text:
Okinawa Indigo Exhibition
Exploring indigo dyeing techniques and manufacturing methods
Kim Nov 30, 2020 - 1 min read
Dec 1st
The event flyer (Photo: Kim)
Venue : Okinawa Prefectural Museum & Art Museum When : Dec 1st - Jan 24th 2021, 9:00am - 6:00pm
Indigo dye comes with a unique, striking blue color, and it has a long history in Japan. A special exhibition taking place at the Okinawa Prefectural Museum & Art Museum will look into indigo dyeing and weaving techniques from all around the world, with a special focus on the ancient indigo manufacturing method and its background in Okinawa. The event will also showcase a variety of dyed and woven products that were created using Okinawa indigo.
Adult admission to the event is priced at 1000 yen.
The Okinawa Prefectural Museum & Art Museum is located around 10 minutes on foot from Omoromachi Station, served by the Okinawa Urban Monorail (Yui Rail).
Buses are also available to the museum. From Naha Airport, take bus 99 and alight at the Omoromachi 3-Chome bus stop. The museum is around 5 minutes on foot from there.
For those who plan to drive, free parking is available on-site.
Kim @kim.b
I'm an expat who has lived abroad for almost a decade, including 7 years in Japan. I've also visited 44 of 47 prefectures and hope to get to the last three someday! I'm particularly fond of exploring off the beaten path destinations, gardens, and tea houses, and have a real interest in Japan's gr...
Okinawa Prefectural Museum
By Muneerah Bee
Okinawa Prefectural and Art Museum
Shopping at T Galleria, Naha
Tokashiki Island Ferry
By Bonson Lam
December 1st - January 24th 2021
Okinawa Prefectural Museum & Art Museum
3 Chome-1-1 Omoromachi, Naha, Okinawa 900-0006, Japan (Directions)
okimu.jp
Hakodate Ropeway
Tokyo's Top 3 Travel Rankings
Awamori and Karate
Awamori and Pork Curry
Mihama American Village
Okinawa Zoo & Museum
Ogimi Village
Cherry Blossom in Okinawa
Make Man
Bise Village, Okinawa
Japan's Last Jungle


Now that Wi-Fi® has been in deployment for two decades, it's time for some significant changes to keep up with the evolving needs of consumers.
The World's first product to receive Wi-Fi EasyMesh certification from the Wi-Fi Alliance.
High-quality, cost-effective Android TV capable products for IP, cable, satellite and terrestrial TV.
Flexible, upgradable CCAP™ for integrated DAA and 10G EPON deployments.


Aishwarya Rai Walks The Ramp At Longines Event In New Delhi. Aishwarya Rai Bachchan was dressed in a Dolce and Gabbana short jacket over a Dior gown at the event. She sported a watch from the newly launched Longines Saint-Imier collection unveiled to mark its 180th anniversary. Aishwarya is all set to mark her comeback and currently reading the scripts so wwe may have to wait a bit but its coming. Checkout Aishwarya Rai Pictures.


How long does it take for someone to establish their first impression of you? 10 minutes, 5 minutes or could it be as little as 7 seconds?
Every time you meet someone new, an impression of you is formed. Whether it is a business relationship, or a social one, the first impression you create is often concretely established and difficult to alter or undo.
Numerous studies have been conducted wherein the encoding of a repeated object results in a bias towards the attributes of its first presentation. This demonstrates that when people see something more than once (whether it be a person, place or thing), psychological associations are made with the initial impression made. Essentially, all subsequent exposures to the particular person, place, or thing are clouded by judgment and conclusions made on first impression. This is known in psychology as the primacy effect.
Everything you do after making an initial impression, gets filtered through that impression. In other words, you never get a second chance to make a first impression.
Here are 10 tips to help you make the right impression, the first time, every time!
We have all heard it before, failing to plan is planning to fail. The best results are not reached by merely winging it, but by planning, preparing, and then performing. It has been said that winning is the science of being prepared. This isn't rocket science. Being prepared ensures you get to present the best version of yourself.
By being prepared, you will feel at ease in new introductions, giving you a greater feeling of self-assurance. Attitude resonates, and when you exemplify and express self-confidence you assure those around you that you mean business! Confidence often gives you a natural high that allows you to bypass feelings of anxiety. Feeling good is contagious, and when you are confident, not only do people notice, but they can feel it too!
Ensure a well put together image. Nobody likes things that are unkempt. Take the time to manage your image and work to create a style that speaks for itself. Be physically active, and eat healthy, take care of your personal hygiene, and maybe toss on a special tie or some make-up to spruce things up. If you want to be viewed as responsible, organized, and put together then you must look as such.
It's not always what you say, sometimes it is how you say it! Non-verbal communication is harder to fake because interpersonal communication includes implicit messages, both intentional and unintentional, conveyed through body language. Managing your non-verbal behaviour is critical. Ensure you are mindful of maintaining your posture, but remain relaxed. You don't want to appear timid, but you also don't want to appear to uptight.
One of the easiest ways of making someone like you, is to make them think you are the same, or at least very similar. Find some commonalities, such as interests, hobbies, causes, etc., and use these to your advantage. Keep up to date on the news, and ensure you are well-read, this will keep you informed and sharp! People are more receptive to those they feel they can relate to.
If you are meeting someone and there is a pre-established appointment, then do not be late! I repeat, do not be late! This is a sure way to taint any first impression. Not being timely displays disorganization, disinterest, and irresponsibility. Being on time, or even a little early, not only demonstrates organization and responsibility, but also shows eagerness and interest.
Nobody wants to meet a faker, so let your guard down a little bit for once! Don't try to be inhumanly perfect. Because guess what? Nobody is perfect and we all have flaws! Often times attempting to present yourself as an all around gift from God, makes people suspicious of what you may really be hiding! Don't be afraid to show some flaws, because not only do flaws make us human, they also make us appear more relatable and similar to those around us. When you seem more natural, it relaxes other and promotes them to act in kind.
Notice things, ask questions and share! You don't want to keep the conversation all about yourself, so ensure you are asking questions, or inciting conversation about interesting topics. Share pieces of information about yourself to appear open and trustworthy, but don't share too much or you may appear self-absorbed or narcissistic. Show interest and offer value in your conversation.
Ultimately, think about what you would seek in a first impression, and then surpass that. Reflect on what type of person you would like to meet. How does this person speak, behave and look? What type of person are you more susceptible to? What traits make you feel welcome, comfortable and relaxed in a social situation? Try your best to be the ideal person you would like to meet!
Last but not least, smile! Having a smile on your face is more welcoming, plain and simple! People will be more open to approaching you or engaging with you if you present yourself in a welcoming manner. Everyone has bad days, but it is important to try your best to smile through your distractions to ensure you are not unconsciously pushing away an opportunity!


Without doubt, more important than anything else, a prophet must attract the trust of the general public in such a way that his words contain no possibility of being lies or erroneous, otherwise, his position of leadership will be a shaky one.
If they are not immaculate, using the excuse that the prophets have erred, people who seek the truth from what they say will begin to doubt their invitation. It will not be accepted, or, at least, their words will not be accepted with all of their hearts.
This reason which can be called 'trustworthiness' is one of the most important reasons for their being immaculate.
In other words, how is it possible that God give His Commands for His people to follow a person who is not truthful for if this person were to err or sin, people would not follow him. If they do, they have erred and if they do not, they have weakened his position of leadership, in particular, since the position of the leadership of the prophets completely differs with the leadership of others for people receive their entire program of life from the prophets.
saying that the command for Absolute obedience is because the Prophet is immaculate as well as 'being charged with authority'. The pure leaders like the Holy Prophet are referred to as 'being charged with authority'. If not, God would never give the command to unconditional obedience to them.
Another way of proving the immaculateness of the Holy Prophet in relation to any sin is that any factor of sin is condemned to defeat within the very being of the Holy Prophet.
The explanation of this is: when we turn to ourselves, we see that we, too, are immaculate in relation to some sins or evil or unacceptable deeds.
Can you find an intelligent person who thinks about eating fire or trash or filth?
Can you find an intelligent person who will walk naked through the streets and bazaars?
Clearly not! If we saw such deeds from someone, we will be assured of the fact that he is no longer normal and has become insane because an intelligent person would never do these things.
When we analyze such behavior, we see that the ugliness of such deeds is so clear that an intelligent person would never even consider them.
It is here that we can imagine what this short phrase means and say that every intelligent and healthy person is 'free of' unacceptable deeds.
From this stage, we take a step further. We see some people who are free from unacceptable deeds.
For instance, an aware physician and expert who knows the various kinds of microbes well is never prepared to drink the polluted water of the dirty clothes of a person who has one of the most dangerous contagious diseases whereas an illiterate person , perhaps, would be indifferent to such a thing.
With another simple example, we reach the point that however much the level of a person rises in the area of awareness, they are less likely to do evil or ugly deeds.
Taking into consideration that if a person's faith and awareness were to rise and have so much faith in God and His court of justice, so that everything that he sees is present before his eyes, such a person will be free of all sin and every ugly deed in relation to him, like walking naked through the streets, will be in our eyes only.
For such a person, the property of something forbid den is just like the flames of fire, and just like we do not put fire in our mouths, he does not put something which is forbidden into his mouth.
We can then conclude that the prophets, because of the extraordinary knowledge, awareness and faith which they have, tame the motives of sin and the most exciting factors causing sin will not prevail upon his intellect and faith. This is why we say that the prophets are immaculate; they are insured against sin.
Some people who do not understand the meaning of purity and the factors of immaculateness and being free from sin are not aware of the fact that if God prevents one from sin and destroys the factors which cause sin, this will not be an honor for that person!
This is coercive purity and therefore is not considered to be a virtue.
The freedom of the prophets from sin in no sense is a coercive one. Rather, it is born from their strong faith and absolute certainty, their awareness and extraordinary knowledge and this is the greatest honor for them.
If an aware physician takes care of and treats a person with the worst of diseases is this a sign of his being forced to do so?
If such a person were to follow the rules of health, would this be Considered to be a virtue?
If a person, a lawyer, were to take the disgraceful considerations into effect of a dreadful crime and try to prevent it, is this a virtue?
Thus, we reach this conclusion that the fact that the prophets are free from sin is both one of their own choice and great honor for them.
1. How many branches are there to being immaculate?
2. If prophets were not free from sin, what would happen?
3.What is the truth of the station of immaculateness?
4. Other than the examples given here, can you point out another example of someone who is immaculate in relation to another group?
5. Is the immaculateness of the prophets coercive or a result of free will? Why?


