Dear Gasim 

Power system monitoring and control in real time can be done with the help of state estimator (SE) program. SE periodically computes an estimate of the operating state of the sub network of interest there by produces an approximate model of the true operating state of the system. Where as load flow analysis is used in contingency analysis for each contingency case to obtain complete and accurate solution of complex bus voltages at system buses. 

Dear Salah,

I think the most important difference is about the possible composition of the input vector into both classes of techniques.

Power flow analysis requires you to provide exactly enough information as needed to determine all state variables of the simulated network. And not more than that. Power flow analysis techniques (such as Newton-Raphson) cannot handle measurement redundancy (a surplus of information, which among themselves can not be independent). Therefore power flow analysis are ill-suited for monitoring real networks, in which you would take more measurements than you actually need in order to be able to compensate for slight errors and detect large errors.

This is where State Estimation comes into play. To the best of my knowledge the current state of the art technique was first published by Prof. Schweppe, MIT, et. al. in 1970 as a publication triplet:

Schweppe, F. C. (1970). Power System Static-State Estimation, Part III: Implementation. Power Apparatus and Systems, IEEE Transactions on, (1), 130–135. doi:10.1109/TPAS.1970.292680

Schweppe, F. C., & Rom, D. B. (1970). Power System Static-State Estimation, Part II: Approximate Model. Power Apparatus and Systems, IEEE Transactions on, (1), 125–130. doi:10.1109/TPAS.1970.292679

Schweppe, F. C., & Wildes, J. (1970). Power System Static-State Estimation, Part I: Exact Model. Power Apparatus and Systems, IEEE Transactions on, (1), 120–125. doi:10.1109/TPAS.1970.292678

This technique is able to handle measurement redundancy (so, over-determined cases) and minimises the error between the theoretical observations you would see if the estimate was accurate and the really observed measurements. But it also cannot handle under-determined cases (or 'measurement deficiency') and requires all state variables to be determined from the available measurement data; which is sometimes hard to realise.

I hope this helps. If you have further questions, just ask.

regards,

    Olav

Great thanks dear Dr. Olav. Your help is highly appreciated.

OK, what if we compared state estimation on a side and SCADA and phasor measurements and Wide Area Measurement System (WAMS) on the other side ..

Thank you so much ..

Dear Salah,

from what I can see in recent publications, phasor measurement units have frequently been used to reduce state estimation problems down to a linear problem. If you know all currents/voltages with magnitude and (relative) phase angle, you're back to the nodal admittance matrix for interpreting them; but nowhere close to a real monitoring system.

From my understanding SCADA implies a relatively local, close to process level, control, while WAMS is focused on transmission systems. Conditions and requirements are quite different here. I'm an neither an expert on SCADA, nor on WAMS. But I consider them being two extreme ends of the same problem, with the common topic being hard real-time capabilities (for different reasons though).

Traditional State Estimation techniques are hardly deployable in either scenario, due to their iterative nature (they cannot guarantee neither convergence nor execution time). I haven't followed WAMS development closely, but I can tell from current research (own and by others) that state estimation techniques based on linearisation perform reasonably well on SCADA systems; and under hard real-time conditions. What you essentially need is a sensitivity analysis (analytic or sampled) of input to output values. This is super fast and does (mathematically) always work. But it has significant precision problems with branch flows in meshed networks (especially on low loaded lines).

But what are you currently looking at research or project-wise?

best regards,

   Olav

That is great .. Thank you so much Dr. Olav.

I am trying to discover to extend and enhance my background ..No a specified direction .. ..

Actually load flow analysis has been considered in power system analysis courses while I have only heard about state estimation. I do not know why it is not included .. It seems to me that it state estimation as the name points is closer to real time sensing of power system operating variables for real time control.

Power flow analysis is the determination of all bus voltages, bus angle and line flows by systematic calculations wither using NR, Gauss Seidal etc.

SE is the estimation of remaining  bus voltages, bus angle and line flows by giving input details of certain/limited bus voltages, bus angle and line flows.

