extended to the broader class of non-linear nodal reconfigura- - suggest them some initial solutions (single topological tions at substations. In this paper, we present an expert system action) if they exist within that representation. to automatically discover such topological remedial actions on congested grid states. It comes with a new adapted grid - allow them to go beyond the machine proposal and find representation, conditional to the congestions of interest, which more complex remedial actions based on this representation. can be interpreted by operators. To test our expert system, we Even in the case no toplogical remedial action is found, independently run it on thousands of realistic congested French they can indeed interpret the visual representation to ap- grid states from 2012 to 2014 with a remedial action discovery prehend quickly the situation and the limits of this expert success rate of 75%. Our exploration is quite efficient, since it is limited to single substation topological action and is usually system, further guiding the search with more expertise. successful on first try, even in the case of overloads above 30%. This philosophy of collaborative human-machine interac- tions is actually a driver of a larger RTE R&D project, named I. INTRODUCTION Apogee, whose ambition is to build a personal assistant for In the era of smart grids, new flexibilities are needed our control room operators. Related to this work, previous for congestion management to handle new power flow dy- work [4] have investigated labeling of historical operator namics without expanding the grid with heavy investments. preventive actions to learn from them. Unfortunately, few Controlling injections seem the most intuitive way to deal contingencies occur in reality. Hence not every curative with such congestions and has been widely explored [1], [2]. actions can be observed. Currative actions that were not Nevertheless, it imposes some constraints on external actors implemented cannot be learned in the same fashion, which such as producers to gain grid flexibility, which comes at justifies the need for this complementary avenue. Those a cost. But power flows are also determined and influenced two approaches however both rely on a same foundation: a by the grid topology. For TSOs who own and operate their counterfactual approach to replay realistic scenarios to learn grid, topology can be changed at negligible cost. But those from, which uses detailed power system simulators at our changes are often highly non-linear and need more advanced disposal on top of historical operational data. algorithms to be controlled. Branch switching [3] is a first The paper is organized as followed. Section II is dedi- step in that direction. However it is only a percent of what cated to the method, where we describe our counterfactual could be done if considering a more general class of topology approach coupled to some expert knowledge to rank a priori reconfiguration: nodal reconfiguration at substations. New the most efficient topological actions. Section III illustrates remedial actions or more robust ones could be implemented. our method on a didactic example: the IEEE14 case. Section In communication networks, topology switching at high IV further dives into the analysis of topological sensitivities. frequencies is a crucial aspect of information routing. In Section V eventually provides systematic results when run- power grids however, we have been more cautious with such ning our expert system on the French Power Grid, measuring actions given the hazardous nature of electricity. Indeed there its performance. Section VI gives conclusions. is an associated risk of short circuit that can be harmful or damaging for assets which has to be considered. Neverthe- II. METHOD less, some TSOs such as RTE, have been successfully using A. Problem statement: Congested powerflow a fraction of possible topological remedial actions for years, In this section, we suppose that we have at our disposal a thanks to operator studies and proper asset management. simulator Sim which, given injections vector and a reference In this paper, we are interested into curative topological topology (P bus, T opon ), compute the power flows P f n on actions. Our goal is to automatically offer our operators many n lines in service, and detect k overloaded lines Ov n : efficient options to manage a stressed grid in a strategic manner, avoiding them the search of such options iteratively (Ov n , P f n ) = Sim(P bus, T opon ) (1) in a study as it is today. Our operators know some efficient ones