Although in the previous lectures, we have developed a synchronous machine model using the basic parameters like the inductances, mutual inductances, resistances etcetera. In the previous lecture, we had introduced the concept of system identification or obtaining the parameters of the model from measurement and we discussed one simple frequency response test which could actually give us some parameters of the model. Currently, when we do a test like a frequency response test, what we actually get are the coefficients of a transfer function that is obtained by fitting the frequency response obtained by measurement onto a transfer function of a certain order. So, that was what we get from measurement and after we get that from measurement, we need to back calculate the basic parameters from it, but the major issue there is that if you do not have an adequate number of measurements, you may not be able to get all parameters required for the model. So, that was the basic point which I tried to emphasize in the previous lecture. Now, in today's class, we will try to get a synchronous machine model based on parameters obtained by measurement and the title of today's lecture therefore, is synchronous machine models using standard parameter. We will quickly recap our synchronous machine model if you recall the basic parameters of a synchronous machine were obtained as follows. So, you have essentially the flux current relationships psi d psi f psi h are the d axis coils the flux in the d axis coils and they are related to the d axis currents. This model of course, is in the basic parameters and it is obtained with k d is equal to root 2 by 3 and there are of course, two differential equations associated with the field winding and the H damper winding. We also have a differential equation which is missed out being written here that is corresponding to the d axis flux psi d.  We call that v f s v f of s is the field voltage the voltage applied to the field winding. So, this is the nature of the transfer functions you get from this model of course, in addition to these differential equations let me again emphasize there is an additional differential equation corresponding to d psi d by d t which you have not written here, but we shall write it down shortly. But if I want to get a transfer function relationship between psi d and i d by eliminating psi f f of s psi h of s i f of s and i h of s, I essentially use the algebraic equations the first three equations which are algebraic equations. The latter two equations are also algebraic equations, but they are obtained effectively from differential equations on which we apply the Laplace transform. So, all of them in fact are algebraic equations. So, what we see that it eventually leads us to a second order transfer function l d of s and g dash of s and the nature of the transfer function looks like this of course, the coefficients a n b n a d and b d and a g are in fact related to the basic parameters. So, if you just solve these algebraic equations and get a transfer function relationship of this form you shall find that b n a n b d a d a g are related to the basic parameters by these equations.  So, these are essentially what we get from the original model. So, from the original model we can get a transfer function the transfer function is in terms of basic parameters. Now, if you carry out a measurement with v f is equal to 0 this is something we discuss in the previous lecture. If we get carry out a measurement what we will effectively get are again the coefficients of the transfer function or equivalently we will get this time constants t d dash t d double dash t d 0 dash t d 0 double dash and l d. Now, of course, a n b n b d n a d are related to these time constants by the four equations given there. So, what we have here is some parameters obtained from measurement the a n b n b d a d parameters obtained from measurements and the basic idea is that why do not we back calculate the basic parameters from these. Now, if we could calculate the basic parameters for these from these we could actually use our model in realistic studies. So, that is what the basic idea is, but you will notice that there is already a low road block if you just use this one measurement then we have a problem. Why is there a problem because the number of basic parameters are more than the parameters obtained from measurements. So, what we obtain from measurement are simply l d t d dash t d double dash t d 0 double dash and t d 0 double dash which are the effectively give you the coefficients of the transfer function from which we have to back calculate the basic parameters. Now, of course, you could do another measurement for example, you could obtain the transfer function g dash of s that is you obtain a transfer function of psi d with respect or other psi d given v f as an input and obtain this transfer function given here with i d is equal to 0. So, effectively if you look at this transfer function if I said i d is equal to 0 and say give v f as an input and they take out the transfer function g dash of s we will essentially obtain m d f by r f and t d c double dash. So, m d f by r f as a whole we will obtain and the time constant t d c double dash. So, this will this is what the transfer function will yield or this measurement will yield of course, it presumes that you know t d 0 dash and t d 0 double dash from the previous measurement also. So, this is what we get of course, this t d 0 dash and t d 0 dash double dash also can be obtained from this measurement itself by curve fitting the frequency response. So, this is what we can get if we carry out two measurements, but unfortunately in most of the synchronous machine literature they do give us the parameters obtained from one measurement. So, we typically do not have this transfer the value of t d c double dash and m d f by r f in most studies actually it is not very difficult to get this, but often the data set which is provided to you will not have the information relating to this m d f by r f as a whole and t d c double dash this is typically not available, but in principle it could be. So, what I will describe to you is what typically will be available to you and what you can do with it.  So, this is what you need to get from the standard parameters, but unfortunately you cannot get all of them because the number of parameters exceeds though the standard parameters. So, we cannot back calculate it what we have effectively is from this if you look at this we can get 5 things 5 equations from here we can get l d and we have got this 4 algebraic equations which you can equate to a n b n b d n a d which are in fact these, but obviously if the number of equations is less than a number of parameters then you cannot back calculate all the basic parameters. So, the standard parameters are lesser than the number of basic parameters. So, we cannot really get all of them of course, the solution to this is have more measurements, but I am describing you to you a situation where you have only these parameters given to you. So, one cannot get a unique solution for the model parameters with just one transfer function measurement, but this is what is typically available to you. Of course, we also require stator resistance is something I did not did not emphasize we also require stator resistance it is usually a very small value, but it can be obtained separately. So, whenever I talk of standard parameters implicitly I also mean the stator resistance which can be obtained easily from measurement. So, we have got 5 measurements 5 standard parameters here given here and we have to get the basic all the basic parameters it is not possible to do that. So, we are actually having a kind of a situation where we have we cannot get all the parameters required for the synchronous machine model which we have derived. So, let us see how we can work around this. Now, if you look at a similar situation exists in the q axis winding. So, this is the basic equations of the q axis excluding the differential equation corresponding to d psi q by d t. The differential equation which tells us how d psi q d psi q by d t is related to the other variables is missing from here, but we shall include it later. Now, if you look at this also a similar situation exists if you take out the transfer functions as before this is what we get of course, there is all the damper windings are of course, shorted you do not have any voltage applied to the damper winding. So, you do not really have that additional transfer function g dash of s as in the q d axis. So, of course, the coefficients of this transfer function are related to the basic parameters by these equations again we follow the same procedure to obtain the basic parameters, but we end up with the same problem that you have got eight basic parameters on the q axis and typically the standard parameters are only five. So, getting back the basic parameters becomes a bit tricky. Now, so what is the way around this there are three possibilities. Now, one of the possibilities is use a state space model which requires fewer parameters you can do that I mean we require eight parameters to get the original model in the original states that is the stator and rotor fluxes, but