Here it is remember that system details including line data, load data are preliminary requirement in both cases of Power Flow and SE.

Dear Salah,

that's right. For monitoring of a real system you would always want to use State Estimation, because it can handle over-determinacy. This allows you to put some measurement redundancy in the monitoring system, what in turn allows you to compensate for small errors, detect large errors (and exclude this data --> Bad Data Detection) and even handle loss of communication to some extend (as long as the remaining measurement data still 'covers the whole network'.

If you want to explore the current State-of-the-Art I can recommend an amazingly comprehensive and helpful book (and just to make sure: I am neither one of the authors, nor associated with them)

Abur, A., & Expósito, A. G. (2004). Power System State Estimation: Theory and Implementation (Power Engineering (Willis)) (1st ed.). CRC Press.

Really well written, quite comprehensive and the references are extremely helpful if you want to know more about a specific technique. 

regards,

    Olav

That is really nice dear Dr. Olav ..

Your help is very highly appreciated. You gently dedicated many papers and a helpful book ..

Will touch these materials and refer to you later ..

Great thanks and best regards.

Load flow analysis is basically calculation of flow of power through the network and hence change in the value of voltage and angle of corresponding buses of the network and state estimation is a digital algorithm to provide raw data to reliable data and it usually provides the value with minimal error and SE tries to capture true condition of voltages ,angles etc.

Hi Salah,

to know the steady state condition of a network means to solve a power flow problem, as well as an optimization problem. Normally you know the input (powers) and by supposing that the network parameters are well known, you obtain the output (voltages)

To estimate the network's state means capture the input (powers) and the output (voltages) for knowing which are the real physical states of the network.

By designing an observer you know the real input and the real output to obtain the paramenters that can be, for example, time variant.

State estimation = close to reality normally you obtain a dynamic system

Power flow = well defined but just in some condition (resistance = constant, capacity = constant ecc)   

Dear all,

I always wanted to try this. I will try to give an explanation as to what is behind the traditional state estimation not in a purely mathematical way, but in a figurative way.

Please provide me with some feedback as to if it is understandable, or which parts of the explanation might need some more work.

So, let’s start! The fundamental problem of any power flow analysis or state estimation is that the available information is not the one we’re after. We usually have information about nodal power balances, line currents, etc., but we want to have a coherent internal state, represented by the complex-valued voltage profile of the network.

Mathematically we have two different spaces (or domains), the _state space_ (domain of complex nodal voltages for power systems) and the _measurement space_ (domain of actual observations, which are directly measurable). Both domains are mathematically linked through a set of (normally non-linear) equations (the _measurement system_), which, sadly, only work in one direction – from state space to measurement space. But this is the wrong way around, so we have to find a way to invert this measurement system.

The method of choice to still translate an observation M into a corresponding state X is through iterative improvement using a Newton approach. In any case this starts off with an initial guess of a possible internal state, which is hopefully not too far from the actual solution. Usually a ‘flat’ voltage profile with all voltage magnitudes at nominal voltage and with zero voltage phase angle differences is used. From there the _theoretical observations_ are calculated. So to speak, the measurement data you should be seeing if a) the assumed system state was accurate and b) all measurement data was 100% accurate. If the mismatch between actual observations and theoretical observations is too high, an system state improvement step would follow and be repeated until the mismatch satisfies a _convergence criterion_ (e.g. being close enough to zero).

In both power flow analysis and state estimation the improvement step would be about inverting a linearized approximation of the measurement system. The linear approximation is the Jacobian matrix of the measurement system in the assumed system state. And it is the inversion process where power flow analysis and state estimation differ. In power flow analysis, the required structure of the provided measurement data (Slack, PV or PQ buses) ensures that the Jacobian is non-singular and can be inverted. (Side comment: This is not always the case, especially under heavy load conditions, where the Jacobian can turn singular for a number of different reasons. But under ‘regular’ conditions this is generally true). With the Jacobian mapping a change to the system state to an approximate of the corresponding change in observations (measurements), the inverse maps a change of observations (measurements) into an approximate of the corresponding state change. In power flow analysis this is used to find a state change that would ‘remove’ the observed mismatch between actual and theoretical observations. With the Jacobian just being a linear approximation of the measurement system, this is not absolutely precise, but relatively good. Repetition of this improvement step allows to iteratively converge into system state corresponding to the actual observations (measurements).