text:
Phone886-6-2757575 Ext. 62000
Emailem62000@email.ncku.edu.tw
Websitehttp://www.me.ncku.edu.tw/enes/
238 Patent
126 Paper
Technology transfer in the design of adjustable linkages
Tao, D. C. & Yan, H-S., 1979 Jan 1, In : Journal of Mechanical Design, Transactions Of the ASME. 101, 3, p. 495-498 4 p.
LINKAGE CHARACTERISTIC POLYNOMIALS: ASSEMBLY THEOREMS, UNIQUENESS.
Yan, H. S. & Hall, A. S., 1980, In : American Society of Mechanical Engineers (Paper). 80 -DET-9
LINKAGE CHARACTERISTIC POLYNOMIALS: DEFINITIONS, COEFFICIENTS BY INSPECTION.
Linkage characteristic polynomials: Definitions, coefficients by inspection
Yan, H. S. & Hall, A. S., 1981 Jul, In : Journal of Mechanical Design, Transactions of the ASME. 103, 3, p. 578-584 7 p.
Rapid solidification of subcooled small metallic drops
Gill, W. N., Jang, J. Y. & Mollendorf, J. C., 1981 Oct 1, In : Chemical Engineering Communications. 12, 1-3, p. 3-31 29 p.
Rapid solidification
Linkage characteristic polynomials: Assembly theorems, uniqueness
Yan, H-S. & Hall, A. S., 1982 Jan 1, In : Journal of Mechanical Design, Transactions Of the ASME. 104, 1, p. 11-20 10 p.
Structural synthesis of planar linkage chains with multiple joints
Hwang, W-M. & Yan, H-S., 1982 Jan 1, In : Journal of the Chinese Institute of Engineers, Transactions of the Chinese Institute of Engineers,Series A/Chung-kuo Kung Ch'eng Hsuch K'an. 5, 4, p. 187-193 7 p.
Thermal buckling of initially stressed thick plates
Chen, L-W., Brunelle, E. J. & Chen, L. Y., 1982 Jan 1, In : Journal of Mechanical Design, Transactions Of the ASME. 104, 3, p. 557-564 8 p.
Thermal effects
Nonlinear equations
EXPERIMENTAL STUDY OF SOLIDIFICATION HEAT TRANSFER IN AN OPEN RECTANGULAR CAVITY.
Ho, C-J. & Viskanta, R., 1983 Jan 1, In : Journal of Heat Transfer. 105, 3, p. 671-673 3 p.
solidification
Flow visualization during solid-liquid phase change heat transfer II. Melting in a rectangular cavity
Gau, C., Viskanta, R. & Ho, C. J., 1983 Jan 1, In : International Communications in Heat and Mass Transfer. 10, 3, p. 183-190 8 p.
liquid-solid interfaces
Large amplitude vibration of an initially stressed moderately thick plate
Chen, L. W. & Doong, J. L., 1983 Aug 22, In : Journal of Sound and Vibration. 89, 4, p. 499-508 10 p.
thick plates
Galerkin method
Galerkin methods
Large-amplitude vibration of an initially stressed thick circular plate
Chen, L. W. & Doong, J. L., 1983 Sep, In : AIAA journal. 21, 9, p. 1317-1324 8 p.
METHOD FOR THE IDENTIFICATION OF PLANAR LINKAGE CHAINS.
Yan, H-S. & Hwang, W-M., 1983 Jan 1, In : Journal of mechanisms, transmissions, and automation in design. 105, 4, p. 658-662 5 p.
Postbuckling behavior of a thick plate
Chen, L. W. & Doong, J. L., 1983 Aug, In : AIAA journal. 21, 8, p. 1157-1161 5 p.
A study on the application of circular biarcs fitting to numerically controlled machining
Lee, R. S. & Liang, N. J., 1984 Oct, In : Journal of the Chinese Institute of Engineers, Transactions of the Chinese Institute of Engineers,Series A/Chung-kuo Kung Ch'eng Hsuch K'an. 7, 4, p. 225-232 8 p.
AXISYMMETRIC VIBRATION OF AN INITIALLY STRESSED BIMODULUS THICK CIRCULAR PLATE.
Doong, J. L. & Chen, L-W., 1984 Jan 1, In : Journal of Sound and Vibration. 94, 4, p. 461-468 8 p.
circular plates
resonant frequencies
Natural frequencies
BUCKLING OF A THICK CIRCULAR PLATE.
Doong, J. L. & Chen, L-W., 1984 Apr 1, In : Chung-Kuo Chi Hsueh Kung Ch'eng Hsueh Pao/Journal of the Chinese Society of Mechanical Engineers. 5, 1, p. 107-112 6 p.
Loads (forces)
Heat transfer during inward melting in a horizontal tube
Ho, C. J. & Viskanta, R., 1984 May, In : International Journal of Heat and Mass Transfer. 27, 5, p. 705-716 12 p.
Heat transfer during melting from an isothermal vertical wall
Ho, C-J. & Viskanta, R., 1984 Jan 1, In : Journal of Heat Transfer. 106, 1, p. 12-19 8 p.
shadowgraph photography
Inertia effects in the laminar radial flow of a power law fluid with an electromagnetic field
Cha'o-Kuang, C., Kuo-Huei, C. & Wu, C-Y., 1984 Apr 2, In : Wear. 95, 1, p. 45-57 13 p.
radial flow
Inward solid-liquid phase-change heat transfer in a rectangular cavity with conducting vertical walls
Ho, C. J. & Viskanta, R., 1984 Jul, In : International Journal of Heat and Mass Transfer. 27, 7, p. 1055-1065 11 p.
liquid phases
Linkage path code
Yan, H-S. & Hwang, W-M., 1984 Jan 1, In : Mechanism and Machine Theory. 19, 4-5, p. 425-429 5 p.
Mechanical properties of a composite wax model material simulating plastic flow of metals
Lee, R. S. & Blazynski, T. Z., 1984 May, In : Journal of Mechanical Working Technology. 9, 3, p. 301-312 12 p.
Plastic flow
METHOD FOR THE COMPUTER-AIDED STRUCTURAL SYNTHESIS OF PLANAR KINEMATIC CHAINS WITH MULTIPLE JOINTS.
Hwang, W-M. & Yan, H-S., 1984, In : American Society of Mechanical Engineers (Paper).
Degrees of freedom (mechanics)
MICROPROCESSOR-BASED NONCONTACT DISTANCE MEASURING CONTROL SYSTEM.
Wang, J., Wambold, J. C. & Henry, J. J., 1984 Dec 1, In : Transportation Research Record. p. 42-48 7 p.
Microprocessor chips
Pass design and redundant strains in forward tube extrusion
Blazynski, T. Z. & Lee, R-S., 1984 Jan 1, In : Journal of Mechanical Working Technology. 9, 3, p. 313-324 12 p.
Rapid solidification of subcooled small metallic drops: Internal nucleation
Gill, W. N., Jang, J. Y., Mollendorf, J. C. & Adam, C. M., 1984 Jan 1, In : Journal of Crystal Growth. 66, 2, p. 351-368 18 p.
Interfacial energy
SYNTHESIS OF FOUR-BAR FUNCTION GENERATORS BY CONSTRAINED FLEXIBLE POLYHEDRON METHOD.
Chiou, S. T. & Yan, H-S., 1984 Apr 1, In : Chung-Kuo Chi Hsueh Kung Ch'eng Hsueh Pao/Journal of the Chinese Society of Mechanical Engineers. 5, 1, p. 19-26 8 p.
Vibrations of an initially stressed transversely isotropic circular thick plate
Chen, L. W. & Doong, J. L., 1984, In : International Journal of Mechanical Sciences. 26, 4, p. 253-263 11 p.
Analysis of free coating onto a rotating roll
Wu, C-Y., Weng, C. I. & Chen, C. K., 1985 Jan 1, In : Chemical Engineering Communications. 33, 1-4, p. 245-254 10 p.
COMPARATIVE STUDIES OF FORMULATING THE DYNAMICS OF RIGID-BODY SYSTEMS USING MACSYMA - A CASE STUDY.
Ju, M-S. & Mansour, J. M., 1985, In : Developments in Mechanics. 13, p. 185-186 2 p.
Computational efficiency
Creative design of a wheel damping mechanism
Yan, H. S. & Chen, J. J., 1985, In : Mechanism and Machine Theory. 20, 6, p. 597-600 4 p.
Effects of convection heat and mass transfer on the flow about an oscillating vertical plate under magnetic field
Lien, F. S., Wu, C. Y. & Chen, C. K., 1985 Jan 1, In : International Communications in Heat and Mass Transfer. 12, 5, p. 587-596 10 p.
Grashof number
NUMERICAL SIMULATION OF MELTING INSIDE A CYLINDRICAL ANNULUS.
Ho, C-J. & Lin, K. C., 1985, In : Modelling, simulation & control. B. 3, 3, p. 25-48 24 p.
annuli
Natural Convection
Ring or annulus
SHAPE OPTIMIZATION OF ELASTIC HOLLOW BARS.
Hou, J. W. & Chen, J. L., 1985 Jan 1, In : Journal of mechanisms, transmissions, and automation in design. 107, 1, p. 100-105 6 p.
Shape optimization
Keyways
Materials properties
The role of axial edge effects and cavitation in lubrication for short journal bearings
Buckholz, R. H., Lin, J-F. & Pan, C. H. T., 1985 Jan 1, In : Journal of Applied Mechanics, Transactions ASME. 52, 2, p. 267-273 7 p.
journal bearings
cavitation flow
Vibration of a bimodulus thick plate
Doong, J. L. & Chen, L-W., 1985 Jan 1, In : Journal of Vibration and Acoustics, Transactions of the ASME. 107, 1, p. 92-97 6 p.
VIBRATION OF THERMAL ELASTIC THICK PLATES.
Chen, L-W. & Li, C. C., 1985 Apr, In : Chung-Kuo Chi Hsueh Kung Ch'eng Hsueh Pao/Journal of the Chinese Society of Mechanical Engineers. 6, 1, p. 35-43 9 p.
Mindlin plates
ANALYSIS OF TUBE EXTRUSION USING UPPER BOUND ELEMENTAL TECHNIQUE.
Lee, R. S. & Shaw, H. C., 1986 Dec 1, In : Chung-Kuo Chi Hsueh Kung Ch'eng Hsueh Pao/Journal of the Chinese Society of Mechanical Engineers. 7, 6, p. 463-472 10 p.
Computational method for optimization of structural shapes
Hou, J. W., Chen, J. L. & Sheen, J. S., 1986 Jan 1, In : AIAA journal. 24, 6, p. 1005-1012 8 p.
DESIGN FOR AUTOMATIC MANUFACTURE OF SELF-TAPPING SCREW DIES.
Hwang, W-M. & Shih, J. M., 1986 Apr, In : Chung-Kuo Chi Hsueh Kung Ch'eng Hsueh Pao/Journal of the Chinese Society of Mechanical Engineers. 7, 2, p. 109-113 5 p.
Milling (machining)
EFFECTS OF INTERFACIAL CURVATURE AND INTERFACE ATTACHMENT KINETICS ON THE FREEZING OF SPHERICAL CRYSTAL NUCLEI.
Jang, Y. Y. & Jeng, W. C., 1986 Oct 1, In : Chung-Kuo Chi Hsueh Kung Ch'eng Hsueh Pao/Journal of the Chinese Society of Mechanical Engineers. 7, 5, p. 373-378 6 p.
Ordinary differential equations
Influence of austempering temperature on fracture toughness in bainitic nodular cast iron
Doong, J. L., Ju, F. C., Chen, H. S. & Chen, L-W., 1986 May 1, In : Journal of Materials Science Letters. 5, 5, p. 555-558 4 p.
Nodular iron
Fracture toughness
INWARD SOLIDIFICATION OF A SUBCOOLED METALLIC SPHERE.
Jang, J-Y. & Wu, A. S., 1986 Apr 1, In : Chung-Kuo Chi Hsueh Kung Ch'eng Hsueh Pao/Journal of the Chinese Society of Mechanical Engineers. 7, 2, p. 67-73 7 p.
Fusion reactions
Liquid phase sintering of austenitic stainless steel powders with silicon additions
Wang, W. F. & Su, Y-L., 1986 Jan 1, In : Powder Metallurgy. 29, 4, p. 269-275 7 p.
liquid phase sintering
austenitic stainless steels
Austenitic stainless steel
Mechanical properties, corrosion resistance, and high temperature oxidation resistance of sintered duplex stainless steels
Thermooxidation
Numerical simulation of melting of ice around a horizontal cylinder
Ho, C. J. & Chen, S., 1986 Sep, In : International Journal of Heat and Mass Transfer. 29, 9, p. 1359-1369 11 p.
Outward melting in a cylindrical annulus
Ho, C. J. & Lin, K. C., 1986 Sep, In : Journal of Energy Resources Technology, Transactions of the ASME. 108, 3, p. 240-245 6 p.
SHAPE OPTIMIZATION OF ELASTIC BARS IN TORSION.
Chen, L. Y. & Chen, L-W., 1986 Apr 1, In : Chung-Kuo Chi Hsueh Kung Ch'eng Hsueh Pao/Journal of the Chinese Society of Mechanical Engineers. 7, 2, p. 99-107 9 p.
Nonlinear programming
STRUCTURAL SYNTHESIS OF CONTRACTED GRAPHS.
Hsu, C. H. & Yan, H-S., 1986 Apr 1, In : Chung-Kuo Chi Hsueh Kung Ch'eng Hsueh Pao/Journal of the Chinese Society of Mechanical Engineers. 7, 2, p. 125-135 11 p.

redpajama_set_name: RedPajamaCommonCrawl


text:
\section{Introduction}

In this study,
we develop a theoretical model of strategic equilibrium bidding and price-setting behaviour
by heterogeneous and boundedly rational electricity producers and a grid operator in a single electricity market
under uncertain information about production capabilities and electricity demand.

We compare eight different market design variants
and several levels of centralized electricity production
that influence the spatial distribution of producers in the grid,
their unit production and curtailment costs,
and the mean and standard deviation of their production capabilities.

Our market design variants differ in three aspects.
Producers are either paid their individual bid price (``pay as bid'')
or the (higher) market price set by the grid operator (``uniform pricing'').
They are either paid for their bid quantity (``pay requested'')
or for their actual supply (``pay supplied'') which may differ due to production uncertainty.
Finally, excess production is either required to be curtailed or may be supplied to the grid.

