The first item of business this afternoon is a member's business debate on motion number 13845 in the name of Christina McKelvie on halt welfare reform. This debate will be concluded without any questions being put, and I would be grateful if those members who wish to speak in the debate could please press the request to speak buttons now. I call on Christina McKelvie to open the debate seven minutes please. Thank you very much, Presiding Officer. Can I take this opportunity and open in the debate to thank all of my colleagues across the chamber who signed the member's motion to allow it to be debated today? Can I also pay tribute to the work of and say thank you to HIV Scotland and that SAMH and the Disability Benefits Consortium and Pat Unions who is the inspiration behind this motion? Last week, my colleague on Westminster, Angus Robertson, asked the Prime Minister about the suicide of Mr Michael O'Sullivan, a 60-year-old disabled man and father of two. His death followed his work capability assessment. Mr Robertson asked the Prime Minister to publish some 60 investigations by the Department of Work and Pensions, which could expose many more tragic cases of this kind. So far, he has refused to do so. Meanwhile, the coroner has warned that there is a risk of further deaths. We must keep sight of the fact that welfare reform is costing lives, bringing misery and debt into families and all in the name of putting the UK into surplus. Even his own backbenchers are questioning the Prime Minister's approach. Although the chancellor himself has suddenly decided that the House of Lords is profoundly undemocratic, that is what you say when the vote isn't in your favour. Even if the notables and the geriatrics and the Tory donors are rejecting Mr O'Sullivan's plan and calling for a rethink. Last week, the Tory MP for South Cambridge in our maiden speech, Heidi Allen, has suggested that ministers were losing sight of the difficulties of working people and their single-minded determination to achieve a surplus. Reform is not a spread sheet, she said, and she fears the way her government is going about the whole process is all wrong. Conservative Johnny Mercer urged the chancellor to do, and I quote something, anything to ease, the harshest as he put it, effects of the cuts on vulnerable people. He also said that my duty and indeed our duty is to shout for the most vulnerable. On Sunday, we were told that three cabinet members, unnamed, have expressed their concerns about George Osborne's planned cuts to working tax credits, and we can see the mess that that has created this week. Ruth Davidson, too, has also expressed her anxieties. She has said, we can't have people suffering on the way the government needs to look at this again. When you have this kind of rebellion in the governing party at Westminster, you most certainly do need to look again at your proposals. Presiding Officer, this SNP Government is shouting out for the most vulnerable, but Westminster isn't listening. Even going by Prime Minister's questions today, they are still not listening. There can be no trade-off between people's lives and national debt. Are we all going to sit us around and say, all well, collateral damage, a term that I abhor? Are people who happen to have a disability, whether mental or physical, or who struggle to find employment that they can manage, are to be punished? Are those folk who have been forced into debt and down to the food bank meant to feel that they are the undeserving poor? Honestly, Presiding Officer, does anyone actually want those so-called welfare reforms? We hear all sorts of dodgy claims by the Westminster Government that cutting benefits is the only way forward. After yesterday's welfare reform committee, Presiding Officer, I remain completely unconvinced. I don't claim to be an economist, but I do understand that the more money a national government pulls out of an economy, the lesser it is available for people to spend. That being so, then, how can you grow and develop your economy? I am sure that I will be accused of oversimplification, but it seems abundantly clear to me that if you pull money away from people, you take it out of the local spending so that people have less to spend and the Treasury then receives less tax. More brutally and more honestly, this Government is literally taking bread out of the mouths of babes. The most disadvantaged are those with the already added strain of long-term health problems and those whose quality of life is already compromised. In my constituency in Hamilton, Larkhall and Stonehouse, 3,400 families in work with 5,800 children are going to feel the loss of tax credits where it hurts most on the lives and wellbeing of their children. So much for making work pay. Here are families desperately struggling to make in-meats, often in low-paid jobs or on zero-hour contracts, and they are being told that the Government sees fit to take more money out of their pockets to the tune of around £1,000 a year on average. For many families, the figure is twice that. The people who suffer most are the least able to get heard. The bankers, public school politicians and affluent aristocracy are already and regularly given a voice. Those at the bottom of a pecan order get little but abuse. Pat Onions is a constituent of Lanarkshire. Her ceasefire campaign calls for an emergency halt to sanctions, timing out and the distress and repeated assessments for sick and disabled people. The evidence shows that, despite the Government's claims, sick and disabled people in the work-related group activity are not finding employment. What is the Government's reaction? Is it to punish them some more, to harass them and blame them for the predicament that they find themselves in? They are attacked as benefit scroungers, lazy or not, or being too picky. Work done to make reasonable adjustments to the workplace for those with disabilities is a great achievement, but it isn't enough. Some people have conditions that mean that the reasonable adjustments cannot compete as effectively as fit people in the ruthless competitive open job market. We need to discuss the extra cost that more major changes will bring to an employer, but no one discusses sheltered working arrangements, quotas or subsidies to help. I have already met many constituents who are suffering a major drop in their income under the changes to DLA. Many have lost that benefit and others will find it extremely difficult to attain PIP. Because of the UK Government's 2010 decision to reduce the DLA budget by 20 per cent, very few of those people will actually get PIP. If PIP is not halted, those people will lose all their vital support. It makes no sense to implement that change. The Scottish Government is repeatedly on the record as having opposed. Fixing the damage would cost as much in health and social care and cost terms than the roll-out would. In Hamilton, Stonehouse, there are 840 people of working age who receive the low rate of DLA and will not qualify for PIP. The impact on those individuals, their carers, who will no longer qualify for carers allowance either, their families and communities could be catastrophic. We have our Parliament with its limited powers, but we have Westminster and we have the issue that they just don't seem to listen. The introduction of evil diminishes our power massively, turns our MPs into second-class elected drapes and smacks very much of a revenge attack. It is our ever-just one example of the means by which Westminster will continue to defer and determine our future in Scotland. That is something that we must counter for the sake of all those silence voices, suffering the cruelty of conservative policies, even though that Government has had only one MP in Scotland. He is not in Hamilton, Lackall or Stonehouse, so I say call a halt and call a halt now. Thank you very much. We now turn to the open debate speeches of four minutes or so, and I call Neil Findlay to be followed by David Torrance. Presiding Officer, I hate the term welfare when it is used in the context that is being used here today. One dictionary definition of welfare is the good fortune, health, happiness and prosperity of a person, group or organisation. While none of those descriptions are fitting for what people and benefits are experiencing at present, I prefer the term social security defined as a Government programme that provides economic assistance to persons who are faced with unemployment, disability or agedness. Social security has been at the heart of our welfare status, a series of policies that have, since its creation, helped to civilise our society with the principle of a safety net through which no one would fall.  