by experience after many years of studies. But their Those overloads create congestions that grid operators breadth of search has been limited, and their understanding have to manage to ensure grid security. They indeed look for topological actions t at substation b (atb ∈ AT opon ), From our GOv , which defines a relevant influence zone to changing the topology from its reference T opon , to relieve explore, we want to identify topological spots to route our t the k detected overloads such that Ov ab = 0: congested flow. To do so, we first extract some meaningful t t structure from the graph as on Figure 1 to reason on: (Ov ab , P f ab ) = Sim(P bus, T opon atb ) (2) • the constrained P athc , that is the connected flow path In other words, we would like to route the flow of those to the overload with negative distribution. congested paths towards other parallel electrical paths. In a • upstream U a and downstream Da areas relative to the meshed grid, we know they exist, since flows we observe overload given the initial flow direction on GP f . are actually a superposition of flows, shared over multiple • Parallel P ath// with positive distribution, paths that paths. But how can we detect them as we are only observing supply similar loads downstream than P athc . a resulting grid state of entangled flow superposition? • Loop P athl , a P ath// also connected upstream to When interested in a specific variable, a proper way to P athc : flows are also supplied by similar productions. discover what influences it is to directly intervene on it. • local routing spots: Hub as nodes intersecting P athc Interventions have proven very useful in the field of causality and P ath// or P athl , multi node substations nmulti [5]. In our case, ”what if” our overloaded line was not and Open circuit lines Loc . available? If power could not flow through it, where would it Based on the detection of such structural elements, we can flow? This virtual flow distribution will actually unveil those further identify 4 different GOv cases we can encounter: latent mutually interacting parallel path with our power flows • Looped GOv if we have at least one P athl of interest, helping us identifying interesting topological • Parallel GOv if we have at least one P ath// spots to influence our congested flow. With a simulator at • Multi Nodes GOv if we have at least one nmulti our disposal, let’s hence run this counterfactual reasoning • Unmeshed GOv if there is no meshing option. through a topological sensitivity analysis by switching off our overloads Of f (Ov n ) leading to n-k active lines: C. Expert knowledge: identifying routing buses Let’s now introduce some expert knowledge to rank the (Ov n−k , P f n−k ) = Sim(P bus, T opon Of f (Ov n )) (3) topological actions that could help us route the flow differ- (∆Ov n−k , ∆P f n−k ) = (Ov n−k , P f n−k ) − (Ov n , P f n ) ently. It relies on two expert principles, that is modifying (4) the relative impedance of electrical paths or creating a new injection pathway between 2 zones at different phase B. Overload distribution Graph: a congested influence zone potentials. More specifically: 1) Hub are the most interesting spots because you can On top of this sensitivity results, we can now build a locally route flow by splitting nodes and pushing new representation of the grid, the ”Overload distribution the incoming or outgoing injections towards P ath// , Graph” (GOv ). It is similar to the usual representation of connecting them together, while isolating from those a directed power flow graph GP f over a grid, with the injections our P athc , and as a result from our overload. same connectivity and directions, but whose edge weights 2) On P athc we would like to increase its impedance to are ∆P f n−k instead of P f n (see Figure 1). However it is hinder the flow by node splitting or branch switching. rather different as it is not a global graph over the grid, 3) On P ath// we would like to decrease its impedance but it becomes a local influent zone when only considering to ease the flow. To do so we can merge nmulti or sensitive flow distributions over a threshold th (th = 5% for switch on Loc . French Power Grid), below which we truncate our GOv . 