one can imagine that one can take out a states space model which requires fewer parameters and is in terms of other states states which are algebraically related to the stator and rotor fluxes. We discussed this in the previous lecture where it was there is no unique way to obtain a state space model from a transfer function. So, what we can do is if you have got a transfer function do not put a condition that you should write the equations in terms of the basic the old the original states that is the stator and rotor fluxes, but we will write it in terms of states such that the states space model requires fewer parameters can you do it yes you can do it we shall show you shortly. So, the first possibility is use a state space model which requires fewer parameters, but the states cannot be easily related to the original states which are the stator and rotor fluxes. So, that is model A the other possibility is use a state space which requires fewer parameters, but by making certain approximations in assumptions we try to obtain the state space model in terms of states which can be related very easily to the original states. That is so I write down my state space model and the model which I get essentially is in terms of states which can be easily for example, it is proportional to some for example, we can have a state you know psi you know maybe psi f dash as I will show you shortly which is proportional to the original state which is the rotor flux psi f. So, we can try to write down the equations in terms of states which are related to the original states very easily. So, we of course, we need to make some assumptions as I mentioned shortly. So, we do of course, need to back calculate from the standard parameters the parameters required for this state space model. So, we will call this model 1. So, model A is a model without any approximations, but is a state space which requires fewer parameters, but the states cannot be easily related to the original states which are the stator and rotor fluxes. The second possibility is we will use a state space which requires fewer parameters, but it is an approximate model which makes certain assumptions, but the good thing about this model 1 is that the states are very easily related to the original states. The third possibility exists is to use a state space which requires fewer parameters and has all the properties of model 1, but the good thing about this model 2 which I shall also talk about is that you do not have to do this extra step of back calculating the basic parameters. You will write down the state space in terms of the standard parameters itself. Now, this all may be sound a bit confusing to you it is somewhat confusing, but as we go through the models I am sure you will understand what I am trying to say. So, just let us look at model A. Suppose, I have got the standard parameters. So, let us just go through model A. So, model A is a state space model which requires fewer parameters. In fact, it will directly use the standard parameters, but the states cannot be easily related to the original stator and rotor fluxes. So, remember that model A, model 1, model 2 will have the same transfer function, but remember the main thing theme or main crux of what I was trying to say is that we try to take out a state space model which use the standard parameters in some way. So, let us focus our attention on first the Q axis. The Q axis transfer function is given by L Q into the second order transfer function. So, in fact, rather I should say that this is a second order transfer function and it has got 5 parameters here. Four time constants and one overall you can call it again L Q. Now, one point one small diversion which we shall have right now is that you can write the same transfer function in this form. How is this form different from this form? First of all this is the transfer function of psi Q with respect to i Q psi Q s upon i Q s. i Q s upon psi Q s is simply the reciprocal of this transfer function.  You know I rewrite it in this fashion, but you will notice that instead of using t d 0 double dash and t d 0 dash I am using now new parameters L Q dash and L Q double dash. So, this transfer function is the reciprocal of the earlier transfer function is written in terms of L Q dash L Q double dash and the time constants t Q dash t Q double dash and L Q. Now, before you start getting a bit confused about what I am getting at what I really want to say is that instead of giving you L Q t Q dash t Q double dash t Q 0 dash and t Q 0 double dash. I can just as well give you L Q L Q dash L Q double dash t Q 0 dash and t Q 0 double dash. Now, what I mean to say is that I can give you either the first set of parameters or the second set of parameters or the third set of parameters, but they are all interrelated. So, they are basically five standard these five four time constants and L Q, but you can also give instead three inductances that is L Q L Q dash and L Q double dash and two time constants with the understanding of course, that all these parameters are related to each other. So, the same transfer function can be written like this where the time constants and the reactances are related to each other in this fashion. So, you may find sometimes the data which you get you may find the first five set of parameters given to you or you may find the next set of parameters given to you or you may find L Q t Q dash t Q double dash L Q dash and L Q double dash given to you and of course, the stator resistance also will be given. Now, all these sets of data are equivalent in some way because there is a relationship between L Q double dash L Q dash and the time constants. So, if you look at this relationship again it is this, this can be easily checked by equating you can actually write this in numerator polynomial by denominator polynomial form and let us take the reciprocal of this and equate it to this. If you do that you will get this interrelationship. Now, why did I have to get this suddenly into the picture because the model A which I am going to describe to you can be conveniently written down in terms of reactances and the time constants t Q dash t Q double dash. Coincidentally I have not described to you why what these inductances and time constants are called L Q dash and L Q double dash in these equations are in fact called the transient and sub transient inductances of the synchronous machine and t Q dash and t Q double dash t Q dash and t Q double dash are called the short circuit time constants of the synchronous machine. The short circuit transient time constant is t Q dash the short circuit sub transient time constant is t Q double dash. Similarly, t d 0 double dash t d t d 0 t Q 0 dash is the transient open circuit time constant and t Q O double dash is the sub transient open circuit time constant. So, we have got t Q dash and t Q double dash which are the short circuit time constants L Q dash and L Q double dash which are the transient and sub transient reactance inductances and t Q 0 dash and t Q 0 double dash which are the open circuit transient and sub transient time constants. This is what they are called why are they called so this is this will become clear in a couple of lectures from now when we do the short circuit and open circuit analysis of a synchronous machine. The model A let us again get back to what we are getting at we are trying to get a model based on the standard parameters which uses just the standard parameters, but I just introduce one small issue or point here that the instead of giving you 4 time constants and the reactance and the inductance L Q sometimes you are given 3 reactances and 2 time constants, but the point is that they all interrelated. So, if you get this data do not get suddenly perturbed you can get the time constants from the reactances by this interrelationship. So, you are normally given these any of these 3 sets of parameters they can be you know they are all the parameters are interrelated by this. So, what I will do is now give you a Q axis model it is a state space model. Which is using only the standard parameters instead of of course, T Q 0 dash and T Q 0 double dash I am using the inductances L Q dash and L Q double dash, but remember that they can be obtained from one another. So, really we are in fact using the 5 standard parameters itself. Now, one of the points which you should remember here that psi what I have done is psi Q is of course, the state we know psi g and psi k I have used the upper case subscripts to denote that these are not the original psi lower case g and psi lower case k. These are states psi upper case g and psi upper case k are states which are linearly related to psi g and psi k, but that in fact that interrelationship is something which we do not know all we know is that this is one model which will also give you this is also give you the same transfer function as before. So, this is something you should this is what I want you really to get that this particular transfer function which you are getting here this particular sorry this particular state space model which you are getting here is in fact using only the standard parameters, but psi upper case g and psi upper case k are we know they are related to psi lower case