That is the inevitable consequence and deliberate consequence of adherence to neoliberal economics and doctrine. Progressive taxes on wealth have shrunk as regressive taxes have increased, with the poor now paying 47 per cent of their income and tax, whilst the rich pay 35 per cent, while wages at the top have fallen while the wealth at the bottom have fallen while the wealth at the top has soared. Pensions have been cut, pay the loan used spiralled, food banks have become an almost accepted part of our culture, what a dammin indictment that is. All the while, corporate welfare through bank bailouts, tax cuts, tax allowances, quantitative easing, EU subsidies, privatisation and tax avoidance dishes out, eye-watering sums of money to the biggest and most profitable corporations. And who is it that is paying the price of the global banking crash? Is it the investment bankers? Is it the hedge fund managers, the gamblers in the city? Of course it's not. It's the people who always pay. It's the people on low pay. It's the people in insecure jobs and the people who rely on our social security system and it's the same here as it is in Ireland, as it is in Spain, as it is in Greece, in the US and elsewhere. But of course, aren't the Tory party relishing ripping apart that safety net? Claiming that they have to do this to balance the books so they pay the likes of ATOS, NGOs, working links and other agencies billions through the failing work programme or via the brutal work capability assessments and they implement a sanctions regime that is regularly cruel and often absurd. And they've created a horrendous and horrible culture around the benefits system, which is humiliating and degrading for claimants and miserable and demoralising for the staff who work there as we heard yesterday at the welfare reform committee. And things are just simply going to get worse. Christina McKelvie's referred to the shambles over tax credits, but we've also got the roll-out of universal credit. Without doubt, the worst and most ill-judged decision of them all, and that is the payment of housing benefit to landlords, tenants rather than landlords. As a former housing officer, I can think of no worse policy that they could have come up with. It's as if they've sat round a table and said, right, let's come up with a plan to see how we can get the most people evicted possible. Thankfully, we will be able to do something different in Scotland. And then we see the move to personal independent payment, which is designed to take millions of pounds worth of benefits, disability benefits from disabled people. Now, I think no one would disagree with the view that the social security system needs reform. It's complex, it's bureaucratic and it's at times indecipherable, but it needs reform to make it simpler, fairer, more humane, and a service that helps people and doesn't humiliate people. Any of us could experience periods of unemployment, any of us could experience mental health or a disability. I'm sure none of us would want to go through a system that we see at the moment. Thank you very much. I now call David Torrens, who will be followed by Alec Johnston. Thank you, Presiding Officer. I'd also like to thank Christine McKellway for bringing this important motion to Parliament today. Living in such a prosperous country, I'm concerned that we are confronted with more cuts to welfare benefits. However, I work on this opportunity in the chamber to highlight the devastating impacts austerity has on our communities, whether it is families, adults or children. Today, I joined Christine McKellway in rejecting the austerity agenda settled by the Westminster Government. This agenda taps into people in and in work poverty by targeting the most vulnerable members of our society. New statistics indicate that welfare reforms will push more than 6 million people in and in work poverty across the UK. In terms of specific entitlements, 105,000 disabled people in Scotland are in danger of losing their benefits. While tax credit reforms are predicted to reduce the income of up to 280,000 Scottish families, overall, austerity measures are predicted to cost Scotland's economy £1.5 billion annually. An OECD study has further demonstrated that growing inequalities caused by benefit cuts are to a severe obstacle to economic growth. With those numbers in mind, I believe that we also have to acknowledge the multifaceted effects of welfare cuts are beside the deepening social inequality UK Government austerity plans, so there is little respect and dignity for those affected. Currently, in the Westminster's direction, the Scottish Government has strongly opposed the austerity and has taken its own initiatives in reducing the worst effects of austerity on individuals. In fact, reducing inequality and creating a fairer society lie at the heart of its policies. The Scottish Government's efforts include fully mitigating the bedroom tax in Scotland, enabling additional support through the Scottish welfare fund and community care grants, and establishing the Scottish independent living fund to help more than 2,800 disabled people across Scotland. I welcome those endeavours in easing the burden of people who are less fortunate. However, welfare cuts are not just about numbers, statistics and political bargain, welfare cuts are real people, including many unemployed disabled people and young people. Nothing will fix this better than a sharp increase in the usage of food banks across Scotland. The Truswell Trust has reported 1,117,689 people visiting Scottish food banks between 2012-13 and 2013-14 who have organised, as the nation noted, a 398 per cent increase. When the Truswell Trust launched an equality among food bank users, one of the most common reasons for accessing the service was the dartsing in their welfare entitlements. By tonight's talk about these national trends, I want to use this opportunity to mention some of the examples in my Cercodi constituency. Cercodi Food Bank was launched in 2013. It works as an independent community-based organisation. It relies on the nations and help of volunteers. Nothing less is committed to support local residents is invaluable. Over a period of 12 months, starting in December 2013, it prepared emergency food packages for 4,685 individuals. This past September, it prepared 240 food parcels that serve 3,870 meals. Grown demand shows how essential these services are, unless I want to commend all voluntary staff members of the Cercodi Food Bank who invest much of their time and effort into ensuring that both adult children do not have to go to bed hungry at night. As we are facing further tax credit cuts, more people are under a risk of falling beneath a poverty line, especially low-income families with children who are most likely to suffer. In Cercodi, approximately one in five children grow up in poverty. Connysent to this, we have to be led that this number can rise further. Given each child, the best possible starting life is too important in creating a fair and equal society. However, I am concerned that growing up in poverty will cause many obstacles to this goal. In addition to increasing number of families and children affected by austerity, the way welfare cuts are being implemented is problematic. An example highlighting some of the discriminations practices used against welfare seekers was brought to me by one of my constituents. He was sanctioned for six weeks as he has missed one day of his triage course, even though I informed him that he would not be there, due to his father's funeral. Before I conclude, allow me to make one more important point. Economically derived country, we carry a social responsibility to our citizens. Our responsibility to treat all individuals with dignity and respect. Our responsibility to support those unable to work. Our responsibility to provide families with a basic income that does not make them rely on food banks. Presiding officer, austerity impedes us from taking up the responsibility. Therefore, I support this motion to halt welfare reform. Many thanks. I now call Alex Johnstone to be followed by George Adam. Thank you very much, Deputy Presiding Officer. It is traditional in these debates to congratulate members for having been able to bring forward a subject for debate. I would like to do that and go a stage further today and pay tribute to Christine McKelvie for the persistence with which she has brought this issue before this Parliament. It is important that we address it and address it regularly and her work, particularly in members' debates, is worthy of note. However, the issue that we discussed today is one on which Christine McKelvie and I will, I am afraid, probably tend to disagree now and into the future. The necessity for welfare reform was something that was identified some time ago. In fact, the right time to reform welfare, I would suggest, is at the peak of the economic cycle rather than at the bottom or during a recovery phase, as we currently are. It was for that reason that it was perfectly right that Frank Field, a minister in the last Labour Government in 2007, brought forward his initial proposals for welfare reform. I would suggest that, if the Labour Party had had the courage of its convictions and had taken that programme forward back then, we would perhaps be in a better position today than we are. Nevertheless, we are where we are and we have to deal with it. There are a couple of points that I think are fair to raise during the course of this debate. The first is the issue of disability benefits. There are criticisms that are being made over the transfer from DLA to PIP, and that 20 per cent cut in the expenditure that is expected within that budget heading is regularly brought up. We must remember that the change in entitlement to PIP will result in a 20 per cent reduction in those who are entitled to claim, but those people will not lose their benefits. They will be entitled to the same benefits as those who are looking for work at the moment, and they will receive the same assistance to find work. They should be the 20 per cent who are most able to make that transition. It is an appropriate thing, I believe, for Government to attempt to help those people back into the workforce in the way that they will. However, the other issue that I think is important that we raise here—and it has already been raised by