After formally deriving producers' and grid operator's optimization problems
and finding their analytical intractability,
we then use numerical simulations to study their resulting strategic behaviour
in an agent-based model slightly similar to \cite{mureddu2015green} with 200 producers on 100 grid nodes
for 50 repetitions of each of the eight markets and ten different synthetically generated network topologies.

We analyse results w.r.t.\ several aggregate indicators such as
the average bid price-to-cost ratio, market price, bid quantity-to-mean production ratio,
balancing needs, total economic costs, producers' profits, consumers' costs,
and total grid workload.

Overall, we find the combination of uniform pricing, paying for requested amounts, and required curtailment
to perform best or second best in many respects, and to provide the best compromise between the goals
of low economic costs, low consumer costs, positive profits, low balancing, low workload, and honest bidding behaviour.

\section{Model}

Our model simulates the bidding and price-setting decisions
of a number of heterogeneous electricity producers and their power grid operator
under eight different generalized market designs
and different degrees of (de-)centralized production.
We focus on the market for a specific time-slot $T$,
e.g., a certain 15-minute interval of the day,
and assume that decisions have to be taken at an earlier time $t < T$,
so that certain quantities such as demand and actual production at time $T$
are uncertain at time $t$ and have to be described via random variables.

\paragraph{Power grid.}
We use an ensemble of ten different {\em single-level power grids} consisting of $n=100$ nodes each
placed at positions chosen uniformly at random from a square territory
and connected via the synthetic random power-grid generation algorithm developed earlier in \cite{schultz2014random}.
To simplify power flow computations, we assume the grid to be tree-shaped and consist of lossless lines.
See Fig.\,\ref{fig:grid} for an example grid.

\begin{figure}
\begin{center}
\includegraphics[width=\textwidth]{grid.pdf}
\end{center}
\caption{\label{fig:grid} Sample grid generated according to \cite{schultz2014random}.}
\end{figure}

\paragraph{Electricity demand.}
At each node $v_a$, there will be an electricity {\em demand} at time $T$
whose uncertain value is described at time $t$ by a random variable $d_a$.
We assume $d_a$ to be independently normally distributed
with mean $\mu^d_a$ and standard deviation $\sigma^d_a = \mu^d_a / 4$,
where $\mu^d_a$ is larger for more decentral nodes, representing the fact that demand is rather decentralized.
We measure a node $v$'s centrality by the standard metric of {\em closeness centrality} from complex network theory,
which is given by $CC(v) = 1 / \sum_{v'} d(v,v')$,
where $v'$ runs over all nodes and $d(v,v')$ is the number of transmission lines one has to pass to get from $v$ to $v'$.
We enumerate all nodes by ascending closeness centrality,
so that $CC(v_1)\leqslant CC(v_2)\leqslant \ldots \leqslant CC(v_n)$,
and put $\mu^d_a = (n + 1 - a) / n (n + 1)$.
{\em Total demand} $D$ thus has mean $\mu^D = \sum_a \mu^d_a = 1 / 2$
and standard deviation $\sigma^D = \sqrt{\sum_a (\sigma^d_a)^2} \approx 1 / \sqrt{3 n} \approx .057$,
i.e., with a relative variability of about 11\%.

\paragraph{Production capabilities.}
Electricity is produced by $N=200$ independent and heterogeneous {\em producers}
which range from large-scale utilities to smallest-scale producers such as single households with a number of PV panels.
The spatial distribution of producers onto grid nodes is governed by a
{\em centralization parameter} $-1 \leqslant  Z \leqslant 1$,
where $ Z = 1$ generates a rather centralized production structure dominated by traditional large-scale utilities,
while $ Z = -1$ generates a rather decentralized production structure dominated by variable renewable energy sources (VRES).
Depending on $ Z$, producers are placed onto nodes at random,
either favouring more central nodes (for positive $ Z$) or more decentral nodes (for negative $ Z$).
More precisely, each producer $i = 1\ldots N$ is then placed at a random node $v(i)$,
where $v(i) = v_a$ with probability $(1 +  Z (2a - n - 1) / n) / n$.

Each producer $i$ will either produce or not produce electricity at time $T$.
If they produce at time $T$, they will produce an amount of electricity
that is only known with some uncertainty at time $t$,
so {\em production} is described by a random variable $u_i$.
To simplify calculations, we assume $u_i$ to be
uniformly distributed between two known limits $\mu_i (1 - \varrho_i)$ and $\mu_i (1 + \varrho_i)$.
To represent the fact that decentralized production tends to by smaller-scale and more variable,
we assume that mean production $\mu_i$ is positively correlated with the centrality of $i$
and $\varrho_i$ is negatively correlated with centrality,
by putting $\mu_i = a \mu_0 / n$ and $\varrho_i = (n + 1 - a) \varrho_0 / n$,
where $a$ is the node index of $v(i) = v_a$.
We chose $\mu_0$ so that the {\em mean total production potential} $\sum_i \mu_i = 1$,
i.e., equals twice the mean demand $\mu^D = 1 / 2$
to get a considerable but fixed amount of {\em competition} between producers.
We put $\varrho_0 = 1/2$ so that the most decentral nodes will have an uncertain production
ranging from $\mu_i / 2$ to $3\mu_i / 2$, while the most central nodes have an almost certain production.

Note that for simplicity, we ignore the actually existing but nontrivial spatial correlation
in both demand and production in this study.

\paragraph{Production, balancing, and curtailment costs.}
Producer $i$'s {\em unit production costs} $c_i$ are assumed to be known for certain and also depend on centrality,
$c_i = a / n$, where $a$ is again the node index of $v(i) = v_a$,
representing the fact that renewable energy sources have lower production costs.
Hence {\em expected mean unit production costs} are $\bar c \approx (3 +  Z) / 6 \in [1/3, 2/3]$,
which will serve us as a reference point for the emerging market price later
and represents a potential production cost reduction of 50\%
when going from rather centralized production to rather decentralized production.

If at time $T$, actual power supply falls short of demand,
the grid operator needs to buy upward balancing energy.
Since we do not want to study interactions between different markets such as spot and balancing market here
but focus on the design of one market stage only,
we assume here that the {\em unit upward balancing costs} $c^+$ are fixed and known already at time $t$,
and we put $c^+ = 2$, i.e., between three and six times the mean unit production costs $\bar c$,
depending on the degree of centralization $ Z$.
Analogously, if supply exceeds demand, the grid operator has to buy some downward balancing demand
at a fixed price $c^-$.
We choose a relatively large value of $c^- = 1/4$
to represent the assumption that in view of the need to reduce energy demand,
society must give the grid operator a considerable incentive to avoid excess supply.

In some of our market designs, if producer $i$ produces more than agreed with the grid operator,
$i$ is not allowed to supply this excess production to the grid but is required to ``curtail'' it.
If this is the case, we assume $i$'s {\em unit curtailment costs} are $c^0_i = c^0_0 (n + 1 - j) / n$,
representing the fact that smaller, more decentralized producers tend to have larger curtailment costs.
On average, however, we assume that curtailment is rather cheap, being only one percent of mean production costs,
$c^0_0 = c_0 / 100$.

\paragraph{Penalties.}
In all of our market designs, we assume that producers
actually supplying more or less electricity to the grid than agreed with the grid operator
have to pay some penalties to the latter.
These penalties serve a double purpose,
they provide an incentive for the producers to make realistic quantity bids
and they compensate the grid operator for balancing costs caused by supply excesses or shortfalls.
Because of the latter,
we assume that for each unit of electricity supplied more than agreed one has to pay
a {\em unit excess supply penalty} $c^>$ that equals downward balancing cost, $c^> = c^-$,
while for each unit supplied less than agreed one has to pay
a {\em unit supply shortfall penalty} $c^<$ that equals upward balancing cost, $c^< = c^+$.
Note that penalties have to be paid regardless of whether at time $T$ there is actually any need for balancing.
One may consider alternative market designs in which penalties reflect actual instead of potential balancing costs,
but it turns out that finding optimal bids in such a scenario is much more complicated than in our setting,
so we leave this possibility for future research.

\paragraph{Overall market procedure.}
At time $t$, each producer $i$ places a {\em price-and-quantity bid} $(p_i,q_i)$,
thereby stating that they offer to supply $q_i\geqslant 0$ units of power at time $T$ for a unit price of $p_i\geqslant 0$.
They are free to choose any combination of $p_i,q_i$,
hence {\em bid price} $p_i$ is not required to be related in any way to unit production costs $c_i$
and {\em bid quantity} $q_i$ is not required to be related in any way to mean production $\mu_i$.
However, as we assume producers to be boundedly rational
and will chose a combination of $p_i,q_i$ that seems economically optimal for them,
i.e., for which they expect their profit to be maximal,
in view of their past observation of the emerging market price
and the information available at time $t$ about the uncertain demand and production capabilities.
We will see below that in general, $p_i > c_i$, and typically $\mu_i (1-\varrho_i) < q_i < \mu_i$.

After all bids are made, the grid operator selects a set $A$ of producers whose bids they accept,
trying to minimize their expected total costs in view of the uncertain information available at time $t$.
To reduce the complexity of this optimization problem,
we assume that the grid operator does not consider all of the $2^N$ many possible sets $A$ of producers
but only those sets $A$ that result from choosing a {\em cutoff price} $P\geqslant 0$
and accepting all cheaper bids, i.e., putting $A = \{ i:p_i \leqslant P \}$.
This is motivated by the fact that if production capabilities and demand were certain,
the cheapest way to meet demand $D$ would be to place the bids into a ``merit order''
so that $p_1\leqslant p_2\leqslant \ldots\leqslant p_n$
and then choose $P$ so that $\sum_{i:p_i\leqslant P} q_i\approx D$.
In princinple, when $D$ and $u_i$ are uncertain,
such a scheme for choosing $A$ might not actually be optimal
since in view of the high potential costs of balancing mismatches,
it may sometimes be preferable to accept a more expensive but more certain bid (e.g.\ by a traditional power plant)
rather than a cheaper but more uncertain bid (e.g.\ by a small PV installation).
For two reasons,
we ignore this fact here and still assume that the grid operator accepts all bids below a certain cutoff price.
For one, the more general optimization problem would require much more information about production uncertainties
and would be much harder to solve in reality, so that using the simpler scheme can be interpreted as some form of bounded rationality.
Second, using the more general scheme would probably result in a bias towards traditional electricity producers
which we do not want to assume here as it would contradict the observable political tendency to rather favour renewable production,
so we choose a scheme that is more unbiased between the two forms.

After the cutoff price $P$ was set at time $t$,
all producers with $p_i\leqslant P$ will produce some actual amount of electricity $u_i$ at time $T$,
leading to production costs $c_i u_i$,
may have to curtail the excess production $e_i = \max(u_i - q_i, 0)$ (in some marked designs),
leading to curtailment costs $c^0_i e_i$
They then {\em supply} some amount $s_i$ to the grid,
where either $s_i = \min(u_i, q_i) = u_i - e_i$ or $s_i = u_i$,
depending on whether curtailment was required or not.
Since supply may still deviate from the requested amount of electricity that is given by the accepted bid quantity, $r_i = q_i$,
this may lead to either a positive amount of {\em excess supply} $s^+_i = \max(s_i - r_i, 0)$
or to a positive amount of {\em supply shortfall} $s^-_i = \max(r_i - s_i, 0)$,
and thus to total penalties $c^+ s^+_i + c^- s^-_i$ they pay to the grid operator.
The grid operator, on the other hand, pays each producer with $p_i\leqslant P$
either for the requested amount $r_i$ (``pay requested'')
or for the actually supplied amount $s_i$ (``pay supplied''),
and either at a uniform price $P$ (``uniform pricing'')
or at each producer only at their bid price $p_i \leqslant P$ (``pay as bid''),
depending on the market design variant.

\paragraph{Market design variants.}
The option of either requiring curtailment (``curtail'') or not (``don't curtail''),
paying for either requested or supplied amounts, and paying either a uniform price or as bid,
we thus get $2^3 = 8$ different market design variants to compare,
each of which sets different incentives for producers and grid operator
and will thus imply different optimizing behaviour regarding the choice of $(p_i,q_i)$ and $P$,
leading to different strategic equilibria and finally to different
total economic costs of the system, total producers' profits,
total curtailment and balancing, total workload on the grid, etc.