So much for the well known Newton-Raphson.But what about the State Estimation introduced by Schweppe et. al.?

The general problem with State Estimation is, that you have more observations (measurements) than state variables – the system is so called ‘over-determined’. This leads to the Jacobian being rectangular, with more rows than columns. (Note: I am not touching on under-determined conditions here, since they cannot be solved with Schweppe et. al.).

With the Jacobian being rectangular, there is no inverse. But we still have to map a point from measurement space to state space. How to do this? I will try to explain the traditional approach in a more figurative way here:

Although the rectangular Jacobian not being invertible, it still related the state space to the measurement space. You can think of it as each column vector of the Jacobian mapping one state variable to a specific direction in the measurement space – all with a certain ‘stretching factor’. But the direction is more important. So, we do have a 2n-dimenional state space (n being the number of nodes of the network) being mapped to a 2n-dimensional sub-space of the measurement space by the column vectors of the Jacobian matrix (it hase to be 2n-dimensional, since the Jacobian has to be of rank 2n to not have an under-determined system). So, in some way the column vectors do span the sub-space where our ‘perfect’ theoretical observations would lie, but they are not independent, not of unity length and generally ‘all over the place’. But they do still relate them back to the state variables.

So, a genuine first step to find the state vector corresponding to a measurement vector would be to determine ‘how much’ of each column vector might be in the measurement vector. This will not give us a real inverse, but it will provide us with some understanding of how a measurement vector relates to the different state variables. This is the first step of State Estimation, where a measurement vector is multiplied with the transposed of the Jacobian matrix to determine ‘how much’ of each column vector is in the measurement vector by calculating the scalar products with them. This will translate from measurement space to state space (so, it is some kind of inversion), but this is not a ‘clean’ inversion, since the column vectors are neither independent nor of unity length.

(1) x = H^T*m

This is where the second part of the traditional State Estimation comes in: What if we could quantify this error or ‘uncleansiness’ of this imperfect inversion? If we knew about how much this process distorts the inversion, we could correct the results obtained from using the transposed Jacobian for an ‘unclean’ inversion.

So, let’s assume we have an unspecified, but known, system state (or system state change) x. What would be the approximate corresponding measurement (or measurement change) vector m? We can use the Jacobian here, with

(2) m = H*x

So, what would roughly be the ‘state distortion’ – or the error – introduced by the ‘unclean inversion’? By reusing (2), the estimate of the measurement (or measurement change) vector to a undetermined, but known, state (or state change) vector x, the ‘distorted state’ x_d can be approximated by probing the ‘unclean’ inversion process with the measurement vector generated form the know state vector. This is multiplying the transposed Jacobian (unclean inversion) with the Jacobian (the generation of the measurement vector)

(3) x_d = H^T*H*x

This gives us an understanding of how much a state gets distorted by the unclean inversion. But again, we need it the other way around. We do have a ‘distorted state’ and what to know what the actual state is. To correct a distorted state into its original, we can use the inverse of (3), which exists as long as H is of rank 2n. This translates a distorted state back to its original state and, when combined with (1) allows us to find the state (or state change) x corresponding to the measurement (or measurement change) m.

(4) x=(H^T*H)^-1 * H^T * m

Well. That’s basically it. (4) gives you an inverse that translates the 2n dimensional sub-space of the measurement space of ‘perfectly coherent measurements without any errors’ back to the 2n dimensional state space. When using (4) with an erroneous measurement vector, you are projecting this vector onto this 2n dimensional sub-space, effectively mapping you’re erroneous measurement vector to the ‘closest’ non-erroneous one. And with Euclidean distance and root mean squares sharing the same definition, you are finding the system state minimizing the root mean square error between theoretical observations and actual observations.

The matrix W in the technique is just for weighing inputs with their estimated precision.