Neil Findlay and others—is that of the activity this week, particularly in the House of Lords, relating to working tax credits. The policy of reducing working tax credits and replacing them with higher wages in the workplace and other measures for support, including childcare support, for example, is, I believe, a sound policy, and one that we should all aspire to make work. The problem is—and it has been pointed out by many within the Conservative Party, most notably Ruth Davidson herself, who has taken the opportunity to raise the matter with the chancellor—that, if you are going to make that transition, you have to make sure that people have the extra money in their pockets before you take the support away. The proposals appeared to indicate that the support was going to be taken away first, and then, ultimately, the higher wages and the better support measures for childcare in other aspects would kick in. That is simply unacceptable as a process, and it is necessary for us to get that in the right order. Does he therefore agree that the action of the House of Lords the other evening was absolutely right? I agree that it was the mechanism that was available to us to take forward this matter in a way that was better for us all. However, I would point out that it is interesting that the decision by members of the Conservative Party, including Ruth Davidson, to take action to further that objective and the measures that were taken by members of the Labour Party to put forward the changes in the way they did, were ultimately extremely effective in obtaining the outcome that we wanted in the short term. I suggest that the actions of the SNP have been an example of how the Scottish National Party's position can be disadvantageous and ineffective, and that the alternative routes have proved to be rather more effective in this instance. I hope that we can come to a conclusion, and I am drawing my remarks to a conclusion at this time. It is vital that, as we go forward, we understand that the reform of welfare is necessary, and that it is our duty to ensure that we reduce dependency on the state wherever we can and that we deliver real independence for all those who are able to take it up. The issue of welfare reform will remain a central debate in this and other parliaments, but it is one that we cannot afford not to address. We need to make welfare deliver. We need to make welfare less significant as time goes on, because we need to get people back into the workforce, back into the workplace and back into a position that they have more control over their own lives, and that is what I aspire to under the welfare reform heading. I can also take this time to thank Christina McKelvie for bringing this debate to the chamber, because I know that it is an important issue to her, and I know that it is an important issue to most of us in our constituency work, because, as most of you know and will be aware, I am convener of the cross-party group on multiple sclerosis, and recently the MS Society Scotland brought this report out. MS, enough, makes sense of welfare, because more and more people with MS have been struggling to either access benefits or to retain what benefits they had, and one of the issues with MS in particular is that most people are diagnosed between their 20s and 30s, so it means that it is during the peak of their working life. They go from being a professional person, being able to do everything that they want, working, paying their bills, to someone who is having to rely on the state now only because of their medical condition, and one of the problems of the legislation is that it does not take long-term, disability or long-term conditions into account. It is as if it is just a spreadsheet to get that person off of that spreadsheet because they need to do something else, and that is the problem that we are seeing. That is the picture that has been painted in our constituencies, and I do not think that that is good enough for us to be going down that route. The MS Society Scotland's report has said that 11,000 people in Scotland have MS, and it is a lifelong condition, and there is no cure. When they are asking to make welfare, it makes sense. They are saying that MS must be at the heart of shaping the system, and I would say that that would be about any long-term condition that when you are dealing with a welfare, because the whole idea of welfare is to support people in their time of need. If we are going to be doing that as a society, people who are disabled or have long-term conditions are the very people that we are wanting to help. I think that the system is wrong at the moment, and that is why I am supporting Christina McKelvie. However, when they did their report, they found out that 65 per cent of people with MS agreed that, without disability benefits, they would be unable to afford essential items such as food and heating. 85 per cent agreed that, without disability benefits, their independence would be negatively impacted, and 91 per cent found the process of claiming disability benefits stressful, which the irony of that is, with a condition like multiple sclerosis, is that the actual pressure of going through the system could trigger another attack and make it actually probably qualify for the PIP one day, as opposed to not qualify for it. The way that the system decides whether a person is using PIP as an example, can the person walk 20 years if they get MS 20 metres? Yes, they probably could, but they will probably be in their bed for the next 24 hours, because of the chronic fatigue that will follow on after that. Those very practical things must be taken into consideration, because that is about people and the people that we serve. One of the things that MS is enough, is that it is difficult enough to live with it without having to deal with Westminster's so-called reforms. Mormore Simkins, the director of MS Society in Scotland, said, it is simply not good enough that people in Scotland who have MS are being forced to make difficult choices between heating their homes and attending hospital appointments. That is the situation that the Tories have now got many people dealing with long-term conditions in now, and that is not what this should be about. It is not good enough for Alec Johnson to say, we are where we are, that is not good enough. We are dealing with people's lives, and the quality of that life is the important aspect as well. Because of that, I follow Christina McKelvie's call to have Westminster halt the so-called reforms now. Many thanks. I now invite Margaret Burgess to respond to the debate. Thank you, Presiding Officer. I would also like to thank Christina McKelvie for bringing this issue to the chamber, which all who have spoken in the debate have agreed is an important issue and one that we should keep revisiting. Today's debate has given members an opportunity to reflect on the consequences of the continuing austerity programme being forced on the whole of the UK by the UK Government. It will see £12 billion removed from welfare expenditure each year by 2019-20, with around a billion cuts being made in Scotland. Those draconian cuts, undertaken by the UK Government, are why the Scottish Government continues to do what it can with the limited resources that we have to mitigate the impact of welfare reform and help those who are affected. It is very clear that we in Scotland have a very different ideological position to the UK Government on the importance of social security. Like Neil Findlay, we should talk about it as social security. We see it as an inclusive safety net that, at some point in our lives, almost all of us will use. I find it difficult to imagine any Government of any persuasion in this Parliament taking forward some of the UK measures in terms of social security. We know that individuals and families across Scotland are bearing the brunt of those reforms. The Scottish Government analysis shows that the impact is being felt by the most vulnerable people in our society. Christina McKelvie and George Adam have highlighted some of the groups of people who are being badly affected by those reforms. Sanctions hit young people hardest. The group was likely to be affected by the benefit cap as lone parents. Disabled people, as we have heard, are particularly affected by the bedroom tax and many lose facing some or all of their disability benefits due to reassessment from disability living allowance to PIP. I heard what Alex Johnson said about that, that 20 per cent that will lose their benefit can get into work. I would suggest that he applies the same theory to that as he was making for working tax benefits. Let's see if people can get into work, let's support them into work before we actually take away their lifeline of benefit, and I think that it applies across the board. The point that I was trying to make at the time in my speech to which he refers is that those who are no longer entitled to disability benefits will continue to be entitled to other out-of-work benefits, so they will not lose their support entirely. No, I think that that's semantic there. They might not lose their support entirely, but they will lose a considerable part of their income that they require to make ends meet at the moment, and they're going to lose that if they lose their PIP, which is additional to any other benefits they may get, so I really don't accept Alex Johnson's point on that. I think that it's very clear that it was made by David Torrance that we're talking here about people that come to