\paragraph{Experiment design.}
We assume the market is run repeatedly under similar conditions,
e.g., each day of similar weather conditions and for the same time of day $T$,
so that producers can form expectations about the market price $P$
that they can incorporate into their optimization
by treating $P$ as a random variable whose distribution matches the past distribution of observed values of $P$.
Since this leads to a relatively fast convergence of bidding behaviour over time,
we run each market variant 50 times in sequence for each of the ten power grids from the ensemble,
resulting in a sample of 500 observations per market variant,
so that statistical averages over this sample will have a standard error of only
$\sqrt{1/500}\approx 4.5\%$ of their respective standard deviation,
which we will use in testing statistically whether market variants differ significantly
with respect to the above-mentioned indicators.

\begin{table}\begin{center}\begin{tabular}{ll}\toprule
 $-1 \leqslant  Z \leqslant 1$ & degree of centralization \\
 $d_a$ & uncertain demand at grid node $v_a$ \\
 $D = \sum_a D_a$ & uncertain total demand \\
 $u_i \geqslant 0$ & uncertain production of producer $i$ \\
 $c_i > 0$ & known unit costs of production \\
 $c^+ > 0$ & known price of upward balancing by grid operator \\
 $c^- > 0$ & known price of downward balancing by grid operator \\
 $c^<$ & known penalty for supplying one unit less than requested \\
 $c^>$ & known penalty for supplying one unit more than requested \\
 $c^0_i > 0$ & known costs of curtailment \\
 $p_i,q_i \geqslant 0$ & producer's strategic bid price and quantity \\
 $P\geqslant 0$ & grid operators strategically chosen cutoff price \\
 $r_i \in \{0, q_i\}$ & resulting quantity requested from $i$ \\
 $s_i, S = \sum_i s_i \geqslant 0$ & actual producer's and total supply \\
 $s_i^< = \max(r_i - s_i, 0) \geqslant 0$ & producer's supply shortfall \\
 $s_i^> = \max(s_i - r_i, 0) \geqslant 0$ & producer's excess supply \\
 $S^< = \sum_i s_i^< \geqslant 0$ & total supply shortfalls \\
 $S^> = \sum_i s_i^> \geqslant 0$ & total excess supplies \\
 $B^+ = \max(D - S, 0) \geqslant 0$ & actual upward balancing needs \\
 $B^- = \max(S - D, 0) \geqslant 0$ & actual downward balancing needs\\\bottomrule
\end{tabular}\end{center}\caption{\label{tbl:notation}Overview of symbols}\end{table}

\subsection{Producers' and grid operator's behaviour}
The central ingredient of the model is our assumption of how producers and grid operator
make their choice of $(p_i,q_i)$ and $P$.

\paragraph{Producers.}
Let us consider the optimization problem of a fixed producer $i$,
and thus drop the index $i$ from all quantities for now.
In all market variants, $i$'s profit $\pi$ is either zero (if $P < p$)
or of the general form
\begin{align}
	\pi &= \beta q + \gamma p q + \delta P q + \varepsilon u + \zeta p u + \eta P u
\end{align}
(if $P \geqslant p$ and $u \leqslant q$) or
\begin{align}
	\pi &= \beta' q + \gamma' p q + \delta' P q + \varepsilon' u + \zeta' p u + \eta' P u
\end{align}
(if $P \geqslant p$ and $u > q$),
with coefficients $\beta,\beta',\ldots,\eta,\eta'$ that depend on the market design variant,
see Table~\ref{tbl:coeffs}.

\begin{table}\begin{center}\begin{tabular}{lllllllll}\toprule
 & \multicolumn{4}{l}{uniform pricing}               & \multicolumn{4}{l}{pay as bid} \\
 & \multicolumn{2}{l}{pay supplied}
 						   & \multicolumn{2}{l}{pay requested}
 						                             & \multicolumn{2}{l}{pay supplied}
 						                                                       & \multicolumn{2}{l}{pay requested} \\
 & don't curtail & curtail & don't curtail & curtail & don't curtail & curtail & don't curtail & curtail \\\midrule
$\beta'$  & $c^> $ & $ $ & $c^> $ & $ $ & $c^> $ & $ $ & $c^> $ & $ $ \\
$\gamma$  & $ $ & $ $ & $ $ & $ $ & $ $ & $ $ & $1 $ & $1 $ \\
$\gamma'$ & $ $ & $ $ & $ $ & $ $ & $ $ & $1 $ & $1 $ & $1 $ \\
$\delta$  & $ $ & $ $ & $1 $ & $1 $ & $ $ & $ $ & $ $ & $ $ \\
$\delta'$ & $ $ & $1 $ & $1 $ & $1 $ & $ $ & $ $ & $ $ & $ $ \\
$\varepsilon'$   & $ -c-c^>$ & $ -c-c^0$ & $ -c-c^>$ & $ -c-c^0$ & $ -c-c^>$ & $ -c-c^0$ & $ -c-c^>$ & $ -c-c^0$ \\
$\zeta$   & $ $ & $ $ & $ $ & $ $ & $1 $ & $1 $ & $ $ & $ $ \\
$\zeta'$  & $ $ & $ $ & $ $ & $ $ & $1 $ & $ $ & $ $ & $ $ \\
$\eta$    & $1 $ & $1 $ & $ $ & $ $ & $ $ & $ $ & $ $ & $ $ \\
$\eta'$   & $1 $ & $ $ & $ $ & $ $ & $ $ & $ $ & $ $ & $ $ \\
$\theta'$   & $ -c^>$ & $ $ & $ -c^>$ & $ $ & $ -c^>$ & $ $ & $ -c^>$ & $ $ \\\bottomrule
\end{tabular}\end{center}
\caption{\label{tbl:coeffs}Nonzero optimization coefficients by market design variant.
Always $\beta = -c^<$, $\varepsilon = c^< - c$, and $\theta = c^<$.}
\end{table}

The random variables $P$ (assumed to be distributed as observed in the past) and $u$
are independent, hence expected profit given some choice of $(p_i,q_i)$ is
\begin{align}
	E \pi &= \int_p^\infty dP\,\phi_P(P)\left[
		\int_0^q du\,\phi_u(u) [ \beta q + \gamma p q + \delta P q + \varepsilon u + \zeta p u + \eta P u ] \right. \nonumber \\
	&\quad\quad\quad\quad\quad\quad\quad\left.
		+ \int_q^\infty du\,\phi_u(u) [ \beta' q + \gamma' p q + \delta' P q + \varepsilon' u + \zeta' p u + \eta' P u ]
	\right] \\
	&= \int_p^\infty dP\,\phi_P(P)\left[
		\Phi_u^<(q) [ \beta q + \gamma p q + \delta P q ]
		+ E_u^<(q) [ \varepsilon + \zeta p + \eta P ] \right. \nonumber\\
	&\left.\quad\quad\quad\quad\quad\quad\quad{}
		+ \Phi_u^>(q) [ \beta' q + \gamma' p q + \delta' P q ]
		+ E_u^>(q) [ \varepsilon' + \zeta' p + \eta' P ]
	\right] \\
	&= \Phi_P^>(p) \left[
		\Phi_u^<(q) [ \beta q + \gamma p q ]
		+ E_u^<(q) [ \varepsilon + \zeta p ]
		+ \Phi_u^>(q) [ \beta' q + \gamma' p q ]
		+ E_u^>(q) [ \varepsilon' + \zeta' p ]
	\right] \nonumber \\
	&\quad
	+ E_P^>(p) \left[
		\Phi_u^<(q) \delta q
		+ E_u^<(q)\eta
		+ \Phi_u^>(q) \delta' q
		+ E_u^>(q) \eta'
	\right],
\end{align}
where
$\phi_x(\cdot), \Phi^<_x(\cdot)$ and $\Phi^>_x(\cdot) = 1 - \Phi^<_x(\cdot)$
are the probability density, cumulative and decumulative distribution functions
of random variable $x$,
and we introduced the abbreviations
\begin{align}
	E_x^<(y) &= \int_0^y dx\,\phi_x(x) x,\\
	E_x^>(y) &= \int_y^\infty dx\,\phi_x(x) x.
\end{align}
For a maximum of $E\pi$ with $p,q>0$, these first-order conditions must be met:
\begin{align}
	0 = \partial_p E \pi &= - \phi_P(p)\left[
		\Phi_u^<(q) [ \alpha + \beta q + (\gamma + \delta) p q ]
		+ E_u^<(q) [ \varepsilon + (\zeta + \eta) p ] \right. \\
	&\quad\quad\quad\quad\left.
		+ \Phi_u^>(q) [ \alpha' + \beta' q + (\gamma' + \delta') p q ]
		+ E_u^>(q) [ \varepsilon' + (\zeta' + \eta') p ] ]
	\right] \\
	&\quad\quad
	+ \Phi_P^>(p) \left[
		\Phi_u^<(q) \gamma q
		+ E_u^<(q) \zeta
		+ \Phi_u^>(q) \gamma' q
		+ E_u^>(q) \zeta'
	\right], \\
	0 = \partial_q E \pi &= \Phi_P^>(p) \left[
		\phi_u(q) [ \Delta\alpha + \Delta\beta q + \Delta\gamma p q ]
		+ \phi_u(q) q [ \Delta\varepsilon + \Delta\zeta p ] \right. \\
	&\quad\quad\quad\quad\left.
		+ \Phi_u^<(q) [ \beta + \gamma p ]
		+ \Phi_u^>(q) [ \beta' + \gamma' p ]
	\right] \\
	&\quad\quad
	+ E_P^>(p) \left[
		\phi_u(q) [\Delta\delta q + \Delta\eta]
		+ \Phi_u^<(q) \delta
		+ \Phi_u^>(q) \delta'
	\right],
\end{align}
where $\partial_p = \frac{\partial}{\partial p}$, $\Delta\alpha = \alpha - \alpha'$ etc.
Although this has no closed form solution,
it allows us to find $i$'s optimal values $p_i,q_i$ given the distributions $\phi_{u_i}$, $\phi_P$
numerically,
and it turns out that there generally $E\pi_i$ depends concavely on $p_i$ and $q_i$,
hence the unique local maximum is the global maximum.
In general, there is an incentive to bid a low price to increase the chances of being selected,
but depending on the market variant,
there is a counteracting incentive to bid a higher price to make sure that the paid price is high enough to offset production costs and penalties.
Also, it may be optimal to bid a quantity lower than average production, to avoid costly curtailment or excess suppy penalty,
or to bid above average production to avoid penalty for shortfalls and/or get excess payments for oversupply.
If quantity bids are rather low, the merit order will be steeper,
so the resulting $P$ will be larger to meet expected demand,
which will explain part of the observed price differences.

\paragraph{Grid operator.}
In view of all bids $(p_i,q_i)$ and the uncertain demand $D$ and production capabilities $u_i$,
the grid operator's expected profit given some choice of $P$ is
\begin{align}
	E\Pi &= \sum_{i:p_i\leqslant P}\Big[
		\Phi_u^<(q) (\beta_i q_i + \gamma_i p_i q_i) + E_u^<(q) (\theta_i + \zeta_i p_i)
        + P ( \Phi_u^<(q) \delta_i q_i + E_u^<(q) \eta_i ) \nonumber\\
    &\quad\quad\quad\quad
        + \Phi_u^>(q) (\beta'_i q_i + \gamma'_i p_i q_i) + E_u^>(q) (\theta'_i + \zeta'_i p_i)
        + P ( \Phi_u^>(q) \delta'_i q_i + E_u^>(q) \eta'_i )
		\Big] \nonumber\\
    &\quad
    	- c^+ EB^+ - c^- EB^-,
\end{align}
where the expected balancing amounts $EB^+,EB^-$ are determined as follows.
Supply $s_i$ of producer $i$ with $p_i\leqslant P$ has expected value $Es_i = \mu_i$
in the ``don't curtail'' market design variants, and
\begin{align}
	Es_i &= \left\{\begin{array}{ll}
		q_i   & \text{if~} q_i \leqslant q^l_i \\
		\mu_i & \text{if~} q_i \geqslant q^h_i \\
		\frac{(q_i^2 - (q^l_i)^2) / 2 + (q^h_i - q_i) q_i}{q^h_i - q^l_i} & \text{otherwise}
	\end{array}\right.
\end{align}
in the ``curtail'' market variants,
where $q^l_i = \mu_i (1 - \varrho_i)$ and $q^u_i = \mu_i (1 + \varrho_i)$.
The corresponding variances are
$Var(s_i) = (q^h_i - q^l_i)^2 / 12$ for ``don't curtail'', and
\begin{align}
	Var(s_i) &= \left\{\begin{array}{ll}
		0   & \text{if~} q_i \leqslant q^l_i \\
		(q^h_i - q^l_i)^2 / 12 & \text{if~} q_i \geqslant q^h_i \\
		\frac{ (q_i - q^l_i)^3 / 12}{q^h_i - q^l_i} & \text{otherwise}
	\end{array}\right.
\end{align}
in the ``curtail'' case.
As we assume production at different places to be independent and since $N$ is large,
total supply $S$ is thus approximately normally distributed
and its mean and variance can be computed as
$ES = \sum_{i:p_i\leqslant P}Es_i$ and $Var(S) = \sum_{i:p_i\leqslant P}Var(s_i)$.
Since production capabilities are independent of demand,
excess demand $D - S$ is thus also approximately normally distributed
and its mean and variance can be computed as
$m = E(D-S) = \mu^D - ES$ and $v = Var(D-S) = (\sigma^D)^2 + Var(S)$.
Finally, $EB^\pm$ is the expected value of $B^+ = \max(D - S, 0)$ and $B^- = \max(S - D, 0)$,
given by
\begin{align}
	EB^\pm &= \exp(-m^2 / 2v) \sqrt{v/2\pi} \pm m [1 + \text{erf}(\pm m / \sqrt{2v})] / 2,
\end{align}
where erf is the error function.