I hope this helps and is somewhat understandable. Feedback on line of arguments is greatly appreciated.

Regards,

     Olav

State estimation is to control and monitor the modern power system. In load flow analysis, the best possible values of the bus voltage magnitudes and angles by processing the available network data

Dear all,

With people moving on to so called dynamic estimators which are focused in estimating generator parameters.., can somebody explain me how that differs from transient stability studies? 

I do understand that measurements and that too erroneous form the basic formulation of a state estimator and that may not be focused in transient stability.. Still is there any other difference?

Dear Olav Krause,

Your answer is quite insightful. Can you please tell me from where do we get the data to simulate the state estimation with a new algorithm? On some websites, data of power flow, bus-bus impedance, etc. are given. But how do we derive the Jacobian matrix (or the h() function that maps state space to measurement space) from these data?

Meera,

Let me try this.

State estimator is used primarily to observe and estimate the entire system status (yes, including generator status), so that system operators can have better understanding of the 'system'. It does NOT collect generator constants/parameters, which are needed in the transient stability types of studies. Typically, if the updated generator constants/parameters are NOT available, system operator/reliability engineers would use the previous or typical values. If updated gen parameters are available, all the better. But, these constants do not change frequently. So, why bother....but they don't stay constant all the time, so frequent updates are important.

Moving towards 'dynamic estimator model' is probably geared towards modeling and understanding 'dynamic world'. Traditional state estimators are used for modeling and understanding 'steady-state world'. I would always treat them as two different kinds of analyses for two different reasons!! 

I hope this answers your questions.

/J

Dear all,

 To the best of my knowledge ‘dynamic’ state estimation is a relatively new term and I agree with Jeremy. In other contexts I have seen ‘dynamic state estimation’ being used for approaches where the (for lack of a better word) ‘inertia’ of demand would be used to identify a plausibility interval for readings coming in from certain load points. The basic idea seems to be that sudden, drastic changes in load behavior (perceived as being the ‘dynamic’ of the load) are very unlikely. But I think this is a very misleading use of the term ’dynamic’, which in power systems is reserved for ‘true’ dynamics in time domain.

Anyway. What I really wanted to add to this enjoyably persistent thread is a little test implementation I’ve developed in MatLab. This addresses Varun’s question (since it has all the standard functions’ Jacobians defined) and somehow refers to Jeremy’s comment that state estimation would be used to estimate the state of an entire network, or “system status” as he called it. Yes. That’s current state of the art and a consequence of Prof. Schweppes formulation of his Weighted Least Mean Squares State Estimation I talked about in one of the earlier posts. If there isn’t enough information in the in input vector to determine all state variables in full, the inversion in eq. (4) fails. This leads to the very undesirable feature in network monitoring systems that they tend to black out once they loose comms with a sufficiently large part of the SCADA system. When this happens the resulting ‘gaps’ in the input vector are filled either with historic data or rough estimates in order to get the system running again until comms are reestablished. Jeremy, correct me if I am wrong here. But I think that’s the current state. At least it is down here in Australia.

The technique we’ve developed goes a bit beyond what’s possible with Prof. Schweppe’s approach. The technique does not require the input vector to allow determining the entire system state in full, but decomposes the system state into independent (for lack of a better word) ‘state components’. For a network with n nodes you would have 2n state components, which can be either determined or undetermined by the available input data. These components are not tied to individual state variables, but can affect multiple ones.

The technique identifies the independent state components from the provided measurement model, solves the state estimation problem for the state components that are determined and indicates which state components aren’t determined (and thus deemed unobservable). In a second step, when the estimated state is used to calculate operational variables of interest from the state estimate (such as line currents, nodal voltages and alike), the information regarding the unobservable state components can be used to decide whether or not such variable is subject to the unobservable state components (or: state changes that could happen without you noticing this from the available measurement data). If a variable shows to be insensitive to all unobservable state changes, then it is deemed observable; and unobservable otherwise.