our surgeries, people that live in our communities, and we know that many of those people are turning to advice agencies for help in their time of need, and the Scottish Government is doing what it can to help those affected. That includes investing £23 million across three years to 2016 to provide advice and support services to mitigate the impact of welfare reforms. The Smith commission gives Scotland opportunities on social security, although only around 14 per cent of social security spending will be devolved to the Scottish Parliament. Powers over disability benefits and carers allowance will provide opportunities to have a more joined-up system, and we've already started to indicate how we plan to use those powers to better support people in Scotland. I think that the First Minister has already announced that, if that Government continues, we would increase carers allowance in line with job seekers allowance. Neil Findlay talked about universal credit and some of the changes to universal credit. The flexibility that the Smith commission will give us and universal credit will give us some the frequency of payment to the claimant and payment to the housing costs element direct to social landlords will be able to do that with the flexibilities, and I would certainly agree with Neil Findlay that tenants are telling us that that's how they would like their payments made direct to the landlord. However, as the Scotland bill, as it stands, fails to deliver a coherent set of powers that will allow us to tackle long-standing, entrenched issues, but rest assured, we will take an intervention. Neil Findlay mentioned earlier that 14 per cent of benefits would be devolved. Almost 50 per cent of benefits is the state pension. I don't think that the minister is asking for that to be devolved. Can she clarify? As Neil Findlay was very clear in the white paper that we produced when we were looking at an independent Scotland, we very much asked for all social security powers to be devolved to Scotland, including the state pension. However, what we have been very clear about is that, unless we get all the other levers of the economy and the power to raise all our own finance, in those circumstances we would not be asking for the state pension to be devolved. We will do what is best for Scotland and the environment that we have for Scotland. We are making progress in some key areas, but we also need to ensure that the wider fiscal framework is in place and will not accept a deal that is not fair for Scotland. The Smith commission was also clear about how it expected employment support to be devolved. It said that all employment programmes that are currently contracted by DWP for the unemployed should be devolved. That would include, but not limited to, contracts to deliver the work pension and work choice. Smith also called for a new governance mechanism to be established, which integrated the reserve functions of Jobcentre Plus in Scotland. As in the proposals for welfare devolution, we are concerned that the Scotland Bill does not deliver Smith's proposals on employment support. However, the limitations of the Scotland Bill will not deter this Government, and we remain engaged in a discussion about how to create a fairer Scotland, conversations, meetings and events are being taken place across the country about the type of country that we want Scotland to be. It is not a traditional consultation. The process is designed to encourage and add to the conversation that is already going on throughout Scotland about how we create that fairer, better place to live and work. We are determined, and I believe that it is vital, that instead of doing things to communities, Scottish Government will do things in partnership with communities. A stocktake paper has already been published, which provides an update of what we have learned throughout the process so far, and we plan to bring forward a social security bill in the first year of the new Parliament. The true cause of the UK Government's austerity programme has been especially felt by those least able to carry the burden, so it is entirely right that we demand that the UK Government abandon those plans. To conclude, the Scottish Government welcomes the motion from Christina McKelvie, which gives me the opportunity to reiterate our opposition to the UK Government's continued austerity. Many thanks. That concludes Christina McKelvie's halt welfare reform debate, and I now suspend this Parliament until 2 o'clock.


Hi everyone, Basel Chapman here. This is the Tiger Financial News Network 4 p.m. closing bell number and what did we have today? Years and years ago when I used to hand chart these, whenever there was a zero percent change I would make a little circle and develop a whole bunch of techniques based on it. To get a zero percent change, that was one thing when you're trading in the three thousands and two thousands, or even going back to the crash of 1929 to 40 level if you go back in the charts. This is 32,944.78, we are up 59 cents, it's a zero percent change towards the low. That's really important because it means that if there is a 150 point close on the downside tomorrow, you've got to be careful of key support on the left side and if there is a 150 or more priced rally on a closing basis tomorrow, it says gee, we could have a little bit with the Fed coming up, we could even have a really good balance. So these are the numbers to watch. You've got the S&P right now, had a much weaker session down 31 at 41.73, look at these three lows that are being made here. It has to hold the 41.50 area, it's going straight down to 41.14, so by tomorrow you've got to get some kind of a relief rally, QQQs took out the left side low and that H pattern went to 317.45 low, which is now gone and closed, no it hasn't, 318.17, yes by a fraction is closed underneath the left side low of the 24th of Jan, this is not so good, IWM the Russell 2000 also had not a good day, it's down at 192.83, what's really important at this particular point is the gold is pulled back, the gold, that was just a huge move to the upside, you can understand down from the 2078 level to 1955, you could even come down to the 1930s, even touch 1900, but there should be some support because this is a geopolitical, it's the yellow icon of fear and that's what we, I look at the gold as, but if you're looking at the TLT, this is something altogether, the TLT is the 20 year churchy bond front, it went to a lower low, it took out the low from back in March of 2020, is it 2021? Yeah, 173.19 was the low, not a good sign and Crudall is pulling back, so we're in a very critical area, there needs to be some kind of relief rally that holds up a wonderful evening, we'll see you all tomorrow again, see you again, thank you for being here and thank you


TFNN headline news update. Good afternoon, everybody. I'm Tommy O'Brien, coming to you live from TFNN, 2 PM Eastern time on Wednesday. It is Fed Day. We're gonna get an announcement as we speak. Right now, markets in positive territory, quite a day ahead of the Fed announcement. We have a press conference as well, Chairman Powell will see what he has to say. Right now, S&P's up 69 points, trading at 29.33, got the Dow up 235, trading at 89.56. Excuse me, Nasdaq up 240, trading at 89.60, Dow up 505, 24,551, putting this on a little bit of a shorter term timeframe. You see the volatility starting to come in the market in the S&P's. We'll get the Fed decision in a moment, we'll start things off, we'll jump over to the charts and we'll start it off with the indices. There we go, Dow 30, check out the run. We're above 24,600 in the last 45 minutes, currently trading 245.41, been an upward trend for most of the day early. We were trading 24,182, now trading a solid 400 points above that level. S&P's 29.35, you back it up to where we started the week in terms of Sunday futures. We were almost 100 points lower, 28.20, Sunday night futures. Right now trading at 29.35. And as we get the news, I'm gonna pull it over so we can see the headlines right here. You have the Fed pledging to keep rates near zero until full employment and inflation comes back. That is your headline, the market gonna like that. The market had an idea that might be happening. That's why you saw, I think, an acceleration even today ahead of that news. The Fed pledging to keep rates near zero until full employment. Federal Reserve painted a dour picture of the current conditions, a pledge Wednesday to continue. It's historically aggressive policy stance until it's comfortable that the US economy is back on its feet. Following this week's FOMC meeting, the central bank said it would maintain its current interest rate target between 0% and 1 quarter percentage point basis points. The ongoing public health crisis will weigh heavily on economic activity, employment and inflation in the near term and poses considerable risk to the economic outlook over the medium term. The committee said in its post meeting statement, the committee expects to maintain this target range until it's confident that the economy has weathered recent events market. Like in that news, holding the gains up about 67 points. Don't forget folks, Tom O'Brien. He's coming up at four o'clock, but tomorrow at 9 a.m., timing the trade webinar, all-day webinar on the front page of TFNN, great time to check that out. Lots of earnings, folks. It's Fed Day. We got Facebook, Tesla, all that action after the bell. Stay tuned, folks. Dave White at two. Tom O'Brien at three. We'll be right back.