\section{Results}

\begin{sidewaystable}[p]
\begin{footnotesize}
\begin{center}
\begin{tabular}{ll|rrrr|rrrr}\toprule
centrali- &  & \multicolumn{4}{c|}{uniform pricing} & \multicolumn{4}{c}{pay as bid} \\
zation  &  & \multicolumn{2}{c}{pay supplied} & \multicolumn{2}{c|}{pay requested} & \multicolumn{2}{c}{pay supplied} & \multicolumn{2}{c}{pay requested}   \\
$Z$ &  & \multicolumn{1}{l}{don't curtail} & \multicolumn{1}{r}{curtail} & \multicolumn{1}{l}{don't curtail} & \multicolumn{1}{r|}{curtail} & \multicolumn{1}{l}{don't curtail} & \multicolumn{1}{r}{curtail} & \multicolumn{1}{l}{don't curtail} & \multicolumn{1}{r}{curtail}  \\ \midrule
1 & price $P$ & \textbf{0.84064} & 1.25805 & 1.19578 & 1.20318 & 1.42060 & \color{red}\bf2.01057 & 1.61220 & 1.61784  \\
 & total economic costs & 0.61720 & 0.44271 & 0.44379 & \textbf{0.39156} & 0.58410 & 0.44417 & 0.42890 & \textbf{\textit{0.40245}}  \\
 & std. total economic costs & 0.03546 & 0.04000 & 0.03391 & 0.03247 & 0.03589 & 0.06420 & 0.03419 & 0.01820  \\
 & producers' profits $\pi$ & \color{red}\bf-0.00083 & 0.14278 & 0.15460 & \textbf{\textit{0.19179}} & 0.16811 & \color{red}\bf0.58631 & 0.33890 & \color{blue}{0.42652}  \\
 & std. producers' profits & 0.01166 & 0.02381 & 0.01400 & 0.01985 & 0.01617 & 0.03587 & 0.01450 & 0.01900  \\
 & grid workload & \textbf{1.04979} & \textbf{1.04126} & 1.09562 & \textit{1.06110} & 1.17799 & 1.27188 & 1.14883 & 1.16823  \\
 & std. grid workload & 0.15185 & 0.15531 & 0.09036 & 0.10222 & 0.16500 & 0.20746 & 0.13520 & 0.13990  \\
 & curtailment & 0.00000 & 0.02257 & 0.00000 & 0.02176 & 0.00000 & 0.03096 & 0.00000 & 0.02340  \\
 & upward balancing $B^+$ & \color{red}\bf0.23808 & 0.07222 & 0.08013 & 0.03093 & 0.18250 & 0.00040 & 0.05399 & 0.00251  \\
 & downward balancing $B^-$ & 0.00000 & 0.00011 & 0.00000 & 0.00045 & 0.00000 & 0.05574 & 0.00001 & 0.02365  \\
 & $(q_i-\mu_i)/\varrho_i\mu_i$ & -0.30039 & -0.14183 & -0.00525 & -0.02410 & -0.29392 & -0.08736 & 0.07148 & 0.06535  \\
 & bid price-to-cost ratio $p_i/c_i$ & \textbf{1.89554} & 2.35714 & 2.43711 & \textbf{\textit{2.07482}} & 3.07774 & 3.90803 & 3.31576 & 3.22720  \\ \midrule
0.5 & price & \textbf{0.74170} & 1.19551 & 1.13596 & 1.13354 & 1.37618 & \color{red}\bf2.06409 & 1.57352 & 1.57957  \\
 & total economic costs& 0.63976 & 0.42089 & 0.42092 & \textbf{\textit{0.37836}} & 0.57897 & 0.46414 & 0.43300 & \textbf{0.37394}  \\
 & std. total economic costs& 0.03341 & 0.03956 & 0.03643 & 0.03416 & 0.03908 & 0.14286 & 0.03873 & 0.01800  \\
 & producers' profits & \color{red}\bf-0.02028 & 0.11986 & 0.13960 & \textbf{\textit{0.16936}} & 0.15698 & \color{red}\bf0.64996 & 0.31956 & \color{blue}{0.41058}  \\
 & std. producers' profits & 0.01017 & 0.02092 & 0.01548 & 0.01777 & 0.01672 & 0.18815 & 0.01607 & 0.01635  \\
 & grid workload & \textbf{0.93604} & 0.96808 & 1.02369 & \textbf{\textit{0.96542}} & 1.13220 & 1.25796 & 1.08555 & 1.05780  \\
 & std. grid workload & 0.15379 & 0.11895 & 0.17079 & 0.12828 & 0.17196 & 0.35750 & 0.14155 & 0.14310  \\
 & curtailment & 0.00000 & 0.02469 & 0.00000 & 0.02657 & 0.00000 & 0.04010 & 0.00000 & 0.02591  \\
 & upward balancing & \color{red}\bf0.26836 & 0.07175 & 0.08070 & 0.03873 & 0.19133 & 0.00038 & 0.06960 & 0.00386  \\
 & downward balancing & 0.00000 & 0.00026 & 0.00000 & 0.00006 & 0.00000 & 0.09052 & 0.00008 & 0.01537  \\
 & $(q_i-\mu_i)/\varrho_i\mu_i$ & -0.26047 & -0.12842 & -0.00500 & -0.02639 & -0.25559 & -0.07131 & 0.06967 & 0.06123  \\
 & bid price-to-cost ratio $p_i/c_i$ & \textbf{2.21957} & 3.25872 & 4.02303 & \textbf{\textit{2.92172}} & 4.72686 & 6.39770 & 5.46417 & 5.11118  \\ \midrule
0 & price & \textbf{0.61963} & 1.09598 & 1.04492 & 1.05081 & 1.30614 & \color{red}\bf2.26680 & 1.52834 & 1.54028  \\
 & total economic costs& 0.67889 & 0.40734 & 0.42732 & \textbf{\textit{0.36805}} & 0.57942 & 0.58338 & 0.42273 & \textbf{0.34457}  \\
 & std. total economic costs& 0.03692 & 0.03707 & 0.03661 & 0.03284 & 0.04469 & 0.19144 & 0.04018 & 0.02213  \\
 & producers' profits & \color{red}\bf-0.03667 & 0.08520 & 0.11065 & \textbf{\textit{0.14226}} & 0.14174 & \color{red}\bf0.89434 & 0.30625 & \color{blue}{0.40691}  \\
 & std. producers' profits & 0.01338 & 0.01984 & 0.01641 & 0.01614 & 0.01953 & 0.31197 & 0.01754 & 0.01836  \\
 & grid workload & 0.96603 & \textbf{0.89847} & 0.93219 & \textbf{0.89505} & 1.04123 & 1.42193 & 1.06795 & 1.01569  \\
 & std. grid workload & 0.13985 & 0.12508 & 0.12458 & 0.11826 & 0.15021 & 0.33491 & 0.13610 & 0.12944  \\
 & curtailment & 0.00000 & 0.02991 & 0.00000 & 0.02823 & 0.00000 & 0.06547 & 0.00000 & 0.03201  \\
 & upward balancing & \color{red}\bf0.30591 & 0.08268 & 0.10572 & 0.05605 & 0.20781 & 0.00009 & 0.08169 & 0.00864  \\
 & downward balancing & 0.00000 & 0.00004 & 0.00000 & 0.00000 & 0.00000 & 0.23065 & 0.00000 & 0.00889  \\
 & $(q_i-\mu_i)/\varrho_i\mu_i$ & -0.22589 & -0.10612 & 0.00842 & -0.01501 & -0.22483 & -0.04297 & 0.08519 & 0.07803  \\
 & bid price-to-cost ratio $p_i/c_i$ & \textbf{2.73163} & 4.49091 & 6.52608 & \textbf{\textit{4.11396}} & 6.99135 & 10.20656 & 8.69645 & 7.87349
\end{tabular}
\end{center}
\end{footnotesize}
\end{sidewaystable}
\begin{sidewaystable}[p]
\begin{footnotesize}
\begin{center}
\begin{tabular}{ll|rrrr|rrrr}
\color{white}centrality & \multicolumn{1}{l}{}  & \multicolumn{1}{l}{\color{white}don't curtail} & \multicolumn{1}{l}{\color{white}curtail} & \multicolumn{1}{l}{\color{white}don't curtail} & \multicolumn{1}{l}{\color{white}curtail} & \multicolumn{1}{l}{\color{white}don't curtail} & \multicolumn{1}{l}{\color{white}curtail} & \multicolumn{1}{l}{\color{white}don't curtail} & \multicolumn{1}{l}{\color{white}curtail}  \\
-0.5 & price & \textbf{0.49363} & 0.96849 & 0.91063 & 0.92646 & 1.23838 & \color{red}\bf2.36502 & 1.45549 & 1.48011  \\
 & total economic costs& 0.68711 & 0.39233 & 0.40382 & \textbf{\textit{0.35677}} & 0.55519 & 0.58779 & 0.38721 & \textbf{0.30770}  \\
 & std. total economic costs& 0.03894 & 0.04061 & 0.04014 & 0.03495 & 0.04759 & 0.16097 & 0.04466 & 0.02421  \\
 & producers' profits & \color{red}\bf-0.04955 & 0.04783 & 0.07391 & \textbf{\textit{0.10305}} & 0.14026 & \color{red}\bf1.00328 & 0.29239 & \color{blue}{0.40000}  \\
 & std. producers' profits & 0.01023 & 0.02839 & 0.01806 & 0.01900 & 0.02243 & 0.29001 & 0.01794 & 0.02319  \\
 & grid workload & 0.98527 & \textbf{\textit{0.80879}} & 0.81490 & \textbf{0.78057} & 0.96520 & 1.28332 & 0.91835 & 0.83154  \\
 & std. grid workload & 0.12699 & 0.10531 & 0.09217 & 0.09410 & 0.13563 & 0.26973 & 0.14056 & 0.11437  \\
 & curtailment & 0.00000 & 0.03622 & 0.00000 & 0.03593 & 0.00000 & 0.09426 & 0.00000 & 0.04276  \\
 & upward balancing & \color{red}\bf0.32013 & 0.09993 & 0.11872 & 0.07830 & 0.20966 & 0.00032 & 0.08401 & 0.01489  \\
 & downward balancing & 0.00000 & 0.00001 & 0.00000 & 0.00000 & 0.00000 & 0.28077 & 0.00002 & 0.00583  \\
 & $(q_i-\mu_i)/\varrho_i\mu_i$ & -0.20856 & -0.09722 & 0.00506 & -0.01985 & -0.20794 & -0.02952 & 0.08030 & 0.07368  \\
 & bid price-to-cost ratio $p_i/c_i$ & \textbf{3.18489} & 5.13785 & 8.61435 & \textbf{\textit{4.70348}} & 8.79295 & 13.49640 & 11.41692 & 10.00518 \\ \midrule
-1 & price & \textbf{0.44077} & 0.79917 & 0.77089 & \textbf{\textit{0.75874}} & 1.13505 & \color{red}\bf2.05625 & 1.31326 & 1.32840 \\
 & total economic costs& 0.63303 & 0.35337 & 0.35574 & \textbf{\textit{0.32651}} & 0.49881 & 0.46149 & 0.36595 & \textbf{0.28619}  \\
 & std. total economic costs& 0.15669 & 0.06126 & 0.07288 & 0.05162 & 0.09085 & 0.14501 & 0.05254 & 0.03019  \\
 & producers' profits & \color{red}\bf-0.04854 & 0.00925 & 0.04089 & \textbf{\textit{0.05118}} & 0.14386 & \color{red}\bf0.78859 & 0.25067 & \color{blue}{0.33845}  \\
 & std. producers' profits & 0.04715 & 0.04348 & 0.01912 & 0.02765 & 0.06272 & 0.27698 & 0.03040 & 0.02223  \\
 & grid workload & 0.95493 & 0.80361 & 0.86136 & \textbf{0.78869} & 0.95681 & 1.12602 & 0.90801 & \textbf{\textit{0.80521}}  \\
 & std. grid workload & 0.16581 & 0.10706 & 0.09843 & 0.11226 & 0.15517 & 0.22130 & 0.16142 & 0.14145  \\
 & curtailment & 0.00000 & 0.04751 & 0.00000 & 0.04487 & 0.00000 & 0.11157 & 0.00000 & 0.04792  \\
 & upward balancing & \color{red}\bf0.29178 & 0.09387 & 0.10582 & 0.08024 & 0.18455 & 0.00115 & 0.09190 & 0.02957  \\
 & downward balancing & 0.00081 & 0.00030 & 0.00055 & 0.00053 & 0.00044 & 0.21056 & 0.00052 & 0.00074  \\
 & $(q_i-\mu_i)/\varrho_i\mu_i$ & -0.23269 & -0.11270 & 0.00912 & -0.03703 & -0.23992 & -0.02526 & 0.10508 & 0.08204  \\
 & bid price-to-cost ratio $p_i/c_i$ & \textbf{3.51436} & 4.74751 & 8.34417 & \textbf{\textit{4.61745}} & 9.67136 & 14.62034 & 12.16332 & 10.87470  \\ \midrule
all & price   & \textbf{0.62495} & 1.06822 & 1.01734 & 1.02063 & 1.29958 & \color{red}\bf2.17382 & 1.50435 & 1.52118  \\
 & total economic costs  & 0.66027 & 0.41095 & 0.41669 & \textbf{\textit{0.36963}} & 0.56793 & 0.52624 & 0.41019 & \textbf{0.34287}  \\
 & std. total economic costs  & 0.06926 & 0.05277 & 0.04879 & 0.04159 & 0.05739 & 0.16733 & 0.04887 & 0.04524  \\
 & producers' profits   & \color{red}\bf-0.03309 & 0.07900 & 0.10412 & \textbf{\textit{0.13224}} & 0.14631 & \color{red}\bf0.81035 & 0.30225 & \color{blue}{0.40211}  \\
 & std. producers' profits   & 0.02646 & 0.05275 & 0.04128 & 0.04906 & 0.03016 & 0.29618 & 0.03112 & 0.03226  \\
 & grid workload   & 0.96249 & \textbf{0.90007} & 0.95591 & \textbf{0.90254} & 1.05353 & 1.30934 & 1.03098 & 0.98037  \\
 & std. grid workload   & 0.15382 & 0.15631 & 0.15673 & 0.15551 & 0.17851 & 0.33428 & 0.17115 & 0.18755  \\
 & curtailment  & 0.00000 & 0.03041 & 0.00000 & 0.03061 & 0.00000 & 0.06819 & 0.00000 & 0.03483  \\
 & upward balancing  & \color{red}\bf0.29114 & 0.09003 & 0.10216 & 0.06062 & 0.20148 & 0.00073 & 0.07773 & 0.01079  \\
 & downward balancing & 0.00009 & 0.00011 & 0.00006 & 0.00015 & 0.00005 & 0.18835 & 0.00008 & 0.01076  \\
 & $(q_i-\mu_i)/\varrho_i\mu_i$  & -0.23453 & -0.10850 & 0.00377 & -0.02055 & -0.23273 & -0.04645 & 0.07848 & 0.07033  \\
 & bid price-to-cost ratio $p_i/c_i$ & \textbf{2.73045} & 4.14358 & 6.20152 & \textbf{\textit{3.79583}} & 6.78798 & 9.93891 & 8.39833 & 7.60097  \\ \bottomrule
\end{tabular}
\end{center}
\caption{\label{tbl:results}
Aggregate simulation results by degree of centralization and market design variant.
Averages and some standard deviations,
each based on a sample of size $500$ (10 networks with 50 time steps).
\textbf{Boldface} and \textbf{\color{red} red boldface} mark best and extreme values in a row,
\textbf{\em boldface italics} 2nd best values or values considered to be a good compromise, {\color{blue} blue} values considered too large.
}
\end{footnotesize}
\end{sidewaystable}