We first published the core idea in “Generalized Static-State Estimation”. You can find the publication here on RG: https://doi.org/10.13140/RG.2.1.3765.4480

I’ve also added a zip file to this publication record as a supplementary resource (you can download it from the RG record linked above).

 It contains two MatLab files that only use very basic MatLab functions and I assume (although I haven’t tested it) that it would run in Octave too…

The two files are:

- ASE.m - contains the actual algorithm

- ASE_Estimation.m - contains an example of how to use it.

I’ll only give you a brief run through the ASE_Example.m file. If you want to know more about the inner mechanics of ASE.m, I’m happy to discuss.

First Part of ASE_Estimation.m: Network model.

 Straightforward: Nodal admittance matrix and line admittance matrix. Note that nodes and branches inherit their indices from here. Whichever line a node or branch corresponds to in these two matrices, that’s its position in all following vectors.

Second Part of ASE_Estimation.m: the input data.

 Inputs have to be provided in the vectors initialized in this section (have a look at them and you’ll understand what I mean). If a value shouldn’t be provided as part of the input vector, it’s element need to be set to NaN (Not a Number). All vectors are initialized to NaN, so you can simply not overwrite the elements you don’t want to provide data for.

 Note that all inputs are given as complex numbers, which is obviously nonsense. But… the real part is the actual measurement, while the imaginary part is the assumed first standard deviation of the measurements error. I’ve done it this way to make it less likely to mix things up.

 The whole section contains values, which are coherent over the provided network model and should contain next to no error. As you can see, most of them are commented out, which means they won’t be available to the estimator. If you want to see what happens if you add a certain value, simply remove the comment % of that line.

Third and fourth part are just calling the ASE and displaying the results.

Please try it out and if you have any questions just let me know.

Best regards,

    Olav

Conference Paper Generalized Static-State Estimation

How is State Estimation applied in Transmission network Capacity determination?

Kind Regards,

... Daniel

Dear Daniel,

State Estimation doesn't do this. State Estimation merely produces an estimate of the likely system state as it currently is (or was at the time of recording the measurement data). The term 'capacity' isn't this easy to define and usually means the set of loading patterns that do not lead to operational issues with the power system. And there is a whole range of possible operational issues that you want to stay away from. To assess if these issues are already likely to occur you would use simulation techniques (for most steady state related issues that would be power flow analysis). Here you would then start a series of 'what-if' simulations. What if this line dropped out? what if that generator failed? How much can I increase the generation at these generators before I get line overloads or voltage band violations.

So, State Estimation just tells you what the current (or past) conditions were and allows you to use this as a starting point in a whole range of secondary analyses. Examples are:

- (N-1) assessment

- short circuit simulation

- optimal dispatch (at least reactive power, where active power dispatch is done market-based)

- topology optimisation

- etc...

In a sense that's another good example of what the difference between State Estimation and Power Flow Analysis is. SE is only to determine the starting point for the power flow analysis based assessment and simulation tasks. And it's mainly there where specific answers, like the one for the remaining 'capacity', are answered using purpose made assessment methods.

I hope this helps.

with best regards,

     Olav

Thanks so much Olav for the clarification. It indeed helped. But what method/Strategy can I use to determine the operational capacity of a transmission line and the transmission network as a whole? For example, IEEE 14 Bus standard network?

Kind Regards,

...Daniel

Dear Daniel,

that's an extremely complex task and I am not aware of any definite answer. Before suggesting possible ways forward, let me just add a couple of word about my understanding of the problem. 'Capacity' of a network as you use the term, and I largely agree with it, is perceived to be the set of feasible set point combinations under the capacity constraining operational limits of the individual network elements plus some security-related constraints (mainly related to dynamic and static stability issues). In a relatively simple scenario the 'capacity' of a network is defined as the set of feasible combination of control variables to generators and the behaviour of loads. So, the constraints are essentially defined in another domain than where we need them (just another inversion problem in power systems analysis).