g and psi lower case k which are the original rotor fluxes, but we actually do not know what that interrelationship is all we know that this is a state space model which will yield the same transfer function as before. Actually this is not a really a big problem in fact psi g and psi k psi upper case g and psi upper case k are states which are related to psi lower case g and psi lower case k, but unless we are really interested in knowing the fluxes to the damper winding or the currents to the damper winding for that matter it is to use this model. So, psi q is of course, as before which is the flux through the q axis winding, but psi upper case g and psi upper case k it is difficult to assign of you know they are related to psi g and psi k or lower case g and lower case k, but unless we are really interested in knowing what the damper winding fluxes are it is alright to use this model because as far as the stator is concerned as far as the transfer function we obtain from this model is exactly the same as can be model obtained from the original state space model. So, this is an acceptable state space model which yields the same transfer function as this transfer function let us show I will show it to you. So, you can actually work this out it is a bit of an exercise, but you can show that this particular transfer function at this particular state space model will give you the same transfer function relationship between psi q and i q as given here. So, this is something which you should you can actually work it out all you have to do is for example, take the Laplace transform of psi g the first differential equation and the second differential equation and the third algebraic equation and you should be able to get this interrelationship. In this particular state space model I have also written down the differential equation for psi q d psi q by d t. So, just to make things a bit clearer I will just indicate the steps you need to go through to verify that model A indeed gives you the transfer function which I had just shown you sometime back. So, for example, what you need to do is you take the transfer function of the first differential equation s into d psi g of s is equal to 1 upon. So, this you can write as t q dash is equal to minus psi g of s plus psi q of s and this is t q double dash s psi k of s this is upper case k just to differentiate this from the original state. So, this is what we get. So, in fact, you can from this you get psi g of s is equal to psi q of s upon 1 plus s t q dash and psi k of s is equal to psi q of s 1 plus s t q double dash. So, and we also have psi q of s is equal to L q I q of s I q of s plus L q dash minus L q double dash upon L q dash psi k of s plus L q minus L q dash upon L q psi g of s. So, you can look at the slide what we I have essentially done is obtained the Laplace transform of these equations the first three equations and if you look at the if you follow the steps now it is quite straight forward what we need to do is of course, psi g of s sorry psi q of s is now equal to L q double dash I q of s plus L q dash minus L q double dash upon L q dash into psi q of s now psi q of psi k of s psi upper case k of s is nothing but psi q of s upon 1 plus s t q double dash plus L q minus L q dash upon L q L q double dash on L q dash into psi q of s upon 1 plus s t q dash. So, what we are really doing here now is must be quite apparent to you we are trying to get the transfer function relationship between psi q s and i q s of course, the next step would be take this on to this side this whole term also on to this side and thereby get relationship between i q of s and psi q of s and what you need to verify is that this yields this particular equation eventually will lead you to this which is equivalent to this. So, this is what I need you to just work out. So, our q axis model a we can actually use this model the q axis model note that it also includes the differential equation of psi q d psi q by d t is equal to omega psi d minus r a into i q minus v q this model can be used directly now for the q axis. If you have got the standard parameters given to you just use this model if somebody ask you what is for example, tell me the flux the flux in tesla of the damper winding g damper winding the answer is I cannot find it out why because the state psi g and psi k the upper case states are valid states of course, but they are related to psi lower case g and psi lower case k which is the original rotor fluxes, but that relationship is not known this is something I am not giving you all I am assuring you is that by using this particular state space model you can get the same transfer function is before this is a valid state space model of which yields the same transfer function. So, you can use it you can use it provided you do not require to know what actually psi up psi the actual g and k damper winding fluxes or currents are just remember that, but nonetheless in most studies we do require do not require to know exactly these fluxes you only need to know what effect these fluxes have on the stator side in that sense this is a valid model because it gives you the correct transfer function relationship between the observables on the stator side that is psi q and i q. So, that is the important point in the d axis if you remember that the transfer function relationships are as shown here remember that there is an additional transfer function here because you have got an input the input is of course, the field voltage again instead of specifying 4 time constants or writing down the transfer function in terms of 4 time constants I can write them in terms of 3 react 3 inductances and 2 time constants that is because the time constants and these inductances in fact related by the relationship which is shown here. So, this is something you can work out it is not very difficult to do that what you need to do is of course, equate this transfer function to the reciprocal of this the first transfer function given in this equation. So, it is not it is not very difficult to verify that this relationship holds. So, if you are given l d t d dash t d double dash t d 0 dash and t d 0 double dash you can in fact, get the 3 react the inductances l d dash and l d double dash. So, your standard parameters could be in any form the either the first set the second set or the third set shown in this slide, but with this you have got essentially whatever you require you do not have to the because of the inter relationships which exist. So, you will be given either of the set of the either this the first set or the second set or the third set, but using this any of these sets you could get the model you desire because there is a inter relationship between reactances and the time constants. Stator reactances can also be obtained from measurement. So, I am not explicitly of course, mentioned this, but yes you can obtain stator resistance also from measurement. Now, if you look at the d axis model remember that the state space model will have an input the rather I should say the rotor differential equations corresponding to the rotor fluxes rather I should say the rotor the differential equations corresponding to the rotor fluxes will have an input term. This is not unlike the q axis in the q axis the damper windings have no voltage input the q winding of course, does have an input v q, but there is no equivalent of a field voltage in the q axis damper windings. So, damper windings are simply shorted, but in the d axis one of the damper windings is shorted the field winding has an input v f and of course, v d is an input to also to an input to the d winding. So, if you look at the inputs you have got v f and v d. Now, what you notice is this is a state space model this I am directly writing it down I am just stating it without proof that this is a valid state space model which yields the transfer function relationship this. So, all you need to do here of course, to verify this is take the Laplace transform of the first three equations and get the interrelationship between psi d and i d psi d of s and i d of s you can verify that you will get exactly the same transfer function as given here. So, this is the nature of the model on the d axis, but remember there is one catch here model a the state psi upper case h and the state psi f upper case f are not equal to psi lower case h and psi lower case f. Remember that psi lower case h and psi lower case f are in fact, the fluxes to the h and f winding respectively, but if you look at the differential equations written here they are not they are using the upper case subscripts just to indicate that these states are not the same as the original states. In fact, the relationship exists a linear relationship you know you can transform from these states to psi h and psi f lower case, but that interrelationship is not known and if you notice this state has some you know you know some contribution of the input also included. So, obviously, this cannot be the original damper winding flux and this cannot be the original field winding flux because now v f is kind of distributed amongst these two you know in some sense there is the input affects directly affects psi upper case h and psi upper case f. So, these states