4) Over Da on P athc , we might want to merge nmulti or switch on Loc as well but with the intent of bringing power from elsewhere. Looking at nodal phase poten- tials, we can guess in which direction power will flow when merged. This tells us if it should be beneficial or not. Conversely for U a looking for loads. D. Ranking topologies with Expert knowledge We eventually assess by simulation topologies at sub- stations ranked along these categories 1 to 4. When two substations belong to the same category, we prioritize the one with the most ingoing or outgoing, negative or positive, flow Fig. 1. On the left, two local grid representations around the overload: distribution on GOv . In the case of Unmeshed GOv , topology a zoomed GP f and the GOv . On GP f , grey flows are insensitive ones is inefficient, the only solution will be load shedding: we can to Of f (Ov n ) and do not appear on GOv . On GOv , blue lines have decreasing flow while red lines have increasing flow. Expert labels are hence detect infeasible cases. represented. On the right, a real GOv example on case 6515rte. Congested Finally, for a given substation, we also rank topologies, as line l4815 in dark blue and remedial substation Bus4225 in green. on Figure 2, since there are very often more than 20 possible configurations with the same active lines. The main goal is to ”break” P athc , to increase this path impedance, setting ingoing and outgoing P athc on 2 different nodes. Second, you want to route as much flow as possible on P ath// . Given those two principles, if you are on U a, you want to connect on one node outgoing P athc towards the overload to non-sensitive ingoing and outgoing flows, plus local loads. On another node you connect the remaining sensitive flows, ingoing P athc , P ath// , and production. Conversely on Da. Fig. 4. IEEE14 system and its power flow on the left. Red nodes for production and blue for loads. On the right, our G10 , the overload distribution graph for our powerflow of P f5 → 6 . Red edges for flow increase, blue for flow decrease and grey for non-sensitive flows. • P athc = 5 → 6 → 13 (U a = {5} and Da = {6, 13}) • P athl1 = 5 → ... → 9 → ... → 6 • P athl2 = 5 → ... → 9 → ... → 13 • Hubs = {5, 6, 13} Over the P athl , we can further discard any substation that Fig. 2. How to preferably reconfigure electrical nodes in U a or Da, given is not a hub and whose topology is fully connected as a single the related GOv elements for a given overload (bold blue), plus the local electrical node, that are substations {4, 7, 8, 9, 10, 11, 14}. productions and loads as well as the non-sensitive grey path. Indeed, as explained in Section II) C), while we would like Our overall expert system is finally depicted on Figure 3. to push more flow over such paths, we can only perform here a node splitting operation for those nodes, which will increase the path impedance and hence repel flows. Hence it will not ease the flow on l5 → 6 but load it even more. C. Topology reconfiguration at Bus 5 and 6 as remedial actions We are now left with buses on the constrained path here, especially our Hubs, to solve our problem. Bus6 is the most promising and ranked first as in section II) D), since it is a hub in the middle of P athc , which we can ”break” while still supplying the loads from a parallel path, and it has a Fig. 3. Expert System Algorithm for topological curative action discovery. high ingoing distribution flow (45 MW). Being in Da, we perform the following node splitting on Bus6 (Figure 2) : III. A DIDACTIC EXAMPLE • connect the ingoing P athc to outgoing non sensitive A. The IEEE14 case path and to local productions or ingoing flows, that is N ode1 = {10, 12} For illustration, we will consider the IEEE 14 power • connect the ingoing P athl to outgoing P athc , and local system and apply our algorithm to it. Considering line 10 loads. that is N ode2 = {11, 13, load6 } connecting bus 5 to 6, an interconnection between the high voltage and low voltage grids, we can imagine it getting This indeed results in a 15 MW decrease, corresponding overloaded when load demand is high. We will hence study to 30% of the initial power flow, which is quite effective. how to reroute part of this powerflow from our reference Of course, you should avoid making new congestions and meshed topology as on Figure 4. While changing topology, monitor the powerflow on other loaded lines. load6 could we don’t want any line being turned off as it is often more be switched to node 1 here as an alternative topology for a robust to operate all of them to increase grid’s capacity. smoother flow distribution, resulting in a 4 MW decrease. For the two remaining Hubs, Bus5 is better suited than B. Overload Distribution Graph over line l5 → 6 Bus13 since about 85% of our overload fictively got redis- From Figure 4, we can observe our influence graph after patched there based on GOv , compared to 40% at Bus13 opening l5 → 6 : this is a Looped GOv we computed