In my dissertation (sadly only in German) I worked it out for a simple network with one reference node (modelling an infinitely stiff and powerful upstream network) and a number of PQ nodes (nodes where the equipment is controlled for their active and reactive power balance with the network). I found a way to approximate the set of feasible active and reactive power combinations at all nodes that would not lead to voltage band violations at any node or over-current in any branch. That's as close to a definition of the 'capacity' of a network as you can get. One core finding was that for the network setup as described the set of feasible active and reactive power combinations is not convex - which has quite some implications for state optimisation. The approach worked like a charm, but only for very small networks. Very small meaning something like maybe up to 6-7 nodes. So, it's unusable for any practical purposes.

With the 'true' set of feasible combination practically indeterminable, there are still a range of approximation techniques that get relatively close to it. What you seem to be looking for seems to be related to the optimal power flow (OPF) problem, where the dispatch of generators/demand response and reactive power are optimised under operational limits of the interconnecting network (which you can call the 'capacity'). I recommend looking at how the inequality constraints (which are the way the capacity limiting influence of operational limits of individual components is modelled) are generated in AC OPF and (a bit simpler) DC OPF. I think this is what you are truly looking for. If you want to consider not only steady state related limitations, but also limits deriving from stability issues, you might want to also look at Security Constrained Optimal Power Flow (SC OPF). But I would start with AC OPF and DC OPF.

I hope this helps.

with best regards,

    Olav

Thanks so so very much Dr. Olav Krause!

Let me work on your suggested ideas and get back to you ASAP!!

Kind Regards,

...Daniel

Hello . Thanks to everyone, it is really informative discussion.

I have a question. While performing state estimation whether we have to assume loads as constant or loads are also needed to be estimated. Thanks in advance

Hi Aslam,

In state estimation you would (normally) only use data from a real system. So, even if the active power at one load point would not be explicitly measured, the information about it would still be implicitly included in the other available measurements (as long as the network is fully observable). As such your unmeasured nodal active power balance could be calculated from the estimated system state which means, in a way, it is estimated as well.

As a side node: in state estimation you don't make assumptions about the behaviour of loads or generators, as you are analysing a concrete manifestation of their behaviour. Assuming constant power load is only needed to predict network states (e.g. through simulation). For predictions it is important to understand and model how the connected components react to changes of the network state to increase precision of the prediction (e.g. to improve convergence speed). This becomes extremely important if you want to build a state optimisation on top of you state estimation, as this such system would need to understand very well what the response to its control actions would be.

But for state estimation you just take the values as they are. 

I hope this helps.

best regards,

    Olav

Sir, Thanks a lot for your precious comment. The idea is cleared.

Sir, one thing more (may be the question is little off-topic of discussion) about voltage measurement accuracy of Voltage Transformers, if we assume the devices are working in good condition. Is the accuracy of those used in distribution system (mounted on poles)  are same as those in transmission system (or less accurate ). I tried to search for related article but could not find in detail. If kindly refer some related articles, I shall be grateful .

Thanks in advance

Hi Aslam,

I have to admit this is beyond my personal experience. I really don't know, but would be interested if you found info on this.

best regards,

   Olav

Thanks Sir, 

Sure, if I find out some useful related knowledge, I will definitely share here. 

Regards 

Aslam

Dear all,thank you for such informative answers.

I think,in power system estimation,the system operating conditions cannot be determined by analytical set of equations.State estimation is different from load flow studies in that the number of input variables ‘m’ should be greater than (2N – 1), the dimension of the state vector.

Hello all,

I can try to summarize the difference between state estimation and load flow analysis in the most short way.

If we talk about transmission network of electrical power system, there are more number of measurement as compare to what is actually required to have the complete knowledge about the whole system.

Suppose you are one of the system operator and you always want to have the update about your entire system at regular time interval, it can be in seconds or minutes or hours.(entirely depends upon on system)

Case 1 : system operator can have all the information about the system like voltage magnitude, phase angle, frequency etc at all buses or nodes or terminal. This process is really simple once the system operator have all the measurement from the system he can perform the load flow analysis and get the information about the whole system.

Case 2 : system operator can have update about the system by state estimation(either centralized approach or decentralized approach).  