are not the original states, but remember what I am trying to get at this is a valid state space representation which yields the same transfer function. In so far as the stator winding stator effects that is the relationship between psi d and i d and the effects on the stator winding are concerned you will get the same answer, but if somebody ask you the question what is the field winding flux or what is the field winding current or what is the h axis damper winding flux you will not be able to answer this question if you use this model because these states are not directly or easily related to the original states or rather I should say this the relationship is not known all I can say that this yields the same transfer function as yields the correct transfer function or yields the correct interrelationship between the stator flux and the stator current psi d and i d, but just remember this point this is a valid state space model. Now beta 1 and beta 2 of course, are rather complicated expressions this is something you can verify at leisure. So, this is something I state without proof this is a directly d axis model. So, in fact, if you do not want if you do not want to know if you do not want to know what the stator what is the rotor flux rotor h winding flux or the field winding flux you can still use this model for understanding the effects on the stator. So, this is one thing which you should keep in mind. So, this is a valid model model a now we go to model 1 now just because it is possible that this is it is kind of gets a bit tedious. So, let us just go back a few slides and remember what we are trying to do we have got these parameters just from one measurement if you had more measurements we could have back calculated all the basic parameters required for the original model which is in terms of rotor and stator fluxes, but what we are doing what I shown you just now is model a which requires few parameters, but the states in model a cannot be directly related to the original stator and rotor fluxes. In fact, the stator fluxes I must make a small correction here the stator flux psi q and psi d are retained in the model model, but the rotor fluxes in fact you know are something are not retained in model a. So, model a is a parameter you can use this model d and q axis model, but you will not be able to answer the question of any question about what the flux in the field winding and h winding individually are. Model 1 is a model with approximation. So, now let us try to understand what we are going to do we cannot get a model in the original parameters, original basic parameters because we do not we often do not we are not given adequate number of parameters from measurement. So, what we are going to do now is use model introduce to you a model called model 1 which will use some assumptions and approximation and what we will do is we will create a model using the original states or a small you know like states which are proportional to the original states and what we will do is back calculate a parameters of this model from the standard parameters. So, this may again appear a bit confusing it is a bit confusing, but I am sure after you we go through the model you will understand what I am getting at. So, let us talk about model 1. Now, remember that the original equations on the d axis this is the original model in terms of the basic parameters. Now, what I will do is I will try to obtain the same state space model in terms of new variables. So, the new variables are psi f psi h dash so or prime. So, we are going to use psi f prime psi h prime i f prime and i h prime which are related to the original states, but remember that this interrelationship which I am going to talk about is very straight forward it is simply a proportional relationship. In model a which we just discussed I told you that there exists a relationship between the upper case or the new states and the lower case states, but that interrelationship is not given it is not clear what does this interrelationship it is a linear transformation from one states to the other. Here also we are in fact using a linear transformation we are just, but the interesting thing is psi f dash is just dependent on psi f. So, there is a direct kind of direct relationship between the new state variables which I am going to use and the old state variables. So, this relationship is direct or easy to understand it is simply a proportionality relationship. So, if you look at the new d axis variables these are in terms of the old variables, but the combination or the relationship is very straight forward. I say straight forward what I mean is psi f dash is just dependent on psi f in model a in fact this is not true psi f the psi upper case f could have been dependent on psi lower case f as well as psi lower case h, but in this particular model we have got a direct relationship and. So, you can even look at this interrelationship as if it is like referring the variables of the flux to the stator side. So, you have got distinct windings here f and h and what we are doing is we are not bothering about what psi f and psi h are, but we will refer them we are not bothering we are not bothered in the sense that we are seeing what it its effects are as when they referred to the stator winding stator side. So, what we are doing is doing a kind of turns ratio kind of transformation. So, it is similar to referring the variables to one side of the transformer now.  So, these are in fact the interrelationships which we are going to use. So, what if I use this interrelationship now what will happen is since I have changed the variables your equations in the new variables will look like this. So, all the variables kind of have this prime except psi d i d which are going to remain as it is, but all the other variables are in fact replaced by the corresponding prime variables.  So, let us just define them remember the psi f prime i f prime psi h prime and i h prime are defined by these variables that these relationships. So, of course, it is easy to find see it is easy to find that the new coefficients of these algebraic equations are actually given by these relationships it is not very difficult to see this. This must be appearing to you similar to referring variables or you know resistances and inductances to one side of a transformer. So, in fact, it is similar this whole operation is in fact similar. Now what we will do is make some simplifications let us call them approximations or assumptions to reduce the number of parameters. Now if you look at this model which we have actually we are not reduced any parameters the differential equation of the state space model in fact looks just as complicated as before. Now to reduce the number of parameters what we will do is we will choose this alpha h choose it. So, this is a very important word we choose alpha h. So, that m d h dash is equal to m d f dash. So, what we are going to do is choose alpha h now. So, if I am choosing it. So, that this relationship is satisfied it means that I am using it in fact alpha h is something I do not know, but I am choosing it. So, that this relationship is being satisfied. Now this also means that since I am choosing it to you know reduce the number of parameters its original meaning as a turns ratio is no longer valid. So, alpha h is no longer the exact turns ratio between the damper winding and d h damper winding and the stator winding it is been chosen. So, that we are reducing the number of parameters this is because with this is if we do not want to eventually know what exactly the current in the damper winding is in amperes. If somebody ask you what is going to be the damper winding current in amperes if you make the first approximation first you know if you have chosen alpha h such that m d h is equal to m d f m d h dash is equal to m d f dash we will not be able to tell eventually what actually the damper winding current in amperes is because I have chosen alpha h to satisfy this criterion rather than you know using the actual turns ratio. So, I am imposing a condition you know I am using alpha h not the actual turns ratio, but a value which will yield this.  So, we will talk of another parameter in fact it is an addition to the standard parameters this l l is a leakage reactance leakage inductance. So, if alpha f is an actual turns ratio if I use actually the turns ratio between the stator winding and the field winding then we shall see that in fact l l is a leakage inductance.  So, actually by assuming this I am reducing the need for one parameter. So, in fact this is an ad hoc assumption without any justification we have not given any justification for this. In fact, there are leakage, leakage is which have to be accounted for. So, the third assumption is an ad hoc assumption it is not based on some very realistic or very correct kind of reasoning, but just an assumption made to reduce the number of parameters. So, obviously now we are talking in terms of approximation. So, what we are going to get is an approximate model it is not the exact model. Model A was an exact model it was an valid state space model this is also going to be a valid state space model, but what we have made an assumption here. So, it is an approximate state space model alpha h is chosen based on trying to equate to mutual inductances. So, it is not going to be actually the turns ratio we have chosen alpha h. So, that this is satisfied. So, we tweak the value of alpha h. So, that m d h dash and m d f dash are equal alpha f is the actual turns ratio between the field winding and the state of winding.  