One of the most important loads category of loads are those formed by induction machines. In fact, we also discussed in the previous class that induction machines are used in another context as generators in many wind farms. Now, so it was in the previous class I told you how from a basic synchronous machine model for example, the 1.1 model the model in which you have got one rotor winding on the d axis and 1 on the q axis. You can modify it so as to get a induction machine model for that you would have to set the field voltage to 0, remove all kinds of salient behavior for example, x d and x u you would have to make to a to a value x and x d dash and x q dash also would be equal. So, if you did that kind of thing and even made a time constants on both axis the same you would come across induction machine model from the original synchronous machine model. So, let us just review what we are going to do in today's lecture. Today is the 32nd lecture and we will be continuing a bit of a discussion on induction machines and we will try to cover a bit of transmission line modeling also in this lecture. So, if you recall in the previous class we had done static and dynamic models of we had discussed the nature of static frequency and voltage dependent loads and we had begun on our induction machine model. Now in the previous class the point at which we left off was some of the issues when it came to induction machine models although I did mention that you can have in fact induction machine model obtained from the synchronous machine model there are few issues which naturally will come to your mind. For example, what do you mean by rotor angle in a in a situation where there is really no saliency in the machine. So, you cannot really align your axis to any particular in any particular direction with respect to the rotor because the rotor is exactly symmetrical. So, that was one issue which we need to tackle. So, if you look at the synchronous machine equations they seem to be having a rotor angle dependence. So, how do we actually show that induction machines in fact are not dependent on the rotor angle although you can get an induction machine model by you know just modifying a synchronous machine model. So, if you look at the basic equations which we had discussed last time that if the induction machine model is obtained from a synchronous machine model by neglecting E F D and setting all the transient time constants and transient reactances and of course, the steady state reactance is equal on the D and Q axis. So, this was the model for the 1.1 model on the D axis and for the Q axis this is what we have. So, what you notice here of course, is in both these equations both on the D and the Q axis the last equation for example, here is dependent on V D and the next one here the Q axis equations you have got V Q here. Now, if you assume a three phase sinusoidal source a sinusoidal balance source of a constant frequency and you use Parkes transformation that is depending on the rotor position. Then you will find that V D and V Q become delta dependent as I mentioned sometime back delta is only notional it is a kind of a abstraction in the context of induction machine it can be anywhere, but the point is does it affect eventually the observables are choice of the D the D axis and the Q axis. So, in other words thus the rotor angle matter eventually the answer is no and proving it is not is not just you know it is not cannot be shown for example, in a couple of steps here. What we will do is this something which will come in coming useful even later what we will do is reformulate the same equations using another transformation. Now, this seems to be a kind of a kind of a complication, but sooner or later as I just start working in power system dynamics you will kind of get used to this change of reference frames. So, our normal reference frame of course, before we go there let us just repeat what we did last time that is the x to be used in these equations is nothing, but in terms of the typical parameters of a induction machine x is equal to x s the leakage reactance of the stator plus the mutual reactance of the stator x dash in fact, is obtained from the second equation in this x r is the rotor leakage referred to the stator and t dash similarly is defined at the bottom with r r r r being the resistance of the rotor winding. So, this kind of these are the parameters which are used in the model 1.1 model, but for an induction machine they can be related to the cell the leakage as well as the mutual reactances as shown in this slide. Now, remember that torque equation is the same its i d i q minus i q i d and we have used in this equation the Parkes transformation. So, where theta is the position of the rotor it is omega t plus delta. Now, let me introduce you to you another transformation C k in fact, it is also called Kronz transformation the difference between the transformation before and now is that instead of theta which is omega naught t plus delta you have got in this transformation the argument of the cosine and sines contain just omega naught t they do not have delta. So, this is not the same as the previous transformation. So, if I use this transformation to transform to the new set of variables from a b c as shown in this slide that is instead of transforming to the small d q lower case d q 0 variables you transform a b c using C k into the variables f d f q f and f naught. And it is you can really show that eventually the lower case f d f q and f 0 are related to the f upper case d q and 0 by the relationship which is given below that is f q plus j f d upper case is equal to f q plus j f d lower case into e raise to j delta this is a compact way of writing this.   So, from this if you evaluate this it can be compactly written down in fact f 0 of course, in these both in these transformation f 0 are the same, but f d and f q upper case are related to f d and f q lower case by this transformation. Now, this is I will not derive it here, but you can compactly write it as shown in the slide that is f q plus j f d is equal to f q plus j f d into e raise to j delta. What I am trying to say here is since the rotor angle in the case of a induction machine or rotor position in case of an induction machine is a bit of an abstraction the rotor angle is a bit of an abstraction because there is no saliency in the rotor. It makes sense to reformulate our differential equations not in terms of the Parkes transformation, but in terms of the Kranz transformation which is a which contains omega naught t as the arguments of the sines and the cosines and omega naught of course, is a constant in this case there is no delta coming into the picture. So, we use such a transformation instead of Parkes transformation. So, this is what is very important. So, if I actually reformulate the equations you know in the capital D Q frame of reference I will call it the capital D Q frame of reference or the Kranz frame of reference. The equations look similar with this additional term. So, if I write down you know for example, d psi capital D by d t the equations for it look the same except here you get omega naught. So, this is one change you will see another important thing is I have also changed the variables psi capital G and psi capital F to the new frame. So, actually if you look at the new variables psi g k and psi f k in fact, they are related to these old variables. So, if I do that you know I just substitute for the old equations with the new variables your differential equations look like this in the new variables. So, you have got now new variables psi f k psi capital D on the d axis and similarly on the q axis psi g k and psi q.  So, why are we writing down the equations in terms of different variables? Now, the important thing here is if your source is a three phase balance source of frequency omega naught you will find that v q v capital Q or upper case q and v capital D are in fact, independent of delta. In fact, you will find that there are constants which are independent of delta. So, although the earlier differential equations of the induction machine was certainly valid what we have done is come to a form in which the inputs v d and v q are in fact, constant in the new variables in the new transformed variables they are not dependent on delta. So, it is better to get rid of the concept of delta or the abstraction of delta in case you do not have a salient pole machine like in an induction machine. So, the important thing of course, is something which you can prove using this basic relationship which I have shown you here on the written slide you can show that of course, and i d plus j i q sorry is equal to i q sorry this should be q and this should be d and this should be q and this should be d. So, if I actually compute psi d i q minus psi q i d delta turnout that it is equal to psi d i q minus psi q i d. So, what I want to say here is of course, that the torque equation also the electrical torque is independent of delta it is not dependent on delta. So, I have formulated my equations in the Kranz variables or using a transformation which is you can say rotating at a constant frequency instead of using Parkes transformation I am able to formulate my equations of an induction machine. So, that it is independent of delta and of course, that also means that the rotor angle is not important in some sense. So, we know for example, that an induction machine under steady state conditions under load or no load in fact, under loaded conditions its speed is not equal to the frequency or the electrical speed of the machine is not equal to the frequency of the source to which it is connected to.  