In general we can say that, state estimation is the most efficient way to determined the state of any over-determined system.

One of the major advantages of state estimation could be, it reduces the size of data to be transferred. If system operator will go with the approach of determining system state with load flow analysis then transferring the large number of measurement data could be the big handling issue.

There are many cases where you will find state estimation over load flow analysis in general.

Thank you. 

some already answered the question in a lengthy manner.

Here's my two-cents:

The purpose of load flow analysis is to use available known variables (input) and attempt to find the unknown variables (output) of a power system. In the load flow, these known variables are user-defined variables (simulated?) or came from field data (real-life data). There is an assumption that all these known variables are 'good'.

The purpose of state estimation (SE) is to use the real-life known variables (input) and 'estimate' the remaining unknown variables. There is a load flow analysis embedded in the state estimation. But, the key purpose of state estimation is to estimate the values of those variables that have bad data or unknown or missing, based on the known and good input data.

On the surface, load flow and SE seems to be similar. But, they are different at a deeper level. The use of SE is very much confined in the SCADA, control center-based operational environment while the load flow is done in many other areas of the power system applications, not just in system operation.

Keep in mind that none of these - load flow and SE - are based on optimization method, but SE appears to minimize the least-squared error as part of the SE math problem.

In conventional power flow studies, we assume that the input data ( Loads at load nodes, P V at the generator nodes) is available correctly and completely which cannot be taken for granted. Some of the data may be corrupted or may not be available at all. 

In such case we cannot process the load flow algorithm. How to get over this?. To be on the safe side, we take extra measurements which are functionally related to the data lost or corrupted and this over-determined set of data is used to to get the expected output( :Voltage magnitude and voltage angle at each node,  

Thanks to the now available PMUs the state estimation  problem is linear and therefore can be processed very fast.

Hi dear all,

thanks to those who gave us the meaning of the difference between power flow and state estimation. I have a question related to 'dynamic' state estimation.Can we apply it for an estimation of static state variables(i.e voltage and current magnitudes or phases)?

Best regards

Consider State Estimation like an estimation problem, where you have a lot of measurements available, you know the system model and you estimate the unknown variables by setting up an overdetermined system of equations.

Powerflow analysis, on the other hand, is a mathematical solution of power system state when you are given all the loading information.

Why power system transient stability studies are initialized using load flow rather than optimal power flow?

My guess is that there is no optimization part or needed in transient stability studies. The optimal power flow is our desired state, but not necessarily the 'current state'. Know the difference. And OPF is defined in many different ways.

In my opinion, the basic assumptions of both methods are the same, but in ‘normal’ condition, there is a main difference. In fact, State estimation (SE) can provide a more realistic and reliable solution to the system operator because its input data is based on measured data while Power Flow (PF) is essentially based on unverified data. Hence, if the input data is incorrect, PF solution will be certainly incorrect, but SE can still provide a more accurate solution by checking it with the valid measured values.

Before the advent of state estimation, the power system operator had responsibility for many real-time control center functions, including scheduling generation and interchange, monitoring outages and scheduling alternatives, supervising scheduled outages, scheduling frequency and time corrections, coordinating bias settings, and emergency restoration of the system. All of this was done with operating guides produced by the planning department after running a large number of load flows. As is always the case, the actual events faced by the operator were occasionally unexpected and had not been included in the planning cases. The solution was to supply the operator with a load flow program installed in the control center. The operator could manually enter data describing the current situation and get a load flow corresponding to the real world. Unexpectedly, the operator’s load flow did not work well. The problems were caused by insufficient data, nonuniform data, and errors in the data and in the model. It was important that the operator’s load flow be accurate so that the outage relief would be accurate. It was also recognized that the planning load flow was not exactly what the operator needed. What was required in the control center was a process of using a large number of imprecise measurements to estimate the existing state of the system. Early state estimation algorithms used measurements of line flows, both real and reactive power, to estimate the bus voltage angles and magnitudes. The complex bus voltages are the state of the system since given an accurate model of the network the bus voltages determine the complex power flows in the lines and all the complex power injection.