So, this is fine. So, the first and second points which are mentioned in the slide here are in fact, in the sense there is nothing wrong in what we have done here, but the third thing is certainly an assumption which will make our model approximate. So, let us just recap what we are doing model 1 is a state space model using certain assumptions. So, the state space is in terms of states that can be related to the original states easily what do I mean by that this is an easy relationship alpha h and alpha f are in fact, can be looked upon as turns ratios we have simply referred things to one side of a transformer. So, that is essentially. So, what we have done is writing down the state space equations in terms of referred states, but since referred states are simply proportional to the original states this is not really a very this is a kind of a reasonable or useful approximation to make. Alpha f we will keep as the actual turns ratio. So, psi f dash is in fact, going to give you the referred field winding flux sorry the turns alpha f is in fact, the turns ratio we will use it as the turns ratio alpha h is something we choose. So, that we make two mutual inductance is equal. So, alpha h need not be the original turns ratio between the damper winding and the stator winding. So, this is something which we should remember alpha h is chosen by us. One interesting thing is that if I write down my transfer functions in terms of the new states the original transfer function does not get changed the form is exactly the same of course, it is in the equation also look similar the only using primed quantities everything else looks the same which is not surprising, but the important thing is because of the assumptions we have made. In fact, not the assumption this one assumption we have made and one additional parameter which we have to obtain from measurement.  So, we now actually can actually compute this is what I wanted to say actually the parameters for this model are these and the parameters from measurement are the ones given below.  So, what we have effectively got here now we have reduced the number of parameters by the one assumption we have made by the choice of alpha h the choice of alpha h member and this extra leakage measurement which will be required. So, this is model one now alpha f is the terms ratio, but actually when we write down this model we will not require alpha f at all provided v f dash is used in all the calculation the referred voltage. So, although I have introduced this concept of alpha f or rather this terms ratio alpha f it is not required in any of the calculations provided of course, in all my calculations and all my studies I am going to use v f dash which is referred voltage. So, I will never specify what the field voltage is, but I will always specify what v f dash which is the referred voltage a similar thing can be. So, the summary of the model in the model one on the d axis is this.  So, using these you can back calculate all the parameters required by this model. So, actually this is an interesting and important and in fact most books and the literature follow this kind of model. So, this is an important model the model on the d axis, actually this is something which you have mentioned sometime back the q axis can be similarly found. So, model one is the model on the d axis and the q axis this uses parameters back calculated from the standard parameters, but it does make some approximations. In fact, once we if we use these model on the d axis and the q axis and we get our answers one thing we know psi g dash which we get and psi k dash psi f dash and psi h dash are going to be proportional to the field winding fluxes and the damper winding fluxes. So, there is a kind of a direct and direct relationship between the states the prime states and the original states. So, this is a more satisfying kind of model because the new states are in fact related to the old states. Now, what about model A? Isn't model A valid? The model A is also valid, but in model A it is difficult or not possible to tell what the actual field flux or the damper winding flux is going to be not even the referred value. In model one we at least know the referred value of these fluxes and currents we can do that. Model A though an exact model obtained from standard parameters you cannot do this. So, this is the difference between model one and model A. Model A is correct exact uses standard parameters model one is an approximate model, but the fluxes here and rather I should say the states here and the currents here are easily related to the original states. Now, in the next class what we shall do is talk about another model model two which uses a distinct approximation, but it has an advantage that this back calculation step will not be there. If you look at model one there is a back calculation step involved in the sense that you have got a standard parameters, but you still need to back calculate if you look at this slide you still need to back calculate L f f dash L h h dash R f dash and R h dash and L L. This is not a problem really, but we shall just look at another model model two which is more convenient. So, this back calculation step we can avoid. So, let me just clarify again what we are trying to do and summarize today's lecture. We have got the standard parameters obtained from measurement. If we do not have adequate number of measurements are we given a limited amount of measurement data which is typically the case will be given limited amount of measurement data. We have to build our model we can build in fact the model a state space model which uses fewer parameters, but we are stuck with the problem that the rotor fluxes there and rotor currents there in that model cannot be easily related to the original rotor fluxes and currents. On the other hand if you use model one we call this model one which is most popular model in some ways. We can use we are using fluxes and currents which are related very simply you know simply by a proportional relationship or a referred relationship with the original states, but of course, model one does involve an approximation. We shall in the next lecture introduce to you model two another model which uses a distinct assumption, but does not require this back calculation step which is required as shown in this slide here. You need to back calculate these parameters from the standard parameters using the relationships these relationships. Remember that model one involves an assumption. The if dash and psi f dash obtained from this model i f prime and psi f prime rather which you get from this model are directly going to give you the referred value of the field winding field winding flux and currents i h dash and psi h dash or i h prime on psi h prime are in fact going to be proportional to the damper winding flux and current, but the exact proportionality relationship cannot be obtained from this model. In fact, if somebody ask you the question if I use this model can you tell me what the damper winding current in amperes is going to be he will not be able to answer this question. If somebody ask you what is the field current going to be in amperes you still cannot answer this question, but if somebody actually tells you the turns ratio between the field winding and the state of winding yes you can answer that question. So, this is the important thing to be kept in mind. So, we can have a d axis and a q axis model one which is the most popular model which is used in the literature. In the next class we shall do model two and shall also discuss equivalent circuits and the per unit model. So, using this we will be all set to study a synchronous machine and do in fact realistic studies because these are the parameters standard parameters of the parameters which will be available from measurement is it ok. So, we will continue our discussion in the next lecture.