Now, if you took the classical definition of delta that delta is nothing but theta is equal to omega t is equal to omega naught t plus delta. You see that in case the speed of the induction machine is different from the speed of the transformation and therefore, also as I have told you it is also equal to the frequency of the voltage it is connected to voltage source to which the induction machine is connected to. We will see that delta is constantly varying if omega naught equal to omega naught and you know that induction machine can operate stably even this is even if this is true in fact, there is always a steady state slip when you load the machine. So, what I have done here is come to a formulation using the Kranz transformation which is completely independent of theta and the induction machine in some sense can happily operate at a speed which is different from the omega naught. Now, this is not true of a synchronous machine in a synchronous machine in fact, you will find that you will find that the torque in fact, is a function of delta it is related in some way to delta. So, in case delta is not a constant in such a case you will find that the torque is also not a constant, but this is not true as far as an induction machine is concerned. So, it may be a good idea in an induction machine to formulate your equations in the capital D Q frame, but you could formulate your equations in the you know the Parkes reference frame as well, but the changing delta whenever there is a slip is of no consequence eventually. So, that is what really I wish to tell you here. So, you can get the induction machines as equations as I mentioned to you a few more points. First thing is what is the torque equation of a of the machine? I told you we are working with the torque equation in fact, is exactly the same this is the per unit torque of a machine in fact, this is correct where t is nothing, but what I had written sometime before it is this. So, this is the differential equation which you have to use along with the differential equations of the various fluxes that is psi d psi q psi g k and psi f k alternatively you can also use psi d psi q psi g and psi k, but remember delta will keep on varying in this equations. So, in steady state you will not find psi d psi q psi g and psi k as constants. Since, this is not a function of delta t is not a function of delta you do not really actually have to write the separate equation for delta itself. Nothing if you formulate your equations this way you do not really have to write the delta equation at all the differential equation corresponding to delta at all because delta never appears in any of these equations. Now, one of the important things of course, is this is the equation of an induction machine in fact, it is derived from the equation of the synchronous machine, but if you want to operate you want to really study the operation of a motor instead of a generator it is important to remember that we when we first formulated this swing equation or this in case of a synchronous machine the directions of t m and t were as follows. We assume that your machine is moving in this direction t is like this t m is like this. So, it is correct to say that the speed of the induction machine is equal to t m minus t in a motor in a motor remember that t m is in fact, in the opposite direction of the speed of rotation.  So, you do not have t m in a synchronous machine a synchronous generator t m would have been the prime over torque, but now the load torque on a motor would be minus t l. So, if I am writing down the equation this is the speed of the machine rate of change of the speed of the machine this is not slip remember this speed of the machine is equal to minus of t l in case it is a motor with t l in this direction then you will have minus t l minus. Now, just remember of course, that whenever we are writing this is a correct equation there is nothing wrong in this equation. So, it is minus t l minus of this psi d i q minus this. So, this is correct there is nothing wrong in this equation you see the direction of speed t is this expression for t is in this direction t in this direction is given by this expression t l is in this direction. So, this is the correct equation, but one more small or other somewhat minor point is in case you are studying a motor another change you would probably like to do is assume that the currents i d and i q are going into the motor rather than coming out of the motor in a generator convention we had assumed that the currents are going out. So, these currents are in fact the currents coming out of the machine. So, all the in all the equations wherever current appears it is referring to the current going out of the machine. So, of course, if you change the direction of the current this will have a positive sign here and similarly in other places you will have to change the sign in case you change the direction of the current. So, this is something which you should remember that in case you are taking the direction of current inward then you have to change the sign of this then our equations are absolutely self consistent there is no problem with them. So, this is regarding the motor convention. The second point which I would like to talk is about T L itself. T L itself is the mechanical load on the machine a particular load has a you know normally we would like to characterize each mechanical load also by some torque speed characteristic. Now, for example, a fan you know you can have a if you have a fan you will find that its torque speed characteristic is something like this the torque versus the speed. So, this is the torque speed this is the load this is the load torque versus speed characteristic and of course, if you have got an induction machine which is driving this fan then the operating speed is given by the point at which both these things intersect. So, this is the operating speed of the machine. So, or rather the steady state speed of the machine. So, this is the steady state speed of the machine. Now, one of the points which you should appreciate at this juncture is that in case. So, if you look at a torque speed characteristics of an induction machine the electrical torque versus speed and this is the load characteristics. This is the load versus speed for a fan type load for a maybe you may can also I think of constant power torque loads for example, if you are lifting up something you know like a through a lift then the torque is a constant it is not a function of the speed torque is nothing, but the mass into gravity means its proportional to the mass and the gravity which is being lifted the mass which is being lifted against the gravitational force. Now, the operating speed as I mentioned was this. Now, suppose an interesting point here is that suppose this of course, frequency here is omega naught at when the slip is 0 or the speed of the mechanical speed of the machine becomes equal to omega naught the electrical torque becomes 0. Now, an interesting thing is if a frequency changes what happens to the torque? If frequency changes you will find the torque speed characteristic in fact, the torque speed characteristic in fact changes and it becomes 0 at some other mechanical speed because of this you will find. So, if there is a small change in the torque you will find this point slightly shifts and operating speed also changes in fact, the amount of the even the torque changes. So, what you find is if you are driving a fan type load you will find that if the electrical frequency changes from omega naught to omega naught dash. So, the source frequency changes from omega naught to omega naught dash the power output of such a motor would reduce and therefore, the input power also would reduce to a certain extent.  So, this is something which in fact, this is one of the mechanisms by which load becomes frequency dependent. We will conclude this our discussion of induction machine with a simple interesting dynamical example this is not something to do with our classical power systems analysis, but nonetheless we are at a point where we can actually analyze this system that is the behavior of a induction machine which is connected to just a set of capacitors.  So, there is a prime mover which is rotating the induction machine at a constant speed and the induction machine stator is not connected to a voltage source, but it is connected to a bank of capacitors in such a case a very interesting thing is which is observed in practice is that the induction machine self excites that is you will find that some voltage appears here. So, if there is some residual magnetism in the machine or there is some residual charge on the capacitor you will find that automatically if you of course, connect an appropriate value of these C's this is a balanced star connected C you will find that the machine suddenly self excites. This is by the way a very from physical perspective a very very interesting phenomena it practically says that if you have got a bank of capacitors which is basically just you know metal and dielectric and you have got a machine which is just a ferromagnetic material in copper and you rotate the machine low and behold you have got some voltage appearing at the terminals of the machine you know without having any other magnet or battery available with you. So, this is something very interesting about self excitation as a phenomena and what I wanted to tell you here today is that with the tools which you have right now at your disposal you should be able to show that self excitation occurs. What exactly is self excitation you rotate a machine with you know practically you know with no self excitation source except the fact that the machine is being rotated by a prime mover at a certain speed say the rated speed and what you want to show is that if there is some you know small however, small and initial condition you will find that voltage grows and the machine self excites eventually of course, what you normally find in practice is that the voltage grows up to a point and settles down because of saturation of the ferromagnetic material which constitutes the induction machine. So, if you look at it from a mathematical perspective an analytical perspective what you have to do is write down the equations of the induction machine. So, we have for example, written down the equations of induction machine you do not worry about the torque will assume that the prime mover is somehow maintaining the speed of the machine a constant. So, the equations of the induction machine are as shown in these slides. So, the first three equations two differential equations and one algebraic equation and the q axis equations. So, these are the equations of the induction machine you will have to just interface them with the equations of the capacitor bank in the d q frame of reference. Now, remember we are not written down the zero sequence equation will assume absolutely a balance setup and therefore, the zero sequence equations are completely decoupled. So, we do not have to include them in this analysis the decoupled completely from this our set of d q equations. So, what do you need to do well what you need to do here is write down the equations of the capacitance capacitors. So, if you look at the equations as they given here you will find that the equations of the capacitor are c c and c d b n by d t is equal to the current I a I b and I c. So, what you get here is if you transform these using the transformation c k what you will find is this something I leave as an exercise to you d v d by d t is equal to. So, in fact this will be omega s omega naught. So, if actually if I write these equations again. So, we will have d v d by d t is equal to minus omega naught v q plus I d by c and you will have of course. Now, we can write this in per unit form in which case you will have d v d by d t is equal to minus omega naught v q. Now, these are in per unit plus I d per unit divided by c per unit, but in case you are in per unit you can also write it the c in per unit is the same as the susceptance in per unit. So, this one. So, normally you will be given the susceptance in per unit. So, that is why I am writing it in this form.  