\def0.18\textheight{0.18\textheight}
\begin{figure}[p]
\begin{center}
\begin{tabular}{cc}
	\includegraphics[height=0.18\textheight]{plot_1_False_False_False_1.pdf} &
	\includegraphics[height=0.18\textheight]{plot_1_False_False_True_0.pdf} \\
	\includegraphics[height=0.18\textheight]{plot_1_False_True_False_2.pdf} &
	\includegraphics[height=0.18\textheight]{plot_1_False_True_True_0.pdf} \\
	\includegraphics[height=0.18\textheight]{plot_1_True_False_False_0.pdf} &
	\includegraphics[height=0.18\textheight]{plot_1_True_False_True_0.pdf} \\
	\includegraphics[height=0.18\textheight]{plot_1_True_True_False_0.pdf} &
	\includegraphics[height=0.18\textheight]{plot_1_True_True_True_0.pdf} \\
\end{tabular}
\end{center}
\caption{\label{fig:trajectories1}
Sample trajectories for all eight market design variants for the centralized casee $Z=1$.
In all cases, bidding and price-setting behaviour converges almost immediately to a strategic equilibrium.
}
\end{figure}

\def0.18\textheight{0.18\textheight}
\begin{figure}[p]
\begin{center}
\begin{tabular}{cc}
	\includegraphics[height=0.18\textheight]{plot_0_False_False_False_1.pdf} &
	\includegraphics[height=0.18\textheight]{plot_0_False_False_True_0.pdf} \\
	\includegraphics[height=0.18\textheight]{plot_0_False_True_False_1.pdf} &
	\includegraphics[height=0.18\textheight]{plot_0_False_True_True_0.pdf} \\
	\multirow{2}{*}[1.8cm]{\includegraphics[height=0.18\textheight]{plot_0_True_False_False_0.pdf}} &
	\includegraphics[height=0.18\textheight]{plot_0_True_False_True_1.pdf} \\
	&
	\includegraphics[height=0.18\textheight]{plot_0_True_False_True_0.pdf} \\
	\includegraphics[height=0.18\textheight]{plot_0_True_True_False_0.pdf} &
	\includegraphics[height=0.18\textheight]{plot_0_True_True_True_0.pdf} \\
\end{tabular}
\end{center}
\caption{\label{fig:trajectories0}
Sample trajectories for all eight market design variants for no centralization or decentralization ($Z=0$).
Now, in the ``pay as bid, pay supplied, curtail'' variant,
an additional run with non-converging but increasing price and profits is shown.
In all other cases, bidding and price-setting behaviour converges almost immediately to a strategic equilibrium.
}
\end{figure}

\def0.18\textheight{0.18\textheight}
\begin{figure}[p]
\begin{center}
\begin{tabular}{cc}
	\includegraphics[height=0.18\textheight]{plot_-1_False_False_False_1.pdf} &
	\includegraphics[height=0.18\textheight]{plot_-1_False_False_True_1.pdf} \\
	\includegraphics[height=0.18\textheight]{plot_-1_False_True_False_1.pdf} &
	\includegraphics[height=0.18\textheight]{plot_-1_False_True_True_0.pdf} \\
	\multirow{2}{*}[1.8cm]{\includegraphics[height=0.18\textheight]{plot_-1_True_False_False_0.pdf}} &
	\includegraphics[height=0.18\textheight]{plot_-1_True_False_True_0.pdf} \\
	&
	\includegraphics[height=0.18\textheight]{plot_-1_True_False_True_4.pdf} \\
	\includegraphics[height=0.18\textheight]{plot_-1_True_True_False_0.pdf} &
	\includegraphics[height=0.18\textheight]{plot_-1_True_True_True_0.pdf} \\
\end{tabular}
\end{center}
\caption{\label{fig:trajectories-1}
Sample trajectories for all eight market design variants for the decentralized case $Z=-1$.
Again, in the ``pay as bid, pay supplied, curtail'' variant,
an additional run with non-converging but increasing price and profits is shown.
}
\end{figure}

Our results are summarized in Table~\ref{tbl:results},
individual trajectories are shown in Figs.~\ref{fig:trajectories1}--\ref{fig:trajectories-1} for $Z\in{1,0,-1}$.

Overall, we find that in all but one marked design variant,
bidding and price-setting behaviour converges  to a strategic equilibrium
already after a very small number of repetitions.
The only exception is the ``pay as bid, pay supplied, curtail'' (henceforth BSC) variant,
where for $Z\leqslant 0$ in some runs, price bids start to increase linearly after a varying number of repetitions
(almost immediately in Fig.\,\ref{fig:trajectories0}, somewhat later in Fig.\,\ref{fig:trajectories-1}),
causing the market price and hence the producer's profits to increase as well,
without affecting the total economic costs however (i.e., only causing an evergrowing transfer from consumers to producers).

\paragraph{Bid price.}
In general, bid prices are at least around twice as high as production costs,
being lowest under the ``uniform pricing, pay supplied, don't curtail'' design in the centralized case $Z=1$ ($p/c=1.89$ on average),
highest under the BSC design in the decentralized case $Z=-1$ ($p/c=14.62$ on average),
which may be partially because of the increasing bid effect mentioned above,
but almost as high under the ``pay as bid, pay requested, don't curtail'' designs in the decentralized case ($p/c=12.16$ on average).
Bid prices are always lower under uniform pricing than under pay as bid,
since by bidding a lower price under uniforma pricing,
a producer will not risk getting a lower payment price (which equals $P$) but will only increase their chance of being selected,
hence the only incentive to not make a too low bid is to make sure that when selected,
$P$ is large enough to cover production costs and expected penalties.

\paragraph{Bid quantity.}
For most designs, average bid quantities are below mean production capabilities:
producers bid conservative quantities since shortfall penalties are higher than excess supply penalties.
Only under ``pay as bid, pay requested'' for all values of $Z$
and under ``uniform pricing, pay requestes, don't curtail'' for $Z\leqslant 0$,
bid quantities are usually higher than mean production capabilities.
This is because in the ``pay requested'' designs,
shortfall penalties are effectively lowered by the fact that the grid operator still pays for the (higher) bid quantity rather the (lower) actual supply.
The other two design choices (uniform pricing or pay as bid, and curtailment yes or no) were not found to have such a clear effect on bid quantities.

\paragraph{Market price and requested amount.}
Because of the lower bid prices,
also market price is always lower under uniform pricing than under pay as bid,
typically by a factor of around 1.5 to 2.
The extremes are
$P=2.37$ on average under BSC with $Z=-0.5$,
and $P=0.44$ on average under ``uniform pricing, pay supplied, don't curtail'' with $Z=-1$,
which is even below the average production costs, and consequently producers' profits are negative in this case,
making this a non-feasible design.
The lowest price that makes production profitable is generally realized under ``uniform pricing, pay supplied, don't curtail'' for most values of $Z$,
resulting in $P\approx 1$, i.e., 1.5 to 3 times the mean production costs,
with profits still only being $\approx 0.15$ for $Z=1$ and $\approx 0.04$ for $Z=-1$
due to excess/shortfall penalties that grow with decreasing centralization.

The relationship between requested amount $R=\sum_{i:p_i\leqslant P}q_i$ and actual demand $D$ differs widely between variants.
For all values of $Z$, they match closest under ``uniform pricing, pay requested, curtail'' and almost as well under ``uniform pricing, pay supplied, curtail''.
For $Z=-1$, they also match well under ``uniform pricing, pay requested, don't curtail''.
Under-requesting $D - R$ is largest under the ``pay supplied, don't curtail'' variants and still significant under the ``pay requested, don't curtail'' variants.
This is in part because if producers need not curtail excess production,
the grid operator expects excess supply, knowing that bid (and thus requested) quantities
are considerably (under ``pay supplied'') or at least moderately (under ``pay requested'') below mean production.
In contrast, in the ``pay as bid, curtail'' variants, $R$ is usually slightly larger than $D$.