Hey, this is Brett, and this 2015 Chevy Silverado 2500 Crew Cab Short Box LTZ is stock number 12864Z. I am here at Summit Automotive in Von Lack, Wisconsin, near New and used heavy-duty truck headquarters. This 2015 Chevy Silverado has the 6.6-liter Duramax diesel engine. It's the LML engine, which puts out 397 horsepower. It's paired up with the Allison 6-speed heavy-duty transmission. This truck has been fully-safetyed and inspected by our service shop, has a fresh oil and filter change, all the fluids have been checked and topped off, and this truck is 100% ready to go. I'm going to go all the way around in this video, inside, underneath, start it up and take a look under the hood, Summit White is the color, and I shoot all my videos in 4K, so if you have HD capabilities on your computer, tablet, smartphone, or television, I highly recommend turning them on right now because it is your best way to check out the quality, condition, and options, and of course, cleanliness of the vehicle before seeing it in person. As you go down this side, very nice and clean. Paint is reflective and no damage to it, looks really good for a 15. If you liked the video, you can subscribe to my YouTube channel, which is youtube.com slash Summit Auto, and this one has very nice method, polished aluminum race wheels. They're in very nice shape, and see any major scuffs or scrapes on there. Has Nitto Terra Grappler tires, and these are LT28565RA teams. They have a very good amount of tread left, I would say probably 80, 90% of the tread left on those tires. This one does have the Z71 off-road suspension package with the rancher shocks, and you can see the frame is in very nice, clean condition, very little to no corrosion, maybe a little dusty, but I always say a little bit better, being dusty than rusty. Production or projector lamp headlamps, factory fog lights, front bumper is in excellent shape, you do get the front bumper parking sensors on there. The grille is in very nice condition as well, and the hood, I didn't see any major dents or dings on there. Passenger side front fender looks really good as well, and the passenger side rim, no major scuffs or scrapes. Now as you go down this side of this 2015 Chevy Silverado, take note of how clean that body is once again, how reflective and mirror like that paint is. I take these HD videos, so if you are far away, or even if you're close by and you just cannot make the trip down, but you're still interested in purchasing the vehicle, you can see the truck, hear the truck, and have confidence in the vehicle that you're looking at before you even get here. Also when you do get here, there's absolutely no surprises, and you can make a smart and informed buying decision from wherever you're at. If this video helps you do that, let your salesman know that you saw the video that it was helpful, and that brat sent you.  Once again, frame and underbody, very little to no corrosion. It's really amazing for a 2015, I would imagine this is a Southern truck. It's really good, has all the remaining factory exhausts, and the lower rockers and cab corners are in excellent shape. As a factor, actually these are DZ chrome step bars. They look like factories. Coming around to the back, rear bumper is in great shape, does have the back of parking sensors, rear bumper steps, full towing package which includes a receiver hitch four pin and seven pin wiring, the only thing I know is one little ding there that does not affect the performance of the truck. Tailgate is in excellent shape, didn't see any denser dings in there. Has a locking tailgate, shock down assist tailgate, spray and bed liner. This is a pro liner, and the bed itself is in fantastic condition. That pro liner goes on to the tailgate which is very nice. Has a Truxedo low pro soft roll up tonneau cover, same tonneau cover I have on my truck, I love them. Mud flaps which keeps your lower rockers looking good, and the back room for full disclosure is in excellent shape. Down the rest is side once again, doors and cab all look really good, does have the telescopic tome or is built in directional signals LED side lights. They do telescope out like that and fold in, and I'm pretty sure they power fold in, which I'll show you in just a second, which they do. Inside the LTZ package gives you the gray leather interior. You get the captains or bucket seats in the front here, both these front seats are heated and cooled.  And these mirrors do power fold in, I was like showing both sides so you know that both sides are working properly. We'll take a quick look at the back seats and then we'll check out the Myles radio and start it up. Back seats are in excellent shape, has latch child safety system, power sign rear window with the built in rear defrost, headliners in gray shape, and this one does have an advent DVD player up there. So that's a really nice feature if you have kids throw a DVD in for a long car ride, very nice weather tack floor mat back here, keeps your carpeting looking like new. The side curtain airbags on this truck and the bottoms of the doors all look really, really good on this vehicle. I will show you the tire and loading information as well as the VIN sticker here so you can see the gross vehicle weight rating and all that good stuff. All right, we'll hop inside, check out the Myles the radio and everything that this truck has to offer and then start it up. You can see that this one has 34,293 miles, it does have a digital speedometer and compass display. You get that very nice Z71 instrument cluster, comes with the heated leather wrap steering wheel, Bluetooth and information center controls and the right cruise controls on the left forward collision warning controls and heated steering wheel controls on the left as well. This one does have the Allison heavy duty six speed automatic transmission with the optional tap shift comes with the Chevy my link radio AM FM and serious XM radio capabilities. You can see it does have the factory navigation system and that is highway 41 right there so that is working nicely. There is your FM and serious and you also have all your different apps on here. It does have the CD player, heated cooled seat buttons, dual climate controls, stability control, power pedals. That's for your cargo lamps. That's how you also turn on your LED side lights. This one does have lane departure, warning parking sensors, downhill assist control and factory exhaust break. You do get three USBs, two 12 volt power points and then a 110 volt, 150 watt plug in passenger side format and seat are in fantastic condition. And once again, the headliners in great shape does have the home link buttons for your garage door security systems and lane systems, power sliding window button and your map lights up there on star and SOS buttons in the mirror. We'll start it up and take a look under the hood starts right up. No check engine lights or anything like that. And yeah, we'll take a look under the hood. I just checked the buyer's guide and this one came out of Iowa. We were curious. Has the LED side lights on there. They are super bright. I would personally like to thank you for checking out the video today and hopefully from this HD video you've been able to verify the quality condition options and cleanliness of this truck all the way around. Inside out under the hood, we have the 6.6 liter Duramax diesel engine based very clean runs very smooth. And once again, this truck has been fully safe and inspected by our service shop as a fresh oil and filter change on the fluids have been checked and topped off. And this truck is 100% ready to go. I would highly recommend this truck from a quality and condition standpoint and to see more pictures of this truck and one of our other 550 new used cars, trucks, SCVs, minivans, wranglers, you name it, we got to go to that website. There's summonauto.com full pictures and descriptions of every single vehicle from two locations all at summonauto.com. And if you'd like to check out more HD videos you can go to youtube.com. So I have summonauto. I'm at two likes, subscribe and share on this video and all the videos that you see there. In fact, the second you see a link to subscribe to my YouTube channel on the upper left. Links to more Chevy 2500 truck videos like this one in the upper right, link to this vehicle on our website in the lower left. And a link to one of our latest YouTube videos in the lower right. Click those checkers out. We're super excited to have you look at this ultra clean 2015 Chevy Silverado 2500 for your Camp Short Box LTZ in Summit White Quickgoat. Thanks again for checking out the video. Remember to like, subscribe and share on the YouTube channel. I really appreciate it. Thanks again.


Income tax 2023-2024, itemized deductions, state and local real estate taxes. Get ready and some coffee so we can recognize the code cracks when doing income tax preparation 2023-2024. Most of this information can be found in the instructions for Schedule A Tax Year 2023, which you can find on the IRS website at irs.gov, irs.gov. Looking at the income tax formula, we're focused on what I would call the below-the-line deductions. More specifically, the itemized deductions. Remember, the first half of the income tax formula is basically a funny income statement. Most income statements having income minus expenses resulting in net income. Here having income minus various deductions resulting in taxable income, noting for taxes, deductions good. Therefore, we're looking for more of them. The difference between the above-the-line deductions or adjustments to income and the below-the-line deductions include the fact that the adjustments to income do not have to clear a hurdle such as the standard deduction before we get a benefit from them, whereas when we're looking at the itemized deductions, they do typically have to clear the hurdle of the standard deduction before they benefit us as taxpayers. Looking at the first page of the Form 1040, we're focused on line number 12, standard deduction or itemized deduction. We're focused on the itemized deduction, which we would take if it's greater than the standard deduction. And if that were the case, we would include the Schedule A. The Schedule A is the itemized deduction schedule. First, a word from our sponsor. Yeah, actually, we're sponsoring ourselves on this one because apparently the merchandisers, they don't want to be seen with us.  