through after intervening on l5 → 6 . Not to mention that Bus13 cannot Matpower [6]. The flow distribution highlights a zone of be split into 2 nodes here while preserving a meshed grid, topological influence to consider, mainly the low voltage having only 3 lines and not a minimum of 4. Being in U a, grid, while discarding the high voltage grid. More precisely, we should perform the following node splitting on Bus5 : buses being discarded at this stage are: {1, 2, 3, 12}. In terms • connect the outgoing P athc to outgoing non influential of structure on the graph, we identify several paths: path and local loads, and to minimum ingoing injection paths, that is N ode1 = {5, 10, load5 } • connect the outgoing P athl to local productions and to θb = Fbbus × (P bus − P busshif t ) (7) maximum ingoing injection paths, so N ode2 = {2, 7} Putting it into equation (6), and introducing This indeed results in a 2.5 MW or 6% decrease. Another P busshif ted = P bus − P busshif t , we have: option could be connecting all outgoing paths on N ode1 = {5, 7, load5 } and all ingoing paths on N ode2 = {2, 5} 1 P fij = (F bus − Fjbus ) × P busshif ted resulting in a 6 MW decrease as on Figure 5 but it is more xij i (8) brutal as it changes the topology mesh and flow direction. = P T DFij × P busshif ted Here appears the well-known Power Transfer Distribution Factors (PTDF) used to study power flow sensitivity to injections. In our case, we are interested into Topology Dis- tribution Factors, an extension of Line Outage Distribution bus Factors (LODF). We can further get the contribution Cij of every P bus to each powerflow P fij on this grid state: m X m X P fij = P T DFijb ∗ P busbshif ted = b Cij (9) b=1 b=1 Fig. 5. Topology reconfiguration on IEEE14 at identified Hubs, Bus5 and For a given topology T opon , we can hence detect the most b Bus6 . On the left, the flow distribution after Bus6 most promising node influent P busk on P fij given their related contribution Cij . splitting. On the left, the flow distribution after Bus5 node splitting. By selectively analyzing the evolution of those specific sen- sible influences (busb0 ∈ S(P fij )) under atb , and discarding Topological reconfigurations at buses 5 and 6 happen to others, we can get an estimate on how much our powerflow be potential remedial actions when line 10 gets overloaded. of interest changes, to anticipate atb ’s effectiveness a priori: They are actually the only topological ones that keeps a   P b0 ,n meshed grid. We knew it a priori based on our expert system  |P fij − 0 0 C b ∈S ) ij |  without any greedy search. Of course, this could be found by S(P fij ) = argminS 0 ⊆Buses |S 0 | | <= 10%  P fij  other methods on such a small example. But our method can hopefully scale to much larger grids, such as RTE French (10) power grid with about 6000 buses, 500 of which having m m  more than 7 connected power lines making the meshing more  atb X b0 ,at X b0 ,n complex and the search space much bigger. If our method     ∆P fij = C ij b − Cij b0 =1 b0 =1 seems already effective, can we rank the topologies more b0 ,at 0 0 X ≈ (P T DFij b − P T DFijb ,n )P busbshif ted  formally, and interpret those results more globally?     0 b ∈S(P fij ) IV. A NALYSIS OF TOPOLOGICAL SENSITIVITIES (11) A. From local expertise to global and formal analysis Moreover, we can interpret more globally, and not only Beyond this expertize which helps prioritizing buses to in terms of local flows, as we did based on our GOv , how look at qualitatively, we could investigate some theoretical long distance injection influence evolves to explain a change foundation for it. Doing so, it could be possible to use more in powerflow. This could be further understood as a relative global quantitative measures to better rank the topologies. change in effective resistance Req, between our overload and We are interested into influencing power flows, which are those influent injections, to highlight which path impedance mainly driven by active power. The DC approximation is really changed. Indeed Bbus+ and Req are closely related: often good enough to screen the space of flexibilities at Reqij = Bbus+ + + ii + Bbusjj − 2Bbusij (12) our disposal with about 5% accuracy loss. Given Bbus, the Laplacian adjacency matrix, θ, the node potentials, and x, the In terms of computation, Bbus+ (T opon atb ), and further line impedances, we have the following load flow equations: PTDF, coefficient can be computed efficiently, incrementally and with parallelism, from original Bbus+ (T opon ) under a P bus = Bbus × θ + P busshif t (5) topological change [7]. Authors in [8] give additional insights 1 for interpretation by detecting flow cycles while defining a P fij = (θi − θj − θshif t ) (6) dual representation of the network. xij Bbus being a Laplacian, we can compute its pseudo- B. IEEE14 case: topology sensitivity interpretation inverse Bbus+ (T opo) = [F1bus | ... | Fm bus ]. Bbus and Based on this derivation, let’s compute our injection con- + Bbus only depend on the topology T opo. Once computed, tributions on our IEEE14 example to interpret more deeply we can actually get at every bus b the contribution factor what happened under our influential topology changes. On Fbbus of every P bus to the potential θb . Figure 6, one can see the contribution evolution of every ations over those cases, we looked for illustrative ones for our method. One was the following: on case 6515, after a contingency on l4816 , l4815 gets overloaded when setting the thermal limit to its 95 MW value. The related Looped GOv can be seen on Figure 1. The influence zone is quite large but we can extract from it our structural elements P athc , P athl and Hub to guide our search: • P athl1 = 2541 → ... → 3947 • P athl2 = 2540 → ... → 3947 • Hubs = {2540, 2541, 3947} Hub 3947 is the most promising, belonging to 2 looped paths. And indeed, there is a topological remedial action that has really been implemented on the grid in the past, Fig. 6. Evolution of injection influence to P f56 under different topologies in colors, relatively to injection values in grey, to interpret topology impact. with 2 electrical nodes leading to 12 MW decrease and resulting in a flow of 92 MW. Even if the bus is 3 hops away from our overload, and there can be many other buses injection to our powerflow P f56 . P f56 is mostly driven by to consider at this distance, it is the first choice of our expert the main production at bus 1, the loads at buses 6, 12,13,14 in system.It actually appears that is the only relevant one beside the West consumption area. It also feels the loads at buses 3, opening some lines. We here illustrated the expert system 4 and 5 which rather pull the flow in the opposite direction, effectiveness at being selective even on a larger zone, proving masking some of the influence of production 1. However, to be really helpful in the remedial action search. our powerflow does not feel the loads in the East Part of B. Systematic results on thousands of realistic cases the grid because East and West are actually balanced, with similary meshed subgrids to supply them. In this case, we To test our expert system systematically on a larger grid, have S(P f56 ) = {1, 3, 4, 5, 6, 12, 13, 14} we had to generate a realistic database of congested situations When we change the topology at Bus6 , the West Part based on French historical snapshots between 2012 and 2014, Load influence decreases and Bus9 influence becomes sensi- given that we rarely observe any overloads on real snapshots. ble. Indeed, the electrical paths through Bus6 became longer To be representative, we selected 9am, noon, 4pm, 7pm with greater impedance, giving more importance to Bus9 to snapshots over the days, on which we run security analysis. now supply the loads all over the distribution grid, breaking We then studied the overloaded situations, with at least 2% the subtle subgrid balance. Contributions of production 1 and overload, that could have occurred after a contingency. On loads 3 and 4 diminishes consequently but proportionally. As average, there are 80 risky contingencies per snapshot to a1 study, over 10.000 power lines. a results we estimate ∆P f56bus6 ≈ −10.8M W . When we change topology at Bus5 in the second configu- To consider realistic topological actions, we restricted ration, we make our line relatively closer to loads 3 and 4 and ourselves to the ones that have been applied at least once in a further from production 1 compared to previously. This pulls snapshot in the past. This makes 52.539 possible topologies the flow in the opposite direction, hence decreasing it. This over 6.091 substations. Our heuristic will only pick up to 20 is even more true in the second node splitting configuration topologies among these, up to 5 per substation, and try to at bus 5 for which production 1 gets far away, leading to find as many remedial actions as possible. We also tested up a1 a2 to 3 branch switching on P athc per congested situation. ∆P f56bus5 ≈ −3.0M W and ∆P f56bus5 ≈ −5.6M W . Scores from 1 to 5 are given to an action: 5 if every Even if our estimates are rough approximations on such overloads disappeared, 4 if an overload disappeared