There is no other source of excitation there is no other source of excitation will assume speed is constant. So, we do not write down the prime over mechanical equation we just assume that the speed is constant. Now, what you need to do is of course, what are the equilibrium conditions x is equal to 0 I mean all the states are equal to 0 is an equilibrium condition. Then what you need to do is find the Eigen values of A for different values of B c and what you will find very surprisingly is that such a system will have Eigen values with real part less than 0 if B c is greater than a certain value. In fact, B c is greater than a certain value which is related to the reactances you can actually get the condition explicitly. So, very very interesting thing can be analyzed mathematically that self excitation will occur in an induction machine if connected to a bank of capacitors and driven by a constant speed prime over you will find that at a certain value of those capacitors the system is unstable at the equilibrium point as a result of which you will find that you know you will find that some voltage appears you know for any non-zero initial condition which exist. So, it may be some residual flux in the machine or some residual charge on the capacitors and the machine will just simply self excite. So, it is a very you know interesting and exciting phenomena. Of course, one important point which in this case is very critical is that the equations which I have derived for the synchronous machine as well as the induction machine are shown to be linear. Now, remember that if you have got a linear system and it is stable it you will find that for any non-zero initial condition of the states it will simply the system will simply blow up it will just go on increasing to infinity. This does not happen in practice and the reason is that the ferromagnetic parts of the machine tend to saturate. Now, if that happens it what it also means is that our model here linear model here is inadequate to capture that phenomena because it is a linear model. So, in fact sometime before I had mentioned to you that there are you know ways which are not very theoretically you know provable kind of ways to account for saturation of a synchronous of a synchronous or any induction machine. If you actually did manage to account for saturation and make this model non-linear in that case you ought to have been able to show that there would be another equilibrium point and the system would go to that new equilibrium point that equilibrium point is not a zero equilibrium point. So, what I mean to say is that with saturation the system becomes x dot is equal to f of x this is a linear system which we are handling right now. What we have we what the thing which you can prove is that if b c is greater than a certain value you will find that at the equilibrium point x is equal to zero this system is unstable and therefore, the system tends to self-excite. If you take a non-linear system first of all you may be having more than one equilibrium point if you take into account saturation and one of the equilibria is stable and the other is unstable. So, if you look at self-excitation you will find that the system kind of you know settles down to a new you know let us say an equilibrium periodic equilibrium. So, that is one interesting thing which you can further chew upon. I will now show you a an videographed experiment which really shows the self-excitation phenomena what we will be seeing in this demonstration is in fact, self-excited induction generator which is driven by a DC generator which maintains the speed practically a constant rather induction self-excited we will just do this again once more. What I will be showing you now is a experimental demonstration of self-excitation phenomena in this experiment we have an induction generator which is driven by a DC motor which keeps the speed of keeps the speed of rotation constant and we will connect a bank of capacitors across the induction machine. What we will see is of course, that if the amount of capacitance is adequate you can actually have a voltage build up at the induction generator at the output of the induction machine terminals. So, that really shows you what is known as self-excited induction machine phenomena. So, now let us see the demonstration. So, what you are seeing here is a DC machine DC motor which is cup and this of course is the bank three banks three banks of delta connected capacitors each with a switch which we shall connect across the induction machine terminals. So, the DC motor will drive this induction machine which you are seeing and we shall of course, monitor the output voltage through one of these probes which is fed to this oscilloscope. So, what we will do now is start this machine DC motor there is one more motor one more machine right in the middle also, but that is playing no role as it is not energized there is one in the middle also here. So, the DC motor has been started the machine on the left. So, we build up the speed and you see that the output voltage of the induction machine there is probably some residual magnetism because which you get little bit of voltage, but it is not really much. So, what is happening is now I will switch on one of the banks of the capacitors, but you see that really there is no voltage really building up at the induction machine terminals there is just a little bit probably due to the residual magnetism. One of my students is removing an additional probe which is not required for this experiment it is no bearing on the outcome of the experiment of course. Now, we will switch on the second bank and what you see is the voltage builds up spontaneously at the terminals of the induction machine. So, this is an example of self excitation if I switch off the capacitor bank one of the one of this capacitor banks then you see that the machine gets the excited and you will voltage will no longer be sustained. So, we will do this experiment again we will switch on this capacitor bank again, but remember that the capacitor bank may have some residual charge on it. So, what we need to do is discharge these capacitors the de-agent energize capacitors. So, we will just discharge it through a resistance. So, we see what that is what we are doing right now we will discharge it. There is no need of doing that because it is not energized it was not energized anyway. So, now we will just redo that. So, you see that the induction machine self excites again. So, you can have an induction machine self excitation by connecting capacitors across it. So, this is so much about induction machine models remember that when you have a large induction machines you may have to model them in power system studies. So, for example, large power plant auxiliaries or induction machines in large industries you may have to model it by a dynamical model. Alternatively you can try to even model smaller induction machines or in some cases even larger machines depending on the nature of the study you are interested in by a static polynomial kind of model. I told you that an induction machine would say with a fan load if you look at its static characteristics it shows a frequency dependence. So, let us now move on to another you know equipment or another component of a power system which is absolutely important is a transmission line. You know transmission line is an element it is a distributed parameter element in the sense that it is defined by you know if you look at the if you look at it from first principle in fact all electrical equipment from first principles would satisfy Maxwell's equations. But if you look at some the low frequency behavior of transmission lines you can model them by distributed parameter equivalent where you have got shunt capacitances and series inductances, but these are distributed parameter devices. So, the basic mathematical equations which describe a transmission line are given as follows. So, if I just write down this the equations. So, if you have got a point k this analysis practically follows what is given in Sauer and Pies book. So, if this is I call x is equal to 0 point of the transmission line this is x is equal to d it is a transmission line element with of length d in that case and x is measured in this fashion. So, you have got this is v of x and we will assume current is in this direction I of x then the equations of the transmission line are this is something of course, I would not derive it is a big exercise in itself to from the basic Maxwell's equations to show that these are the roughly the equations which describe the transmission line for 50 hertz kind of behavior. So, these are the equations of the transmission line they are partial differential equations and the current directions and voltages at a distance x are described by these equations. Now, R L G and C are per unit length parameters. So, just one small note of caution because you may think L is in Henry no it is Henry per unit length and C is capacitance per unit length. So, just this is an important thing these are the partial differential equations which describe transmission line you know especially for power you know power frequency behavior. So, most of our these equations are valid for that kind of