Like our crunchy numbers is my cardio product line. Now, I'm not saying that subscribing to this channel, crunching numbers with us, will make you thin, fit, and healthy or anything. However, it does seem like it worked for her. Just saying. So, you know, subscribe, hit the bell thing and buy some merchandise so you can make the world a better place by sharing your accounting instruction exercise routine. If you would like a commercial free experience, consider subscribing to our website at accountinginstruction.com or accountinginstruction.thinkific.com. We have some of the items on the left-hand side, although this is not the full schedule page. This has given us a layout of the standard deduction, the hurdle that we would have to clear, dependent largely on the filing status. Single filers having a standard deduction $13,850, married filing joint doubling to $27,700, head of household in the middle $20,800, and if over an age or blind, you would then have the added standard deduction depending on if one or two of those items are checked off for single versus one through four for two people if married and head of household, qualified widow and so on and so forth. All right, so now we're going to be continuing on with the state taxes. You will recall that in a federal income tax system, the general idea of an income tax is that we should be able to deduct those things that we have to consume in order to generate revenue so we're taxed not on gross income but net income, a concept most clearly seen with the Schedule C business deductions where we have in essence an income statement, income minus the expenses we had to spend in order to generate the income, the net income, then being the thing we apply the tax to. The Schedule A has a bunch of things that kind of deviate from that standard rule where we have personal items that we get a deduction from for whatever reason in the past. Now, this often comes up with complexities related to them. We're now looking at the state taxes, remembering state taxes and local taxes are different than the federal income taxes. Clearly, we can't deduct federal income taxes typically, at least like the income tax in order to then calculate the income tax because we would result in a circle reference. But what about the state taxes? Normally the answer would be in a pure kind of income tax system. No, you wouldn't get to deduct them because they're personal unless they were spent for the business. You bought something business related and had to pay state taxes, then you would think it would be like a business expense. But the IRS for whatever reason said we're going to deduct the state taxes. And so now we have the capacity to deduct certain state and local taxes. We talked about in the past, some of those being the state tax, like an income tax that the state might set up to take care of the things they are responsible for, such as local police firefighting and so on and so forth versus the federal government that should be mainly focused on protecting us, military. And then on the local side, they could pay for that with an income tax or possibly like a sales tax, whatever they wanted to do. We talked about those options. What about like real estate? That's another big one where we have basically a property tax type of situation on the main piece of property for most people that being a home. And this is probably one of the big factors that really helped the itemized deductions of the state taxes to stay in place on the schedule A. And I would think it's because of the lobbyist. My skeptical mind would say, well, it's because all of the people that are in the housing industry wants subsidies for housing. And therefore, mortgage interest, a personal expense and the real estate taxes related to the purchase of the home become very beneficial for those those interests. Right. So now we have the taxes on the home. Can we deduct the taxes on the home remembering that usually it's going to be a more well off individuals that have the ability to itemize because they have more itemized deductions and the main thing that pushes people over from taking the standard to itemize deductions is the ownership of the home primarily because of the loan or mortgage related to it and the interest expense on that mortgage, which could be deductible, but also significant to the ownership of the home are real estate taxes, which are often quite high in many areas. However, remember the real estate taxes have been limited a lot in a few years ago. So if you're in a high cost of living area, it's quite common that you could get capped on the deductibility of real estate taxes as they're included to like total state taxes. Also just keep in mind that you probably don't want to buy a house just so that you can itemize your deductions unless you've you've really calculated it out because there could be a big gap between the standard deductions you're taking and being able to itemize. And so we might touch in on that when we get to the software example problem, but just realize if someone says, hey, you get to deduct all 6000 of the taxes, plus you get to deduct the real the loan interest on the mortgage interest. And that's true. And you say, well, that's like 20,000 of a deduction. But if you were married before, you still might not be clearing it might not be enough to clear the itemized deductions or barely clear the itemized deductions. So the actual amount of benefit that you're getting could be substantially less than the itemized deductions that you're claiming on the Schedule A. So we'll see that more in the example problems. Tip. So if you are a homeowner who receives assistance under a state housing finance agency hardest hit fund program or an emergency homeowners loan program, you could see publication 530 for the amount you can include online 5B. So enter online 5B the state and local taxes you paid on real estate you own that wasn't used for business, but only if the taxes are assessed uniformly at a like rate on a real property throughout the community and the proceeds are used for general community or government purposes. Okay, let's take a look at that one more time. Enter online 5B the state and local taxes you paid on real estate. So we're basically talking about property state property taxes, real estate taxes, usually on the home because that's the property that most individuals own. But we're talking real estate taxes that wasn't used for business. Now you might say well why if it was used for business. That's when I should get the deduction because then I pay taxes as a normal ordinary business expense. And you might you might get the taxes deducted there but not on the schedule E. I mean, a in that case not an itemized deduction. You might then be able to take the deduction on a schedule C or whatever the business form was that you use for the business, which could be legitimate. That would be make more sense. However, if you use your home for both personal and business, we're going to see that we run into this kind of confusing problem again, in that we might have part of the deduction that maybe we can deduct on say a schedule C. And part of it that then possibly could still be deductible on a noting that we can't double dip deducting the same amount in both places. Okay, so but only if the taxes are assessed uniformly at a like rate on all real property throughout the community. So no special kind of arrangements and what not. So anyways and the proceeds are used for general community or governmental purposes. In other words, the money that's being used is not like it's going into a fund for you or something like that. It's used for the general governmental purposes of the state or locale. So our publication 530 explains the deductions the deductions homeowners can take. So you could take a look at that for more detail. Don't include the following amounts online 5B foreign taxes you paid on real estate. So we're talking about United States taxes here. So we're talking about the property taxes in the United States for real estate. So itemized charges for services to specific property or persons, for example, a $20 monthly charge for house per house for trash collection, a $5 charge for every 1000 gallons of water consumed, a $5 charge for mowing a lawn they had grown higher than permitted under a local ordinance. You can see this kind of makes sense because that's not exactly property tax. It's kind of like maintenance or required maintenance kind of things that are basically taking place in essence charges for the improvements that tend to increase the value of your property. For example, an assessment to build a new sidewalk. So clearly, if you would think it would kind of be a form of double dipping if you're paying if you're paying something in order to in order to increase the value of your property because obviously the incentive to do that would most likely to be to improve and increase the property value, which means you're getting kind of a benefit from it already. And so you would think it'd be kind of like double dipping if you got if you got