\paragraph{Balancing needs.}
Interestingly, under the ``don't curtail'' variants, the grid operator's expectation of excess supply (i.e., positive $S - R$)
turns out to be incorrect and consequently there is need for considerable upward balancing.
Except for the BSC design, upward balancing needs are generally significantly larger than downward balancing.
Under pay as bid, balancing needs are generally somewhat lower than under uniform pricing.

\paragraph{Total economic costs.}
Total economic costs, i.e., the sum of all production, curtailment, and balancing costs, but without penalties (which are only flows within the economy),
vary largely over the eight market design variants,
being largest under ``uniform pricing, pay supplied, don't curtail'' ($0.66$ on average) due to the large upward balancing needs,
and smallest (only half as high) under ``pay as bid, pay requested, curtail'' ($0.34$ on average).
This difference becomes larger for smaller centralization $Z$.
The second-best design w.r.t.\ total costs is ``uniform pricing, pay requested, curtail'' ($0.37$ on average).
In general, the choice between uniform pricing and pay as bid does not exhibit a consistent influence on total costs.
With the exception of ``uniform pricing, pay supplied, don't curtail'',
costs decrease with decreasing centralization $Z$, reflecting the lower production costs of VRES.

\paragraph{Producers' profits, consumers' costs.}
For an economic evaluation, producers' profits are the second most interesting indicator besides total economic costs.
They also vary largely over the eight market design variants,
being negative on average under ``uniform pricing, pay supplied, don't curtail'',
making this an economically infeasible design,
are slightly positive ($0.079$ on average) under ``uniform pricing, pay supplied, curtail'',
and are largest ($0.81$) under BSC.
Notably, under the overall cheapest design, ``pay as bid, pay requested, curtail'',
profits are large ($0.4$),
while under the second-cheapest design, ``uniform pricing, pay requested, curtail'' (URC),
they are only a third as high ($0.13$).

Note that in our model, the grid operator's total costs equal total economic costs plus producers' profits,
and these can be interpreted as the consumers' total electricity costs.
Consequently, for ``pay as bid, pay requested, curtail'' these are about $0.34+0.4=0.74$ on average,
while for URC they are only about $0.37+0.13=0.5$.
When going from centralized to decentralized, this ratio increases from about $3/4$ to almost $1/2$.
Consumers' costs are even slightly smaller under ``uniform pricing, pay supplied, curtail''
($0.41+0.08=0.49$, with a strongly statistically significant two-sample $t$-test),
which is however considerably more expensive overall.
Hence consumers would prefer the latter design, producers would prefer BSC,
a social planner not interested in welfare effects would prefer ``pay as bid, pay requested, curtail'',
and a social planner caring for welfare effects would probably prefer the compromise design URC.

\paragraph{Grid workload.}
As an overall indicator of the stress placed onto the grid, the potential needs for extending it, and the overall likelihood of line trippings,
we look at the total power flow summed over all grid lines, here called the ``grid workload'',
computed by standard power flow calculations on the underlying grid topology.
Overall, workload is smallest under the two ``uniform pricing, curtail'' variants,
with no statistically significant difference between the two,
and is highest and most volatile under BSC.
Except for the latter design, workload coefficient of variation is generally around $1/6$,
interestingly not varying much between the centralized and decentralized situations,
but suggesting that lines need a considerable amound of excess capacity to avoid tripping.

\section{Conclusion}

In view of the above results,
this study suggests that the best compromise between the eight possible designs studied here
might be given by the URC market design
in which producers are paid a uniform market price instead of their bid price,
are paid this price for the requested (i.e., the bid) quantity of electricity,
regardless of whether their actual supply falls short of their bid quantity,
but have to pay a fixed penalty for each unit of electricity not supplied
and are not allowed to supply more than bid but have to curtail any excess production.
As seen above, this combination seems to lead to an almost optimal overall level of total economic costs of electricity production,
an almost optimal optimal level of consumers' costs,
a robust but moderate profitability for electricity producers,
a low level of balancing needs,
a moderate market price for electricity,
``honest'' bid quantities close to expected production capability,
and the smallest level of grid workload (i.e., higher reliability of supply).

All other studied designs seem to perform considerably worse than URC in one or several aspects.
The ``pay as bid'' variants have higher price bids,
hence higher market prices and higher total consumers' costs,
less honest quantity bids,
higher workload,
and (except for ``pay requested, curtail'') higher total economic costs.
The ``pay supplied'' and ``don't curtail'' variants have
higher balancing needs, hence higher total economic costs,
and (except for ``uniform pricing, pay supplied, curtail'') higher workload.

In view of the rather conceptual nature of this study,
we recommend focussing in future research on
(i) simulating several coupled markets (e.g., day-ahead, intraday, balancing),
(ii) using real-world demand profiles and cost distributions for production, curtailment, and balancing,
(iii) distibnguishing different types of producers (traditional plants and utilities, small VRES producers, virtual power plants, etc.)
more explicitly than here, where we used a kind of continuum of producer types,
(iv) compare simulated bidding and price-setting behaviour over time with real-world data
to assess the amount of bounded rationality in real-world agents and improve the model.

\paragraph{Acknowledgements.}
The authors gratefully acknowledge the support of the German Federal Ministry of Education and Research (BMBF), CoNDyNet, FK. 03SF0472A,
and the European Regional Development Fund (ERDF), the German Federal Ministry of Education and Research and the Land Brandenburg
for supporting this project by providing resources on the high performance computer system at the Potsdam Institute for Climate Impact Research.

\bibliographystyle{aer}

redpajama_set_name: RedPajamaArXiv


CARW Members take monthly actions for racial justice, attend quarterly membership meetings, and make meaningful financial contributions to support CARW and our partner organizations' work.
Our remaining 2019 quarterly meetings for 2019 are on July 12 and October 2.
CARW holds quarter anti-racism workshops that give folks an opportunity to learn about our foundational analysis and how that informs our work.
The next workshops for 2019 are on May 19, August 11, and November 17.
Follow us on Facebook or Sign Up for upcoming events.
We are all more likely to take accountable actions when we do so together. Learn more about the different ways you can plug in and get involved!


text:
Titans #24 Review
Deathstroke's new crew takes aim at Lex Luthor.
By Dan Phillips
Updated: 8 May 2012 4:17 pm
Posted: 10 Jun 2010 4:48 am
It's tough to take the name of DC's new "Brightest Day" branding very seriously when writers like Eric Wallace, along with JT Krul and James Robinson, continue to produce issues that deal heavily in loud, stupid, adolescent hyper-violence. The fact that books such as Titans and Justice League: Rise of Arsenal actually fit under the "Brightest Day" banner is so ludicrous you can't help but wonder if the folks responsible have a sick sense of humor, and are aware of the ridiculous contrast between the name of this new line-wide direction and the content of the issues. And if that is not the case, and "Brightest Day" isn't a moniker heavily soaked in irony, then I'd hate to learn what DC's idea of dark comics might be.
Wallace's Titans #24 isn't as offensive or blatantly misogynistic as recent issues of Rise of Arsenal, but it is almost as stupid. The book may not assault good taste as eagerly as Krul's train wreck of a mini-series does, but it is equally as guilty of taking a sledgehammer to rationality and story logic. In both cases, the plot exists merely as a crude foundation to prop up the writer's ideas of shocking acts of violence and plot twists, none of which make much sense if you think about them for more than a few seconds. And for that, Titans and Rise of Arsenal, and the names Wallace and Krul, are inexorably linked in my mind as the chief culprits of DC's recent devolution into the worse sort of sophomoric, "grim and gritty" superhero comics.
After an introductory issue that saw Deathstroke's new band of villainous Titans brutally murder Ryan Choi for no other reason than to prove to readers that Wilson Slade really means business this time around, Titans #24 sees the team inexplicably set their murderous sights on Lex Luthor, freshly repositioned as the legitimate head of LexCorp after the events of War of the Supermen. But wait, are they really trying to murder the infamous Superman villain, or are their efforts to eviscerate heaps of LexCorp bodyguards really just a big ploy to do something else entirely? You'll have to wait until the issue's final pages for the answer – just don't expect it to make a lick of sense. This is, after all, a comic in which characters' actions are determined first and foremost by the direction of the inane plot.
Deathstroke may be the leader of this new team, but Osiris is without a doubt its star and the source of many of the issue's most cringe-worthy scenes. Scenes like the one in which the troubled super-teen pushes Wonder Girl away and literally announces that no one understands him, or another in which he loudly proclaims that he doesn't want to hurt anyone before blowing a LexCorp guard to smithereens. Why does he do such a thing despite his best intentions and the fact that he screams "No" loudly before committing the act? Again, it's apparently too much for these characters to act in accordance to any rhyme or reason.
In addition to the loud, dumb melee at the heart of the issue, there's also a few brief, feeble attempts on Wallace's part to lay down subplots. These include the aforementioned Osiris/Wonder Girl scene as well as a sequence in which Osiris and the new villain Cinder both prove how annoying and angst-ridden they can be. There's another in which Cheshire and the Tattooed Man tangle with villains from Cheshire's past, with little explanation as to what's going on or why it is important.
The issue is drawn in the same painterly style seen in Cry for Justice, although here the art of Fabrizio Fiorentino and Mike Mayhew is far more uniform than the hodgepodge of different styles found in that unfortunate James Robinson mini-series. That's Titans #24 in a nutshell for you – the issue is bad; just not nearly as bad as the recent issues to which it is so similar. But does that really make it anywhere near respectable? Of course not.
Titans Vol. 2
PublisherDC Comics
Release DateSeptember 9, 2009


The MIDI BUS was designed to be a MIDI interface for the eurorack system, and more specifically to offer MIDI inputs and outputs for our TRAX performance sequencer.
This device provides opto-isolation of the MIDI input and buffers all MIDI signals.
The MIDI BUS provides MIDI IN/OUT/THRU inputs and outputs on 3.5mm TRS jacks. Three 3.5mm to 5-pin DIN MIDI cables are included with each MIDI BUS product. These MIDI cables conform to the TRS MIDI B Spec Class, currently supported by Arturia, Novation, and 1010 Music devices.
The MIDI BUS uses the power bus cable to receive and transmit MIDI at the +3.3 volt standard. In order to do this, the MIDI BUS repurposes what the eurorack standard defines as the INT GATE line of the power bus for MIDI IN signals, and the INT CV line of the power bus for MIDI OUT signals.
To prevent conflicts with other signals that may be using these lines of the power bus, we recommend using the special MIDI BUS power cable provided with this unit, or our optional Flying Bus power cable when using the MIDI BUS with the TRAX product or any other products using this new MIDI standard.
The MIDI BUS power cable that is provided with your MIDI BUS will allow only a single device in your system to send and transmit MIDI.
The optional Flying Bus power cable allows multiple modules connected to this cable to share MIDI data with one another and also receive the proper power from the system, without connecting MIDI signals to other modules in your system.


text:
TPG to conduct due diligence on Billabong: Midday roundup
Engel Schmidl
TPG has been granted permission to conduct due diligence on Billabong, following an offer from the private equity group to buy the struggling surfwear retailer.
In a statement this morning, Billabong said the move would hopefully reduce the conditionality of the TPG proposal and improve the company's understanding of the chain's value.
But it also said the move doesn't guarantee a deal.
"In fact, the board of Billabong does not believe that the proposal reflects the fundamental value of Billabong in the context of a change of control transaction," the company said.
TPG has offered $1.45 a share for the company – 32% higher than the company's last closing price.
It originally offered $850 million earlier this year, which Billabong rejected.
Carbon tax complaints falling: ACCC
The number of complaints received every day by the Australian Competition and Consumer Commission relating to the carbon tax has continued to fall, the agency has said.
The ACCC says while it originally received about an average of 63 complaints per day when the tax came into effect, it now only receives about 45.
It also says this is relatively low compared to the amount of complaints received about other matters.
"The majority of contacts to the ACCC have been about general price increases not specific complaints about carbon price misrepresentation," the ACCC said.
"This is especially the case with electricity complaints where cost increases reviewed by the ACCC have been of the order expected. The sectors that continue to record the most complaints are the energy, landfill, refrigerants, and building and construction sectors."
Shares rise after strong offshore leads
The Australian sharemarket has opened higher this morning, after strong offshore leads following remarks from European Central Bank chief Mario Draghi that it would do "whatever it takes" to preserve the strength of the Euro.
The benchmark S&P/ASX200 index was up 32 points or 0.8% to 4180.2 at 12.00 AEST, while the dollar remained at $US1.03c.
In the United States, the Dow Jones Industrial Average rose 211 points or 1.7% to 12,887.
Caltex closure out of government's hands, NSW Premier claims
New South Wales premier Barry O'Farrell has said the closure of a Caltex refinery is out of the NSW Government's hands.
The closure will result in the loss of as many as 600 jobs.
"The decision has been made, it's been two years in the making," O'Farrell told Fairfax Radio.
"Regrettably we're going to see anywhere between 100, (and) as the company says, 600 estimated jobs lost."
"That's bad for NSW and just reiterates our concern about creating the economic conditions in NSW to get others to invest here."