thing. Now, the solution of the general solution of these equations is something which you have done in your undergraduate years in a course on electromagnetic or perhaps even in maths or power systems itself is the current at any time t and distance x from from one end is given by just a moment we just have this in view. So, v of x at a distance x from this side is given by so, we are just following the notation of software and pi where in this when you are this of course is true only for a lossless line that is R is equal to G is equal to 0 the resistance and the conductance shunt conductance per unit length is actually 0. So, in that case we get what is known as the wave solution of these partial differential equations and where C is equal to 1 by root L C and Z C is equal to root of L of C this is the dimensions of ohms of a resistance and this is in fact the speed propagation of velocity. So, it is got the dimension of distance per unit time. So, of course it is important to note that this equation this solution is valid only for a lossless line. EHV lines in fact you will find that they come to this close to this lossless behavior. The resistance is low compared to the reactive components that is the resistance per unit length as compared to the x per unit length is much smaller. Remember that this functions f 1 and f 2 really dependent are dependent on the what are the conditions on the boundary. So, if I tell you about the conditions at the boundary for example, what is connected at one end and what is connected at the other end and I tell you its behavior with respect to time. In that case I should be able to tell you what the behavior of i at any other i or v at any point on the line. So, this is a solution which is valid for a lossless line. Now, the point of course which I want to make here is that this is the solution of a transmission line under transient conditions of a lossless line under transient conditions. If you are talking about the sinusoidal steady state, if you are talking of sinusoidal steady state behavior in such a case you must be recalling that if I take a transmission line this is k and this is m. I will be able to mimic or at least capture the behavior under sinusoidal steady state conditions what I mean by sinusoidal steady state conditions. For example, I apply a voltage source here and a weight for all the transients to settle down and then I measure for example, the terminal behavior here. I find out for example, what is the voltage which appears here say this line is open circuited. Then when I say sinusoidal steady state means that after all the transients have died down what is the behavior. So, you have already done this sometime previously in your undergraduate years. So, if I call this as you know Z S and Y S S H Z series and Y shunt you will find that Z series is equal to Z bar into sin of gamma bar D by gamma bar D sin H hyperbolic cinch function and this Y S H is equal to Y bar by 2 hyperbolic tan function. So, in fact, so if you take the sinusoidal steady state response you can use this pi circuit you can use this pi circuit with an impedance Z series impedance and the shunt admittance given by these values where Z bar is equal to R dash D. D is of course, the distance and Y bar is equal to G dash D plus J omega S and omega S is of course, the frequency of the sinusoidal sources. So, when you are talking of sinusoidal steady state the frequency which corresponds to those sinusoid sinusoids are omega S and of course, root of Z Y Z bar Y bar divided by D square. So, this is the sinusoidal steady state representation of a transmission line as a two port network. Remember that this is this solution is valid only for sinusoidal steady state conditions. So, as is mentioned in the book by sovereign pi it we should resist the temptation of trying to use this lumped pi equivalent two port equivalent of a transmission line under sin which is valid under sinusoidal steady state conditions. We should resist the temptation of using it for all kinds of transient analysis.  And then write down the transient equations L di by dt lumped transient equations like this. Now, is this correct or no that is the basic doubt you may have. So, let me just tell you what the situation is you have got the differential partial differential equation corresponding to the behavior of a transmission line which to some extent can be said to be physically valid for the studies normally encountered at for power system in power system analysis. You can use the distributed parameter differential partial differential equation model it has got a wave like solution in transients it has got traveling wave kind of solution. Under sinusoidal steady state conditions you will find that the behavior of a transmission line can be represented by a two port network consisting of lumped a lumped pi network. Now, can we the question is can we utilize this lumped pi equivalent which comes the R and L corresponding to the lumped pi you know you have got the this impedance z series and y shunt which we just wrote down. Can we use them for example, if you look at this y series and shunt if you look at the equations which come about you will get basically a plus j b then you divided this b divided by omega s that will give you the equivalent inductance to be used in this sinusoidal steady state model and then used use the lumped parameter differential equation once we get the L from this and then use it in our analysis for transient behavior we should avoid this temptation because of rather we in fact we do it sometimes. So, the question is is it valid the answer is strictly speaking you know it is not valid, but under certain circumstances you will get close behavior to what you observe rather you can use this kind of approximation of representing a transmission line by lumped parameters obtained from a sinusoidal steady state model. But of course, you will be committing some errors because this is not really how the transmission line behaves during transient it is a traveling wave behavior. So, there is a example given in sovereign pi's book which is very apt and in which he is asked us to find out yeah it is basically an example here from sovereign pi you have got a voltage source V s and it is connected to a resistance of 10 ohms this voltage source is switched on this voltage source is a sinusoidal voltage source it is 230 kilo volts line to line. So, we are just talking of a single phase model of a transmission line it is a 230 kilo volt line to line system. So, the phase to neutral of this will be 230 divided by root 3 and the peak value is 230 into root 2 by 3. So, this is the voltage source here it is a sinusoidal voltage source of 60 hertz. So, your 2 pi into 60 into t this is switched on through a resistance of 10 ohms to a 100 mile transmission line distributed parameter transmission line with parameters L and C given as 1.5 milli Henry per mile and capacitance per unit length is 0.02 micro farad per mile. Now, the thing we need to check is when we do the simulation of this how to do the simulation of this is something we will discuss in the next class when you do the simulation of this and compare it with what we get if we simulate a lumped equivalent same same system except that now we are going to use a lumped equivalent I am sorry you will have an induction series induction lumped equivalent of the lossless line. So, we have to compare the behavior of this model of a distributed parameter model of a transmission line with what happens if you take a lumped equivalent of a transmission line based on the sinusoidal steady state representation. So, that is an interesting thing and we will compare the results and discuss this problem in more detail in the next class.


Thermo4 catalytic cracking process provided significant improvement over the hodry cat cracking in terms of thermal efficiency. Now this improvement came with the change in the reactor configuration from fixed bed in hodry to moving bed of catalyst now. So the catalysts are not fixed but they are moving by gravity so that the reaction can be now conducted in just one reactor instead of having multiple reactors and switching between those reactors. There was an improvement in catalyst as well instead of using natural silica alumina. Now there are synthetic alumina silica beads with more controlled activity more homogeneous activity of the sites that cracking goes on which of course makes the control of the reactions better compared to the hodry cat cracking. So integration of the the reactor and the catalyst regenerators as you will see has increased the thermal efficiency very significantly over the fixed bed hodry cat cracking. Now you can see that the feed is introduced along with the catalyst from the top of the reactors so the particles move down with gravity at controlled flow rates along with the feed so as the cracking goes on on the catalyst surfaces there is the activation there's still a coking going on on the catalyst particles so by the time they reach the bottom of the reactor flowing with gravity the catalyst reactivity has been reduced to a significant extent the catalysts are now ready to be reactivated or regenerated. Steam as you can see is introduced from the bottom of the reactor to strip off all the volatile products during cracking and the products are sent to a fractionator for separating into gas, gasoline, lco, heavy oil and so forth. So the used catalyst then leaving the reactor is sent to a furnace where hot air is introduced to burn off the coke on the surface of the catalyst to regenerate the act of sites and the regenerated catalysts the hot particles now are put on bucket elevators to be sent up to the top of the reactor to close the catalyst cycles. So the thermal integration here is such that the heat that is generated by burning the coke heats the catalyst particles and these are hot enough to actually have the cracking take place on the surface you see that there is no external heater in this scheme reactors scheme in thermal for cat cracking but there are still heat losses especially in this bucket elevator system transporting the hot catalyst particles to the top of the reactor. Thermal efficiency although much improved over the hodry fixed bed process there is still a lot of room for improvement in thermal efficiency through integration of endothermic and exothermic reactions.