a tax deduction with it too. But in any case the cost of property improvement is added to the basis of the property. So meaning the value of the property it might be included to the basis. Because that do the basis is kind of like the cost of the property. So when you sell the property, then you might have to calculate a gain or loss on the property if it's real estate property it might be like a capital gain or loss. But if it's personal property, then it still would be capital but you might have an exemption for it. But the general idea is that you would like to have a higher basis or cost in the property when you sell it. Because then when you calculate the gain, gains are bad for taxes. They're good in general but bad for taxes because they might trigger a tax event. So then you have the sales price minus the cost or basis. If you get to increase the value of the basis, then you're going to have less of a gain when you sell it and that could be a tax benefit. However, it might be totally wiped away if it's your home in any case because there is a substantial exclusion on the sale which we might talk about when we get to the capital gains. So however, a charge is deductible if it is used only to maintain an existing public facility and service. For example, a charge to repair an existing sidewalk and any interest included in that charge. So if your mortgage payments include your real estate taxes, you can include only amount the mortgage company actually paid to the Taxing Authority in 2023. So this gets a little bit into the logistics of this. So note that if you're dealing with somebody or yourself who is itemizing, most likely because you own a home which is a type of real estate. And that pushes you over because you're going to have a loan on it typically, a mortgage, which means you're going to be paying mortgage interest which is usually quite significant and something that the bank will typically tell you about. You're going to get forms documentation related to the mortgage interest which will help you to populate the mortgage interest part or deduction on Schedule A. Property taxes, though, what's the documentation that we're going to get with relation to property taxes? Now if it's not being paid through your mortgage company, which it may not, you might just be paying your own property taxes, then you might not get any documentation. Because the people that the state and the locale doesn't have a responsibility typically to inform the IRS and you of the property taxes with like a 1099 or 1098 or something like that. Therefore, you're just going to have to keep the bills and make sure that you are properly recording the property taxes typically in the year that you paid them mainly on a cashed-based system, although you have to be careful if you try to come up with a scheme of prepaying your property taxes, right? Because the IRS will limit that kind of thing typically. But sometimes when you pay your financial institution, they're going to say, hey, look, we'll make it easy on you. We'll just include the property taxes in the amount that you pay us. So when you pay your mortgage company, you're going to be paying them the principal and interest on the loan as well as an amount that will be evenly allocated monthly. That would be easier to budget. That would be their argument on why you might do that. And then they will take that money and pay it to the state and locale to pay your property taxes in essence for you. So if that's the case, you will probably get the form from your financial institution telling you the amount of interest you paid in the year, which could be deductible on Schedule A as interest. And the property taxes will be reported basically separately. What you don't get a deduction for is of course the principal, the pay-down of the loan itself. It's only the interest and the property taxes. Okay, so if you sold your home in 2023, any real estate tax charged to the buyer should be shown on your settlement statement. And in box six of any form 1099S you received, this amount is considered a refund of real estate taxes. See refunds and rebates later. So any real estate taxes you paid at closing should be shown on your settlement statement. So things get messy when there's a purchase and a sale of the real estate. So in the year of purchase or the year of sale, then as part of the agreement when there's a sale of real estate that takes place, there could be property tax that's outstanding at that point in time. And part of the agreement could be well who's going to be in charge of paying the property tax? Is it the person selling or is it the person purchasing? And those kind of details will typically be in the closing statement of the real estate transaction. And you might have to go to the closing statement to make sure that you're properly allocating and picking up the property taxes and who's basically paying for the property taxes. Once the sale has been made, then hopefully after the year of sale or purchase, whichever side of the transaction you're on, it should be fairly easy because then you're just going to be dealing with the property taxes. And you're going to be dealing with the mortgage, which includes the mortgage interest, most of which will be reported by the financial institution, at least the mortgage interest possibly even the property taxes. If you're paying it through them, otherwise you track the bills for the property taxes. So prepayments of next year's property taxes. So we noted when do you deduct things for income taxes, typically on a cashed based system when you pay them. So you might get the bright idea of, well, hey, look, I made more money this year than I'm going to make next year. Why don't I prepay the next five years of property tax this year, deduct it all this year when I'm in a higher tax bracket. And then next year when I'm in a lower tax bracket, that'll be work out for me for my taxes. But the IRS is going to be skeptical of that kind of things. The manipulation, that's why the cash based system, by the way, is not the preferred system used by corporations. They have auditors and audits and whatnot to make sure that people aren't manipulating the cutoff dates by manipulating cash flow, for example, because it distorts the financial statements, right? So same thing happens here. Cash basis is the easiest way to do it. That's what we're on. It's the easiest. We don't need audits or, you know, like a standard audit of financial statements to figure it out. It's simple to do. But you can come up with schemes like this of saying, well, I'm going to manipulate. When I pay the cash, manipulating the cutoff dates, and the IRS, of course, is going to try to come up with rules to stop that, right? So that's the idea. So only taxes paid in 2023 and assessed prior to 2024 can be deducted for 2023. State or local law determines whether and when a property tax is assessed, which is generally when the taxpayer becomes liable for the property tax imposed. So refunds and rebates. If you received a refund or rebate in 2023 of real estate taxes you paid in 2023, reduce your deduction by the amount of the refund or rebate. If you received a refund or rebate in 2023 of real estate taxes you paid in an earlier year, don't reduce your deduction by this amount. So we have a similar scenario as we saw with like a state tax refund, for example. However, this is one that does not come up as often because when you pay your real estate taxes it's unlikely that you're going to get a refund. That doesn't happen all the time as it does happen all the time with a state income tax system designed similar to a federal income tax system in which you overpay and will basically be expecting some kind of refund typically. But if you did get a refund because you overpaid the taxes for whatever reason, if it happened in the same year, then of course you would just reduce, you already know about it so you would reduce the amount of taxes you paid by the refund. If, however, you got a refund say in 2023, for real estate taxes you paid in 2022, the question as with the state tax refunds, same concept is did you get a benefit from the payment in 2022? If you itemized and deducted it, you got a tax benefit. So then you would think, well that means that I should just reduce the property taxes deduction I get to pay in 2023. But no, that's not how we do it because maybe you're in a situation where you didn't have property taxes in 2023 or something. Instead of adjusting your deductions you're going to include it in income. So if you got a benefit from it last year and then you got the refund back, you're not going to refund the prior, you're not going to amend prior year return, you're not going to adjust your deductions but rather the typical concept is you put it and include it in income in the current year. So that shouldn't happen like all the time but as it does happen all the time with the state income tax for example if someone is itemizing. So instead you must include the refund or rebate in income on schedule 1 form 1040 line 8Z if you deducted the real estate taxes in the earlier year and the deduction reduced your tax. So see recoveries in publication 525 for details on how to figure the amount to include in income.