For the federal constituency formerly represented in the Dewan Rakyat, see Sitiawan (federal constituency).
Sitiawan (alternate spelling: Setiawan; origin: from Malay, a portmanteau of Setia Kawan, meaning "Loyal Friend") is a region in Manjung District, Perak, Malaysia.
The region covers an area of 331.5 square kilometers (128.0 sq mi) and as of year 2000, its population was 95,920 and has risen to more than 150,000 by 2015. Sitiawan town, the principal town of Sitiawan sub-district (mukim), is located at 4°13′N 100°42′E / 4.217°N 100.700°E / 4.217; 100.700.
Folklore mentions Sitiawan as Kampung Sungai Gajah Mati. It became a thriving settlement for industrious migrants from Foochow (Chinese: Fuzhou). They were mostly from the district of Kutien in Fuzhou, China.
According to legend, Kampung Sungai Gajah Mati (literally: "Dead Elephant River Village") was the place where two large elephants drowned after one of them, overladen with tin ore, got stuck in the mud of the Dinding River at low tide. Efforts to save the elephant were in vain and eventually, everyone gave up and left. However, the second elephant refused to budge and hung on to its friend, resulting in them drowning together in the rising tide. Thus the setia kawan (loyal friend) name was derived.
In the late 19th century, tin, together with rubber sheets, formed the main commodities of commerce. They were often carried by elephants and loaded onto waiting steamships destined for Penang. In the 1870s, when an outbreak of smallpox struck the settlement, and in line with the Chinese belief of naming a place to enhance its feng-shui, the locals chose to name the locality Setia Kawan—the "loyal friend" -- to harmonise with nature and appease the dead elephants. The name eventually became shortened to Sitiawan.
Another folklore mentions about the ancient tree that is located in Sitiawan, and how an old man's spirit is often found wandering around the tree. Nowadays, the ancient tree, located at the famous Shi Zi Lu (crossroad), has become a common area for people waiting for bus to travel around Malaysia. Instead of a spirit, a middle age old man nickname "Hei Ren" can be seen often selling bus tickets.
In September 1903, the settlement got a boost with the arrival of more than 360 Christian Foochows desperate to escape the violence against the Qings Dynasty.The Chinese Christians were attacked by the Boxer party also known as Yihetuan in Chinese 义和团 and the Qing Dynasty government support the cause causing mess in Fujian in 1901 also known as Boxer Rebellion. They were led by two Chinese pastors and settled down in what is today known as Kampung Koh. Most of these immigrants worked in rubber plantations in Sitiawan. The Foochows also built four wells, two in the 1930s and another two in the 1950s. These heritage wells still exist but are no longer used.
Chin Peng, who led the Malayan Communist Party for many years, was born in Sitiawan in 1924.
Sitiawan has a Tropical Rainforest Climate (Af).
Sitiawan consist of 45.6% Chinese, 37.3% Malay and 16.9% Indian and 0.2% others.
Sitiawan is one of the driest places after Kuala Klawang Town (Jelebu), Malacca City (Malacca) and Lubok Merbau (Perak) in Malaysia with average annual rainfall just a bit below 2,000 mm (79 in). Most of the time, the average rainfall is just above 100 mm (3.9 in) with October and November being wetter months while June is the driest month of the year.
In recent years Sitiawan has suffered from haze swept in by winds from raging open fires in Sumatra, Indonesia.
Sitiawan grew from a small settlement with rubber tapping and latex processing as its main economic activities. The town was flanked by various Chinese settlements composed mostly of the descendants of immigrants from the Kutien district of Fuzhou, China. The original settlers were encouraged by the British to plant rice. The settlers, however, found that paddy-planting is not suited to the soil of the region and so they switched to livestock farming before discovering that the land was much better suited for rubber plantations.
The development of the town had been rapid in the 1990s. One of the main reasons was the establishment of the Royal Malaysian Navy's Naval Base in Lumut, approximately 10 km from the town centre. The Naval Base is currently the largest in Malaysia. The base has acted as a catalyst for the development of commercial activities in the town, serving both the residents of the base and sailors visiting from other countries.
Located at the western coast of Perak with direct access to the Straits of Malacca, it is no surprise that port-related activities, marine services and industries play a major role. Its main port, Lumut Port consists of the Lumut Maritime Terminal (LMT) and Lekir Bulk Terminal (LBT) and it serves the surrounding regions and the state of Perak. LMT, a Royal Malaysian Customs Gazetted Port, is a river port, located along the banks of the Dindings River. The Terminal is an integrated common user port facility, and is International Ship Port Security code compliant. Since 1995, the Terminal has been improved and upgraded and its facilities have been extended to include additional open and covered storage. The main berth has been extended for another 280m in 2001, with the alongside depth of 12m ACD, resulting in a total overall linear berth length of 510m.
LBT is a deepwater seaport, and with a natural depth of 20 metres, LBT is currently South-East Asia's largest dry bulk unloading facility. The terminal is capable of berthing an entire range of vessels in Panamax and Capemax ships up to 165,000 DWT. LBT is designed to handle dry bulk cargoes. It currently is a dedicated terminal to handle coal for Station Janakuasa Sultan Azlan Shah (TNBJ) in Seri Manjung.
An industrial zone, Lumut Port Industrial Park (LPIP), located within Lumut Port itself with direct sea,trade access, is home to various industries and companies. LPIP is home to companies such as Sapura Kencana Petroleum Berhad, an oilfield service company, Kencana Torsco Sdn. Bhd., B.I.G. Industrial Gas Sdn. Bhd., IMPSA, etc. In recent years, bio-diesel, oleo and palm-oil based companies have been set up due to the proximity to its raw material source.
A secondary jetty, located at Teluk Rubiah is built and managed by Vale Malaysia Minerals Sdn Bhd, a Brazilian mining giant. It was built as a transshipment hub for iron ore. The raw material is brought in from Brazil in gigantic 400,000 DWT bulk carriers some 360 metres in length. The Vale Jetty serves a maximum 90 million tonnes per annum of iron ore and functions as entry and exit points for all material including iron ore, sinter pellets, blast furnace pellets and pelletizing plant additives. The jetty is designed to bring in incoming iron ore from the largest bulk carrier of 400,000 DWT Valemax, and to export it with a maximum of 80,000 DWT panamax size vessel.
The project has been controversial due to environmental concerns. Fears expressed by civic groups and local residents concern the destruction of the environment, the livelihood of locals, particularly fishermen, and beach-side tourism. Nevertheless, the nearby Outward Bound School has alleged that part of the jungle is inaccessible to its teams. Other education and training institutions are also barred from entering the area.Consumer and environmental groups have joined in the condemnations with claims that the ecosystem of the area, formerly gazetted as a forest reserve, would be destabilised. The plant is located on a 450-acre site which was originally a Permanent Forest Reserve but the state government re-gazetted it to an 'Industrial Zone'. The Perak Department of Wildlife and National Parks said that the area is rich in flora and fauna and protected under the Wildlife Protection Act 1972. The site is surrounded by mature and regenerating natural primary forest whilst the bird life and mammals are protected by national and international laws. The area is also home to leopards, white-bellied eagles and the endangered palm plant, Phoenix paladosa.
Another major industry is its rich rubber latex resource, YTY Industry Sdn Bhd, a world leader in Nitrile Gloves production for examination and surgical use, TNB JanaManjung Sdn Bhd an independent power generation company, TNB's Sultan Aziz Shah Coal-Fired Power Plant and several other industrial manufacturing and mining companies.
There are many schools in Sitiawan, such as Sekolah Menengah Kebangsaan Ahmad Boestamam, Sekolah Menengah Jenis Kebangsaan Nan Hwa,Sekolah Menengah Kebangsaan Convent Sitiawan, Sekolah Menengah Kebangsaan ACS (Anglo Chinese School) Sitiawan,Sekolah Menengah Kebangsaan Tok Perdana. The first mentioned school is named after Ahmad Boestamam, an historical figure who helped to gain independence from the British.
SMJK Nan Hwa was previously a private Chinese school which had been converted into a partially subsidised government school which uses the Chinese medium. Nan Hwa was founded in 1935 from the amalgamation of the High School section of 4 Chinese primary schools (Chung Cheng Primary School, Kuok Min Primary School, Uk Dih Primary School and Uk Ing Primary School) in the Sitiawan area. Ong Seok Kim was elected as first Chairman of the School Board in 1936 and again in 1946 to 1947. Its 70th anniversary was celebrated on 1 September 2006 in SMJK Nan Hwa school hall. A thousand-person dinner was held at the Ku Tien Association Hall to commemorate that auspicious day.
There are 24 Chinese primary schools and 5 Chinese secondary schools in the district. Of these, 5 schools were founded by Ong Seok Kim. They are SJK (C) Chung Cheng, Sitiawan in 1920, SMJK Nan Hwa (which split into Sekolah Tinggi Nan Hwa, Ayer Tawar Road in 1984) in 1935, SJK (C) Ping Min, Lumut in 1951 and SMJK Dindings, Lumut in 1953. Ong Seok Kim died in 1964. The following year, the Manjung community established the Ong Seok Kim Memorial Education Fund in his honour. The Fund offers scholarships and loans to students in the Manjung District, irrespective of ethnicity.
SMK Methodist ACS Sitiawan, formerly an English school, was founded by Christian missionaries back in 1903. It is currently a national school under the Malaysian education system and subjects are taught in Bahasa Malaysia. Its 100th anniversary was celebrated in 2003 and it is also the oldest secondary school in Sitiawan. ACS is the first school in Manjung to set up a scout troop.
Sitiawan is known for its strong Foochow heritage. Various traditional Foochow dishes such as Red Rice Wine Vermicelli, "Kompiang" or "Kong Piang" (traditional Foochow buns made with a type of unleavened flatbread stuffed with seasoned pork and baked in a clay oven), as well as "Go- row" (a thick sweet and sour broth cooked with fish maw) are served in Sitiawan restaurants and households alike. Traditional local produce such as red rice wine, and Foochow vermicelli continue to play a vital part in the livelihood of some families from Kampung Koh. Kampong Koh Sauce (M) Sdn Bhd makes one of the finest and widely liked chilly sauces.
Recent intense development on transportation routes between Lumut, Seri Manjung and Sitiawan along the Dindings river have brought both prosperity and pollution to what was once a relatively quiet town. The primary industries within Sitiawan are rubber and Rubber glove manufacturing, palm oil, mineral ore, fishing, prawn farming and shipbuilding. Sitiawan is known for it Vietnam Farms, where patrons can enjoy some beer with the company of Vietnam lasses.
Around the year 2000, Sitiawan residents began to be involved in swiftlet bird breeding activities. This activity was partly attributed to the development of 2 major roads which indirectly "disconnect" Kampung Koh and Simpang Empat from traffics travelling to Lumut. All traffics were directed to the planned township of Sri Manjung. All local government administrative offices were also relocated to Manjung in recent years. This development renders shop and small business owners in Kampung Koh and Simpang Empat obsolete and there were many closures. The empty shop lots were later converted to culture swiftlets and at its peak 8-10 years ago, drove property prices up through the roof. There were also many new independent buildings built on farm started to mushroom which can still be seen from major roads leading to Lumut.
Sitiawan also is known for the Tua Pek Kong temple which is located about 15 minutes from the town, this temple has monumental statues and structure that are quite amazing. Lots of Chinese deities in a garden-like atmosphere in a large compound facing the Pasir Panjang seashore.
Majlis Perbandaran Manjung (Manjung Municipal Council) website in Bahasa Malaysia.
Manjung Land and District Office website.