without a small grid, we can rank them a priori in the right order. stressing the network, 3 if at least 30% of an overload was Especially at Bus5 where it was unclear which configuration relieved, 2 if an overload was relieved but an other appeared will be best a priori with only an understanding of interac- or got worse, 1 as failed if no overloads were alleviated or if tions locally at this bus over our GOv on Figure 4. it resulted in some load shedding or production distribution. V. R ESULTS ON F RENCH P OWER G RID From the result table on Figure 7, we see that most of We will now describe results on the larger grid of interest the feasible situations are Looped ones, meaning meshed to us: the French Power Grid. We will present one more local grids. In these situations, individual topological curative reproducible and relativeley difficult example over the Mat- actions can be quite effective, with an overall success rate power 6515rtecase. Finally, we will share systematic results (score above 4) of 76% to relieve overloads. of our expert system, after running it over thousands of Independently analyzing branch switching and nodal re- situations, and discuss them. configuration, switching leads to a remedial action 55% of the time but if not, worsen the situation (score below 2) A. One More Example: the 6515 RTE case in 39%, while nodal reconfiguration helps in 64% cases Four historical French Power Grid snapshots have been with only 19% worsened situations from the result table on recently released [9]. Running through congested N-1 situ- Figure 8. For Extra High Voltage overloaded lines (30% of Fig. 7. Summary table of most efficient topological action found per congested situation (max 20 topologies explored over 5 substations) by our expert system on French Power Grid. Fig. 9. On the left, histograms of the minimum load flow required to find a topological solution in congested situations in red, and of the number cases), success rate even reach 79% for nodal reconfiguration of successes per topology ranking in blue. On the right, success rate at a substation according to its ranking a priori, when at least 3 substations have while branch switching remains at 57%. Finally, for VHV been explored, summing to 14546 situations. Grey histogram showing the lines in cases of high overloads (above 30% of their thermal sample proportions of situations for a given substation exploration depth limit), we still manage to achieve a high success rate of 73% a median of 8 remedial actions per line. These numbers with nodal reconfiguration. This demonstrates that our expert could be further increased if considering actions that have not system can be very effective at discovering single topological been implemented. It could hence highlight interesting nodal actions for meshed high voltage transmission grids. A control reconfiguration that were not considered, pushing forward room operator can further implement such suggestions on the need for studying such flexibilities and maybe upgrading a congested situation or compose more complex topology substation assets to enable its implementation. reconfiguration from those unitary results. VI. CONCLUSIONS Our expert knowledge system proved to be successful by discovering topological remedial actions a priori, beyond branch switching, in a selective manner, relying on a simple local counterfactual reasoning and few load-flow computa- tions. The underlying ”distribution graph” can further be interpreted by a control room operator to discover more complex remedial actions. This successful counterfactual Fig. 8. Summary Table of most efficient topological action in Looped reasoning can also be jointly applied to the whole grid to congested situations, depending on the type of topological action and the nature of the overload. represent overall zonal segmentation of it [10]. In terms of applications, our expert system can be used in real time to Finally, looking at the relevance of nodal topology recon- make remedial action suggestions or can help initialize a re- figuration ranking overall on Figure 9 bar plots, we notice medial action database given historical snapshots. Systematic that, when we find a solution for a meshed and complex results on RTE’s French Transmission grid when applying situation (at least 10 actions tested on a congested situation), our method highlighted the potential of topological actions we can find a successful one for 70% of cases when testing to make smarter grids, making the point that such flexibilities up to 3 actions. 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